Chapter 1 Introduction

Linear Control Systems CHAPTER 1 INTRODUCTION Prof. Fawzy Ibrahim Electronics and Communication Department Misr International University

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EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

Chapter Contents 1.1 Course Description and Outline 1.2 Course Objectives 1.3 Control systems Classifications 1.4 Control Systems Terminologies 1.5 Examples of Control Systems

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EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

1.1Course Description and Outline Week

Lec.

Items/Topics

Assignments

Chapter 1 Introduction 1

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Chapter 2 Mathematical Model of Systems • Differential Equations of Physical Systems: - D. E. of Electrical Components. - D. E. of Mechanical Components

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- D. E. of Electromechanical Components

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• Review of Laplace Transform. • The Transfer Function of Linear Systems

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• Block Diagram Models

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• Signal Flow Graph Models

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Assignment #1 Representation of Control Systems

• Examples of control systems

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• Course Description and Outline • Control Systems History and Applications • Control systems Classifications • Control Systems Terminologies

Chapter 3 Feedback Control System Performance and Characteristics • Introduction • Test Input Signals • Response of First Order Systems

Assignment #2.1 System Modeling, Laplace Transform and Transfer Function

Assignment #2.2 Block Diagrams and Signal Flow Graph Models

Fifth week Exam

EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

Course Description and Outline (Continue) 11

• Response of Second Order Systems • Higher Order Systems Response

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•  Steady State Errors of Feedback Control Systems

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• Stability Analysis Using Routh-Hurwitz Method

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• Sensitivity of Control Systems to Parameter Variations

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Chapter 4 Analysis and Design of Control Systems using Root Locus Method

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• Root Locus Examples

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• Stability Analysis

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•  Introduction •  Root Locus Construction

Assignment #3.1 2nd Order Response and Steady State Errors

Assignment #3.2 Stability Analysis and Sensitivity of Control Systems

• Compensation and Controller Design using Root Locus

Term Paper Assignment

Midterm Exam

EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

Course Description and Outline (Continue) Chapter 5 Analysis and Design of Control Systems using Frequency Response Method 21 11

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• Stability Analysis • Bandwidth and Cutoff Frequency • Compensation and Controller Design in the Frequency Domain

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Chapter 6 Practical Control Systems Applications

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• Antenna Azimuth Position Control System • Control Systems History and Applications

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• Introduction • The State Variables of a Dynamic System • The State Differential Equation • Alternative Block Diagram and Signal Flow Graph Models

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• The Transfer Function from the State Equation

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Assignment #4 Root Locus Analysis and Design

Chapter 7 State Space Representation of Control Systems

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• Introduction • Frequency Response • Bode Plots • Gain and Phase Margins

Assignment #5 Frequency Domain Analysis and Design

• The Time Response and the State Transition Matrix

Term Paper Submission

• Discrete Time Evaluation of The Time Response

Term Paper Presentation

Assignment #6 State Space Representation

Final Review EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

1.2 Course Objectives Upon successful completion of this course, the student should be able to: 1.  Deduce mathematical models describing control system elements. 2.  Represent a complete control system using transfer function approach. 3.  Reduce control system transfer function using block diagram and signal flow graph models. 4.  Calculate the transient and steady state response of feedback control systems. 5.  Investigate the Stability of control systems. 6.  Check the system stability in frequency domain. 7.  Understand the root locus analysis and design of control systems. 8.  Apply the analysis and design of Control system in frequency domain. 9.  Represent, analyze and design of Control systems using State space approach. 10. Utilize the CAD tools (MATLAB package) to deal with all analysis and design issues of Control system. 6

EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

1.3 Control systems Classifications non-linear system OR linear system time varying system OR time invariant system single variable control OR Multivariable Control Classical Representation OR State Space Representation (Classical Control) OR (modern control) manual control OR automatic control open-loop control OR closed-loop control (feedback control)

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EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

1.4 Control Systems Terminologies 1- Block diagram A control system is any an interconnection of components to provide a desired action. It can be described by a block diagram as shown in Fig. 1.1.

Fig. 1.1 Simplified description of a control system or block diagram

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EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

2- Open-loop control system It is the system in which the control action is independent of the output as shown in Fig. 1.2. 3. A process or plant It is the portion of a system which is to be controlled. The input-output relationship represent the cause and effect of the process. 4- A controller It is device that generates the plant input signals to produce the desired outputs. input or reference

input filter (transducer)

disturbance plant

controller

control signal

actuator

process

output or controlled variable

Fig. 1.2 An open-loop system 9

EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

5- Closed-loop or feedback control system It is the system in which the control action is dependent on the output or the input depends on the output as shown in Fig. 1.3. error or input or actuating signal disturbance reference summing junction plant output or or comparator control controlled signal input filter + controller actuator process variable (transducer)

_

Σ

sensor or output transducer sensor noise

Fig. 1.3 closed-loop or feedback control system 10

EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

Example: A simple feedback control system for controlling the room temperature is shown in Fig. 1.4. heat transfer Qout

desired temperature

_

room temperature

Qin thermostat

switch

air con

+

Σ

office room

Fig. 1.4. A simple feedback control system for controlling the room temperature 11

EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

6- A Multivariable control systems It is the system that has many variables and shown in Fig. 1.5

Fig. 1.5 Block diagrams of control systems: a. open-loop system b. closed-loop system 12

EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

The open-loop system characteristics

Advantages

Disadvantages

•  simple construction •  ease of maintenance •  less expensive •  no stability problem •  no need for output measurement

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•  disturbances cause errors •  changes in calibration cause errors •  output may differ from what is desired •  recalibration needed

EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

The closed-loop system characteristics

Advantages •  high accuracy •  not sensitive to disturbance •  controllable transient response •  controllable steady state error

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Disadvantages •  more complex •  more expensive •  possibility of instability •  recalibration needed •  need for output measurement

EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

1.5 Examples of Control Systems 1 Open Loop Example of a room heating system: control of the room temperature ϕR is changed according to Figure 1.6.

(a) Open-loop control of a

room heating system Figure 1. 6 15

(b)  Characteristic of a heating control

device for three different tuning sets (1, 2, 3)

EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

The Block Diagram of an open loop room heating system: control of the room temperature is shown Figure 1.7.

Figure 1.7 : Block diagram of the open-loop control of the heating system

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EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim

2 Closed Loop Example of a room heating system: control of the room temperature ϕR is changed according to Figure 1. 8. and its block diagram is shown in Fig. 1.9.

(a) The Physical system

(b) The system block diagram

Figure 1.8 Closed-loop control of a room heating system 17

EEG431 Ch. 1 Introduction

Prof Fawzy Ibrahim