Linear Control Systems With Matlab Applications

A comprehensive self contained text covering principles of Linear Control Systems. It provides basic approach for the development of fundamental concepts and Insight in to the subject matter.

The text dealt in the book develops the subject matter in a simplified sequential manner. Theoretical explanation is supported by graded solved examples, which have been framed to help the students in grasping the theoretical principles and its applicability with the coverage of various topics.

In view of the Computer Software application as a supplementary tool for solving control related problems, Solutions to typical examples using MATLAB have been introduced in a way so that the readers can well understand the MATLAB commands and can verify the results of the examples contained in the text.

The book meets the requirements of undergraduate students of Engineering in the area of control systems and also useful for Grad. I.E.T.E. (India) as well as for those who are preparing for Professional competitive examinations.

B.S. Manke, graduated in Electrical Engineering from Madhav Institute of Technology & Science, Gwalior in 1962 and completed postgraduation in Elect. Engg. in 1964 from College of Engg., Pune, where he was awarded Senior Fellowship from 1962 to 1965 under Technical Teachers Training Programme of Govt. of India.

He joined M.A. College of Tech., Bhopal (A Regional Engg. College) as a Lecturer in Electrical Engg. Department in 1965 and was promoted to the post of Asst. Prof, and Prof, in 1974 and 1991 respectively. He also served as the Head of Elect. Engg. Department from 1994 to 1996 in the same institution.

Besides Teaching control systems at undergraduate and postgraduate levels for about three decades, Prof. Manke has been teaching basic courses in Elect. Engg. and Elect. Network Theory.

On attaining age of superannuation Prof. Manke retired from service in Jan. 2002.

In addition to his Academic assignments, Prof. Manke was awarded two Indian patents (No. 141033 of 28.6.1974 and No. 146763 of 28.1.1976) in relation to his experimental work on improvements in electrical spark ignition systems and headlamps for automobiles.

I. INTRODUCTION :
1. An Example of Control Action
2. Open-loop Control System
3. Closed-loop Control System
4. Use of Laplace Transformation in Control Systems
5. Laplace Transform :
i. Derivation of Laplace transform
ii. Basic Laplace transform theorems

6. Solved Examples
Problems

II. TRANSFER FUNCTION :
1. Poles and Zeros of a Transfer Function
2. Transfer Function and Its Relationship with Impulse Response
3. Procedure for Determining the Transfer Function of a Control
4. Solved Examples
Problems

III. BLOCK DIAGRAMS :
1. Block Diagram Reduction
2. Solved Examples
Problems

IV. Signal FLOW GRAPHS :
1. Rules for Drawing Signal Flow Graphs
2. Manson's Gain Formula
3. Drawing Signal Flow Graph from a Given Block Diagram
4. Solved Examples
Problems

V. Modelling A CONTROL SYSTEM :
1. Electrical Networks
2. Mechanical Systems :
i. Translation Mechanical Systems
ii. Rotational Mechanical System

3. Hydraulic System
4. Pneumatic System
5. Thermal System
6. Servo Motors
7. Generators
8. Error Detectors
9. Solved Examples
Problems

VI. TIME RESPONSE ANALYSIS OF CONTROL SYSTEMS :
1. Transient and Steady State Response
2. Input Test Signals
3. Time Response of a First Order Control System :
i. Time Response of a First order Control System Subjected to Unit Step input Function
ii. Demarcation between the Transient Part and Steady State Part of the Time Response in Terms of Time Constant
iii. Time Response of a First order Control System Subjected to Unit Ramp Input Function
iv. Time Response of a First order Control System Subjected to Unit Impulse Input Function

4. Time Response of Second Order Control System :
i. Time Response of a Second order Control System Subjected to Unit Step Input Function
ii. Critical Damping
iii. Characteristic Equation
iv. Transient Response Specifications of Second order Control System
v. Time Response of a Second order Control System Subjected to Unit Ramp Input Function
vi. Time Response of a Second order Control System Subjected to Impulse Input Function

5. Time Response of a Third Order Control System :
i. Effect of First order Term Time Constant on Time Response of Third order Control System

6. Time Response of Higher Order Control System :
i. An Example of third order Unstable Control System

7. Steady State Error :
i. Static Error Coefficients
ii. Type of Transfer Functions and Steady State Error
iii. Generalized Error Coefficients
iv. Performance Indices

8. Sensitivity :
i. Effect of Transfer Function Parameter Variations in an Open Loop Control System
ii. Effect of Forward Path Transfer Function Parameter Variations in a Closed Loop Control System
iii. Sensitivity of Overall Transfer Function M (s) with Respect to Forward Path Transfer Function G (s)
iv. Sensitivity of Overall Transfer Function M (s) with Respect to Feedback Path Transfer Function
v. Effect of Feedback on Time Constant of a Control System

9. Control Actions :
i. Proportional Control
ii. Derivative Control
iii. Integral Control
iv. Proportional Plus Derivative plus Integral Control (PID Control)
v. Derivative Feedback Control

10. Solved Examples
Problems

VII. Stability ANALYSIS OF CONTROL SYSTEMS :
1. Stability in Terms of Characteristic Equation of a Control System :
i. Definition of Stability
ii. Absolute and Relative Stability
iii. Location of the Roots of Characteristic Equation in s-plane as Related to Time Response and Prediction of Absolute Stability Therefrom

2. To Determine the Number of Roots Having Positive Real Parts for a Polynomial
3. Hurwitz Determinants of a Polynomial
4. Routh-Hurwitz Criterion
5. Solved Examples : Routh-Hurwitz Criterion
6. Nyquist Criterion :
i. Procedure for Mapping from s-plane to G(s) H(s)-plane
ii. Determination from the Nyquist Plot the Number of Zeros of G(s)H(s) which are Located Inside a Specified Region in s-plane
iii. Application of Nyquist Criterion to Determine Stability of a Closed-loop Control System

7. Gain Margin and Phase Margin
8. Relative Stability from Nyquist Plot
9. Gain Phase Plot
10. Closed-loop Frequency Response of a Unity Feedback Control System from Nyquist Plot
11. Constant Magnitude Loci : M-circles
12. Constant Phase Angles Loci : N-circles
13. Closed-loop Frequency Response of Control System from M and N-circles
14. Gain Adjustment Using M-circle
15. Nichols Chart
16. Cutoff Frequency and Bandwidth
17. Solved Examples : Nyquist Criterion
18. Bode Plot :
i. Bode Plot (Logarithmic Plot) for Transfer Functions
ii. Graphs for the Gain Term K
iii. Graphs for the Term 1/(jw) N
iv. Graphs for the Term (1+jw T)
v. Graphs for the Term 1 (1+jw T)
vi. Initial Slope of Bode Plot
vii. Determination of Static Error Coefficients from Initial Slope of Bode Plot
viii. Graphs for Quadratic Term wn2 [(wn2 w2)+j2 (wn w]
ix. Procedure for Drawing Bode Plot and Determination of Gain Margin, Phase Margin and Stability
x. Minimum Phase, Non-minimum Phase and all Pass Transfer Functions

19. Solved Examples : Bode Plot
20. Correlation between Transient Response and Frequency Response
21. Root Locus
22. Salient Features of Root Locus Plot
23. The Procedure for Plotting Root Locus
24. Solved Examples : Root Locus
25. Root Contours Problems

VIII. COMPENSATION OF CONTROL SYSTEMS :
1. Phase-lead Compensation
2. Phase-lag Compensation
3. Phase-lag-lead Compensation
4. Concluding Remarks
5. Feedback Compensation
6. Solved Examples
Problems

IX. INTRODUCTION TO STATE SPACE ANALYSIS OF CONTROL SYSTEMS :
1. State Space Representation
2. The Concept of State
3. State Space Representation of Systems
4. Block Diagram for State Equation
5. Transfer Function Decomposition :
i. Direct Decomposition
ii. Cascade Decomposition
iii. Parallel Decomposition
iv. Parallel Decomposition of a Transfer Function having Repeated Roots of its Characteristic Equation

6. Solution of State Equation :
i. Determination of State Transition Matrix
ii. Properties of State Transition Matrix

7. Transfer Matrix
8. Controllability
9. Observability
10. Solved Examples
Problems

X. SAMPLED DATA CONTROL SYSTEMS :
1. Sampler
2. Sampling Process
3. Laplace Transform of Sampled Function
4. Z-transform
5. Z-transform of Some Useful Functions
6. Inverse Z-transform
7. Hold Circuit
8. Reconstruction of Signal : Minimum Sampling Frequency
9. Pulse Transfer Function (z-transfer Function)
10. Stability Analysis of Sampled-data Control Systems
11. Solved Examples
Problems

XI. SOLUTION OF PROBLEMS USING Computer :
1. Introduction to MATLAB
2. Running MATLAB
Solved Examples