The Regulator and Its Functions
Short Description
El regulador y sus funciones en el control d eprocesos...
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INSTRUMENTATION MAINTENANCE THE REGULATOR AND ITS FUNCTIONS
TRAINING MANUAL Course EXP-MN-SI070 Revision 0
Field Operations Training Instrumentation Maintenance The Regulator and its Functions
MAINTENANCE INSTRUMENTATION THE REGULATOR AND ITS FUNCTIONS CONTENTS 1. OBJECTIVES ..................................................................................................................5 2. REGULATION .................................................................................................................6 2.1. DEFINITIONS ...........................................................................................................6 2.2. INTRODUCTION.......................................................................................................6 2.2.1. Behaviour in terms of regulation........................................................................8 2.2.2. Behaviour in terms of slaving ............................................................................8 2.3. CLOSED-LOOP REGULATION ................................................................................9 2.3.1. Operating principle ............................................................................................9 2.4. OPEN-LOOP REGULATION...................................................................................11 2.4.1. Operating principle ..........................................................................................11 3. THE PROCESS AND ITS CHARACTERISTICS ...........................................................13 3.1. STABILITY ..............................................................................................................13 3.1.1. Naturally stable process ..................................................................................13 3.1.1.1. Principle .....................................................................................................13 3.1.1.2. Example of a stable process ......................................................................14 3.1.2. Naturally unstable process ..............................................................................15 3.1.2.1. Principle .....................................................................................................15 3.1.2.2. Example of an unstable process ................................................................15 3.2. PROCESS RESPONSE PARAMETERS ................................................................16 3.2.1. Transient state and steady state .....................................................................16 3.2.1.1. Principle .....................................................................................................16 3.2.1.2. Example .....................................................................................................16 3.2.1.3. Conclusion .................................................................................................20 3.3. STATIC CHARACTERISTIC OF A PROCESS .......................................................20 3.3.1. Static gain........................................................................................................20 3.3.2. Static error.......................................................................................................21 3.3.3. Linearity and non-linearity of a system (process) ............................................21 3.4. DYNAMIC CHARACTERISTIC OF A PROCESS....................................................21 3.4.1. Response time ................................................................................................21 3.4.2. Overshoot........................................................................................................21 4. REGULATORS ..............................................................................................................22 4.1. ROLE OF THE REGULATOR .................................................................................22 4.2. REGULATOR STRUCTURE ...................................................................................23 4.3. PID DIAGRAM REPRESENTATION OF A REGULATOR ......................................27 4.4. REGULATOR CLASSIFICATION............................................................................28 4.4.1. Pneumatic regulator ........................................................................................28 4.4.2. Electronic regulator .........................................................................................30 4.5. REGULATOR ACTION DIRECTION.......................................................................33 4.5.1. Definition .........................................................................................................33 4.5.2. Choice of regulator action direction .................................................................34 5. REGULATOR ALGORITHMS........................................................................................35 5.1. PROPORTIONAL ACTION .....................................................................................35 Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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5.1.1. Definition .........................................................................................................35 5.1.2. Presentation ....................................................................................................36 5.1.3. Operation.........................................................................................................38 5.1.4. Influence of the proportional band ...................................................................39 5.1.5. Band shift ........................................................................................................41 5.1.6. Influence of band shift .....................................................................................42 5.1.7. Functional representation of a proportional regulation ....................................42 5.2. INTEGRAL ACTION................................................................................................43 5.2.1. What is an integral action? ..............................................................................43 5.2.2. Operation.........................................................................................................43 5.2.3. Eliminating the integral action..........................................................................44 5.2.4. Combined PI action .........................................................................................44 5.2.5. Influence of the integral time parameter ..........................................................45 5.3. DERIVED ACTION..................................................................................................46 5.3.1. What is a derived action? ................................................................................46 5.3.2. Operation.........................................................................................................46 5.3.3. Influence of the derived time parameter ..........................................................48 5.3.4. Combined PID action.......................................................................................49 5.3.5. Summary of the PID actions............................................................................49 5.3.6. Advantages and drawbacks ............................................................................50 5.4. THE VARIOUS STRUCTURES OF A PID REGULATOR .......................................51 5.4.1. How to determine the internal structure of a PID regulator..............................51 5.4.2. Series structure ...............................................................................................52 5.4.3. Combined structure .........................................................................................52 5.4.4. Parallel structure .............................................................................................52 6. DETERMINING A REGULATOR'S ACTIONS ...............................................................55 6.1. ZIEGLER AND NICHOLS METHOD .......................................................................56 6.1.1. Response of the open-loop process ................................................................57 6.2. STABLE PROCESS IDENTIFICATION METHOD ..................................................58 6.2.1. Strejc method ..................................................................................................59 6.2.2. Broîda method.................................................................................................59 6.2.2.1. Identifying the open-loop process ..............................................................60 6.2.2.2. Identification in a closed loop .....................................................................60 6.3. UNSTABLE PROCESS IDENTIFICATION METHOD .............................................63 6.3.1. Identification in an open loop...........................................................................63 6.3.2. Identification in a closed loop ..........................................................................64 6.4. THE ADJUSTOR METHOD (BY SUCCESSIVE APPROXIMATIONS) ...................65 7. THE REGULATION LOOP ............................................................................................67 7.1. SINGLE-LOOP REGULATION................................................................................67 7.1.1. Simple regulation loop .....................................................................................67 7.2. MULTI-LOOP REGULATION ..................................................................................67 7.2.1. The different types of multi-loop regulation......................................................67 7.2.1.1. Cascade Regulation ...................................................................................67 7.2.1.2. Ratio regulation ..........................................................................................68 7.2.1.3. Feedforward regulation (combined) ...........................................................69 7.2.1.4. Split-Range regulation................................................................................70 7.2.1.5. On/Off regulation........................................................................................72 8. LIST OF FIGURES ........................................................................................................73 Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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9. LIST OF TABLES ..........................................................................................................75
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1. OBJECTIVES The purpose of this course is to enable the future instrumentation specialist to understand the instrumentation on a predominantly oil-oriented industrial site. The objectives of this course are to allow you to know: what a regulator consists of, what purpose it serves, all its functions, how to adjust the actions of a regulator.
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2. REGULATION 2.1. DEFINITIONS Adjusted variable Physical variable that you want to control. The name taken by the regulation is based on this variable. For example: temperature regulation.
Setpoint value Value that the adjusted variable must take.
Correction variable Physical variable that has been chosen to control the setpoint value. Generally, it is not of the same nature as the adjusted variable.
Disturbance variables Physical variables that influence the adjusted variable. Generally, they are not of the same nature as the adjusted variable (e.g. variation in the ambient temperature).
Setting or control device Element that acts on the correction variable (e.g. regulation valve).
2.2. INTRODUCTION A certain number of parameters have to be controlled for most industrial processes, such as: temperature, pressure, flow rate, level, pH, concentration of O2, etc. It is the task of the regulation chain (and more generally of the slaving chain) to maintain the parameters governing process operation at predetermined levels. All regulation (or slaving) chains include four essential links: the sensor and its transmitter, the actuator (regulation valve, speed variator, etc.), the regulator and the industrial process (heat exchanger, distillation column, etc.). Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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You must therefore start by measuring the main variables that are used to control the process. The regulator recovers these measurements and compares them with the values required by the operator, which are usually called the "setpoint values". In the case where the measured values are not in agreement with the setpoint values, the regulator sends a command signal to the actuator so that it can act on the process. The parameters governing the process are therefore stabilized at all times at the desired levels. If we take the example of a heat exchanger, the adjusted variable is the output temperature (which must be held constant, at a predetermined setpoint value) and the correction variable is the flow-rate of the heat-transfer fluid. The load's flow rate variations and changes in the ambient temperature are considered to be disturbance variables.
Figure 1: Regulation chain schematic diagram The choice of elements in the regulation chain is dictated by the characteristics of the industrial process to be controlled, which means that you must know the process and the way it behaves. In the regulation chain, the three devices that have been mentioned above make up the regulating system, whereas the process constitutes the regulated system. After the regulator's action, two different types of behaviour can be obtained in automatic mode: The behaviour in terms of regulation The behaviour in terms of slaving Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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The instrumentation specialist is ‘subjected to’ the manufacturing process, but he 'chooses' the regulating system (made up of sensors, regulators and actuators).
2.2.1. Behaviour in terms of regulation The setting is maintained constant and a change (or variation) in one of the disturbance inputs occurs. Regulation is considered to be the most important aspect in the industrial world, because the setpoint values are very often fixed. However, to test the performance and quality of a regulation loop, the instrumentation specialist must also look at the slaving aspect.
Figure 2: Unit-step response in process regulation
2.2.2. Behaviour in terms of slaving The operator makes a change in the setpoint value, which corresponds to a modification in the process's operating point. If slaving behaves correctly, it is demonstrated that the "regulation loop" reacts correctly, even when a disturbance occurs.
Figure 3: Unit-step response in process slaving Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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2.3. CLOSED-LOOP REGULATION There are two ways of "qualifying" a closed-loop regulation system: The first one (behaviour in terms of regulation) consists of seeing how it reacts to an external disturbance, The second (behaviour in terms of slaving) consists of seeing how it reacts to a variation in the setpoint value.
Figure 4: Closed-loop regulation schematic diagram This represents normal regulation operation: the regulator is in Automatic mode. The regulator compares the measurement of the adjusted variable with the setpoint value and acts appropriately to make them coincide.
2.3.1. Operating principle The output variable or "correction variable" exerts an influence on the input variable or "adjusted variable" to maintain it within the predetermined limits: this is a closed-loop regulation or slaving system. The action of the correction value on the adjusted variable is obtained via the "process or system" which closes the loop. In a closed-loop regulation system, a large proportion of the disturbances, including the drift specific to certain components in the loop, are automatically compensated for by the counter-reaction through the process.
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Example:
Figure 5: Example of closed-loop regulation In this example: The adjusted variable is the oven's output Temperature Ts, The correction variable is the gas's flow rate, The disturbance variable is the input flow rate Z. The setpoint value is T = 100 °C You do not have to know precisely the laws and behaviour of the various components in the loop, and in particular in the process, even though it will be useful to know the static and dynamic rates of the various phenomena encountered in order to choose the components in the loop. Amongst the drawbacks of closed-loop regulation, we must mention the fact that regulation accuracy and fidelity depend on the measured values and on the setpoint value. Another drawback, no doubt more serious, is that the loop's dynamic behaviour depends on the characteristics of the various components in the loop, and in particular in the process, that we do not have under control: a poor choice of certain components may cause the loop to start oscillating (surging phenomenon).
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Lastly, closed-loop regulation cannot anticipate. In order for the regulation to send a command to the control system, the disturbances or any variations with respect to the setpoint value must have been observed at the output from the process, and this sometimes takes far too long.
2.4. OPEN-LOOP REGULATION We have an "open loop" when we switch the regulator to Manual mode, that is to say it is the operator who makes the process react the way he wants it to by "playing" directly on the setting device.
2.4.1. Operating principle In an open-loop slaving system, the setting device does not react through the process on the measured variable (this is not verified). Open-loop regulation can only be used if you know the operating process perfectly (in other words, you must know the correlation between the measured value and the correction variable). Example:
Figure 6: Example of open-loop regulation This example illustrates perfectly what happens: It is the operator who acts directly on the setting system to obtain the oven output temperature TS that he wants, we do not have any feedback (the value measured by the sensor-transmitter).
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Unlike closed-loop slaving, open-loop control makes it possible to anticipate the phenomena and obtain very short response times. Open-loop control can only be considered when there is no possibility of having a final check; this is equivalent to placing the regulator in manual mode when a transmitter has failed and we have lost the measurement. The major drawback is that there is no way of checking, let alone correcting any errors, drift or accidents that may occur inside the loop. In other words, there is no precision or, above all, fidelity, which depends on the intrinsic quality of the components. Lastly, open-loop regulation does not compensate the disturbance factors.
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3. THE PROCESS AND ITS CHARACTERISTICS For the instrumentation specialist the term process designates a part or an element in an industrial production unit; for example a heat exchanger that includes a temperature regulation or a tank whose level is regulated. Process and regulation form an inseparable whole. The choice of the type of regulation loop and its fine-tuning require a good knowledge of the process's behaviour. The process can also be called a system. For instance, how does the output temperature from a heat exchanger or the level of a tank evolve naturally? There are two classes that cover all the elements in the process: process elements whose behaviour is said to be stable and others whose behaviour is said to be unstable. We usually use the terms: stable process and unstable process. In order to see the industrial process's behaviour, we always place ourselves in an open loop, that is to say the regulator is in MANUAL mode and we act directly on regulator output Y. When we change the regulator's output value in MANUAL mode, this is equivalent to saying we applied a "valve step of X%".
3.1. STABILITY 3.1.1. Naturally stable process 3.1.1.1. Principle A process is said to be naturally stable if a finite variation in the correction variable E corresponds to a finite variation in the adjusted variable S.
Figure 7: Schematic diagram of a stable process Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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3.1.1.2. Example of a stable process
Figure 8: Example of a stable process Let us take the level N in a tank. The output flow rate Qs depnds on the level N ( Qs = K N ). If N is constant, that means Qs is equal to Qe. At time to, let us apply one valve step, the level rises in the tank, which causes the output flow rate Qs to increase. This phenomenon continues until the level is such that it causes a flow rate Qs that is once again equal to Qe. We can therefore see that further to a change in the correction variable Qe, the adjusted variable N reaches a new equilibrium N1. The process is said to be stable. We must insist on the fact that it is effectively the process on its own, because the regulator is in manual mode. Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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3.1.2. Naturally unstable process 3.1.2.1. Principle A process is said to be naturally unstable if a finite variation in the correction variable E corresponds to a continuous variation in the adjusted variable S.
Figure 9: Functional diagram of an unstable process
3.1.2.2. Example of an unstable process Let us modify the process above by replacing the natural flow by a forced flow, obtained by means of a pump with a constant flow rate Q. By repeating the previous test, we can see that, this time, the level N does not stabilize. The process is said to be unstable.
Figure 10: Example of an unstable process Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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Remark: A process is said to be of the integrator type if for a constant input E, output S is a rising straight line.
Figure 11: Functional diagram of an integrator type process
3.2. PROCESS RESPONSE PARAMETERS 3.2.1. Transient state and steady state 3.2.1.1. Principle A system is said to function in a steady state if its operation can be described in a simple way. Otherwise, we talk of a transient state. To pass from one steady state to another, the system passes through a transient state.
Figure 12: Transient and steady states
3.2.1.2. Example We have observed previously the response of a process to determine whether it is stable or unstable. Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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In this section, we are going to determine the process's characteristic parameters from that response. It will be easier to adjust the regulation loop if we know these parameters.
On a stable process Let us consider the regulation scheme for the heat exchanger in the figure below. With the regulator in manual mode, let us generate a step ΔV on the valve signal and observe the change of temperature Ts.
Figure 13: Example of a heat exchanger The response obtained is as shown in the next figure:
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Figure 14: Response of a stable process to a step This S-shape is the typical response of a stable process. The transient state is the time interval between instant to at the beginning of the step and instant t3 where the measurement reaches its final value Mm. Designation
Definition
Tr
Dead time or pure delay
Time interval between application of the step and the start of the change in the measurement: Tr = T1 – T0
teBO
Open-loop establishment time
Time interval between application of the step and the time when the measurement reaches 95 % of its final value Mm. We consider that this time is practically equal to the length of the transient state: teBO = t2 – t0
Gs
Static gain
Ratio between the measurement variation ΔM and the corresponding valve signal variation ΔV
Table 1: A stable process's response parameters Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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On an unstable process
Figure 15: Response to an unstable process step We can clearly see in the figure above that the unstable process is of the integrator type.
Designation
Definition
Tr
Dead time or pure delay
Time interval between application of the step and the start of the change in the measurement: tr = t1 – t0
K
Integration coefficient
The process's characteristic coefficient.
K=
ΔM K unit in mn-1 or s-1 Δt × ΔV
Table 2: An unstable process's response parameters
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3.2.1.3. Conclusion The regulation loop setting operations are often carried out by experienced technicians, who do not necessarily know the value of the parameters (Gs, teBO, Tr, K) of the processes on which they act. Knowledge, even approximate, of these parameters can: constitute an indicator for choosing the type of regulation best suited to a process (single loop, cascade, etc.). provide an indication on the best-suited regulation mode (P, PI, PID, PID selfadapting, etc.). make it possible to find, using calculation methods, the optimum setting actions to be displayed on a regulator to ensure the stability of a regulation loop.
3.3. STATIC CHARACTERISTIC OF A PROCESS The static characteristic is the curve representing the output variable S according to the input variable E: S = f(E). Remark: It is only possible to plot the static characteristic of a stable system.
Figure 16: Static characteristic of a process
3.3.1. Static gain If the system is naturally stable, the static gain G is the ratio between the variation of the input variable E and the output variable S.
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3.3.2. Static error If the system is stable, the static error E is the difference between the setpoint value W and the measurement of the adjusted value X.
3.3.3. Linearity and non-linearity of a system (process) A system is linear if its functioning can be described by means of linear mathematical equations.
3.4. DYNAMIC CHARACTERISTIC OF A PROCESS 3.4.1. Response time This is the system's aptitude to follow the variations in the correction variable. In the case of one step in the correction variable, the increase in the adjusted variable defines the different response times. In the example below, we measure the response time at 10, which is equal to T1 - T0.
Figure 17: Dynamic response of a closed-loop process
3.4.2. Overshoot The first overshoot makes it possible to qualify a system's stability. The greater the overshoot, the closer the system will be to instability. In certain regulation systems, no overshoots are tolerated. In the unit-step response, the first overshoot is 20 (=120% instead of 100%).
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4. REGULATORS We have therefore said earlier that a regulation loop is made up of four main elements: The sensor-transmitter, The regulator, The regulation valve, The process (for example: heat exchanger, distillation column, etc.). And here in this course, we are going to define what a regulator is, what it is made up of and we are going to see all its functions in a regulation loop.
4.1. ROLE OF THE REGULATOR The purpose of automatic system regulation is to hold an operating parameter (adjusted variable) at a constant and predetermined value, despite the influence of uncontrolled parameters (disturbance variables). The regulator is an integral part of the regulation loop, whether it is analogue, pneumatic or digital (software regulator), local, by control desk or display panel, in a control centre. In all cases, the regulator receives two inputs: The measurement signal from the transmitter, The setpoint value (manual or automatic).
Remark: These two variables have been identified for many years, and still are for many people, by the letters "M" and "C". But there is a problem here, the letter "C" also symbolizes the comparator, the sensor or even the command; the letter "M" also stands for Measurement, Measurand (physical value that has been captured).
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That is why the letters have been normalized by an American international system and the letters used for the measured and setpoint value are: X: Measured value W: Setpoint value
It "regulates": Compares the measured and setpoint values: measured-setpoint value difference (e = X - W), Decides what action is to be taken according to the parameters
It delivers: An output signal usually called the "command Y " to the regulation valve.
4.2. REGULATOR STRUCTURE
Comparateur
Figure 18: Regulator structure
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In the diagram above, we can see that the regulator is a set of several elements, it consists of: a comparator making it possible to compare the measured value with the setpoint value, a corrector that is going to correct this difference by performing several setting actions, a selector making it possible to choose between the Manual or Automatic positions. The measured signal X is the image of the adjusted variable, delivered by a sensor and transmitter and transmitted in the form of an electrical or pneumatic signal; The setpoint value W may be internal (provided locally by the operator) or external; Command Y is displayed and generally in physical units for the set and measured values. If a regulator is in automatic mode, its output will depend on the measured and the setpoint value. This will not be the case if it is in manual mode.
Figure 19: Detailed structure of the regulator Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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Whatever the technology used, a distinction is made between: The signals: 1: Measurement input: this signal, delivered by the transmitter, represents the variable to be adjusted 2: External setpoint value: delivered by an external instrument. 3: Output: command signal from the device being adjusted (valve). The most commonly used standard scale is: 4 to 20 mA.
The blocks: 4: Setpoint value generator. 5: PID module: in automatic mode, the output from the block is the same as the output from the regulator. The automatic position corresponds to normal regulator operation.
The adjustments: 9: Adjustment of the internal setpoint value. 10: Adjustment of P, I and D actions. 11: Adjustment of the upper and lower limits. 12: Adjustment of the regulator's output in manual position.
The selectors: 13: Internal setpoint value or external setpoint value selector. 14: Regulator's action direction (direct or inverse) selector. 15: Automatic or manual operation selector.
The indicators: 16: Setpoint value indicator. 17: Measurement indicator. 18: Measured value – Setpoint value difference indicator. 19: Output indicator.
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The table below gives the main symbols and designations used on regulators according to the manufacturers.
Measurement
M PV (Process Value) X
Output
S OUT or OUTPUT Y
Setpoint value
C SP (Set Point) W
(W-X) difference
X DV E
Internal, external setpoint value
INT and EX C.I and C.E L (local) and D (Distance)
Tracking setpoint value
Tracking P.V.T (Process Value Tracking)
Direct, inverse
D and I INC (Increase) and DEC (decrease)
Manual, auto
M and A MAN. and AUT. MANUAL and AUTO
Upper and lower limits
O.L and O.H L.B and L.H
Table 3: Symbols used on regulators
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4.3. PID DIAGRAM REPRESENTATION OF A REGULATOR The instruments used are represented by circles around letters defining the physical variable being adjusted and its/their function(s). The first letter defines the physical variable being adjusted, the following letters define the function of the instruments (see "Drawings used in instrumentation" course and the "Standards used in instrumentation" course).
Figure 20: Example of measuring instrument identification on a PID diagram
Figure 21: Example of regulator identification on a PID diagram Having read the "Drawings and Standards used in Instrumentation", it can clearly be seen that the regulator is a pneumatic regulator whose input measurement is the water flow rate + tank top-up with the steam flow rate.
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4.4. REGULATOR CLASSIFICATION Depending on the signal transmitted by the sensor-transmitter, we will therefore have two types of regulator: pneumatic regulator electronic regulator The pneumatic regulator is a regulator for local regulation, but it is being used less and less. The electronic regulator is the most commonly used type of regulator, it may be on a local control desk or in a centralized control system or a PLC (Programmable Logic Controller).
4.4.1. Pneumatic regulator The pneumatic regulator receives a pneumatic signal (200-1000 mbar) from the sensortransmitter. It is fed via a pressure relief valve set to 1.4 bar. It displays the measurement by means of a Bourdon tube, which will make a pointer move according to the pneumatic signal. The measured/setpoint value comparison is made by means of a nozzle-vane system and the regulator's command signal is amplified by means of a pneumatic relay.
Figure 22: Example of a pneumatic regulator
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Most often, you have two pressure gauges integrated in the regulator, they indicate the feed pressure and the regulator's output signal. The pneumatic regulator is installed close to the measurement point and functions in a single loop. The setpoint value is adjusted by means of a pointer, and you must turn the pointer's knob to change the value. You can always adjust the measurement zero by means of a set screw. Its main advantage is its response speed. And its main drawback is the difficulty in integrating the functions of several regulators spread around the units.
Figure 23: Pneumatic regulator measurement pointer
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4.4.2. Electronic regulator
Figure 24: Front face of an electronic regulator Recent types of regulators use digital technology. The fact that the links with the measuring instruments and regulation valves are made using analogue signals (4-20 mA) means that analogue-to-digital and digital-to-analogue (D-A and A-D) inputs-outputs (I/O are required). The figure above shows the different commands and indicators that can be accessed on the front face of a regulator.
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Two types of digital regulator are available: Single or double loop with control and adjustment on the front face Multi-loop with control and adjustment carried out in a remote station Digital technology provides numerous possibilities: Input signal processing (square-root extraction, measurement filtering, linearization, etc.). Possibility of having several inputs. Choice of input signal (current, voltage, frequency, thermo-electric couple, platinum probe, etc.). Scaling (value and format) of the indicators. Choice of the type of alarm, either on the measurement or on the deviation. Precise display of data such as actions, limits, etc. Automatic balancing (manual to auto transitions, etc.). Choice of derived mode, either on the measurement, or on the deviation. Setpoint value tracking: in manual position, the setpoint value follows the measurement. Self-adaptation of the PID actions. A distinction is made between: Self-regulating regulators which calculate the PID actions at a given operating point, on the basis of human intervention. Self-adapting regulators, which permanently calculate and adjust the parameters of their algorithm (PID or other) according to how the process evolves. A digital link makes it possible to link the regulator and make it communicate with other instruments such as: supervisor, calculator or other regulators. The digital regulator is an analogue regulator but with additional functions at the level of measurement signal processing.
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In fact, it has an analogue-to-digital converter (ADC) and a digital-to-analogue converter (DAC) which makes it possible to receive the standard electrical signal (4-20 mA) delivered by the sensor-transmitter, it processes it digitally and then transmits an analogue type signal to an adjustment device (e.g. regulation valve). This feature allows it to process the measurement information faster than an analogue regulator can. We have said earlier on that it could be on a local control desk (front face of the desk) and also that it could in a control system or a PLC with supervisor. Nowadays, to achieve this, all centralized control and PLC systems include processors with a regulator's basic and complex algorithms. Which is equivalent to saying that in these systems, we declare each PID algorithm that we want directly in the software. This is the most commonly used way these days, because it is very simple: you just have to take the input and output you want, declare them in the algorithm block of a regulator designed for that purpose, it's as simple as that! The operator has direct access to the regulator on his mimic views with all the possible commands (manual, automatic, etc.).
Figure 25: Example of an ABB local digital regulator
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Figure 26: Example of a digital regulator on a control system
4.5. REGULATOR ACTION DIRECTION 4.5.1. Definition A process is direct when its output varies in the same direction as its input. In a regulator, the measurement is considered to be an input E. If it varies in the opposite direction, the process is said to be inverse.
Figure 27: Definition of the action direction
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4.5.2. Choice of regulator action direction If the process is direct: the regulator's action direction must be set to inverse If the process is inverse: the regulator's action direction must be set to direct
Figure 28: Action of the regulator with a direct process
Figure 29: Action of the regulator with an inverse process Remark: In order to have a stable system in a regulation loop, the regulator must act in such a way that it opposes an unwanted variation of the variable X. If X increases, the regulator + process pair must tend to make it decrease.
Figure 30: Action direction of the regulator and of the process in a closed loop
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5. REGULATOR ALGORITHMS We have seen in the structure of the regulator that there is a corrector, and this corrector is going to allow us to make adjustments that will in turn allow us to act on the measured/setpoint value difference (also called "static error"). These adjustments are made by means of the following three regulator actions: Proportional action P: the error is multiplied by a gain K Integral action I: the error is integrated over a time interval Ti Derived action D: the error is derived over a time Td Each of the regulator's actions therefore corresponds to an algorithm. By associating these three algorithms in different ways, they will enable the regulator to adjust a process to a setpoint value that we want, by managing to compensate all the possible disturbances.
5.1. PROPORTIONAL ACTION 5.1.1. Definition Regulator output Y is proportional to the difference between the measured value and the setpoint value (W-X). The proportional action makes it possible to speed up the process's response because it instantaneously corrects any deviation in the variable to be adjusted. In order to reduce the adjustment difference (W-X) and make the process faster, we increase the gain (we reduce the proportional band). Take care, if this action is too great, you will risk having instability in the regulation loop (oscillations). Proportional action regulators are used when you want to adjust a parameter whose precision is not important. For example: to adjust the level in a storage tank Terms used: BP or Xp: Proportional band as a % K or Kp: Gain Y: Regulator command signal sent to the device being adjusted (e.g.: regulation valve). Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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5.1.2. Presentation The regulator's command Y is proportional to the static error (W - X), insofar as possible (Y cannot be negative, or have a value higher than 100). In the proportional part, called the proportional band, we have: B p =
100 K
The proportional band Bp therefore represents the variation in the measured/setpoint value difference as a % which produces a 100% variation in the regulator's output signal. The gain K represents the ratio between the output variation and the input variation. The setpoint value W, the measured value X and the proportional band Bp, are expressed as a % of the full scale.
Figure 31: Diagram of the proportional band according to the regulator's output Depending on the sites, people use different terms: you will hear the words 'gain' or 'proportional band' used.
Example of calculations: I take my regulator's parameters and I see that: The level measurement is X=10% Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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The setpoint value is W= 15% My valve command is Y=50% We are now going to return to my regulator's proportional band and do some small calculations. To begin with, let's calculate the set/measured value difference (W - X) W - X = 15 – 10 = 5% And then we can deduce the proportional band Bp
If we want to have the gain K:
We therefore have a gain K = 0.1
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5.1.3. Operation At the time of a variation in the setpoint value's step, the process has a response that looks like this:
Figure 32: Unit-step response of a proportional action process We are now going to see how to determine the operating point. The regulation of a process can be represented by the figure below. The regulator and the process each define a static characteristic. In the case of stable operation, the operating point in steady state belongs to two curves. The operating point therefore corresponds to the intersection of these two curves. From this construction, we can deduce the value of the static error (W-Xs), and the value of the regulator's command in steady state Ys.
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Figure 33: Proportional regulation in closed-loop operation
Figure 34: Determining the operating point
5.1.4. Influence of the proportional band
Figure 35: Influence of the proportional band in static behaviour Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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Static behaviour (operation in steady state): we can see in graph-form that the smaller the proportional band is, the smaller the error (W-X) will be in steady state. In the figure, Xp1 < Xp2 Here the process's response in static is the green curve. The red and blue curves show the change of value in the proportional band and therefore its influence on the process. Dynamic behaviour (operation in transient state): the smaller the proportional band is, the shorter the system's response time will be. In fact, for a given error, the command delivered is greater than with a larger proportional band. If the proportional band comes close to 0, the system becomes unstable. In fact, On/Off operation corresponds to a nil proportional band (see On/Off regulation chapter).
Figure 36: Influence of the proportional band in dynamic behaviour
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Figure 37: Example of adjustment of the proportional action
5.1.5. Band shift More generally speaking, the formula linking output Y from the regulator to the difference between the measured value and the setpoint value is: Y = ± K (W - X) + Yo Where Yo is the ‘band shift’ or ‘bias’ to be adjusted on the regulator. Where K has become a positive constant, the +/- sign will give us the regulator's action direction. This shift will allow us to choose the operating point and, depending on the manufacturers, the P type regulators can be designed for the following operating conditions: let Yo = 0 ; we when talk of an off-centre proportional band, because the adjustment zone is completely to the left or right of the setpoint value. let Yo = 50% ; we when talk of a centred proportional band, because the adjustment zone is evenly spread on each side of the setpoint value. let Yo be adjustable. So, for an inverse action regulator we have the characteristic shown in this figure:
Figure 38: Band shift characteristic
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5.1.6. Influence of band shift
Figure 39: Influence of band shift on the static error We can see that with a good choice of band shift value, you can very significantly reduce the static error. The influence on the behaviour in transient state mainly depends on the static characteristic. We can deduce from this that, in electronics, a proportional action corrector is a simple ‘amplifier-phase shifter.
5.1.7. Functional representation of a proportional regulation In the case of an inverse action regulation, the figure below represents a regulator in proportional operation. Kp = corrector gain Yo = band shift
Figure 40: Functional representation of a proportional action regulation on its own
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5.2. INTEGRAL ACTION The role of integral action is to eliminate the static error. However, increasing the integral action produces instability. In industry, action I will be used whenever, for technical reasons, we need perfect precision. Example: pressure or temperature regulation in a nuclear reactor. If the process itself includes an integrator (e.g. level), action I is all the same necessary to cancel out the disturbance deviation because, further to variations in the setpoint value, the usefulness of I is slighter as the deviation cancels itself out naturally. Furthermore, it must be underlined that action I is a filter, it is therefore worthwhile using it for adjusting dynamic parameters such as pressure. Action I completes the proportional action, which gives us a PI regulator.
5.2.1. What is an integral action? We want: an action that changes over time; an action that tends to cancel out the static error. This function is fulfilled by the mathematical operator: 'integral with respect to time'. So, in a regulator, we define the integral action from one of the two parameters Ti or Ki with: 1 Ki = Ti where: Ti is the integral time, defined in time units [sec, minutes] or as a number of repetitions per minute (rep/min). Ki the integral gain, defined as strokes per time unit.
5.2.2. Operation In order to study the influence of integral action, we shall look at the response of the onestep integral modulus. The greater Ki is (the smaller Ti is), the more the value of output Y increases quickly. Time Ti is the time required for command Y to increase by the input value E = W - X.
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Figure 41: Influence of Ki on the command Y signal
5.2.3. Eliminating the integral action There are several solutions for cancelling out the integral action, depending on the regulator. If you set the integral action by means of the gain Ki, you just have to set Ki to zero. In cases where the integral gain is set by means of the time Ti, there are two solutions: set Ti to zero, if that is possible; set Ti to its maximum value and the "supp." message will be displayed on the regulator's screen. For regulators on a control desk, everything depends on the manufacturer. For softwarecontrolled regulators (DCS or PLC), you just have to deactivate the integral action.
5.2.4. Combined PI action
Figure 42: Combined PI action Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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Integral action repeats the effect of the proportional action, until the difference between the measured and setpoint values is nil. It integrates the W-X difference as a function of time. Here we can see the behaviour of the output signal Y from the open loop regulator with a PI regulator. This little example makes it possible to observe the behaviour of the regulator's output signal. At time T = 0: we see that the measurement = the setpoint value (W = X). T = Ti = 1 min K=1
5.2.5. Influence of the integral time parameter Static behaviour: whatever the value of the integral action, the static error is nil (if the process is stable). Dynamic behaviour: in the case of a unit-step response such as shown below, the smaller Ti is the closer the process will get to instability.
Figure 43: Influence of the integration time in a closed loop Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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Figure 44: Example of PI regulator setting
5.3. DERIVED ACTION 5.3.1. What is a derived action? A derived action compensates for the effects of the process's dead time. It has a stabilizing effect. The presence of a derived action makes it possible to speed up the process. In industry, a derived action is never used on its own, but in general with an integral action. We recommend that it should be used for setting slow parameters such as temperature. In practice, a derived action is applied to the variations in the measured value and not to the difference between the measured and setpoint values in order to avoid any juddering due to sudden variations in the setpoint value. It is not recommended for setting a variable subject to noise or that is too dynamic (e.g. pressure). By deriving a noise, its amplitude could become greater than that of the useful signal. Its action opposes the integral action. This function is fulfilled by the mathematical operator: 'derive with respect to time'.
5.3.2. Operation In order to study the influence of the derived action, we will look at the response of the derived modulus to a ramp. The greater Td is, the larger the value of output Y will be. Time Td is the time for which input E increases by the value of output Y. Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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Figure 45: Influence of derived time Td on regulator output Y It therefore makes it possible to increase the regulation speed by giving opening and closing pulses to the regulator's output signal. The derived time Td is expressed in minutes.
Figure 46: Output signal from the regulator submitted to a derived action The figure above allows us to see the shape of the regulator's output signal submitted to a derived action. These pulses on output signal Y are called "Dirac peaks". We can see that they act quickly on the measured value X.
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5.3.3. Influence of the derived time parameter Static behaviour: no influence. Dynamic behaviour: the greater the derived time Td, the faster the process will be.
Figure 47: Influence of derived time Td in a closed loop
Figure 48: Example of PD regulator adjustment
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5.3.4. Combined PID action In general, the regulator does not function with a pure derived action (too unstable). It functions as a Proportional Integral Derived (PID) corrector. This is the most commonly used type of algorithm. In general it is available on most of the regulators currently used (PID regulators). It makes it possible to stabilize the measured value on the set point in the shortest possible time.
Figure 49: Output signal from the regulator with three combined actions The figure above allows us to see how the regulator output signal Y evolves with three combined regulator actions: P + I + D.
5.3.5. Summary of the PID actions
Figure 50: Unit-step response of each action of a regulator and of each of its PI, PD and PID combinations Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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5.3.6. Advantages and drawbacks
Regulator action
Advantages
Dynamic Proportional
Precise Stable
Drawbacks
It does not cancel out the static error Permanent residual deviation Surging if the proportional band is too narrow Slow action
Integral
Cancels out the static error Slows down the process Sensitivity to noise
Derived
Very dynamic and faster action
Serious loading of the command device
Faster than proportional on its own. Proportional + Integral
No difference between the measured and setpoint values whatever the variation in the disturbances
Surging if the integral action is too predominating
Anticipates Fast Proportional + Integral + Derived
Precise No deviation of the variable to be adjusted
Surging if the derived action is too strong
Limits the amplitude and length of the adjusted variable's variation
Table 4: Advantages and drawbacks of PID actions
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5.4. THE VARIOUS STRUCTURES OF A PID REGULATOR 5.4.1. How to determine the internal structure of a PID regulator To determine the structure of a regulator, you must isolate the process (do whatever is necessary to ensure it does not act on the measurement) and run it in automatic mode. You then just have to follow the flow chart below (observe the regulator's command Y in response to a measured value step X or a setpoint value step W). You should use the following values to make the measurement easier:
Figure 51: Determining the internal structure of a PID regulator
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5.4.2. Series structure This is the internal structure found in the oldest types of regulator, because it was already used in pneumatic regulators. It can be considered as a variant in the combined structure that we are going to see in the paragraph below.
Figure 52: Series structure
5.4.3. Combined structure This is the most widespread internal structure for local regulators that use electronic or digital technology.
Figure 53: Combined structure
5.4.4. Parallel structure This is the simplest structure, because the three basic corrections are independent. Digital command/control systems nearly always use it.
Figure 54: Parallel structure Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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Figure 55: Electronic schematization of a // PID regulator
P
Equation: S = Gr (M - C) + S’o
PI (series)
Equation: S = Gr (M − C ) +
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Gr Ti
∫ (M − C )dt − S
o
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PD (series)
Equation: S = G (M − C ) + Gr × Td
PID (series)
Equation: ⎛ T + Td ⎞ Gr ⎟⎟ + S = Gr (M − C )⎜⎜ i T i ⎝ ⎠ Ti d (M − C ) + Gr × Td + S0 dt
d (( M − C ) + S0' dt
∫ (M − C )dt
Table 5: Summary of the different types of regulator structure In a PID regulator, there are several ways of associating the P, I and D parameters. The response of a regulator to a measurement step has the same shape whatever the regulator's structure. However, you must know the regulator's structure in order to determine the actions of a regulator by calculation, in order to fine-tune a regulation loop.
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6. DETERMINING A REGULATOR'S ACTIONS Most books dedicated to automatic regulation include a wealth of mathematical developments. These are essential if you want to study the behaviour of servo and regulation systems, the influence of the various disturbances, the effectiveness of the adjustments, etc. In order to implement all these tools, you must have a mathematical model of the process you want to control. To obtain this model, you can start from the laws governing the physical-chemistry phenomena, in particular the laws of chemistry, heat transfer, mechanics, hydraulics, aerodynamics, fluid mechanics, etc. From there, it is possible to describe any operating process in the form of a set of mathematical equations. By solving those equations, it will then be possible to know how the process will rea ct to a modification in one of its inputs or to the arrival of an external disturbance. By knowing this behaviour, it is possible to define the regulator's characteristics that will make it possible to control the process as finely as possible. Unfortunately, there is a gulf between theory and practice. The mathematical descriptions of the processes are often very complex and require considerable skills in highly different disciplines. Furthermore, even if these equations were established, you would have to know the values of the various parameters that they include (calorific capacities, viscosities, Reynolds number, etc.). A colossal task!! So much so that, except in some mechanical processes, these mathematical studies cannot reach any satisfactory conclusion. Several other techniques can be used to calculate the parameters for regulators, all of them based on experimental tests: The Ziegler and Nichols method: this requires the observation of the process's response and knowledge of the regulator's structure. This method makes it possible to calculate the PID actions, without having to determine the process. By identification of the process: if you know the process's parameters and the regulator's structure, you can calculate the actions. This method requires a highspeed recorder. It is used, preferably, for high-inertia processes (e.g. oven temperature regulation). By successive approximations: this technique consists of modifying the actions and observing the effects for the recorded measurement, until the optimum response is obtained.
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6.1. ZIEGLER AND NICHOLS METHOD The Ziegler and Nichols method consists of placing the regulation loop in continuous oscillation. By using the Gain Grc, which you have used to obtain this oscillation, and the period T of that oscillation, it is possible to choose the regulator's adjustment parameters. This method can be used for stable and unstable process. Regul. mode
Actions
P
PI Series
PI Parallel
PID Series
PID Parallel
PID Combined
G rc
G rc
2,2
2,2
G rc 3,3
G rc 1,7
G rc 1,7
T
0,85T
T
4
G rc
2
T
T × G rc 13,3
T 8
Gr
G rc 2
Ti
Max
T 1,2
2T G rc
Td
0
0
0
4
Table 6: Ziegler and Nichols parameters according to the regulator's structure Two variants are proposed for this method, one for open-loop regulation and the other for closed-loop regulation. In the closed-loop method, we only use the proportional command to excite the loop until it starts to oscillate. This is done by applying a disturbance of the step type to the load. Starting from the critical gain value obtained (Grc) or the proportional band, which made it possible to obtain the undamped oscillation, and the value of the oscillation period T, you can deduce the regulator's optimum adjustment values. The coefficients to be applied depend on the regulator's structure. For a series PI regulator, the proportional band must be 2.2 times the band producing the undamped oscillation and the integration time equal to 0.83 times the undamped oscillation's period; for a combined PID regulator, the proportional band must be 1.66 times the band producing the undamped oscillation, and the integration and derived times must respectively be 1/2 and 1/8 of the undamped oscillation's period. In general, these adjustments give acceptable results, but they are not efficient for all the processes under all conditions. Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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Firstly, they are deduced from the Ziegler and Nichols optimum behaviour criterion, defined from the maximum amplitude of the controlled variable and its establishment time (the choice of parameters varies greatly from one process to another). Furthermore, the method consists of applying a step-type disturbance to the load when excitations of the pulse, ramp or sine type are better suited in certain cases. Generally speaking, this method is not suitable for fast loops (flow rates for example) and processes with long delays. However, it can be used for stable and unstable processes.
6.1.1. Response of the open-loop process Most adjustment parameter calculation methods consist of doing calculation on the openloop process's response curves, further to application of a step. The response curve in the figure below is more or less S-shaped, depending on the process.
Figure 56: Unit-step response of an open-loop process to a step In any case, we consider the linear zone where the response curve is at its steepest, we draw a straight line "fitting" this linear zone and we look at this straight's intersection point on the x-axis (time axis): we thus define time Tu. We then define time Tg as being the time it takes the variable being controlled to vary by the same amplitude as the regulator's output, this being done at the maximum variation (you must therefore use the straight line drawn above). These two parameters then make it possible to define the regulators adjustment by using the table below:
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Values recommended by Ziegler & Nichols Regulator P
Adjustment parameters Gr =
TG TU
G r = 0,9
PI
TG TU
Ti = 3,3TU
G r = 1,27
PID
TG TU
Ti = 2TU Td = 0,5TU
Table 7: Ziegler & Nichols parameters depending on the regulator's actions
6.2. STABLE PROCESS IDENTIFICATION METHOD This approach consists of using the one-step response curve to "identify" the process. The purpose of identification is to look for the transfer function, that is to say a mathematical model representing the most faithfully possible the process's behaviour, whether in static or dynamic mode. The search for the parameters of the model's transfer function is carried out using the recording of the process's input (command) and output (measurement) signals. When it is very precisely known, this transfer function makes it possible to determine in the optimum way the adjustment actions for the regulator controlling the process, so as to ensure the stability of the system and control of the variable to be adjusted. The real transfer function of an industrial process is practically impossible to determine, because in general industrial processes are not linear over their whole operating range. This is why we limit ourselves to slight variations around one operating point (and we consider that the process is linear).
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6.2.1. Strejc method Strejc considers a stable process and assimilates the process's unit-step response (further to the application of a step excitation) with the response of a process of the nth order (in the mathematical senses of the term) with a pure delay. By analyzing the shape of the "S" of the process's unit-step response and evaluating the Tu and Tg, parameters in the charts we can determine the values to be assigned to the PID actions. The Strejc method makes it possible to "stick" with a certain degree of precision to the process's unit-step response.
6.2.2. Broîda method Like Strejc, Broîda deals with stable processes, and proceeds to identify an open loop, but he simplifies by considering that the "S" shape can be assimilated with a first order mathematical function with a time constant, associated with a pure delay:
The mathematical function that we have just described above is therefore the transfer function of the process to be identified.
GS: static gain τ: delay time θ: time constant
Figure 57: The process's unit-step response according to the mathematical model To identify the process, we must therefore manage to determine the time constant and the delay time.
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6.2.2.1. Identifying the open-loop process
Figure 58: Unit-step response of the open-loop process submitted to one step Broîda therefore makes the S-shaped unit-step response correspond with the first order function at two points on the y-axis, respectively 28% and 40%, for which he notes the times T1 and T2. He obtains: G S =
ΔC ΔM
θ = 5,5(T2 − T1 )
τ = 2,8T1 − 1,8T2
6.2.2.2. Identification in a closed loop The regulator is in the automatic position, and the integral and derived actions are inhibited.
Figure 59: Unit-step response of the closed-loop process subjected to one step
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Two tests are required for this method. We start by looking for the static gain Gs. To do that, we set a gain (Gr) on the regulator and we apply a setpoint value step ∆C: the measurement varies by ∆M and, after stabilization, there remains a difference e between the measured and the setpoint values. The static gain is given by: G S =
M ε × Gr
The purpose of the second test is to look for the θ and τ parameters. For this test, the regulation loop must be placed in continuous oscillation. Let T be the period of the oscillations and Grc the critical gain to be applied to obtain those oscillations.
Figure 60: Gain Grc to make the loop oscillate The θ and τ parameters are then given by:
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Once we have completed these two tests to obtain the parameters being sought for the process, we can deduce the regulator actions from them using the table below: Regul modes
P
PI Series
PI Parallel
PID Series
Gr
0.8 × θ GS × τ
0.8 × θ GS × τ
0.8 × θ GS × τ
0.85 × θ G S ×τ
Ti
Max.
θ
GS × τ 0,8
Td
0
0
0
Actions
PID Parallel
PID Combined
θ + 0,4 τ
θ + 0,4 τ
1.2 × G S
1.2 × G S
θ
GS × τ 0.75
θ + 0.4τ
0. 4 × τ
0.35 × θ GS
θ ×τ τ + 2.5θ
Table 8: Broîda parameters according to the regulator's structure The choice of regulation mode is linked to the adjustability of the process, determined by the ratio θ / τ. If θ / τ is comprised between 10 and 20: P regulation If θ / τ is comprised between 5 and 10: PI regulation If θ / τ is comprised between 2 and 5: PID regulation If θ / τ is greater than 20: On/Off regulation If θ / τ is lower than 2: limit of the PID algorithm in a single loop (you will have to use multiple loops or correctors).
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6.3. UNSTABLE PROCESS IDENTIFICATION METHOD The identification methods also apply to unstable processes. There too, assumptions have to be made on the process's transfer function. The simplest, is when we consider that the process follows the model of a pure integrator (with an integration constant K) associated with a delay τ:
6.3.1. Identification in an open loop Given the unstable nature of the process, care must be taken when using this method.
Figure 61: Unstable process identification in an open loop We apply a step excitation ∆C and we observe the evolution of the measurement. The delay τ is given by the time that elapses between the moment the step is applied and the moment when the measurement begins to change. To obtain the integration constant K, you must measure the slope of the measurement variation as a function of time (∆M/∆t); from there, we can deduce K:
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6.3.2. Identification in a closed loop The regulation loop must be put into continuous oscillation for this method. Figure 62: Gain Grc for putting the process into oscillation Let Grc be the critical gain making it possible to obtain these oscillations, and let T be the period of the oscillations obtained. The values K and τ are given by the following formulas:
Regul. modes
P
PI Series
PI Parallel
PID Series
PID Parallel
PID Combined
Gr
0,8 K ×τ
0,8 K ×τ
0,8 K ×τ
0,85 K ×τ
0,9 K ×τ
0,9 K ×τ
Ti
Maxi
5 ×τ
K ×τ ² 0,15
4,8 × τ
K ×τ ² 0,15
5,2 × τ
Td
0
0
0
0,4 × τ
0,35 K
0,4 × τ
Actions
Table 9: Unstable process parameters according to the regulator's structure The choice of regulation mode is linked to the adjustability of the process determined by the product K.τ If K.τ is comprised between 0.05 and 0.1: P regulation If K.τ is comprised between 0.1 and 0.2: PI regulation If K.τ is comprised between 0.2 and 0.5: PID regulation If K.τ is lower than 0.05: On/Off regulation If K.τ is higher than 0.5: limit of the PID as a single loop. You must use multiple loops. Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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6.4. THE ADJUSTOR METHOD (BY SUCCESSIVE APPROXIMATIONS) This is a method that does not obey the general rules. The regulator is adjusted in small steps. With the system functioning in a closed loop around the set point: in proportional regulation, we look for the correct proportional band by observing the system's response to a setpoint value step
Figure 63: Adjusting the proportional band
in proportional integral regulation, we look for the correct integral time by observing the system's response to a setpoint value step
Figure 64: Adjusting the integral time
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in proportional integral derived regulation, we look for the correct derived time by observing the system's response to a setpoint value step
Figure 65: Adjusting the derived time
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Field Operations Training Instrumentation Maintenance The Regulator and its Functions
7. THE REGULATION LOOP 7.1. SINGLE-LOOP REGULATION Obviously, we will use at least one closed loop, all the more so if there is no other variable disturbing the process besides the correction variable.
7.1.1. Simple regulation loop This is the regulation that we have been studying until now. The measured value is compared with the setpoint value so that we can calculate the command signal. The greater the dead time the less suitable this type of regulation will be.
7.2. MULTI-LOOP REGULATION In the case where several disturbance variables have been identified, we will use a closed loop as the main loop in which one or more open loops are nested. Each of these open loops intervenes in the closed loop by means of a calculated corrector (generally a summer).
7.2.1. The different types of multi-loop regulation 7.2.1.1. Cascade Regulation Cascade regulation consists of two nested loops. The system can be broken down into two subsystems linked by a measurable intermediate variable. The first loop – the slave loop – uses this intermediate variable as its adjusted variable. The adjusted value of the second loop – the master loop – is the adjusted value of the cascade regulation and it commands the setpoint value of the slave regulation.
Figure 66: Principle of a cascade regulation loop Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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Example of use: Cascade regulation can be used to regulate a level. The slave loop is the regulation of the tank's supply flow rate. This type of regulation is justified when you have a great deal of system inertia with respect to a disturbance on the correction variable, or on an intermediate variable. You must first of all adjust the inner loop, and then the outer loop with the slave regulator closed.
Figure 67: Example of a cascade regulation loop
7.2.1.2. Ratio regulation We use ratio regulation when we want a constant ratio between two adjusted variables X1 and X2 (X2/X1 = constant). In the example below, the control variable X1 is used to calculate the setpoint value of the loop regulating variable X2.
Figure 68: Principle of a ratio regulation loop
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Example of use: You can use a ratio regulation to establish the air/gas ratio of a boiler combustion regulation.
Figure 69: Example of a ratio regulation loop
7.2.1.3. Feedforward regulation (combined) We use the measurement of a disturbance to compensate for its effects on the adjusted variable. The operator may be a simple gain, an advance/delay modulus or a more complex type of operator. This type of loop is useful when a disturbance weighs heavily on the system and the measurement does not vary quickly following that disturbance.
Figure 70: Principle of a feedforward regulation loop Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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Example of use:
Figure 71: Example of a feedforward regulation loop In this temperature regulation, the measurement of the heated liquid's flow rate makes it possible to anticipate the fall of temperature caused by an increase in the water's flow rate.
7.2.1.4. Split-Range regulation We use split-range regulation when we want to control the process by means of two different adjustment devices. These adjustment devices may have antagonistic effects of the hot-cold type.
Figure 72: Principle of a split-range regulation loop Example of use: To avoid cavitation problems, we use two regulation valves with different flow rate capacities (Cv). One valve will be used to control the high flow rates, and the other for the low flow rates.
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Figure 73: Example of a split-range regulation loop With this regulation, the two adjustment devices are controlled by a single command delivered by the regulator. There are two possible solutions: We perform a shift of the zeros and 100% of the valves so that the first one opens at 0% and closes at 50% of the signal, the second will be closed until 50% and will then open at 100% of the signal. Figure 74: Example with two valves adjusted with a shift for the Split range Or we use a calculation block splitting the command into two signals, with each signal commanding an analogue output. The valves are adjusted in a standard way, and no longer shifted, which simplifies maintenance. Figure 75: Example with a calculation block without valve shifting for the Split range
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7.2.1.5. On/Off regulation This mode of action is essentially discontinuous. A lower limit and upper limit must be set in order to use this type of regulation. When the measurement reaches the lower limit, the actuator goes to a particular position (On or Off for a pump, Open or Closed for a valve). Likewise, the fact of reaching the upper limit places the actuator in the opposing position. The measurement therefore oscillates between two extreme values and its variation takes a sawtooth shape. This simple adjustment is cheap, but has the drawback of not being very precise. Furthermore, this system can only be used on installations that have a sufficiently high degree of inertia to cause a low frequency oscillation so as not to load the command devices too often, which would shorten their operating life. I would say that this type of regulation is, in a way, like that used for temperature regulation in a house with electric heating. The thermostat is in fact the On/Off regulator and the actuator is the radiator.
Figure 76: Shape of the measurement signal with On/Off regulation The regulator output Y is either 0 or 1.
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8. LIST OF FIGURES Figure 1: Regulation chain schematic diagram ....................................................................7 Figure 2: Unit-step response in process regulation..............................................................8 Figure 3: Unit-step response in process slaving ..................................................................8 Figure 4: Closed-loop regulation schematic diagram ...........................................................9 Figure 5: Example of closed-loop regulation......................................................................10 Figure 6: Example of open-loop regulation ........................................................................11 Figure 7: Schematic diagram of a stable process ..............................................................13 Figure 8: Example of a stable process...............................................................................14 Figure 9: Functional diagram of an unstable process ........................................................15 Figure 10: Example of an unstable process.......................................................................15 Figure 11: Functional diagram of an integrator type process .............................................16 Figure 12: Transient and steady states..............................................................................16 Figure 13: Example of a heat exchanger ...........................................................................17 Figure 14: Response of a stable process to a step............................................................18 Figure 15: Response to an unstable process step.............................................................19 Figure 16: Static characteristic of a process ......................................................................20 Figure 17: Dynamic response of a closed-loop process ....................................................21 Figure 18: Regulator structure ...........................................................................................23 Figure 19: Detailed structure of the regulator.....................................................................24 Figure 20: Example of measuring instrument identification on a PID diagram...................27 Figure 21: Example of regulator identification on a PID diagram .......................................27 Figure 22: Example of a pneumatic regulator ....................................................................28 Figure 23: Pneumatic regulator measurement pointer .......................................................29 Figure 24: Front face of an electronic regulator .................................................................30 Figure 25: Example of an ABB local digital regulator .........................................................32 Figure 26: Example of a digital regulator on a control system ...........................................33 Figure 27: Definition of the action direction........................................................................33 Figure 28: Action of the regulator with a direct process .....................................................34 Figure 29: Action of the regulator with an inverse process ................................................34 Figure 30: Action direction of the regulator and of the process in a closed loop ................34 Figure 31: Diagram of the proportional band according to the regulator's output ..............36 Figure 32: Unit-step response of a proportional action process.........................................38 Figure 33: Proportional regulation in closed-loop operation...............................................39 Figure 34: Determining the operating point........................................................................39 Figure 35: Influence of the proportional band in static behaviour.......................................39 Figure 36: Influence of the proportional band in dynamic behaviour..................................40 Figure 37: Example of adjustment of the proportional action .............................................41 Figure 38: Band shift characteristic....................................................................................41 Figure 39: Influence of band shift on the static error..........................................................42 Figure 40: Functional representation of a proportional action regulation on its own ..........42 Figure 41: Influence of Ki on the command Y signal ..........................................................44 Figure 42: Combined PI action ..........................................................................................44 Figure 43: Influence of the integration time in a closed loop ..............................................45 Figure 44: Example of PI regulator setting.........................................................................46 Figure 45: Influence of derived time Td on regulator output Y ...........................................47 Training Manual: EXP-MN-SI070-EN Last revised: 17/10/2008
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Figure 46: Output signal from the regulator submitted to a derived action.........................47 Figure 47: Influence of derived time Td in a closed loop....................................................48 Figure 48: Example of PD regulator adjustment ................................................................48 Figure 49: Output signal from the regulator with three combined actions ..........................49 Figure 50: Unit-step response of each action of a regulator and of each of its PI, PD and PID combinations........................................................................................................49 Figure 51: Determining the internal structure of a PID regulator........................................51 Figure 52: Series structure.................................................................................................52 Figure 53: Combined structure ..........................................................................................52 Figure 54: Parallel structure...............................................................................................52 Figure 55: Electronic schematization of a // PID regulator .................................................53 Figure 56: Unit-step response of an open-loop process to a step......................................57 Figure 57: The process's unit-step response according to the mathematical model..........59 Figure 58: Unit-step response of the open-loop process submitted to one step ................60 Figure 59: Unit-step response of the closed-loop process subjected to one step ..............60 Figure 60: Gain Grc to make the loop oscillate ...................................................................61 Figure 61: Unstable process identification in an open loop................................................63 Figure 62: Gain Grc for putting the process into oscillation.................................................64 Figure 63: Adjusting the proportional band ........................................................................65 Figure 64: Adjusting the integral time ................................................................................65 Figure 65: Adjusting the derived time ................................................................................66 Figure 66: Principle of a cascade regulation loop ..............................................................67 Figure 67: Example of a cascade regulation loop ..............................................................68 Figure 68: Principle of a ratio regulation loop.....................................................................68 Figure 69: Example of a ratio regulation loop ....................................................................69 Figure 70: Principle of a feedforward regulation loop.........................................................69 Figure 71: Example of a feedforward regulation loop ........................................................70 Figure 72: Principle of a split-range regulation loop...........................................................70 Figure 73: Example of a split-range regulation loop...........................................................71 Figure 74: Example with two valves adjusted with a shift for the Split range .....................71 Figure 75: Example with a calculation block without valve shifting for the Split range .......71 Figure 76: Shape of the measurement signal with On/Off regulation.................................72
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9. LIST OF TABLES Table 1: A stable process's response parameters .............................................................18 Table 2: An unstable process's response parameters .......................................................19 Table 3: Symbols used on regulators ................................................................................26 Table 4: Advantages and drawbacks of PID actions..........................................................50 Table 5: Summary of the different types of regulator structure ..........................................54 Table 6: Ziegler and Nichols parameters according to the regulator's structure ................56 Table 7: Ziegler & Nichols parameters depending on the regulator's actions ....................58 Table 8: Broîda parameters according to the regulator's structure ....................................62 Table 9: Unstable process parameters according to the regulator's structure ...................64
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