FLIGHT CONTROL SYSTEMS practical issues In design and implementation

FLIGHT CONTROL SYSTE,,MS practical"

" issues In

design and implementation Edited by Roger W. Pratt

The Institution of Electrical Engineers

Copublished by: The Institution of Electrical Engineers, Michael Faraday House, Six Hills Way, Stevenage, Herts. SG1 2AY, United Kingdom and The American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive Suite 500 Reston VA 20191-4344 USA © 2000 Editorial selection and presentation: The Institution of Electrical Engineers For copyright ownership details see final page of each chapter. This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted, in any forms or by any means, only with the prior permission in writing of the Institution of Electrical Engineers (lEE) or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency or Copyright Clearance Centre Inc. Inquiries concerning reproduction outside those terms should be sent to the lEE at the address above. While the authors and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgment when making use of them. Neither the authors nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral right of the authors to be identified as authors of this work has been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing in Publication Data A CIP catalogue record for this book is available from the British Library ISBN 0 85296 766 7

Printed in England by TJ International, Padstow, Cornwall

To Gill, Joanne, Ian and Sara

Contributors

B.D. Caldwell Aerodynamics (W310C) British Aerospace Warton Aerodrome Preston PR4 lAX UK M.V° Cook Flight Test and Dynamics Group College of Aeronautics Cranfield University Cranfield, Bedfordshire MK43 0AL UK L.F. Faleiro Control Design Engineering Institute for Robotics and Mechatronics German Aerospace Center DLR Oberpfaffenhofen Postfach 1116 82234 Wessling Germany R,D. Felton 14 Cromwell Court Eynesbury St Neots, Cambs. PE19 2NZ UK J. Fenton Smiths Industries Aerospace Bishops Cleeve Cheltenham, Glos. GL52 4SF UK

C. Fielding Aerodynamics (W427D) British Aerospace Warton Aerodrome Preston PR4 lAX UK J. Hodgkinson 7022 Starstone Drive Rancho Palos Verdes, CA 90275 USA R.A. Hyde Cambridge Control Ltd Matrix House Cowley Park Cambridge CB4 0HH UK R. Luckner DaimlerChrysler Aerospace Airbus GmbH Flight Mechanics Flight Guidance and Control PO Box 95 01 09 D-21111 Hamburg Germany D.G. Mitchell Hoh Aeronautics Inc. Vista Verde Center 217 2075 Palos Verdes Drive North Lomita, CA 90717 USA

xiv

Contributors

R.W. Pratt Formerly: Department of Aeronautical and Automotive Engineering Loughborough University Loughborough UK Now with: Ricardo MTC Ltd. Midlands Technical Centre Southam Road Radford Semele Leamington Spa Warwicks CV31 1FQ UK S.P. Ravenscroft

Flight Systems (W354C) British Aerospace Warton Aerodrome Preston PR4 lAX UK

T,D. Smith Flight Test (W27K) British Aerospace Warton Aerodrome Preston PR4 lAX UK R. Taylor Ricardo MTC Ltd. Midlands Technical Centre Southam Road Radford Semele Leamington Spa Warwicks CV31 1FQ UK

Preface

If you belong to the school of thought that says 'give me a model and I'll give you a controller' then this book is not for you. If, however, you believe that using linear-control design methodologies to develop flight control laws requires a fuller understanding of the dynamics of the plant (aircraft), the problems associated with implementation and the n e e d to satisfy the requirements of a highly trained h u m a n operator (pilot) then the chapters in this b o o k should help you to develop that understanding. In essence, m u c h of this b o o k is a message to the academic researcher which says: ' I f your work is to be useful to practising engineers in industry, then you n e e d to understand, or at least appreciate, the issues dealt with in this book'. Additionally, young engineers who are beginning their careers in the aerospace industry should find it useful to have a coverage of the key aspects of flight control in a single volume T h e authors were chosen because of their depth of experience and mix of backgrounds, which I believe are reflected in their individual contributions. Additionally, in a n u m b e r of cases the chapters were reviewed by senior managers who have spent their entire careers in the aerospace industry. Hopefully, the experience which lies behind the individual contributions will encourage a new generation of engineers, mathematicians and scientists to b e c o m e involved in this exciting branch of e n g i n e e r i n g - - f l i g h t control systems. In the late seventies and eighties very few texts were p r o d u c e d on flight control. T h e n in the nineties a n u m b e r of books appeared. For readers who are new to flight control it might be useful to attempt to assign a place for this text in the total grouping. Fundamentals of the subject with varying degrees o f emphasis on aircraft dynamics and flight control are covered by a n u m b e r of texts [1-7]. All of these texts should be of use to u n d e r g r a d u a t e students in the final year or years of their courses, as well as to postgraduate students who are in the process of strengthening their knowledge of f u n d a m e n t a l concepts before immersing themselves in their specific topic. The texts by McLean [4] and Stevens and Lewis [7] will extend the r e a d e r ' s knowledge into the realms of research work. The contribution edited by Tischler [8] is significantly different from the other texts in that experienced practitioners, some of whom have contributed to this book, give a strong account of the state of the art, for rotorcraft, combat aircraft and fixed-wing transport

xvi

Preface

aircraft. Our text is seen as bridging the gap between the work on fundamental principles and Tischler's excellent collection of research reviews. The aim of this text is to build on the fundamentals of flight dynamics and flight control as described in References [ 1-7] and embellish these principles by assigning their relevance to the development of flight control systems in the aircraft industry. The first seven chapters cover most of the key areas within the discipline of flight control systems with explicit reference to recent development programmes written by engineers who were closely involved in the work. The last two chapters look at just two of the multitude of m o d e r n control methods which have been the subject of research studies. The text is largely restricted to military and civil fixed-wing aircraft. Only the constraint of space has prevented equivalent material for rotorcraft and missiles from being included. The book comprises nine chapters: Chapter 1 'Industrial considerations for flight control', Chris Fielding and Robert Luckner: the authors set the scene for the whole book by explaining the industry's perspective on flight control systems, giving a comprehensive overview of the subject with more detailed discussions of some particular topics being given in later chapters. The authors have carried through their chapter the parallel themes of military combat aircraft and civil aircraft, an interesting feature which strongly reflects their backgrounds. The Chapter begins by examining the general objectives of flight control and the role of the flight control system (FCS). This is followed by the operational requirements for both types of aircraft and a discussion of the benefits of fly-by-wire (FBW) in the pilot-vehicle system. The systems issues are explored, as are reliability and integrity, the twin versus--verification and validation. The Chapter is rounded off by a discussion of the state-of-the-art and a look at some exciting future developments. Chapter 2 'Aircraft modelling', Mike Cook: the author summarises from his own text [3] the main elements of axis systems and the equations of motion for the longitudinal and lateral dynamics of fixed-wing aircraft. Aircraftresponse transfer functions and state-space representations are then developed from the equations of motion. Any reader who requires a fuller treatment than can be given within the confines of this book is strongly r e c o m m e n d e d to refer to Mike's own text. Chapter 3 'Actuation systems', Steven Ravenscroft: since the advent of powered control surfaces without manual reversion, in the era of the Lightning, actuation systems have assumed great importance. The significance of actuation systems has been further enhanced by the drive to develop highly agile combat aircraft in which a safety-critical flight control system is required to stabilise the unstable open-loop dynamics of the aircraft. This comprehensive chapter begins with an overview of primary and secondary control surfaces and their operation and leads on to a discussion of performance criteria and modelling. The latter sections discuss more

Preface

xvii

advanced topics: nonlinear frequency response, saturation analysis, j u m p resonance and failure transients. Chapter 4 'Handling qualities', J o h n Hodgkinson and Dave Mitchell: uses the response transfer functions developed in Chapter 2 and examines the response of the aircraft from the pilot's viewpoint. The subjectivity which is inherent in the assessment of handling qualities has, inevitably, given rise to a n u m b e r of metrics and these are discussed in relation to the dynamic modes for the longitudinal and the lateral motion. This leads on to stability and control augmentation systems and a discussion of some control design concepts. Clearly, a chapter on handling qualities has to include a discussion of pilot-induced oscillations (PIOs). This topic is given a thorough and up-todate treatment which reflects the very recent research carried out in the United States. Chapter 5 'Automatic flight control system design considerations', J o h n Fenton: this chapter gives a clear and practical breakdown of the tasks which are necessary in the management of the development programme for a complex flight control system. The conciseness of the chapter stems from the detailed breakdown of the main areas, the development programme requirements definition and verification, system design considerations and AFCS architecture, into detailed subtasks. Chapter 6 'Ground and flight testing a digital flight control system', Terry Smith: discusses the techniques which have been employed by the UK's major aircraft manufacturer, British Aerospace, as it has progressed with the development of fly-by-wire combat aircraft. The chapter gives an excellent description of the need to progress a test programme in a way which minimises both risk and cost, from the philosophy, tools and techniques of flight testing through the elements of simulator and rig testing, ground testing and, of course, flight testing. Chapter 7 'Aeroservoelasticity', Brian Caldwell, Roger Pratt, Richard Taylor and Richard Felton: discusses how a safety-critical flight control system can be affected by the elastic behaviour of the aircraft structure, namely the p h e n o m e n o n of aeroservoelasticity or structural coupling. As with the previous chapter, the material draws on the experience gained at British Aerospace with a series of aircraft in which the open stability has been reduced to the point of severe instability in order to enhance manoeuvrability. The contributions from Richard Taylor and Richard Felton are based on the results of research programmes which were carried out at the Universities of Loughborough and Lancaster, respectively. Chapter 8 'Eigenstructure assignment', Lester Faleiro and Roger Pratt: represents one contribution to the work done u n d e r the GARTEUR Action Group on robust flight control in which a group of universities, research establishments and aircraft companies contributed u n d e r Jan Terlouw's (NLR) excellent stewardship. Eigenstructure assignment was chosen in this case because it appeared to offer a more visible methodology than other m o d e r n control techniques. The case study (RCAM) was based on a flight

xviii

Prefa~

profile for a civil aircraft which consisted of a base leg and a two-stage final approach. The chapter is intended as an honest assessment of eigenstructure assignment in this type of application. Chapter 9 'An H0~ loop-shaping design for the VAAC Harrier', Rick Hyde: describes one of the most exciting research programmes which has been carried out in the field of m o d e r n control engineering applied to flight control. H0~ designs were evaluated extensively by piloted simulation and on the VAAC Harrier at DERA Bedford where the controller was in competition with designs from British Aerospace and Smiths Industries. The early work benefited enormously from the rapport between Rick and the RAF's test pilot, Bj6rn Singer. A step-by-step guide is given to the linear loop-shaping design process with a clear description of the use of the knowledge of the aircraft's dynamics. This is followed by the work on implementation and flight testing which explains the approach that was taken to gain-schedule controllers, deal with antiwindup as well as describe the impressive results achieved during flight testing. I would like to thank George Irwin, co-editor for the series, for inviting me 'to write or edit a text of flight control': certainly, there have been moments when I have regretted yielding to George's Celtic persuasion. However, over twenty or so years I have benefited greatly from my association with the control community in the UK and, more recently, this has been equally true o f my association with the guidance, navigation and control activities within the AIAA in the United States and GARTEUR in Europe. My contribution to this book can be viewed as a partial repayment of a very large debt. Obviously, an edited text is the product of a team of authors. I have been extremely fortunate to be able to assemble a very strong team, but more than that, they have been great people to work with. Although, inevitably, experienced people have many calls on their time and from time to time this has caused the usual problems, everyone has come through and I have greatly appreciated their support and friendship throughout the preparation of the text. Additionally, I would like to thank the people who have volunteered to review individual chapters. Tony Lambregts (FAA) and Mike Walker (British Aerospace) are two people who are known to me, others have been acknowledged by individual authors. The process of publishing an edited text with several contributors is a demanding task. I have been extremely fortunate to work with Jonathan Simpson, then the IEE's commissioning editor for the project. Jonathan's quietly efficient style impressed me greatly and on many, many occasions I have been extremely grateful for his support and guidance. I would also like to thank Robin Mellors-Bourne, Director of Publishing, who managed the project in addition to his normal duties during a very difficult period and Sarah Daniels, Book Production Editor, who joined the project at a late stage and injected some much needed energy and enthusiasm. Finally, I would like to express my thanks to Penny Pilkington whose support and commitment I have greatly appreciated throughout this project.

Preface

xix

Penny has acted as the focal point for communications and retyped contributions and patiently, well mostly patiently, e n d u r e d the seemingly endless edits.

References [1] BABISTER, A.W.: 'Aircraft-dynamic stability and response' (Pergamon Press, 1980) [2] BLAKELOCK,J.H.: 'Automatic-control of aircraft and missiles' (Wiley, 1991, 2nd edn.) [3] COOK, M.V.: 'Flight dynamics: principles' (Arnold, 1997) [4] ETKINS, B, and REID, L.D.: 'Dynamics of flight: stability and control' (Wiley, 1996, 3rd edn.) [5] MCLEAN, D.: 'Automatic-flight control systems' (Prentice-Hall, 1990) [6] NELSON, R.C.: 'Flight stability and automatic control' (McGraw-Hill, 1998, 2nd edn.) [7] STEVENS, B.L., and LEWIS, EL.: 'Aircraft control and simulation' (Wiley, 1992) [8] TISCHLER, M.B. (Ed): 'Advances in aircraft flight control' (Taylor & Francis, 1996)

Nomenclature

A B

cg C

cL D

g G h

i, I

I= kq

k~ kw ko kr L m

M M

N N o

P q 1" $

t

state matrix input matrix centre of gravity output matrix drag coefficient lift coefficient direction cosine matrix; direct matrix acceleration due to gravity transfer function matrix height m o m e n t of inertia in roll m o m e n t of inertia in pitch m o m e n t of inertia in yaw identity matrix product of inertia about ox or oz axes pitch-rate transfer function gain constant axial-velocity transfer function gain constant normal-velocity transfer function gain constant pitch-attitude transfer function gain constant turbojet engine gain constant rolling m o m e n t mass pitching m o m e n t 'mass' matrix yawing m o m e n t n u m e r a t o r matrix origin of axes roll-rate perturbation pitch-rate perturbation yaw-rate perturbation Laplace operator time; maximum aerofoil section thickness roll-mode time constant

xxviii

U U

U /] V

V

W X X

X Y Y Y Z

Z

Re

%

A

7/ 0

I"

Nomenclature

spiral-mode time constant numerator zero in axial-velocity transfer function numerator zero in normal-velocity transfer function numerator zero in pitch-rate and attitude transfer functions turbojet engine time constant axial-velocity perurbation input vector total axial velocity axial component of steady-equilibrium velocity lateral-velocity perturbation eigenvector perturbed total velocity; total lateral velocity lateral component of steady-equilibrium velocity steady-equilibrium velocity normal-velocity perturbation total normal velocity normal component of steady-equilibrium velocity longitudinal coordinate in axis system state vector axial-force component lateral coordinate in axis system output vector lateral-force component normal coordinate in axis system normal-force component angle-of-attack or incidence perturbation equilibrium incidence sideslip angle perturbation equilibrium flight-path angle roll-control stick angle pitch-control stick angle rudder-pedal control angle transfer function denominator throttle-lever angle rudder-angle perturbation; damping ratio dutch-roll damping ratio phugoid damping ratio short-period pitching-oscillation damping ratio elevator-angle perturbation pitch-angle perturbation equilibrium pitch angle aileron-angle perturbation engine-thrust perturbation roll-angle perturbation

Nomenclature

¢ ~0 d f-On

% Ws

yaw-angle perturbation dutch-roll u n d a m p e d natural frequency d a m p e d natural frequency phugoid u n d a m p e d natural frequency short-period pitching-oscillation u n d a m p e d natural frequency

SUBSCRIPTS

0 b d e E p q r s u v w

free-stream flow conditions aeroplane body axes dutch roll equilibrium, steady or initial condition datum-path earth axes roll rate; phugoid pitch rate yaw rate; roll mode short-period pitching oscillation; spiral mode axial velocity lateral velocity aeroplane wind or stability axes; normal velocity

(

rudder elevator pitch ailerons thrust

0 ~-

EXAMPLES OF O T H E R SYMBOLS AND NOTATION xu

a shorthand notation to denote a concise derivative, a dimensional derivative divided by the appropriate mass or inertia parameters

.~

a shorthand notation to denote the dimensional Ou

N { (s)

a shorthand notation to denote a transfer function numerator polynomial relating the output response y to the input u

OX

xxix

Glossary of terms

Accident (aircraft): an unintended event that causes death, injury, environ-

mental or material damage Active control technology: the use of feedback control to enhance the performance or controllability and handling of a vehicle Actuator: physical device for producing motion and/or force Adaptive control: real-time parameter identification and controller update Aerodynamic derivative: partial derivative defining changes in vehicle force or moment due to changes in control or motion parameters Air data system: provides flight-condition and velocity vector information from external aircraft measurements Airworthiness: an all-embracing term to describe an aircraft's ability to fulfil its role safely Aliasing: phenomenon in digital systems in which input signal frequencies above half the sampling frequency appear at lower frequencies on the output signal, owing to the sampling process Analogue (computer): using electrical signals that are directly proportional (i.e. analogous) to a continuous physical parameter Angle of attack (AoA): the angle formed by the vector addition of the aircraft body-axis normal and longitudinal velocity components Anti-aliasing filter: function for reducing aliasing by restricting the bandwidth of the signal to be sampled--usually an analogue filter with a natural frequency set to less than half the sampling frequency Authority limit" permissible maximum amplitude of a signal or physical parameter Autopilot- outer-loop automatic control system for reducing pilot workload and/or augmenting weapon-system performance Autostabiliser: simple stability-augmentation system, usually to provide increased damping and often with limited authority Averaging (rolling average): digital process used to provide a smoothing and anti-aliasing function Backlash: a form of hysteresis found in mechanical systems Bandstop filter: see notch filter Bandwidth: range of frequencies over which the amplitude of the frequency response of a device remains essentially constant (numerical definitions vary)

Glossary of terms

xxi

Bode diagram: frequency-response plots covering gain (usually in decibels, dB) against frequency and phase against frequency Break point: frequency at which attenuation (or amplification) appears to occur, for the frequency response of a real pole or zero term Built-in test: checks that are carried out automatically on the system or part of the system by failure-detection algorithms within the flight control system. These checks may be carried out continuously or at specific instances, for example, on start-up Carefree handling: protection of aircraft from both departure and exceedance of loading limits, regardless of pilot-input demands, through the functionality of the flight control system Certification: process for demonstrating that system safety is satisfactory for flight operation Characteristic equation: polynomial defining the linear-stability characteristics of the system (defined by setting the denominator of a transfer function equal to zero) Classical control: range of design and analysis techniques developed early in the 20th century, principally the methods referred to as Bode, Nyquist, Nichols, R o o t - L o c u s . . . Clearance: see certification Closed-loop control: outputs from the aircraft (or system) are measured and fed back to provide corrective action Command path: part of control system between physical input (e.g. pilot's stick) and the point where feedback is applied Conditionally stable: a system that is stable only for a range of values of a particular gain; the system can be made unstable by either increasing or decreasing the nominal gain value by a sufficient amount Control-configured vehicle (CCV): one which incorporates the control system capabilities and limitations at the onset of the project design Control law: architecture containing controller(s), feedback filtering, nonlinear compensation and scheduling Controller: algorithm or filter to provide desired control behaviour, usually acting on an error signal Cooper-Harper rating: a method for quantifying pilot opinion of an aircraft handling task, in terms of perceived controllability and operational effectiveness Crossover frequency: gain crossover occurs when the gain of a system equals unity (0 dB); phase crossover occurs when the phase equal - 1 8 0 degrees. These are the frequencies at which the stability margins are measured Damping: attribute which determines the nature of a response, in terms of the rate of decay of oscillatory behaviour DC block: see high-pass filter Dead-beat (response): exhibiting no overshoot when tracking a step input signal

xxii

Glossary of terms

Dead-zone: nonlinearity in which no output is achieved until the input exceeds some threshold Decade: frequency interval in which the frequency changes by a factor of ten Decibel (riB): defined at each frequency as 101ogl0(g) where g is ratio of powers, or 201ogl0(g) if g is a ratio of voltages or signal amplitudes Defect: the nonconformance of an item to one or more of its required parameters, within the limits defined in the specification Derivative control/action: a function proportional to the rate of change of the applied signal (i.e. differentiation with respect to time) Describing function: approximation of nonlinear behaviour (amplitude dependence) of a system element, by modelling the gain and phase characteristics of the fundamental components of its Fourier transform Digital: described by a function of regularly sampled values Dissimilar redundancy: multiplex arrangement where different lanes use different software a n d / o r hardware to perform the same function Disturbance: an unwanted signal or force which can impair the quality of control Drop back: a reduction in attained angle, following the removal of an angular rate demand Duplex: having two hardware lanes operating in parallel, with crossmonitoring for detection of a single failure Error: a state, resulting from a fault or human mistake, which is liable to lead to incorrect operation Error signal: a control system signal equal to the calculated value between the parameter value commanded and that achieved Failure: an occurrence in which a previously acceptable item is no longer able to perform its required function within the limits defined in the specification Fault: see defect Feedback: signal generated by sensor and applied with the aim of corrective action Feedforward: signal from the command path which bypasses the controller to boost the downstream command to an actuator--improving transient response without affecting stability Flight control laws: control laws (or algorithms) within the flight control system which have broarder capabilities, for example, the monitoring of independent signal channels for possible failures Flight envelope: boundaries which define the limitations imposed on the operation of the aircraft defined in terms of altitude, airspeed/Mach number and load factor Flight management systems: system designed to assist the flight crew in managing the aircraft's systems, for example, fuel and navigational Fly-by-wire (light): connection between pilot's control column, yoke or inceptor made electrically (or by fibre optics) rather than by mechanical

Glossary of terms

xxiii

system consisting of rods, cables and levers Hying qualities: see handling qualities Frequency response: variation of an output signal magnitude and phase characteristics, relative to a sinusoidal input signal, as frequency varies Full authority: allowing the maximum useable range Full-state feedback: all the system states are used as feedback signals Functional requirements document: specification of function requirements (e.g. control laws) Gain: control law parameter for providing a signal-scaling capability Gain margin: the factor by which the gain may be increased or decreased before system instability results Gain schedule: variation of a gain or gains within a control law with respect to some measured scheduling variable (s) Governor: a mechanical system for regulating a controlled parameter Handling (or flying) qualities: piloting characteristics with respect to how easy or safe the aircraft is to fly (for a particular task) Hang-off (also hang-on): transient response characteristics whereby the commanded response fails to achieve its steady-state value within an acceptable time; is associated with undershoot, and with overshoot Hard-over: a failure that causes a control surface to rapidly drive its output to the authority limit Hazard: a state of the system, often following some initiating event, that can lead to an accident High-pass filter: attenuates low frequency signals, allowing high frequencies to pass Hysteresis: nonlinear function in which the i n p u t / o u t p u t relationship for increasing an input is different from that for decreasing the input Inceptor: physical device with variable force a n d / o r motion, for enabling pilot input to the flight control system. Examples might be a centre-stick control column, a side stick or a throttle lever Incidence: see angle-of-attack Incident: an event which results in equipment or property sustaining damage or any person receiving any injury, or which might have resulted in an accident Integrating filter: function for performing integral action on a signal Integrity: freedom from flaw or corruption (within acceptable limits) J u m p resonance: undesirable nonlinear saturation p h e n o m e n o n with a sudden j u m p in its frequency-response characteristics l a n e : a signal path containing all the hardware and functional elements of the control system within a multiplex arrangement Limited authority: having access to only part of the full range available Limit cycle: bounded amplitude and fixed-frequency oscillation of a system, involving nonlinear beahviour Line-replaceable unit or item: equipment fitted into an aircraft Linear system: having no nonlinearities; scaling any input signal scales all the

xxiv

Glossary of terms

outputs by the same factor; the principle of superposition applies Linear quadratic Gaussian (LQG): linear design method which uses a quadratic cost performance and Gaussian noise to determine optimum feedback gains Low-pass filter: function which attenuates high frequency signals but allows low frequency signals to pass Minimum phase: a system which has no zeros in the right half of the complex plane Mission-critical: loss of capability leading to possible reduction in mission effectiveness; compare with safety-critical Mode (FCS): a selectable function of the FCS, e.g. terrain following Modern control: a range of design and analysis techniques developed, generally considered as post 1960 Multi-input multi-output (MIMO) system: a system which has at least two inputs and at least two outputs. Often it is understood that the system possessses significant interaction or cross-coupling Multiplex: having several hardware lanes to enable detection and isolation of equipment failures Multivariable control: theory and techniques for addressing multi-input multi-output systems Natural frequency (damped): the frequency at which a system will tend to respond when excited by a sudden input Nichols chart: frequency response rectangular plot with gain in decibels (dB) plotted against phase in degrees and with frequency varying as a parameter. The chart contains contours of closed-loop gain and phase characteristics superimposed, assuming unity negative feedback Noise: usually, an unwanted signal corrupting the desired signal Nonlinearity: characteristic which introduces amplitude dependency into a system; linear behaviour is not preserved, in that the output magnitude no longer scales with the input Nouminimum phase: having zeros in the right-half complex plane Notch filter: function which produces attenuation over a specified frequency range, normally with minimal attenuation either below or above that range Nyquist diagram: a polar plot of a system's frequency response in the complex plane, with frequency varying as a parameter Open-loop: without the use of any feedback Order: the number of poles in the characteristic polynomial, remembering that a complex pair consists of two poles Overgearing: where the control system gains have been increased beyond the point of optimum performance Overshoot: transient response characteristic whereby the commanded response exceeds its steady-state; usually measured as a percentage Pad6 approximation: a transfer function technique for establishing a loworder approximation to exponential functions (e.g. to model pure time delays)

Glossary of terms

xxv

Phase: the relative angle between a sinusoidal input signal and the corresponding output signal Phase advance filter: function for providing a low frequency phase lead, at the expense of increasing high frequency gain Phase margin: the amount of phase lag (or advance) a system can tolerate before instability is reached Phase-plane analysis: rectangular plot of two system states, usually position and velocity, for analysing system behaviour, particularly when nonlinear characteristics are present Phase-retard filter: function for providing high frequency attenuation, with the associated phase loss being recovered at higher frequencies Pilot-induced oscillation (PIO): p h e n o m e n o n whereby the pilot inadvertently triggers and sustains an oscillation of the aircraft through a control input, owing to adverse coupling with the system dynamics Plant: a device which is to be controlled, for example, an aircraft Pole: real or complex root of transfer function denominator polynomial, sometimes referred to as an eigenvalue of the system Power spectrum: plot of power against frequency where power is defined as the square of the signal magnitude Primary controls: those controls which are fundamental for the safe operation of the system, for example, elevators, ailerons and rudder Proportional, integral and derivative: three-term controller with inherent phase advance and tracking capability Quadruplex: having four hardware lanes for detection and isolation of up to two identical failures Qualification: process for demonstrating that the system meets the customer's requirements Random failure: a failure which results from a variety of degradation mechanisms in the hardware Rate limit: physical or functional limit on rate of change of a parameter, of particular significance in actuation systems Reconfigurable control: redistribution of system functions or hardware following a failure, to maintain satisfactory operation Redundancy: duplication of components or software, to improve system integrity Regulator: a control system in which the design driver is satisfactory disturbance rejection, in order to hold some desired parameter value constant; command tracking is usually of secondary importance Reliability: the probability that a system will be free from faults Resonant frequency: frequency at which the ratio of the magnitudes of a system's output to input is a maximum Rise time: the time taken for the system response to a step input to change from ten per cent to ninety per cent of its steady-state value Risk: the combination of the frequency, or probability, and the consequence of an accident

xxvi

Glossaryof terms

Robustness: the ability of a system to tolerate variations in system parameters

without u n d u e degradation in performance Roll-off: rate of gain reduction at extremes of frequency (usually specified as d B / d e c a d e or dB/octave) Root locus: parametric plot showing variation of closed-loop poles, as a function of a particular system parameter, almost invariably but not essentially, to the controller gain Safe: the state in which the perceived risk is lower than the maximum acceptable risk Safety: the expectation that a system does not, under defined conditions, lead to a state in which human life is endangered Safety-critical: failure or design error could cause a risk to h u m a n life Sample and hold: device for producing an analogue signal from a series of discrete digital pulses Saturation: a state where authority limits, rate limits or acceleration limits are reached Secondary controls: those controls which are not essential for safe operation of the system, but are likely to result in degraded performance if they are not available (for example, flaps) Self-monitoring: capability of a lane of computing to detect its own failures Sensor: physical device for detection of inceptor positions, feedback measurements or scheduling information Servomechanism: control system, literally slave mechanism, in which the design driver is accurate tracking of a varying input signal and where disturbance rejection is usually of secondary importance Servovalve: a hydraulic device applied to a control valve or ram for switching the pressure and controlling the direction and magnitude of flow of hydraulic fluid Settling time: time taken for the c o m m a n d e d response to remain within a specified percentage, often five per cent, of its steady-state value Sideslip: the angle formed by the vector addition of the aircraft body-axis lateral and longitudinal plane velocity components Similar redundancy: multiplex arrangement where different lanes have identical software and hardware to perform the same function Single-input single-output (SISO): system which has only one input with one associated controlled output Stability margin: a measure of system stability--see gain margin and phase margin Validation: process of determining that the requirements are correct and complete Verification): evaluation of results of a process to ensure correctness and consistency with respect to the inputs and standards provided to that process C. Fielding and R. W. Pratt

Contents

Contributors Preface Glossary of terms Nomenclature 1 Industrial considerations for flight control C. Fielding and R. Luckner 1.1 Introduction 1.2 The general objectives of flight control 1.2.1 Military aircraft 1.2.2 Civil aircraft 1.3 The role of the flight control system 1.3.1 History 1.3.2 Military aircraft developments 1.3.3 Civil aircraft developments 1.4 Aircraft in-service requirements 1.4.1 Military aircraft operations 1.4.2 Civil aircraft operations 1.5 The benefits of fly-by-wire 1.5.1 Military aircraft benefits 1.5.2 Civil aircraft benefits 1.6 Flight control systems implementation 1.6.1 Military aircraft--design considerations and systems overview 1.6.2 Civil aircraft--design considerations and systems overview 1.7 Military aircraft--state-of-the-art and future challenges 1.7.1 Eurofighter Typhoon 1.7.2 Future challenges for military aircraft 1.8 Civil aircraft--state-of-the-art and future challenges 1.8.1 The Airbus fly-by-wire family 1.8.2 Boeing 777 1.8.3 Future challenges for civil aircraft 1.9 The flight control system development process 1.9.1 The current situation 1.9.2 The system development process 1.9.3 The flight control laws development process 1.9.4 Cost considerations--recurring and nonrecurring costs 1.10 Closing discussion 1.11 Acknowledgements 1.12 References 2 Aircraft modelling M. V. Cook 2.1 Introduction

xiii xxvfi

1 2 6 6 7 7 9 12 13 13 15 17 18 19 20 20 27 30 30 33 34 34 42 42 43 43 44 46 5O 51 53 53 56 56

Contents

viii 2.2 2.3

2.4

2.5

2.6

2.7

2.8 2.9 2.10

2.11

2.12 2.13

A mathematical framework Axes systems and notation 2.3.1 Earth axes 2.3.2 Aeroplane-body fixed axes 2.3.3 Perturbation variables 2.3.4 Angular relationships in symmetric flight 2.3.5 Choice of axes Euler angles and aeroplane attitude 2.4.1 Linear-quantities transformation 2.4.2 Angular velocities transformation Controls notation 2.5.1 Aerodynamic controls 2.5.2 Engine control The decoupled small-perturbation equations of motion 2.6.t The equations of longitudinal symmetric motion 2.6.2 The equations of lateral-directional asymmetric motion The equations of motion in state-space form 2.7.1 The equations of longitudinal motion 2.7.2 The equations of lateral-directional motion Aircraft-response transfer functions The transfer function matrix Longitudinal response to controls 2.10.1 The longitudinal transfer function matrix 2.10.2 The longitudinal characteristic equation 2.10.3 The short-period pitching oscillation 2.10.4 The phugoid Lateral-directional response to controls 2.11.1 The lateral transfer function matrix 2.11.2 The lateral-directional characteristic equation 2.11.3 The roll-subsidence mode 2.11.4 The spiral mode 2.11.5 The dutch-roll mode Conclusions Reference

3 Actuation systems

57 59 59 60 61 63 64 65 66 66 67 67 67 68 68 69 69 7O 72 72 73 74 74 76 76 79 81 81 84 85 86 87 89 89 9O

S. Ravenscroft 3.1 3.2 3.3

3.4 3.5 3.6 3.7 3.8 3.9 3.10

Introduction Actuation system technology--an overview 3.2.1 Control-surface types 3.2.2 Actuator operation Actuation system-performance criteria 3.3.1 Stall load 3.3.2 Maximum rate capability 3.3.3 Frequency response 3.3.4 Dynamic stiffness 3.3.5 Failure transients Actuation system modelling Nonlinear frequency response Saturation analysis J u m p resonance Failure transients Conclusions Acknowledgements

90 90 90 91 96 98 99 100 104 105 107 109 110 112 112 116 118

Contents 4 Handling qualities

ix

119

J. Hodgkinson and D. Mitchell 4.1 4.2

Introduction Longitudinal flying qualities 4.2.1 Control-input transfer functions 4.2.2 Modal criteria 4.2.3 Phugoid flying qualities 4.2.4 Short-period flying qualities 4.2.5 Criteria for the longitudinal short-period dynamics 4.2.6 Model criteria for the short period 4.2.7 Other short-period criteria 4.2.8 Equivalent systems 4.2.9 Equivalent time delay 4.2.10 The bandwidth method 4.2.11 The Neal-Smith method 4.2.12 Gibson's dropback criterion 4.2.13 Time-history criteria 4.2.14 Flight-path stability 4.3 Lateral-directional flying qualities 4.3.1 Roll mode 4.3.2 Spiral mode 4.3.3 Coupled-roll spiral 4.3.4 Dutch-roll mode 4.3.5 The parameter t%/~a 4.3.6 Phi-to-beta ratio, ~b//3 4.4 Stability and control-augmentation systems 4.4.1 The influence of feedback 4.4.2 The influence of actuators, sensors and processors 4.4.3 Multiple-input, multiple-output flying quality possibilities 4.4.4 Response types 4.5 Notes on some control design concepts 4.5.1 Integration in the forward path 4.5.2 Notch filters 4.5.3 Stick prefilters 4.5.4 Model prefilters 4.6 Pilot-induced oscillations ( P i t s ) 4.6.1 P I t categories 4.6.2 P I t and APC 4.6.3 Criteria for category I P i t s 4.7 Modal P I t criteria 4.7.1 STI high-gain asymptote parameter 4.7.2 A'Harrah-Siewert criteria 4.7.3 Dynamic stick force per g 4.8 Non-modal P I t criteria 4.8.1 Some current criteria 4.8.2 Effectiveness of the criteria 4.9 Effects of rate limiting on P I t 4.9.1 Criteria for category II P i t s 4.9.2 The consequences of rate limiting 4.10 Concluding remarks 4.11 References

119 121 121 121 122 123 124 126 126 127 131 132 132 134 134 136 136 136 139 139 139 140 141 142 142 144 146 147 147 147 149 150 150 150 150 151 151 152 152 155 155 155 156 161 164 164 165 167 167

x

Contents

5 Automatic flight control system design considerations

170

J. Fenton

5.1 AFCS development programme 5.1.1 Study phase/vendor selection 5.1.2 Interface definition 5.1.3 System definition 5.1.4 Software design and code 5.1.5 Hardware design and development 5.1.6 System integration and test 5.1.7 Qualification testing 5.1.8 Preliminary (final) declaration of design and performance (PDDP/FDDP) 5.1.9 Flight testing 5.1.10 Certification 5.1.11 Design reviews 5.2 Requirements definition and verification 5.2.1 Introduction 5.2.2 Design and test methodology 5.2.3 Safety considerations 5.3 System design considerations 5.3.1 Primary considerations 5.4 AFCS architecture 5.4.1 Introduction 5.4.2 AFCS flying control interfaces 5.4.3 AFCS system interfaces 5.4.4 AFCS configurations 5.4.5 Flight control computer data processing 6 Ground and flight testing of digital flight control systems

170 170 172 172 172 172 172 173 173 173 173 173 174 174 175 176 178 178 184 184 184 184 188 189

197

7: Smith

6.1 Introduction 6.2 Philosophy of flight testing 6.2.1 Ground testing 6.2.2 Simulator and rig testing 6.3 Aircraft ground testing 6.3.1 FCS build tests 6.3.2 Ground-resonance tests 6.3.3 Structural-coupling tests 6.3.4 Electromagnetic-compatibility testing 6.3.5 Engine-running tests 6.4 Flight test tools and techniques 6.5 Flight testing 6.5.1 FBWJaguar demonstrator flight test programme 6.5.2 The EAP demonstrator flight test programme 6.6 Conclusion 6.7 Acknowledgements 6.8 References

7 Aeroservoelasticity

197 2O0 201 202 209 210 210 210 211 213 213 214 214 217 223 223 223

225

B.D. CaldweU, R. W. Pratt, tL Taylor and R.D. Felton

7.1 Introduction 7.2 Elements of structural coupling 7.2.1 Flexible-aircraft modal dynamics

225 226 226

Contents

7.3

7.4

7.5 7.6

7.2.2 Inertial excitation of the flexible-aircraft control surface 7.2.3 Actuators, flight control computers and the aircraft-motion sensor unit 7.2.4 Aerodynamic excitation of the flexible-aircraft's control surface 7.2.5 Flexible-aircraft modal aerodynamics 7.2.6 Formulation for solution and design trade-offs FCS-SC structural coupling: design examples 7.3.1 Jaguar-first flight 1968 7.3.2 Tornado-first flight 1974 7.3.3 Experimental aircraft programme (EAP)--first flight 1986 7.3.4 Eurofighter 2000 (EF2000)--first flight 1994 Future developments 7.4.1 Limit-cycle prediction and specification of alternative clearance requirements 7.4.2 Active control for rigid body and structural-mode stabilisation 7.4.3 Flexible aircraft modelling Conclusions References

8 Eigens~ucture assignment applied to the design of an autopilot function for a civil aircraft L.F. Faleiro and R. W. Pratt

8.1 Introduction 8.2 The RCAM control problem 8.2.1 A landing-approach simulation 8.2.2 Performance specifications 8.2.3 Robustness specifications 8.2.4 Ride-quality specifications 8.2.5 Safety specifications 8.2.6 Control-activity specifications 8.3 Eigenstructure analysis and assignment 8.3.1 Eigenstructure analysis 8.3.2 Eigenstructure assignment 8.4 The eigenstructure assignment design cycle 8.4.1 Controller structure 8.4.2 Construction of a desired eigenstructure 8.4.3 Initial synthesis 8.4.4 Methods of controller analysis 8.4.5 Analysis of the longitudinal controller 8.4.6 Analysis of the lateral controller 8.4.70ptimisation of the controllers 8.5 Nonlinear simulation of the controlled aircraft 8.5.1 Performance specifications 8.5.2 Robustness specifications 8.5.3 Ride-quality specifications 8.5.4 Safety specifications 8.5.5 Control-activity specifications 8.5.6 Evaluation using a landing-approach simulation 8.6 Conclusions 8.7 References 9 An H ® loop-shaping design for the VAAC Harrier R.A. Hyde

9.1 Introduction

xi 226 228 230 230 230 234 235 236 237 248 260 260 284 297 298 299 301

301 302 304 305 306 306 306 307 307 307 310 316 316 320 324 324 327 329 330 331 333 337 337 338 338 339 343 346 348

348

xii

Contents

9.2 9.3 9.4 9.5

The VAAC Harrier Ha Loop shaping Linear design for the VAC Implementation and flight testing 9.5.1 Gain scheduling 9.5.2 Anti-windup 9.5.3 Flight modes 9.5.4 Flight testing 9.6 Flight clearance 9.7 The way ahead 9.8 References

350 350 354 359 359 360 362 364 366 371 372

Index

375

Chapter 3

Actuation systems S. Ravenscroft

3.1 Introduction Actuation systems are a vital link in the flight control system, providing the motive force necessary to move flight control surfaces. Whether it is a primary flight control, such as an elevator, rudder, taileron, spoiler or foreplane, or a secondary flight control, such as a leading edge slat, trailing edge flap, air intake or airbrake, some means of moving the surface is necessary. Performance of the actuator can have a significant influence on overall aircraft performance and the implications of actuator performance on aircraft control at all operating conditions must be considered during flightcontrol system design and development programmes. Overall aircraft p e r f o r m a n c e requirements will dictate actuator performance requirements, which can lead to difficult design, control and manufacturing problems in their own right. In this chapter an overview of current actuation system technologies as applied to m o d e r n combat aircraft is presented, and their performance and control requirements are discussed. The implications for aircraft control are considered and an overview of selected modelling and analysis methods is presented.

3.2 Actuation system technologyman overview

3.2.1 Control-surface types Aircraft have a n u m b e r of different flying control surfaces. Some are for primary flight control (control of roll, pitch and yaw manoeuvring and stabilisation) and others are secondary controls (high-lift or lift-dump devices, for example). The type and use of a control surface has a significant impact on the requirements for the actuation system for that surface, in particular the actuator post-failure operation. Primary flight control capability is critical to safety and loss of control in one or more of the primary flight control axes will, in most cases, hazard the © 1999 British Aerospace PLC. Reproduced with permission.

Actuation systems 91 aircraft. The advent of concepts such as active control technology, controlconfigured vehicles and relaxed static stability, resulting in highly unstable combat aircraft to improve performance and agility, have led to an even greater reliance on primary flight control surface availability to the extent that many m o d e r n combat aircraft could not be controlled without the continued operation of the primary flight control surfaces. Accepting that failures within an actuator are inevitable at some time in the life of a fleet of aircraft, the actuation systems for primary flight control of such aircraft are designed to comply with a fail-op-fail-op philosophy; that is the actuator will continue to operate at, or very close to, full performance following one or two failures to meet the safety and integrity requirements. For many secondary control surfaces, it is not necessary to ensure full operation following failures. Although the loss of operation of a secondary surface may introduce flight restrictions, such as requiring a flapless landing or limiting the maximum incidence angle the aircraft can achieve, these will not directly lead to the loss of an aircraft. However, the nature of the failure may, in itself, produce a hazardous situation, such as possible engine flameout if air-intake cowls fail in a closed position, or handling and speed restrictions if an airbrake fails in the open position. In such cases a fail-op-failsafe or simply fail-safe philosophy is used, where one design feature is to ensure that the secondary control surface can be moved to a safe position or simply frozen following a failure. In the examples given above, the actuators may be required to open the intake cowl or close the airbrake following a failure, albeit at a lower rate than would normally be achieved. A similar philosophy exists for landing gear, where the safe state is gear down; the actuators have an extend only capability following loss of normal extend and retract functions. Although secondary flight controls are, of course, very important components of an aircraft and the provision of emergency operation modes can produce interesting engineering challenges, it is the primary flight control actuators that have most influence on basic aircraft stabilisation and handling qualities. T h r o u g h o u t the remainder of this chapter we will concentrate primarily on actuators for primary flight control surfaces.

3.2.2 Actuator operation Most flight control actuation systems on current aircraft are electrically or mechanically signalled and hydraulically powered. Until the early 1970s most actuators were mechanically signalled, but the advent of fly-by-wire technology has led to many actuators now having electrical signalling as the primary, if not only, form of demand. The d e m a n d signal is used to drive a spool valve, opening ports through which high-pressure hydraulic fluid flows. The fluid is metered to the actuator ram, causing the piston rod to extend or retract and providing the force to move the control surface. Movement of the spool valve could be achieved by mechanical input, using mechanical feedback of

92

Flight control systems

actuator r a m position to close the valve when the actuator reaches the d e m a n d e d position; by hydraulic means, using an electrohydraulic servo valve, in effect a mini actuator, to drive the spool; or, as is b e c o m i n g m o r e c o m m o n , by a direct m o t o r drive. These concepts are shown diagramatically in Figure :3.1. Redundancy features such as the n u m b e r of servo valves or m o t o r coils and bypass valves are not shown in this figure. A typical actuator with servo valves providing the motive force for a t a n d e m main control spool valve is shown in Figure 3.2. This particular actuator configuration uses four servo valves to drive the main control (spool) valve, each signalled by one of four flight control computers, four linear variable differential transformers (LVDTs) to measure main-ram displacement and four LVDTs to measure main-control-valve displacement, producing a q u a d r u p l e x r e d u n d a n t actuator. By comparing each of the four signals up to two failed lanes may be isolated, one lane at a time, by a majority vote, to m e e t system safety requirements. Post-failure operation requirements have a significant effect on actuator design philosophy. Redundancy is necessary in primary actuators to ensure continued operation following a failure to m e e t the fail-op-fail-op requirement. This often takes the f o r m of multiplexing, or the addition of a n u m b e r o f identical lanes of control. For example, in the Eurofighter 2000 primary flight control actuators, all feedback sensors are quadruplexed, each o f the four sensors feeding their signal back to one of four flight control c o m p u t e r s (FCCs). T h e four FCCs c o m p a r e signals across a cross-channel data link, to identify whether any of the signals differ significantly from the others. A consolidated or average signal is p r o d u c e d for use in control and m o n i t o r i n g algorithms and each FCC produces an actuator drive signal to one of the four coils in the direct drive valve m o t o r which moves the main control valve to control the t a n d e m actuator. A typical actuator with a direct m o t o r drive for first stage actuation is shown in Figure 3.3. Whereas the Eurofighter 9000 actuators use a linear m o t o r to displace the main control valve, this actuator uses a rotary, brushless DC motor, rotary motion being converted to linear motion through a crank mechanism. A further difference from the Eurofighter 2000 q u a d r u p l e x actuator is the use o f a triplex architecture, with only three coils in the direct drive m o t o r and three feedback sensors (LVDTs) for each main control valve and main ram. For a triplex actuator to survive two similar but i n d e p e n d e n t electrical failures to achieve fail-op-fail-op some element of in-lane fault detection, rather than simply a majority vote between lanes, is needed, for example comparison with a model. T h e level of redundancy refers to the n u m b e r of electrical lanes used and not the n u m b e r of hydraulic supplies. The actuators depicted in Figures 3.2 and 3.3 b o t h use two i n d e p e n d e n t hydraulic supplies with an actuator r a m of t a n d e m construction. In order to maintain separation of the two hydraulic systems the actuator design must minimise, if not eliminate, leakage of fluid between systems and a rip-stop ram design is used to ensure that fatigue

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damage in one side of the cylinder will not cause a crack which will also damage the other side of the cylinder, leading to the potential loss of both hydraulic systems. Following a failure in one of the hydraulic supplies, the remaining hydraulic system will continue to provide enough power to move the actuator against air loads. However, the movement of the ram will cause hydraulic fluid to be pushed into and out of the cylinders on the side o f the failed hydraulic supply, which could cause a drag force to restrict movement of the ram. In order to overcome this drag force, bypass valves are fitted to the actuator in Figure 3.3, to connect each side of the piston in the affected cylinder together in the event of loss of hydraulic pressure. Control of actuator position is achieved with a closed-loop, feedback control system. Ram position is measured, often using an LVDT, although potentiometers or other devices could also be used. Main-control-valve position, which is roughly proportional to ram velocity (excluding the effects o f external loads on the ram, or the effects of nonlinear valve port shapes), is also measured to give improved damping characteristics. Loop closure could be p e r f o r m e d in analogue circuitry, but is more often implemented, at least in part, in digital computers. Typical control loops, for an actuator with servo valves for main valve actuation, are depicted in block diagram form in Figure 3.4. The inner (spool position) loop is analogue, as the high bandwidth of this loop would necessitate a very high sampling rate. In this case outer-loop closure is p e r f o r m e d digitally, with feedback signals sampled at 80 Hz. In analysing the performance characteristics of the actuator it is important not to neglect the effects of digital control, including sample and computational delays, which have an effect on loop stability and actuator frequency response, and nonlinear effects caused by sampling, which can cause such effects as dither.

3.3 Actuation system-performance

criteria

An essential part of a specification for an actuation system is the definition of the system-performance requirements as these requirements will be a primary consideration for the supplier throughout the design phase. Before the airframe manufacturer accepts an actuation system the supplier must demonstrate that the specified performance requirements have been met. With long-lead-time items such as actuation systems and considering the expense involved in the testing of hardware or of modifications late in the design cycle, modelling is an important part of performance assessment both for the supplier and the airframe manufacturer. A primary flight control actuation system has to provide the necessary speed and power of control-surface response to give the aircraft the required stability and manoeuvrability. The basic performance requirements are: • the actuation system should be able to move the control surfaces with a following or opposing load, while maintaining a rate of movement

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adequate for control purposes; • the actuation system should be able to hold the control surface at a required position with a load applied in either direction up to a defined maximum-load magnitude; • the effect of the actuation-system frequency-response characteristics (gain and phase lag) on low frequency (rigid aircraft) FCS loop stability margins should be minimised; • interaction with high frequency (flexible aircraft) vibration modes should be minimised. In addition, requirements for system reliability and integrity, size, weight and installation details and the appropriate technology level have to be considered, in as far as these will have an impact on the actuation system performance. Particular performance requirements that will be considered now in more detail are: • • • • •

stall load; maximum rate capability; frequency response; dynamic stiffness; failure transients.

3. 3.1 Stall load The stall load of an actuator is the maximum force applied directly onto the main ram that can be supported by the available hydraulic supply pressure before the ram will begin to sink. The load can be in either direction (extend or retract) and the criteria will apply equally for both. The stall load is a basic design parameter for the actuator ram and determines the required piston area for a given hydraulic supply pressure available at the actuator. Requirements on the actuator's load capability are usually defined as: • minimum required output thrust (two systems operating with a defined pressure drop across each piston); • minimum single-system thrust (with a defined pressure drop across the pressurised piston, the other being bypassed); • maximum static-output thrust (two systems operating with a defined pressure drop across each piston). These requirements are used by the supplier to determine the size of the actuators within the limitations set by the available standard hydraulic seal sizes. The first two will determine the minimum size (and in particular piston area) to meet load and performance requirements, and the third sets an u p p e r limit on the size to prevent damage to aircraft structure. The magnitude of the design stall load will be based on the maximum aerodynamic hinge m o m e n t predicted at any point in the flight envelope.

Actuation systems 99 This maximum estimated value may be factored upwards to provide the required design stall load. This additional factor is required to ensure that there is sufficient excess capability in the actuator to provide manoeuvring forces in the most severe flight conditions. For unstable aircraft, the loadcarrying capability will be defined such that the maximum load experienced in flight will be no greater than 70 per cent of the single-system stall load, in order to ensure that there is always adequate rate capability for control purposes (following a hydraulic system failure), to maintain control o f the aircraft u n d e r the most adverse conditions. If the aircraft is stable then the maximum flight load may only be slightly less than the single-system stall load on the basis that recovery can be made to a flight condition where thrust capability is adequate. The primary factors affecting the stall load are: • piston area; • hydraulic supply pressure; • n u m b e r of hydraulic systems operating. Secondary factors are: • unequal piston areas on each side of the piston; • force fight in a tandem ram configuration; • cross-piston leakage. When a force is applied that exceeds the stall load the pressure required to support the load is greater than that which is available from the hydraulic supply, the ram stalls and tends to sink and the outer-loop feedback will try to compensate. The dynamic behaviour at this point can potentially be predicted by an actuator model, although post-stall behaviour is not normally regarded as being of significance for performance assessment. When the ram sinks u n d e r the applied stall load a hydraulic flow back through the valve ports against the supply is implied. Because of the main-ram position feedback control the main valve will move hard over to its maximum travel when the ram sinks, so the ports will be fully open for this reverse flow. Some actuation systems are provisioned with non-return valves which prevent reverse flow through the valve ports. If reverse flow is allowed then the sinkage of the ram reduces the static stiffness effectively to zero beyond the stall, causes the normal hydraulic pressure maxima to be exceeded and may even r e n d e r the aircraft uncontrollable.

3.3.2 Maximum rate capability Rate requirements are defined as a required rate, extending and retracting, for a given load and pressure differential across the piston. The required rates are usually defined at no-load conditions and about 60 to 70 per cent of the stall load, for two-system and single-system operation. The supplier uses the rate requirements, along with size information derived from consideration of

100

Flightcontrolsystems

the loading requirements, to d e t e r m i n e the fluid flow needed, and h e n c e the necessary valve size. T h e m a x i m u m rate at which the actuator main ram can be driven corresponds to the m a x i m u m opening of the valve ports. T h e m a x i m u m rate is reduced when the actuator is required to move against the load and increased when required to move with the load. A steady load will be present in practice when a control surface has to be deflected against the airflow, either for a steady manoeuvre or a trim requirement. T h e factors affecting the m a x i m u m rate capability are: • • • • • •

steady load; supply and return pressures; n u m b e r of operating hydraulic systems; piston areas; main-valve p o r t geometry; m a x i m u m main-valve displacement; • cross-piston leakage; • valve-block pressure losses.

From a p e r f o r m a n c e point of view the m a x i m u m rate capability must be sufficient to move the aerodynamic control surface at a speed which is required to give satisfactory pilot-handling qualities. Also, the requirements of automatic flight control systems, including any active control feedback functions where control rate is a factor, must be taken into account, since stability of the aircraft control loops u n d e r large-amplitude motions may be affected by the rate limit. T h e hydraulic supply pressure at the actuator must be maintained close to the nominal design level in order to maintain the m a x i m u m rate capability, as well as other actuation system p e r f o r m a n c e parameters. This must be taken into account when specifying the aircraft hydraulic system supply, including the pumps, accumulators and hydraulic pipe pressure losses at m a x i m u m flow. Figure 3.5 shows a typical plot of m a x i m u m rate capability as a function of steady external load, up to stall conditions for each direction of main-valve opening. The effect on m a x i m u m rate of a cross-piston leak is also given on the plot. With a cross-piston leak there are areas of operation with high steady load for which the main ram will sink against the d e m a n d e d direction as fluid drains across the piston. This should be avoided in an actuation system design by ensuring that valve port size and piston areas are adequate to prevent sink for all operating conditions, taking cross-piston leakage into consideration.

3.3.3 Frequency response Requirements for the actuation-system frequency response u n d e r particular test conditions, e.g. load, amplitude, m e t h o d of loop closure, are defined in the specification d o c u m e n t as boundaries within which the frequency

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response must lie. The gain and phase-lag boundaries are applied to the response of the ram-to-body displacement to an input d e m a n d with representative control-surface inertia loading. An example of typical gain and phase boundaries applied to a fly-by-wire actuation system is shown in Figure 3.6. Bounds are placed on the maximum and minimum gain and on the maximum allowable phase lag, and a particular range of d e m a n d amplitudes is defined to encompass the linear range of operation of the actuation system. The frequency-response boundaries are used by actuator suppliers to assist in determining the distribution of gain around the control loop along with other criteria such as hysteresis, failure transients and valve port size and shape. Frequency-response boundaries are defined to ensure that the effects of the actuator on low frequency (rigid aircraft) modes are minimised with the ram movement to demanded-movement gain of approximately 0 dB and the phase lag at a minimum, while providing sufficient gain roll-off at high frequencies to reduce interaction with aircraft and control-surface structural vibration (flexible aircraft) modes. It should be noted that the gain and phase boundaries are to be respected when control-surface structural modes are included, so it is usually the case that output inertia loading will have to be modelled. T h e frequency response of the actuation system is a very important consideration, since this is a significant measure of the actuation system performance. The total actuation system is normally a fairly high-order system with as many as 12 state variables for a well-specified model (based on current experience), depending on the degree of detail required for analysis. Nevertheless the basic response is a first-order lag resulting from the integration of valve flow (proportional to main-ram velocity), coupled with ram-position feedback. All other states correspond to higher frequency effects such as servo valve or direct-drive valve and inner-loop dynamics, filters, sensors and inertial loads. The basic design and build quality of the actuator is aimed at achieving the required performance for the specified range of frequencies and amplitudes. It is invariably intended that the characteristics are as close to linear as possible. The basic first-order response is the primary factor in determining the actuation-system response bandwidth. The higher-order terms cause variations from the basic response, and can result in undesirable resonances which amplify response at some frequencies. Such linear properties will be evident t h r o u g h o u t the broad mid-range of amplitudes. In specifying the required performance it is necessary to set frequencyresponse gain and phase-lag boundaries which must not be violated and meeting these criteria will determine the feedback control gain, whether electrical or mechanical. Variations from linearity occur t h r o u g h o u t the working range, but these are normally small enough to be acceptable; it is at extremes of input amplitude that significant deviations from linearity become evident on the frequency response.

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The upper-gain boundary is aimed primarily at the linear-system characteristics, to avoid the presence in the system of any excessive resonances. It applies to all amplitudes. The lower gain boundaries apply for very small levels of input excitation and different boundaries are specified for different amplitudes. These levels are taken to correspond with the amplitudes to be applied in the actuation-system tests. The factors affecting low amplitude response are ram and valve friction, valve laps and leakage, hysteresis, electrical tolerances and bearing backlash. Meeting these boundaries will determine the degree of refinement required in manufacturing accuracy of valve ports, ram friction, bearings, components etc. Phase boundaries apply only to maximum allowable phase lag, whether at low or high amplitude. The high-amplitude boundary is intended to define the performance required for the main linear range of operation. Satisfying the phase-lag criterion is important for the flight control system, which is designed assuming a specified standard of actuation-system performance. The usual single number quoted for the actuation system in this regard for comparison purposes is the phase lag at 1 Hz, this being a typical frequency associated with aircraft-handling qualities for pilot control. The large amplitude gain and phase boundaries discussed above can be assumed to apply for the stated amplitudes up to the amplitudes that will result in main-ram rate limiting. No frequency response criteria are specified for very large amplitude inputs that will cause the valve to open to its full extent. The frequency-response boundaries of Figure 3.6 assume that the input is applied directly as an analogue demand. If the input is digital, as when the d e m a n d is injected into a digital computer, then an additional phase lag is incurred in the input path, so the boundaries as shown are no longer applicable and a modified set of boundaries is required. Although it is necessary to meet the gain and phase requirements when the actuator is controlled by the digital flight control computer, it may not be possible for the actuator supplier to test the equipment in this configuration, particularly during the early development stages of an aircraft programme. In practice, a set of frequency-response boundaries is specified covering digital loop-closure methods (the requirement for aircraft control) and analogue loop-closure methods (to allow the supplier to test the actuator before a flight control computer becomes available). Failure cases and external loading conditions are also considered.

3.3. 4 Dynamic stiffness Dynamic stiffness, or impedance, is the ability of the actuator to resist an external oscillatory load, that is, to act as an effective spring and damper. Impedance characteristics are measured by installing the actuator in a suitable test rig, applying a steady load to the ram if required, then applying an incremental oscillatory load at a range of frequencies and measuring

Actuation systems 105 incremental ram displacement relative to jack body. Results are presented as dynamic stiffness, in real and imaginary form representing stiffness and damping respectively, with the units force/displacement ( N / m or lb/in). Impedance requirements are defined in the actuation-system specification as boundaries within which the measured impedance must lie. Typical impedance boundaries, based on those used for a previous fly-by-wire aircraft project, are shown in Figure 3.7. Test conditions are defined, including requirements on steady-load and oscillatory-force amplitude. Impedance considerations will influence actuator sizing and possibly the reversion modes following failures. The criteria usually specified for impedance are based on the need to avoid control-surface flutter. There are no specific criteria set out for the lower frequency range associated with flight control system design, as the impedance which is present in the basic design is generally sufficient and no design constraints need be imposed. At the higher frequencies associated with flutter it may be critical that the actuation system contributes enough stiffness, in conjunction with the stiffness of the back up structure, to the control-surface rotation mode so that the flutter-speed margins are met. The margins with a fully operational actuation system will be greater than when failures are present. When a hydraulic system fails the r a m / b o d y impedance is more or less halved and the impedance boundaries are relaxed. The overall impedance includes the effects of attachment and o u t p u t structural stiffness and so will not be halved when a hydraulic system fails. If the structural stiffnesses are very high relative to the actuator r a m / b o d y impedance, then the overall impedance will be almost halved. If they are relatively very low, halving the r a m / b o d y impedance will have little effect on overall impedance.

3.3.5 Failure transients Requirements for failure transients are usually defined as boundaries on the ram-to-body displacement following the occurrence of the failure. Different classes of failure must be considered, including electrical-lane failures, hardover failures (for example, one lane of a multilane electric m o t o r demands full current, requiring the other lanes to compensate, until the failure is confirmed and isolated, as well as to control the actuator) and hydraulic-supply failures. Figure 3.8 shows typical failure transient boundaries. The actuation system is assumed to be in a state of steady equilibrium prior to the failure, with or without a steady applied force. The class 1 boundaries apply to a first failure or a second failure if the first failed lane has been switched out. The class 2 boundaries apply to a first hydraulic failure and subsequent electrical failures. Failure transients are particularly affected by intersystem force fight and main-valve pressure-gain characteristics, requiring a high-fidelity actuator model to predict results accurately.

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3.4 Actuation system modelling During the design phase of an actuator development programme both the equipment supplier and the airframe company purchasing the equipment will use mathematical models to represent actuation-system dynamics. Models are produced for a variety of purposes from simple representation of the actuator dynamics for use in the overall flight control-system analyses to more detailed representation of the actuator itself for use in control and failure monitor system design or performance prediction. The complexity of the model used will be determined by the type and depth of analysis to be performed and can vary from a first- or second-order transfer function through to highly detailed representations of digital computing effects, magnetic characteristics in direct-drive valve motors and the nonlinear flow and pressure characteristics of hydraulic fluid through a valve block. In the following descriptions, a relatively simple model of an actuator is discussed, referring to the block diagram of Figure 3.4. Sampling effects are repre-

108

Flight control systems

sented, as are nonlinearities in the f o r m of servo valve and main control-valve displacement limits. Nonlinear orifice flow and fluid compressibility effects are neglected, however, with flow rate, and hence actuator rate, being represented in the model as a linear function of spool displacement using flow gains. Such a model could not be used to assess pressure transients in stopping or starting an actuator, and does not include any representation of loading on the actuator, but will allow an assessment of basic frequency response and failure transient characteristics, including the effects of saturation limits. Servo-valve dynamics are represented in the model as a first-order lag with a time constant of 1.3 ms. A gain defining servo valve spool displacement per milliAmp of current d e m a n d and a displacement limit (e.g. + 0.3 m m ) complete the representation of the servo valve. Fluid flows through the servovalve to move the main control valve. The complete dynamics of the servo-valve flow and resultant force on the main valve, including the effects of friction or backlash, could be included in the model if the effects have a significant effect on the analysis to be p e r f o r m e d . H e r e a simple flow gain and integrator links main valve rate (and position) to servo-valve displacement. Again a travel limit is included (e.g. +3.0 m m ) which may be c o m b i n e d with the integrator to f o r m a limited integrator, setting main valve rate to zero when the travel limit is reached. Inner-loop closure is p e r f o r m e d with a differential amplifier, feeding back main-control-valve position measured using an LVDT, the representation of which is a gain ( V / m m ) and a second-order filter associated with the d e m o d u l a t i o n of the raw a.c. LVDT signal into a d.c. voltage. T h e representation of the main ram could take a n u m b e r of forms, f r o m a simple flow gain and integrator to detailed orifice-flow and fluid-compressibility equations, including representations of external loads and mass-springd a m p e r equations to represent the control-surface structure. T h e level of detail depends on the intended use of the model. In the example shown a flow gain and the integrator effect of the main ram are c o m b i n e d to p r o d u c e an overall gain of 60 ( m / s ) / m . No main-ram position limits are included, as it is m o r e usual to provide a d e m a n d limit in the flight control laws, preventing the actuator from being driven onto the r a m e n d stops. Outer-loop closure is p e r f o r m e d digitally. Ram position feedback is measured by LVDTs and sampled at a rate of 80 Hz. It is i m p o r t a n t that the delays due to sampling and computation are included in the model, in addition to the demodulation, anti-alias filter and loop-closure control-filter dynamics, to give an accurate representation of loop stability and overall frequency response. A model of this type would be used for simulation analyses, to evaluate the response to step, ramp, sinusoidal or other input demands. Transfer function analysis could also be p e r f o r m e d , to d e t e r m i n e gain and phase relationships between input and output for a range of frequencies and amplitudes. T h e m o d e l could also be linearised, to allow linear frequency-response calcula-

Actuation systems 109 tions. In the following sections examples of the results obtained from such analyses are presented to give an indication of the type of work carried out with such a model. 3.5 Nonlinear

frequency response

O n e of the main uses of mathematical models of actuators is to d e t e r m i n e the frequency-response characteristics (the response amplitude and phase lag when responding to a sinusoidal input d e m a n d ) . Linear models can be created and the frequency-response characteristics calculated using traditional, linear-analysis techniques. In this way the ability of the actuator design to m e e t specified frequency response characteristics can be proven. This is particularly i m p o r t a n t in flight control system design, as the aircraft control laws are designed with an assumed gain and phase characteristic for the actuators (usually in the f o r m of a second- or third-order transfer function), and any significant deviation from these ideal characteristics can lead to a reduction of aircraft gain and phase stability margins. However, the linear m o d e l only shows actuator frequency response u n d e r m o d e r a t e amplitude conditions, but in reality response characteristics would vary with d e m a n d amplitude. Nonlinear models are used to assess amplitude effects on frequency response, with a transfer function-analysis m e t h o d for analysis of the response to sinusoidal input demands. T h e m e t h o d is very similar to test methods, when a transfer function analyser or spectrum analyser is used to inject sinusoidal d e m a n d s to the actuator, and to analyse the gain and phase relationship between d e m a n d signals and the resulting actuator response. At larger d e m a n d amplitudes the actuator will start to reach internal limits, such as c u r r e n t or voltage limits in motors and spool displacement limits in servo valves and main control valves. The relationship between the limits reached in terms of amplitude and the frequency of the d e m a n d signal at which each occurs has a significant impact on the nonlinear frequency response of the actuator, and can lead to stability problems (see the c o m m e n t s on j u m p resonance, Section 3.7). In the actuator example presented in Figure 3.4, the position limit of the main control valve represents a limit on the rate of m o v e m e n t of the actuator ram, and the servo-valve position limit forms a rate limit on the main control valve and, hence, an acceleration limit on the main ram. If the combination o f input d e m a n d amplitude and frequency is such that one of these limits is reached, the response of the ram will be affected with a consequent effect on frequency-response characteristics. This effect is illustrated in Figure 3.9. These results, p r o d u c e d using a nonlinear model based on the block diagram of Figure 3.4, show that gain reduces and phase lag increases as d e m a n d amplitude increases. A d e m a n d amplitude of 0.5 m m represents a linear response, in this case, as neither the spool n o r the main control-valve position limits are reached. Even at d e m a n d amplitudes up to 2 m m across the

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3.6

Saturation

analysis

An analysis technique closely allied with the production of nonlinear frequency-response data is that of saturation analysis. A linear model of the

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actuator is used to calculate the frequency response from i n p u t - d e m a n d signals to the locations of the various limits, such as servo-valve posidon or main-control-valve position. T h e gain information from this analysis can then be used to d e t e r m i n e the d e m a n d amplitude which will cause the limit to be reached across a range of frequencies. Figure 3.10 shows the results of such an analysis, based on the actuator model of Figure 3.4. From this figure it can be seen that saturation will not occur for sinusoidal d e m a n d s of up to 2 m m in amplitude. For d e m a n d s between 2 and 4 m m the servo-valve position limit will be reached if the frequency of the d e m a n d signal is above 12 Hz, but the main valve limit will not be reached for any d e m a n d signal. For d e m a n d s with a frequency below 12 Hz, the main-control-valve position limit will be reached before the servo-valve position limit, if the amplitude o f the d e m a n d signal is higher than 4 m m . A d e m a n d signal o f 6 m m amplitude will cause the main control-valve limit to be reached if the frequency is above 6 Hz. These results support the findings from the nonlinear frequency response discussed above, giving confidence that no untoward nonlinear effects are likely to affect actuator response. However, it is possible to have combinations

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o f gains and limits around the control loop which can cause a j u m p resonance effect, with serious performance implications for the actuator, as discussed below.

3.7 Jump resonance U n d e r conditions of large amplitude d e m a n d when servo-valve travel limits are e n c o u n t e r e d an actuation system can display sudden large increases in phase lag. This p h e n o m e n o n is described by the term j u m p resonance, although there is no gain peak associated with the sharp phase variation, and is caused by an effective acceleration limit. In practice, if in some extreme manoeuvres it is possible to reach such limits, the additional phase lag caused by the j u m p resonance can lead to severe temporary reduction of aircraft stability margins, with consequent potential handling difficulties. To avoid this problem at the design stage it is important to ensure that the valve ports (for both the main control valve and the servo valve) and travel limits are sized adequately. Increased valve-port width can be compensated for by a reduction of electrical gain, maintaining the overall loop gain required for actuator stability and response. Jump-resonance is characterised by a very rapid increase in phase lag over a narrow frequency band, as shown in Figure 3.11. This figure shows nonlinear frequency response results obtained from a model configured to exhibit jump-resonance effects. As d e m a n d amplitude increases the frequency at which saturation occurs reduces and a reduction in gain is seen, along with an even more dramatic increase in phase lag. The presence of any potential for j u m p resonance can be predicted from saturation-analysis results. Figure 3.12 shows the saturation characteristics for the actuator with j u m p resonance. Saturation of the servo-valve position limit will occur before saturation of main-control-valve position leading to an effective actuator acceleration limit, for the majority of d e m a n d amplitude and frequency combinations. The crossover frequency, where the two saturation loci intersect, is at a relatively low frequency (2.5 Hz), within the bandwidth of aircraft control. An actuator such as this is likely to cause severe handling deficiencies in an aircraft, and the valve ports and control gains would need to be redesigned to give a better balance, and to produce the sorts o f characteristic exhibited in Figures 3.9 and 3.10.

3.8 Failure transients C o m p u t e r models of an actuation system are used to predict the transients which occur following a failure within the system. Although redundancy features are included in the actuator design to ensure continued operation following failures, it is also important that the actuator does not produce an

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excessive transient when transitioning from one level of redundancy to another. Boundaries, within which the transient must lie, are defined in an actuator specification, and failure to comply with this r e q u i r e m e n t will lead to excessive actuator transient m o v e m e n t immediately following a failure, which could p r o d u c e structural damage in the area of the actuator mountings or a high transient acceleration at the crew's stations or at sensitive equipment, owing to aircraft response to control-surface movement. T h e effect of the failure can be countered either by a failure-absorption m e t h o d , where the presence of the failure is countered by the rest of the system with no special action being taken, or by failure rejection, where the failure is detected and an appropriate action removes the effects of the failure, leaving the remaining parts of the system to continue operating. For either a p p r o a c h the transient response induced following a failure must be assessed, and a design be p r o d u c e d which will m e e t the specified requirements. For the failure-rejection approach, the failure detection and isolation

Actuation systems 115 lane 1 v

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algorithms must also be designed. Failure-detection algorithms are often referred to as built-in-test, or BIT. A n u m b e r of levels of BIT will exist on an aircraft actuation system, ranging from start-up checks and preflight checks carried out automatically by the flight control system, through to the continuous monitoring of actuator operation, referred to as continuous built-in test, or CBIT. The level and m e t h o d of CBIT depends largely on the actuator design, but the following typical example will illustrate the principles. Ram-position measurement for feedback control is often p e r f o r m e d using linear variable differential transformers (LVDTs), with three or four used to provide the necessary levels of redundancy. The individual LVDT signals are consolidated in each computer, to produce an average signal which is used for actuator control-loop closure. In this way slight build tolerances, temperature effects etc. on each LVDT can be averaged out, minimising the difference in drive signals between lanes which would produce a force fight on mechanical components. However, this m e t h o d also means that any fault in one of the LVDTs will be propagated to the consolidated ram-position signal in all of the flight control computers. In order to reduce this effect averaging algorithms are used, weighted towards the median to reduce the influence of extreme signals and failed sensors. A typical voter algorithm for a triplex system is shown in Figure 3.13. The incoming signal samples are first sorted to determine the highest, median and lowest values. The voter algorithm then produces a consolidated or averaged value based on the three input values. A n u m b e r of alternative algorithms could be used, including simple averaging of the three values or selection of the median. To minimise the influence of faults on the consolidated value the algorithm will limit the authority of the highest or

116

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lowest signals, weighting the average towards the median. Having produced algorithms that limit the influence of faulty sensors on control-loop closure, it is also necessary to determine which lane is faulty and to reconfigure the voter monitor to ignore that lane. This is the purpose of the CBIT algorithms. In the case of the LVDT monitor u n d e r consideration here, the faulty lane could be identified by comparing each lane's signal with the consolidated value. As we have already established that the influence of the faulty lane on the consolidated signal is limited, any lane which shows a significant difference to the consolidated value (more than a certain tolerance value) can be considered faulty. In order to minimise the n u m b e r of nuisance failure warnings the tolerance value is selected to allow for a difference in build standard of the LVDTs and, to remove the effects of glitches causing spurious failure warnings, a fault must be present for a certain period o f time, such as five consecutive computer iterations, before it is confirmed as a failure and the appropriate action taken. In this case the appropriate action would be to change the voter algorithm to simple duplex averaging, using the two healthy signals only. Simulation is used in defining the voter algorithms to minimise the influence of the faulty signals, and to design CBIT algorithms. An actuator model is produced including various redundancy features and signalconsolidation algorithms. Typical faults can then be simulated and the effects on actuator response predicted, as shown in Figure 3.14. In this Figure a transient response for the actuator model shown in Figure 3.4 is given, as the outer-loop (ram-position) consolidation changes from triplex to duplex.

3.9 Conclusions Actuation systems for m o d e r n combat aircraft flight control are, in general, highly complex devices relying on state-of-the art technology. They are often required to operate at, or very close to, full performance following multiple failures, requiring sophisticated control and monitor algorithms. Closed-loop control systems, often implemented in digital computers, are designed to give actuator performance in accordance with specified requirements, which are driven by the need for high performance and failure tolerance to provide high agility and control basically unstable airframes. Two control loops are usually used, the inner loop with main-control-valve position feedback (similar to main ram rate feedback) and the outer loop with mainram-position feedback. Monitor algorithms, again usually implemented in digital computers, detect c o m p o n e n t failures so that the overall actuatorcontrol system can take the appropriate action to remove the effects o f the failure. This may involve isolation of a servo valve or direct-drive motor coil, or reconfiguration of voter algorithms to exclude signals from faulty feedback sensors.

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Dynamic mathematical models play an important role in the design and analysis of control and monitor algorithms. Both linear and nonlinear models and a wide range of analysis techniques are used to design the control systems, and prove that performance requirements defined in the e q u i p m e n t specification can be met. The complexity of the model will reflect the analysis to be performed, and it is vital that consideration is given to this point to ensure that any model produced is appropriate to the task. In this chapter an overview of typical performance requirements, modelling methods and analysis techniques has been given. For future aircraft projects, flight control actuation may use electro hydrostatic actuators, electro-mechanical actuators or further developments of the more conventional hydraulic actuator. Whichever technology is used, control and monitor systems will be designed using methods based on those defined here.

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3.10 Acknowledgments The author wishes to thank Dr. Robert Stirling of Stirling Dynamics Limited for his assistance in the preparation of this chapter. Thanks are also due to Dowty Aerospace Wolverhampton, for permission to use Figure 3.2, and to John Tucker, Dave Allison, Mike Walker and Peter Chambers of British Aerospace Military Aircraft and Aerostructures for their comments.

© British Aerospace plc, 2000. Published with permission of the copyright owner.

Chapter 4

Handling qualities J. Hodgkinson and D. Mitchell

4.1 Introduction In this Chapter, we first introduce in simple terms what we mean by handling qualities, how we specify them, and how we achieve them. Then we introduce pilot-induced oscillations (PIOs) because they are one of the more serious consequences of failure to design for good handling qualities, and because current PIO studies offer an interesting example of state-of-the-art research in handling qualities. Handling qualities have been variously defined. For our purposes they are those characteristics of the dynamic behaviour of the aircraft that allow precise control with low pilot workload. A major objective of flight control system design is to bestow good handling (or flying) qualities on the aircraft. Engineers, oblivious to the philosophical fact that measuring a quality transforms it into a quantity, define metrics for handling qualities. Precision of flight can be quantified in terms of rounds on target for gun tracking, circular error probability for bombing or sink rate for landing, for example. Workload is more difficult to quantify, and for the time being we simply ask the pilot how easy or difficult his job is. Much of the achievement of handling-qualities practitioners has been in acquiring reliable information on pilot workload from pilots. Goodness is generally with reference to the pilot's comments in flight or in the flight simulator, and as summarised by Cooper-Harper ratings (Figure 4.1). The scale has ten points, where one is excellent and ten represents the worst qualities possible. Coarser gradations, levels 1, 2 and 3, are also defined. The scale is dichotomous. This feature improves repeatability by leading the evaluation pilot through a series of decisions regarding the task performance and the pilot workload. Among the factors affecting pilot opinion are piloting task, what failures are present and atmospheric environment. US specifications have distinguished between different task difficulties by defining flight-phase categories A, B and C [1]. Category A consists of demanding tasks like air-to air combat and refueling, category B includes less demanding tasks like cruise and climbs and descents and category C includes terminal tasks such as landing and take-off. The idea behind incorporating failure probabilities into flying-quality specifications is simply that the more

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Handling qualities 121 likely a failure, the better the consequent and subsequent flying qualities should be. Gusts make an airplane m o r e difficult to fly, so we sometimes p e r m i t worse flying qualities in turbulence. This does not m e a n that the aircraft itself is worse. O u r a p p r o a c h is to use classical control to identify those p a r a m e t e r s in the aircraft response which the pilot uses in p e r f o r m i n g his task. We will then define values of those parameters of the response which c o r r e s p o n d to good through to bad characteristics or, in our language, level 1, 2 or 3. T h e notation in this Chapter largely conforms to the n o m e n c l a t u r e defined at the beginning of this book. The occasional differences are due to the variations in accepted practice between the notations in use in the UK and the United States.

4.2 Longitudinal flying qualities

4.2.1 Control-input transfer functions T h e relevant transfer functions which describe the longitudinal notion were covered in Chapter 2. They are repeated here for completeness. For pitch attitude O(s) to elevator ~/(s) O (s) -

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4.2.2 Modal criteria T h e coefficients in eqns 4.6 and 4.7 describe i n p u t / o u t p u t relationships along with the c o m m o n notation for the modes of motion. These equations also show some useful relationships between the response quantities (these apply to conventional aircraft). T h e two modes are the short period, generally with frequencies f r o m one to ten rad/s, and the phugoid, with frequencies below that. If a m o d e of the

122

Flight control systems

response does not appear in the time response of a particular variable to an input, it will be manifest in the transfer function as a numerator term which cancels or nearly cancels the modal term in the denominator. For example, there is usually very little angle-of-attack variation in the phugoid oscillations, therefore the second-order numerator in N~ is closely equal to the secondorder phugoid in the denominator. Recall that from Chapter 2:

w(s) -_ N~(s) kw(s + 1/T~) (s2 + 2(~w,~s + w 2) 71(s) A(s) = (s2+2(pwps+w~)(s2+2(,w,s+w~)

(2.36)

4. 2.3 Phugoid f l y i n g qualities The phugoid is a long-period (low frequency) mode in which forward speed (kinetic energy) and altitude (potential energy) are interchanged. The resulting oscillations are in pitch, speed, altitude and flight path, but as mentioned already the angle-of-attack remains roughly constant. The denominator of the transfer function for speed and pitch motion is:

+

(4.1)

where U0 is the steady-state velocity, Ue in Chapter 2. Here the constant term, - g Z J U o, is the undamped natural frequency squared, ¢02n,for the phugoid. The derivative: ,

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The first term in the parentheses here is small in subsonic flight. Therefore since:

mg= ~I pU2 SCL for the aircraft, we can substitute this in the remaining expression for the derivative to get: Zu ~ _ 2__g

U0 So the phugoid frequency:

(4.3)

Hand~ngquaKti~

123

-

%=

u0

-u0

g

(4.4)

and the period of the phugoid in seconds, as McRuer et aL [2] point out, is about a fifth of the true airspeed in miles per hour. The above analysis is obtained from a two-degree-of-freedom model of the phugoid. In the three-degree-of-freedom model, the derivative M u appears. Aeroelastic and thrust effects that are highly configuration dependent introduce this parameter. The total damping of the phugoid mode is Xu, which is a measure of the drag of the aircraft. In high-speed flight, altitude can change significantly in phugoid motions and this can affect the phugoid damping because air density changes with altitude. The phugoid period will also be decreased as a consequence of the density gradient. The requirements for the phugoid are in terms of damping ratio for stable phugoids and time-to-double-amplitude for unstable phugoids. For level 1, (p should be at least 0.04 and at least zero for level 2. Time-to-double-amplitude, T2 should be at least 55 seconds for level 3. No distinction is made between classes of aircraft. Time-to-double-amplitude is -0.693/(pWnp and (p is negative if the phugoid is unstable. Pilots can control phugoid oscillations quite readily by closing a low-gain pitch loop. Nevertheless, this does require the pilot's attention and side tasks are difficult if poor phugoid characteristics are present. 4.2.4

Short-period f l y i n g qualities

The short period is a relatively rapid mode which governs the transient changes in angle-of-attack, pitch, flight path and normal load factor that occur at relatively constant speed following rapid control (generally elevator) or gust inputs. The mode is usually a stable underdamped second-order oscillation. For small angles, the angle-of-attack ot~- w~ Uo and L , ~ - Z,0 so we can use: Z. = UoZ~,-~ - UoL,~~ - Uo / To2

(4.5)

Define the parameter n / a in g per radian, as the steady-state normal load factor per steady-state angle of attack, so: n/ a = UoLJ g

This gives us a number of useful relationships which govern the short-period motions and the response variables to elevator input as follows:

Flight control systems

124

For pitch-rate:

sO Ms(s+ L`,) 6 A for angle-of-attack:

8

A

for normal acceleration at the c.g. or 1x ahead of it:

(4.6)

n~ M~n/ a S /X n~p= n~cx+s2OlJg for flight-path:

Y_~. MsL`, 6 sA where It is helpful to look at response ratios, for example to imagine what the response of angle-of-attack is to pitch angle, of flight-path angle to pitch angle, and of normal load factor to pitch angle: a 0

1 s+ L`,

y 0

L`, s+ L`,

(4.7)

• z . •n/OL 0

s+L`,

This is a convenient way of viewing the responses because pitch is the fastest initial response. The other response variables, including flight path, lag it with a time constant of 1/L,,, which is consequently sometimes called the flightpath time constant.

4.2.5 Criteria for the longitudinal short-period dynamics The stick force required to develop unit steady-state normal load factor, stick force per g is the short-period steady-state gain.

Handling qualities 125

stick force per g

short period resonancei /

/

3 pounds/ g

frequency of pilot's stick excitation Figure 4.2 Floor stick force/g specified to prevent sensitivity in dynamic manoeuvres around the short-period resonance

The stick forces in a steady manoeuvre must not be so great that the pilot cannot comfortably attain the maximum g load on the aircraft, and not so light that he inadvertently overstresses the aircraft. Fighters require light forces to avoid fatigue in prolonged manoeuvring up to 9 g for example. Transport aircraft, with their gradual manoeuvring and low maximum g capability, typically have higher stick forces. At flight conditions with low dynamic pressure, i.e. at high altitudes a n d / o r low speeds, the acceleration generation capability of the aircraft is low, so higher overall stick force per g is allowed at these conditions. Similarly, at higher dynamic pressures, we could allow lower stick force per g, Fin, so that the pilot can attain the maximum load factor that the airframe allows without excessive effort. F,/n is therefore specified to be a function of acceleration sensitivity, n/a, the steady-state normal load factor per unit angle-of-attack, n/a is a measure of flight condition, corresponding to high or low dynamic pressure. A floor minimum value of Fs/n is specified to prevent sensitivity problems. Classical airplane dynamics produce a constant Fs/n with flight condition so the variation with n/a is really a concession to aircraft with artificial feel systems and real flexibility effects. Classical airplane dynamics do not produce a constant stick deflection per g. Larger deflections are required for a given g at lower n/a. A dynamic value of Fs/n is also specified by requiring that the floor value be maintained during a sinewave sweep of the pilot's longitudinal controller for a frequency range spanning the effective short period (see Figure 4.2). To understand both the steady and the dynamic Fin, consider the transfer function for nz/F~:

126

Flight control systems

n~

KM~UoL~

~, = g( ;Z + 2(spW,~ s + o92~t,)

(4.8)

where the numerator is just a multiplier depending o n / ~ a measure of the effectiveness of the stick-force-to-elevator system, M n, the surface effectiveness, U0, the true speed and L,~, the dimensional lift-curve slope. The denominator consists only of the gravitational constant and the second-order short-period mode. From this transfer function and the final value theorem, the steady-state for a step input is:

gf.O2p

'

or equivalently:

KM n / a

(4.9)

The minimum stick force per g is determined by plotting the amplitude ratio of the nz/F s transfer function, which will have a maximum at the resonant frequency.

4.2. 6 M o d a l criteria for the short period Short-period natural frequency is specified via the control-anticipation parameter (CAP): O92 nsp

n/a

(4.10)

again, where n / a ~- UoL~/g. CAP boundaries are specified in the form of Figure 4.3. The short-period damping ratio is specified alone as a parameter according to Figure 4.4. The step-time histories and frequency responses of the various damping ratios are shown along with this Figure.

4.2. 7 Other short-period criteria A number of criteria have emerged that attempt to deal with longitudinal dynamics in the presence of feedback control systems. Sometimes these systems have introduced phase lags and delays from various mechanisation features like actuators, sensors, filters etc. The consequent mathematical model of the system becomes far higher than the fourth-order dynamics we

Handling qualities 127 100

I

I

I

I

II I II II I I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

,

,

, ,,~,I0.0

-

i

i llll

v

:iiL .,,l'7~.._u. 0.28 o.~s

short period natural frequency, COnsp,rad/s 10 •-~l ; lineal I ~dl il~.~l

f

, ,, :

1.0

11,, :

~

~ lli

jf 0.1

:

i

it" ~ :

. . . . . .! ! ! ! !

!!!!!

v~,li

~,,ii

:

i

,

1.0

controlanticipation parameter,

. . . .

,

10

:

• "

:

::

(.0 2nsp nAz

ioo

acceleration sensitivity, n/m, g's/rad

Figure 4.3 Boundaries of control-anticipation parameter have mostly considered so far. As an example, the longitudinal dynamics of the F-18 were commonly modelled as a 75th-order system.

4.2. 8

Equivalent systems

The equivalent system concept [3] is simply to match the augmented, highorder dynamics with a low-order equivalent which has the same form as an unaugmented aircraft, plus a time delay to approximate the phase lag of system components. Equivalent systems form the basis of all current modal criteria (longitudinal, lateral and directional) in the military specifications in the United States. The process works best if frequency responses are matched in the range 0.1-10 rad/s for estimating short-period parameters. For the phugoid, extension down to 0.01 generally works. With the gain in decibels, the phase in degrees and a weighting on the phase match around 0.02, a sumof-squares mismatch function is minimised. The approach is a vast improvement on picking one, dominant mode from the s-plane array (see Figure 4.5).

128

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,.o O

Flight control systems

C

e~

01

0

0

]

O

O

~0

¢-

0 t~o

)loelle Io al6Ue

O

O

__tD

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.

phase, deg .

p 'apnl!u6em

.

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~

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.

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oN

0

N~ =9

~

.-,9,

0

Handling qualities

~

~

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",~ ~

~

~

"~.~ .~..~~ ~. ~

-~

129

130

Flight control systems

,..i

\_

"0

e-

II II ~

I I

~uency,ra~,s ~

~[ u ~ eequsinp~acedc ~i on e logsscale I

4.5a

imaginary usedfordominant-~ rootapproximation~

" ~ X ,~=, ,,,,

~1

4.5b

¢.. e~

ill]

I,H~I~LI J~LI~III 1 II II II1~ _ . H H - - ..._ Illl! I I11~,,I11"1.L IIIII "',@l.IJ. IIIII 1~1 IIIII III1'

I~

frequency,rad/s

4.5c

Handling qualities 131 4.2. 9 Equivalent time delay A key addition to the low-order equivalent is a time delay of T seconds. This parameter T approximates the high frequency phase lag generated by the high-order terms in the response. A useful rule of thumb is to look at the additional phase lag at 10 rad/s, and to r e m e m b e r that 0.1 seconds of delay produces 57.3 degrees of lag at that frequency. For demanding piloting tasks for fighter aircraft, a delay of 0.1 s, i.e. 100 ms, is enough to preclude level 1 flying qualities and 150 ms is excessive even for large transports if they are required for precision landings, in-flight refuelling, formation flying or other tight tasks. For fighters, the level 2 limit is 200 ms, and for level 3 it is 250 ms. Delay worsens the pilot loop closure only when the loop gain is increased by the pilot in an attempt to get tighter control and a faster pilot-in-the-loop response. This p h e n o m e n o n - - t h e aircraft becoming more out of control as the pilot works harder to control i t - - i s very disconcerting to the pilot; R.E. Smith has called the effect the flying-qualities cliff. Large delays in demanding tasks often result in pilotinduced oscillations. The degradation in pilot rating has been summarised by plots like Figure 4.6. Unfortunately, there are insufficient research data available to determine whether the stick force or stick-position characteristics should be used in the equivalent system m e t h o d (or in any other method, for that matter). In an attempt to quantify the acceptable mismatch in determining an equivalent system, Wood and Hodgkinson [4] examined the added dynamics that would cause a noticeable difference in pilot rating. When the dynamics (from the Neal-Smith variable stability experiment [5]) were overlaid, they had the form of hour-glass-shaped envelopes of allowable mismatch against frequency, as shown in Figure 4.7. The envelopes show that differences a r o u n d a centralised frequency are more noticeable than at the frequency extremes. The equivalent system form must be appropriate for the response type. If novel response types are used, whatever the axis of control, the equivalent

Figure 4.5 Definition of equivalent-system mismatch, and comparison of po~-zero arrays and frequency responsesfor high-order system, its dominant root approximation, and its low-orderequivalent system 2O

a Minimise cost (i.e., mismatch) functional: = Z ( G2 + KP~): K= 0.02 i=1 - - high-order-response - equivalent response b x O high-order poles, zero X O low-order equivalent poles, zero c - - high-order system dominant-root approximation . . . . equivalent with delay - - - equivalent, no delay (Note: amplitude ratios for equivalent with/out delay, coincide.) -

-

-

Flight control systems

132

Cooper-Harper rating 10

F-8 h~. s" .,u, ,.-stress t" lanoings s"

Navion altitude .... ,.,n~ t,=~,~,, u

~s" /s

(Lateral)\

NT-33

NT--33(lateral)landing

.,t"

s

.~o~-

,oo

i

. ' ",.-"

. • . .

t's"

..s/\/ ,/ _., "'7"'" landings , ; . . ~ _ ~ . . . . t % : ~ ,.............. field-carrier \ - "" ~"" - 7 " ' " " s S _.."" ~ .......... xe ~ ho~,, landing ~ ....~.~,~" ~.'""..~.....:..........~ NT-33 landing (lateral)"'x-" . . ' " ' " s" / . " " . ' 2 " ' . . ......... ~ ..... \ \

Navion

-

•

t" t~...

/ /."

.

.

.

.

.......

.

I

0

Figure 4.6

.°.

.

-" L - ' ; . " , . . . . . ' S .0s~..~

.

.

.......

7>"-""=---=~""

.

~ . . ~ - ~ ~-'; . . . . .

I

0.1

I

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---1

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| " Navion approach and landing, 75 kts I

I

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...... F-8 I o w s t r e s s

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=

aavion approachand landing in turbulence

I

0.2 0.3 equivalent time delay, s

I

I

0.4

I

0.5

Rate of degraduation of Cooper-Harper pilot ratings increases with difficulty of task

form must comply with the physics of the dynamics. For example, a pitchangle command system can generally be matched with a zero-over-second-order equivalent plus a time delay, yielding a damping ratio, natural frequency and time delay which are useful for specifying flying qualities and for comparing the qualities of design changes. The damping and frequency here are not strictly the classical short-period values, and would not strictly be compared with classical criteria since the response is not classical, but we would expect them to be in the same general range of values.

4.2.10 The bandwidth method From the frequency response of the pitch attitude to the longitudinal controller, the bandwidth frequency is the frequency where the phase margin is 45 degrees, or where the gain margin is 6 dB (see Figure 4.8). The bandwidth hypothesis [6] is that the pilot can adequately follow input commands with frequencies up to the bandwidth without causing instability. The phase roll-off or slope at high frequency, that causes this characteristic is essentially the same as equivalent time delay and is measured using a parameter called phase delay, ~'p.Figure 4.8 defines bandwidth and ~-p.

4.2.11 The Neal-Smith method Neal and Smith [5] proposed for pitch-angle control a pilot model of the form shown in Figure 4.9. Here the pilot shifts his parameters so as to reduce

Handling qualities 133 20.0 amplitude ratio, dB

0

s 2 + 11.6s + 4.96 -20.0 0.1

i 1.0

180.0 [--L

~

phase, dB

I 10.0

~

68.89s 2 + 1100.12s- 275.22

I 100.0 frequency, rad/s

e

.0059s

0

.

.

.

.

S2 + 11.66S + .0389 -180.0 0.1

-0.0072s

~

I

i

1.0

10.0

I

[ I

I

100.0 frequency, rad/s

Figure 4. 7 Envelopes of allowable mismatchfor longitudinal equivalent systems

steady-state closed-loop errors to reasonable levels (this is the 3 dB droop) and to reproduce rapid closed-loop commands (this is the fixed bandwidth frequency--not the same definition of bandwidth as we used previously). See Figure 4.10 for a Bode plot of the resulting closed-loop dynamics. The Neal-Smith criterion is a two-dimensional plot of pilot compensation against pilot-in-the-loop resonance (see Figure 4.11, which contains some recommended corrections to the boundaries made by Rickard [8]). Compensation is defined as the phase angle of the pilot's compensation measured at the specified bandwidth frequency, and the resonance (a measure of the pilot-in-the-loop oscillatory tendency) is presented in dB. The boundaries reflect the fact that pilots dislike PIOs and they dislike generating lead or lag. Figure 4.11 summarises the pilot comments corresponding to the

134

Flightcontrolsystems 1;p- 180 - (¢#)2~18o 2m18o

amplitude ratio of e

I ,

Flong

gain margin = 6dB

I s

phase angle of e

F,o.g

phase

............

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

..... .t ....

e';=

Figure 4.8 Definition of bandwidthfrequency and phase delay

different regions on the Neal-Smith plane, and uses a range of bandwidths as a design guide. Figure 4.12 shows that Neal--Smith pilot compensation is strongly correlated to equivalent frequency, as we would expect.

4.2.12 Gibson's dropback criterion Both the equivalent systems and the bandwidth criteria have had problems correlating configurations with excessive lead compensation and Gibson's dropback criterion (Figure 4.13) is a way of screening these configurations. Gibson [9] suggests the ratio of dropback to steady-state pitch rate, dropback/qs s should be less than 0.25 for precision tracking and less than 1.0 for landing.

4.2.13 Time-history criteria A number of workers have proposed measuring features from step-time histories as a generic way of determining flying qualities. Although in a design effort the step history is easily calculated, it is difficult to test and measure. A true step has infinite slope at its leading edge and instantaneously changes that slope to zero following an elapse of zero time. Inputs like this can be approximated electrically, but are quite different from even the most abrupt inputs of pilots.

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Handling qualities 135

136

Flight control systems

Hr, ax I~ T~ ~ . . . . . . . . . . . . . .

~............. ~ ..................... ~J .....

~.......... ~

N

-/(-6~'c) ' I deg I -901

o

log (.o

( BVlOmin

Figure 4.10 Neal-Smith criterion: pilot-in-the-loop tracking standards 4.2.14 Flight-path stability At speeds well above stall, airspeed is generally controlled with power and the flight path is controlled with the elevator. At very slow speeds, however, pilots are trained to add power to bring the flight path back to the desired value and to control the speed by using the elevator. The two control strategies correspond to operation at speeds above or below the speed for minimum drag, or the speed for minimum thrust required. The criteria for flight-path instability are generally stated as a restriction on the slope of the plot of flightpath angle against speed, using elevator control only.

4.3 L a t e r a l - d i r e c t i o n a l f l y i n g q u a l i t i e s Here we are considering the three equations for rolling moment, yaw rate and side force, as we see in Chapter 2, and the modes of motion which result from solving the equations.

4.3.1 Roll mode For an aircraft rolling about its x axis:

sp- Lps = I%

(4.11)

Handling qualities 20 abrupt response, .&.. ~ .. ~

strong PIO @,,.' tendencies, . have to fly it smoothly t 16 / closed-

--,

~

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-20

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-4

11

1/

./." RJckard s. ~ o u n d a r y

8

sluggish response, strong PIO tendencies, have to overdrive it ,..~

strong PIO tendencies

@ i. loop ,.. resonance , 12 Neal and Smith s b o u n d a r y

137

'

J

~"~ Ii I I = I / ~ / kZ,) .~1 A .."

in'~al . response . final response difficultto predict, tendency to overcontrolor dig in, initialforces heavy, lightening up as response develops 40

60

80

100

pilot compensation, deg

key(bandwidth,rad/s)

Figure 4.11

•

1.5

•

2.0

•

2.5

• •

3,0 3.5 4.0

Neal-Smith criterion showing Neal and Smith's boundaries with Rickard's level 1/2 boundary, typical pilot comments for the various criterion regions and the effect of changing Neal-Smith bandwidth on configurations with various pilot ratings Note: Position command, pilot delay = 0.2 s Various LAHOS configurations (Smith, 1978) Pilot rating shown in circles, @

T h e transfer f u n c t i o n for roll-rate response to aileron is then: P_

Le,

~a S--Lp o r in generalised forms: p_ 6~

K T~+I

(4.12)

138

Flight control systems

0

80

pilot compensation. deg

0

40

J Zpc=114"2-33"8me(00~

-40 0

Figure 4.12

1.0 2.0 3.0 equivalent short-period frequency, we, rad/s

4.0

Comparison of pilot compensation in Neal-Smith c~terion against equivalent short-period frequency. (Note: line fitted to data with correlation coefficient of 94 %)

pitch attitude I

4, dropback i' overshoot

~/,,,,~_

(negative dropback)

attitude dropback

time control input removed

Figure 4.13

Gibson's dropback criterion

or

----K/ (1/TR)

(4.13)

in the shorthand notion where (s+a) is written simply (a). Typically, the roll-mode time constant is of the order of one second or so for fighters and somewhat longer for larger aircraft. If it is much longer (the

Handling qualities

139

requirements range from 1.0 to 1.4 s for level 1, 1.4 to 3.0 s for level 2, and 10 s for level 3), the initial slope region of the step-time history persists t h r o u g h o u t roll manoeuvres. The pilot's perception is then that he is c o m m a n d i n g roll acceleration, not rate, as he prefers. The Bode plot interpretation would be that, in the likely piloted crossover region (essentially his usual frequency range of interest) around say 3 rad/s, the response in roll rate drops off, so we would have to differentiate the response (multiply it by s) to make it look like a gain-type response,/~ This means that the pilot would see an sp or ~type response, which is not impossible to control but requires full attention, i.e. it leaves little or no reserve for side tasks.

4.3.2 Spiral mode T h e spiral mode is a slow recovery (or divergence) from a bank-angle disturbance. Usually it is very slow and so can be approximated by the ratio of the low-order coefficients of the transfer function denominator. Specifications prevent too rapid divergence. We often treat the spiral mode separately from the shorter-period roll and dutch-roll modes because it is generally at a far lower frequency and is differently handled by the pilot.

4.3.3 Coupled-roll spiral When bank angle is fed back to aileron, a low frequency oscillation can result. Unusual combinations of stability derivatives can also result in a low frequency oscillatory mode, similar to the phugoid, which is sometimes called the lateral phugoid. Although it is not generally associated with good flying qualities, total damping values (i.e., the product (r~OJn) of 0.5, 0.3 and 0.15 are currently used as the levels 1, 2 and 3 boundaries, respectively, based on data from the variable stability aircraft, NT-33.

4.3.4 Dutch-roU mode T h e dutch-roll mode is the lateral-directional short-period oscillatory mode. It generally occurs at frequencies similar to those of the longitudinal shortperiod mode, i.e. of the order of one to five radians per second or so. T h e dutch-roll mode can helpfully be considered very approximately as the m o d e through which the sideslip of the aircraft is controlled with the rudder. More realistically, the dutch roll is a nuisance mode in the basic roll response to lateral control. Along with its frequency and damping characteristics are specified measures of how much it appears in the lateral response (the magnitude of its residue) and its phasing. T h e r e are parallels between this sideslip response to r u d d e r and the response of angle-of-attack to elevator. The damping term is the sum of the rotational damping, N r and the resistance o f the aircraft to the velocity that generates the sideslip, Yr. The frequency or stiffness is mostly the rotational resistance of the aircraft to the

Flight control systems

140

Level

1

Flight-phase category

Class

Min srd*

Min ~r~fJd* (rad/s)

Min wd (rad/s)

A (CO and GA)

IV

0.40

0.40

1.0

A

I, IV, II, III

0.19 0.19

0.35 0.35

1.0 0.4

B

All

0.08

0.15

0.4

C

I, II-C, IV

0.08

0.15

1.0

II-L, III

0.08

0.10

0.4

2

all

all

0.02

0.05

0.4

3

all

all

0

-

0.4

* The governing requirement is that yielding the large value of (d, except that a (d of 0.7 is the maximum required for Class III. When the product w21 qb/fll is greater than 20 (rad/s) 2, the minimum specified dutch roll total damping ~'dt0,~is increased by A~'dto,,a values as follows; level 1: Asrdto,~= 0.014 (w,,~21¢/fll - 20) level 2:A(dmn=O.OO9(o)na2lqb/[31 20) -

-

level 3: AsrdW.e=0.005 (w.d21¢/fll -- 20)

Figure 4.14

Dutch-roll damping and frequency requirements

velocity w h i c h g e n e r a t e s the sideslip. T h e similarity o f Yv to Zw, Mq to N Ta n d o f N B to M s is q u i t e direct. T h e y can b e c o n s i d e r e d c o n c e p t u a l l y to b e the s a m e derivatives r o t a t e d t h r o u g h 90 d e g r e e s . T h e r a p i d i t y o f t h e d u t c h roll a n d t h e d e g r e e o f its o s c i l l a t o r y d e c a y a r e s p e c i f i e d by t h e u n d a m p e d n a t u r a l f r e q u e n c y a n d t h e d a m p i n g ratio, respectively. T h e s e c r i t e r i a a r e specified in F i g u r e 4.14. N o t e t h a t t h e total d a m p i n g , i.e. the p r o d u c t o f t h e u n d a m p e d n a t u r a l f r e q u e n c y a n d the d a m p i n g ratio, is also specified. T h e r e is c o m m o n l y significant d u t c h - r o l l c o n t e n t in t h e l a t e r a l o r roll r e s p o n s e to lateral c o n t r o l . We n e x t discuss c r i t e r i a w h i c h cover this effect, w h i c h is d e l e t e r i o u s since t h e p i l o t p r e f e r s a relatively p u r e roll r e s p o n s e to control.

4 . 3 . 5 The parameter w 4 J w d T h e l u m p e d p a r a m e t e r r e s p o n s e to lateral c o n t r o l is:

¢ = U ~ , =K¢(s2 + 2~¢wcs+(w2¢) 6a A (TRS+I)(TsS+I)(s2+2(dWnS+W2)

(4.14)

M a t h e m a t i c a l l y , if 56= (d a n d e0¢~ w.,, t h e n the two s e c o n d - o r d e r t e r m s c a n c e l e a c h other.

Handling qualities

141

bank angle, ~)

sideslip angle, -

t

Figure 4.15 Time responsedefinition of 8/,B roll-to-sideslipratio in the dutch roll Physically, the cancellation would mean that the bank-angle response does not contain any dutch-roll oscillations. Often, the parameter e0C/0a,~, which is usually abbreviated to eo¢,/ead,is a measure of the vertical separation of roots in this dipole, and requiring this parameter to be about unity has been used as a crude way of keeping the dutch roll out of the bank-angle response. However, it can be shown that yawing m o m e n t due to roll rate, Np, (the dynamic version of adverse yaw) causes the zero to move in a circular locus a r o u n d the pole, giving lateral root separation. The time-history equation for sideslip following a step aileron input is:

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(4.15)

and the criteria (not reproduced here for brevity) restrict the ratio of oscillatory rolling to average rolling as a function of the phase parameter 4'13 [1].

4.3.6 Phi-to-beta ratio, qS/fl The phi-to-beta ratio distinguishes between dutch-roll oscillations which occur in sideslip, with the wings roughly level, and dutch-roll oscillations which occur in bank angle, with roughly zero sideslip. Figure 4.15 defines qS/fl ratio in terms of time responses, which is readily calculated from the modal response ratios in the transfer functions. Current specifications state that when the product wz,dd?/fl is greater than 20 (rad/s) 2, the minimum specified dutch-roll total damping, (d0~,,t, is increased to prevent high roll accelerations due to side gusts. In addition to roll accelerations due to side gusts, pilots object to lateral accelerations due to roll manoeuvres. T h e specified maximum values of the parameter;

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Figure 4.25 PIO criteria using dynamic stickforce per g

Handling qualities

155

4. 7.2 A'Harrah-Siewert criteria A'Harrah and Siewert proposed their own criteria for prevention of PIO, especially for low-altitude, high-speed flight, in the 1960s. The most mature of these recently resurfaced as the US Federal Aviation Administration searched for ways to regulate against PIOs in commercial airliners. Early draft advisory circulars proposed the A'Harrah-Siewert criteria, but later versions have not. A'Harrah-Siewert PIO criteria [23] use an airplane response metric and a control metric. The response metric is defined as the time to one-tenth amplitude of the short-period response, compu ted as T l / 10 In (0.1) / ((spC0sp), and the control metric is a combination of stick force and position per g, (FJ nL)~x (6/nL), in units of in-lbS/g 4. The PIO boundary for their criteria is shown in Figure 4,24, along with their flight data introduced in Figure 4.23. Correlation is very good for the flight data, as there are only two PIO cases clearly on the nonPIO side of the boundary (and both are at least near the boundary), and two nonPIO cases on the PIO side. This makes the A ' H a r r a h Siewert criteria appear to be very effective. (One significant shortcoming, n o t e d by large-airplane manufacturers, has been that the control metric for wheel-and-yoke transports is orders of magnitude larger than the highest value in Figure 4.24, and this has understandably raised some concern.) =

4. 7.3 Dynamic stick force per g T h e developers of the US military specifications in the 1960s were aware of the work of both STI and A'Harrah and Siewert. Based on research at Cornell Aeronautical Laboratory (later Calspan), however, the choice for the military requirements was a dynamic stick force per g parameter that is primarily a function of short-period damping ratio. The requirements on stick force per g from the military standard [12] are shown in Figure 4.25, along with the now-familiar data collected by A'Harrah and Siewert [23]. The requirements of Figure 4.25 are even more effective at correlating the data, better than either the high-gain asymptote or A'Harrah-Siewert criteria. One PIO case lies on the nonPIO side, and one nonPIO case is on the PIO side of the boundary. Thus, we may conclude that, for conventional airplanes where short-period damping and control response are the primary causes of PIO, dynamic stick force per g is a very effective PIO criterion.

4.8 N o n - m o d a l PIO criteria Flying-qualities criteria introduced up to now have been directed towards airplanes responses for controlling inputs look similar to those of unaugm e n t e d aircraft, whether augmentation is used or not. As long as the basic characteristics of the airplane resemble those of the conventional response type in Figure 4.21, the modal criteria may be applied. The modal criteria are applicable even to less conventional-looking responses if the source of the

156

Flightcontrolsystems

unconventional form is well approximated by a time delay at frequencies below about 10-20 rad/s. T h e n we can apply the equivalent-systems approach and make use of the same criteria, along with a new limit on equivalent time delay. Examples of such high frequency dynamics include the typical noise, structural and anti-aliasing filters applied to the output signals of aircraft motion gyros and accelerometers. T h e r e are cases where this adherence to the traditional criteria breaks down, however. Historically this has been a result of the addition of lag or lead/lag filters in the pilot's command path with break frequencies near the pilot's operating frequency. The dynamics often are not conventional looking on a frequency-response plot, and use of traditional criteria (by applying equivalent-systems techniques to the responses) has resulted in controversy [24]. Another example of the shortcomings of traditional criteria is the unconventional response type, where the basic response form is not even close to that of the conventional airplane. Consider, for instance, the attitude response type where the short-term response to pitch control inputs looks like this: 0

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8e = IS2 + 2~',OS + ,oZl

T h e r e is certainly nothing wrong with fitting an equivalent system to an attitude response type to obtain this transfer function. Note, however, that this equivalent airplane does not have the same form as that for the traditional airplane: it is missing the zero 1~To2 and a free s in the denominator. The second-order lag that dictates the response clearly is not the same as the traditional short-period mode with which we are familiar. Therefore, it would be incorrect to blithely plot this root on the traditional criteria and make judgements about the short-period flying qualities of the airplane. What is needed, then, is a way of judging the flying qualities of aircraft which defy the traditional modal criteria.

4.8.1 Some current criteria Numerous flying-qualities researchers have proposed n o n m o d a l criteria for prediction of category I PIO. Typically these criteria apply well to the database u p o n which they are based, but break down when confronted with data from other experiments. The following is a brief summary of four longitudinal PIO criteria.

Airplane bandwidth~pitch-rate overshoot Pitch-attitude bandwidth criteria were developed for evaluation o f the handling qualities of highly augmented airplanes where more conventional criteria cannot be easily applied [26]. The criteria are included in the

Handling qualities 157 handling-qualities interface standard MIL-STD-1797A[12]. (The limits in MIL-STD-1797A have been found to be much too stringent and have been adjusted significantly, especially with the addition of a requirement on pitchrate overshoot [25].) They have been adapted to the prediction of PIO susceptibility as sketched in Figure 4.26. All of the bandwidth parameters are to be measured with the feel system included at all times (even if force sensing is used for aircraft commands). This differs from the approach taken by most other researchers. The argument is made that the feel system is not transparent to the pilot, and that it will therefore influence both pilot opinion of flying qualities and probability of encountering a PIO [26]. The developers of the bandwidth-based PIO criteria observed that, if a PIO occurs, the likely frequency for the oscillations is well approximated by the pitch-attitude neutral-stability frequency, tol800, with a slight adjustment of an additional 0.5 rad/s [27]. The hypothesis is that, in a PIO, the pilot adds little in the way of dynamics to the pilot-vehicle system (i.e., the pilot displays synchronous tracking behaviour [21]). The added 0.5 is an admitted fudge factor which probably indicates the addition of some small amount of lead as the pilot attempts to cope with the PIO.

Neal-Smith The Neal-Smith criteria [5] were also designed for the evaluation of flying qualities of highly augmented airplanes. The original requirements explicitly referred to handling-qualities levels but only indirectly addressed PIOs (Figure 4.11). Although there is a region (corresponding to handling qualities level 3) where PIO tendencies are mentioned, there is no clear P I O / no PIO dividing line on Figure 4.11. Strong PIO tendencies are indicated throughout the level 3 region, so this is clearly a region where PIO is predicted, but tendencies to oscillate in the middle of level 2 might also signify a milder PIO tendency. As with all the nonmodal criteria considered here, the Neal-Smith criteria are frequency-domain based. Unlike the others, however, application is best performed using transfer function models of the airplane, rather than frequency-response plots (in their original development [5], application was entirely graphical and it was possible to avoid obtaining transfer functions). This is a shortcoming of the criteria, since it raises the issue of the best way to obtain the transfer function, especially from flight test data. A significant complication of the criteria is the requirement to perform closed-loop analysis of the pilot-vehicle system. This requires assumptions about the pilot model to be used. Neal and Smith established several ground rules which they applied to their own flight research data to derive the boundaries. These ground rules have been varied, relaxed, tightened and ignored by other researchers over the years, but there is no real evidence that these variations are significantly more successful than the original version. As

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Handling qualities

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originally developed by Neal and Smith, the parameters in the criteria are obtained by finding the dynamics of the pilot model given in Figure 4.10, i.e.,

by: (TlS+ 1)

Yp= I~ (TLS+ I) e-'P for the pitch-attitude dynamics of the airplane described by Y~= O/bes. The pilot time delay, rp, is a fixed value (Neal and Smith assumed 0.3 s) and K p, 7"/ and TL are varied to meet specific performance constraints. In the original Neal-Smith analysis, the performance criteria were a specified closed-loop bandwidth, BW (where the phase of the closed-loop system, / ( 0 / 0 c ) , is - 9 0 degrees), of either 3.0 or 3.5 rad/s and closed-loop droop of exactly - 3 dB. The parameters of the Neal-Smith criteria are the closed-loop resonance, ]0/ 0clm~,, and the phase angle of pilot compensation, /_pc, at the bandwidth frequency. Determination of the best pilot model is not a trivial task when performed manually. Most users of the Neal-Smith criteria have developed software which will perform the loop-closure process automatically.

Smith-Geddes The Smith-Geddes P I t criteria were developed from basic principles of closed-loop piloted control of pitch attitude and normal acceleration [28]. They were initially aimed towards handling qualities, and they owe as their foundation the Neal-Smith database. The criteria have undergone some revisions as well as extension into the roll axis. Smith and Geddes define three types of P I t . These types are not to be confused with the categories of P I t mentioned earlier. The parameters of the Smith-Geddes criteria, as currently applied [29], are as follows: (i)

Slope of the pitch-attitude-to-stick force transfer function, S, defined between 1 and 6 rad/s, in units of dB/octave. (ii) Criterion frequency, too defined as 6+0.24S. If a P I t is predicted this is the expected P I t frequency. (iii) Phase angle of the O/Fe~transfer function measured at toe If the phase angle /-O/Fe~(jtoc) is more negative than - 1 8 0 °, a type III (attitudedominant) P I t is predicted. (iv) Normal acceleration parameter, ~(/'toc). If the phase is between - 160 and - 1 8 0 o, a type I (acceleration-dominant) P I t is predicted if, in addition, the normal acceleration response at the pilot's station is such that ~(Jtoc) = Ln~/Fs(Jtoc) - 14.3toe ---