Chapter 1 Introduction

Linear Control Systems

CHAPTER 1

INTRODUCTION

Prof. Fawzy Ibrahim

Electronics and Communication Department

Misr International University

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

1.1Course Description and Outline

Assignments

Items/Topics

Lec.

Week

Chapter 1 Introduction

• Course Description and Outline

• Control Systems History and Applications • Control systems Classifications

• Control Systems Terminologies 1

1

• Examples of control systems 2

Assignment #2.1

System Modeling, Laplace Transform and

Transfer Function

Chapter 2 Mathematical Model of Systems

• Differential Equations of Physical Systems: - D. E. of Electrical Components. 3 2 - D. E. of Mechanical Components 4 - D. E. of Electromechanical Components 5

3 _{• Review of Laplace Transform.}

• The Transfer Function of Linear Systems 6

Assignment #2.2

Block Diagrams and Signal Flow Graph

Models • Block Diagram Models

7 4

• Signal Flow Graph Models 8

Chapter 3 Feedback Control System Performance and

Characteristics

• Introduction • Test Input Signals

• Response of First Order Systems 9

5

Fifth week Exam

Course Description and Outline (Continue)

Assignment #3.1

2nd _{Order Response and}

Steady State Errors • Response of Second Order Systems

• Higher Order Systems Response 11

6

•  Steady State Errors of Feedback Control Systems 12

• Stability Analysis Using Routh-Hurwitz Method 13

7

• Sensitivity of Control Systems to Parameter Variations 14

Assignment #3.2

Stability Analysis and Sensitivity of Control

Systems

Chapter 4 Analysis and Design of Control Systems using Root

Locus Method

•  Introduction

•  Root Locus Construction 15

8

• Root Locus Examples 16

• Stability Analysis 17

9 _{• Compensation and Controller Design using Root Locus}

Term Paper Assignment

18

Midterm Exam

19 10

Course Description and Outline (Continue)

Assignment #4

Root Locus Analysis and Design

Chapter 5 Analysis and Design of Control Systems using

Frequency Response Method

• Introduction

• Frequency Response • Bode Plots

• Gain and Phase Margins 21

11

• Stability Analysis

• Bandwidth and Cutoff Frequency

• Compensation and Controller Design in the Frequency Domain 22

Chapter 6 Practical Control Systems Applications

• Antenna Azimuth Position Control System • Control Systems History and Applications 23

12

24

Assignment #5

Frequency Domain Analysis and Design

Chapter 7 State Space Representation of Control Systems

• Introduction

• The State Variables of a Dynamic System 25

13

• The State Differential Equation

• Alternative Block Diagram and Signal Flow Graph Models 26

• The Transfer Function from the State Equation 27

14

Assignment #6

State Space Representation • The Time Response and the State Transition Matrix

Term Paper Submission

28

• Discrete Time Evaluation of The Time Response

Term Paper Presentation

29 15

Final Review

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.

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

)

1.4 Control Systems Terminologies

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

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.

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.

controller

actuator

process

output or

controlled

variable

disturbance

control

signal

plant

input or

reference

input filter

(transducer)

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.

input filter

(transducer)

controller

actuator process

input or

reference

disturbance

_

+

Σ

sensor or

output transducer

sensor noise

control

signal

plant

summing junction

or comparator

error or

actuating signal

output or

controlled

variable

Example: A simple feedback control system for controlling

the room temperature is shown in Fig. 1.4.

thermostat

switch

air con

office room

desired

temperature

room

temperature

heat transfer

Q

_

+

Q

Σ

Fig. 1.4. A simple feedback control system for controlling

the room temperature

6- A Multivariable control systems

The open-loop system characteristics

Advantages

Disadvantages

•  simple construction

•  ease of maintenance

•  less expensive

•  no stability problem

•  no need for output

measurement

•  disturbances cause errors

•  changes in calibration cause

errors

•  output may differ from what

is desired

The closed-loop system characteristics

Advantages

Disadvantages

•  high accuracy

•  not sensitive to disturbance

•  controllable transient response

•  controllable steady state error

•  more complex

•  more expensive

•  possibility of instability

•  recalibration needed

•  need for output

1.5 Examples of Control Systems

1 Open Loop

Example of a room heating system: control of the room temperature ϕ

is changed according to Figure 1.6.

(a) Open-loop control of a

room heating system

(b)  Characteristic of a heating

control

device for three different

tuning sets (1, 2, 3)

The Block Diagram of an open loop room heating system:

control of the room temperature is shown Figure 1.7.

2 Closed Loop

Example of a room heating system: control of the room temperature ϕ

is changed according to Figure 1. 8. and its block diagram is shown in

Fig. 1.9.

(b) The system block diagram

Figure 1.8 Closed-loop control of a room heating system