**Linear Control Systems with Matlab Applications by B. S. Manke, ISBN-13: 978-8174093103**

[PDF eBook eTextbook]

- Publisher: Khanna Publisher (January 1, 2012)
- Language: English
- 695 pages
- ISBN-10: 9788174093103
- ISBN-13: 978-8174093103

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.

This textbook has been written to explain the basic principles of Linear Control Systems

and an effort is made to present the subject in a simple and sequential manner to enable the students to acquire a good grasp of fundamentals of the subject.

The text presented covers the course content of the subject Linear Control Systems of

Indian Universities and is meant for pre-final/final year students of electrical, electronics and mechanical engineering.

The material given in this book has been thoroughly class tested by the author while

teaching the subject of control systems at undergraduate level for the past several years.

This book is divided in 9 chapters. The first four chapters give the basic concepts of the

subject from the view point of control system representation. Chapter 5 presents the

modelling of control systems and the respective * mathematical* models derived therein. The

time response and steady state analysis is given in Chapter 6. Necessary derivations have been derived from the first principles. The stability analysis is described in Chapter 7. The methods of ascertaining stability: Routh-Hurwitz criterion, Nyquist criterion, Bode plot and root locus plot have been explained step by step in a simplified manner to make the explanation easily understandable. The compensation methods and introduction to state space analysis is described in chapters 8 and 9 respectively.

Suitable illustrative examples as well as solved examples have been incorporated in the

text to make the subject clear and interesting. A list of references is given at the end.

Selective unsolved problems have been included at the end of each chapter to help the

student to judge himself whether he has gained sufficient workable knowledge of basic

principles involved. Answers to odd numbered problems being given in Appendix I.

The salient feature of this book is the inclusion of objective type multiple choice questions

given in Appendix II covering the entire text which would be of great help for the students

preparing for competitive examinations.

**Table of Contents:**

1. INTRODUCTION 1-15

1.1 An Example of Control Action … 2

1.2 Open-Loop Control System … 2

1.3 Closed-Loop Control System … 2

1.4 Use of Laplace Transformation in Control Systems … 3

1.5 Laplace Transform … 3

1.5.1 Derivation of Laplace Transform … 4

1.5.2 Basic Laplace Transform Theorems … 6

1.6 Solved Examples … 7

Problems … 15

2. TRANSFER FUNCTION 1624

2.1 Poles and Zeros of a Transfer Function … 17

2.2 Transfer Function and its Relationship with Impulse Response … 19

2.3 Procedure for Determining the Transfer Function of a Control System … 19

2.4 Solved Examples … 20

Problems … 24

3. BLOCK DIAGRAMS 25-61

3.1 Block Diagram Reduction … 26

3.2 Solved Examples … 32

Problems … 58

4. SIGNAL FLOW GRAPHS 62-78

4.1 Rules for Drawing Signal Flow Graphs … 63

4.2 Masons Gain Formula … 67

4.3 Drawing Signal Flow Graph from a Given Block Diagram … 67

4.4 Solved Examples … 69

Problem … 78

5. MODELLING A CONTROL SYSTEM 79-126

5.1 Electrical Networks … 79

5.2 Mechanical Systems … 81

5.2.1 Translation Mechanical Systems … 81

5.2.2 Rotational Mechanical System … 84

5.3 Hydraulic System … 86

5.4 Pneumatic System … 88

5.5 Thermal System … 89

5.6 Servo Motors … 90

5.7 Generators … 97

5.8 Error Detectors … 102

5.9 Solved Examples … 106

Problems … 124

6. THREE RESPONSE ANALYSIS OF CONTROL SYSTEMS 127-215

6.1 Transient and Steady State Response … 128

6.2 Input Test Signals … 128

6.3 Time Response of a First Order Control System … 130

6.3.1 Time Response of a First Order Control System Subjected

to Unit Step Input Function … 130

6.3.2 Demarcation between the Transient Part and Steady State Part

of the Time Response in terms of Time Constant … 131

6.3.3 Time Response of a First Order Control System Subjected to

Unit Ramp Input Function … 132

6.3.4 Time Response of a First Order Control System Subjected to

Unit Impulse Input Function … 133

6.4 Time Response of a Second Order Control System … 134

6.4.1 Time Response of a Second Order Control System Subjected to

Unit Step Input Function … 134

6.4.2 Critical Damping … 139

6.4.3 Characteristic Equation … 140

6.4.4 Transient Response Specifications of Second Order Control System … 141

6.4.5 Time Response of a Second Order Control System Subjected to

Unit Ramp Input Function … 144

6.4.6 Time Response of a Second Order Control System Subjected to

Impulse Input Function … 146

6.5 Time Response of a Third Order Control System … 147

6.5.1 Effect of First Order Term Time Constant on Time Response

of Third Order Control System … 151

6.6 Time Response of Higher Order Control System … 152

6.6.1 An Example of Third Order Unstable Control System … 152

6.7 Steady State Error … 153

6.7.1 Static Error Coefficients … 155

6.7.2 Type of Transfer Functions and Steady State Error … 156

6.7.3 Generalized Error Coefficients … 159

6.7.4 Performance Indices … 162

6.8 Sensitivity … 168

6.8.1 Effect of Transfer Function Parameter variations in an

Open-loop Control System … 168

6.8.2 Effect of Forward Path Transfer Function Parameter variations

in a Closed-loop Control System … 168

6.8.3 Sensitivity of Overall Transfer Function M(s) with respect to

Forward Path Transfer Function G(s) … 169

6.8.4 Sensitivity of Overall Transfer Function M(s) with respect to

Feedback Path Transfer Function … 170

6.8.5 Effect of Feedback on Time Constant of a Control System … 172

6.9 Control Actions … 173

6.9.1 Proportional Control … 173

6.9.2 Derivative Control … 173

6.9.3 Integral Control … 178

6.9.4 Proportional Plus Derivative Plus Integral Control (PID Control) … 181

6.9.5 Derivative Feedback Control … 181

6.10 Solved Examples … 185

Problems … 212

7. STABILITY ANALYSIS OF CONTROL SYSTEMS 216-362

7.1 Stability in Terms of Characteristic Equation of a Control System … 218

7.1.1 Definition of Stability … 218

7.1.2 Absolute and Relative Stability … 218

7.1.3 Location of the Roots of Characteristic Equation in s-plane as

related to Time Response and Prediction of Absolute Stability

therefrom … 218

7.2 To Determine the Number of Roots having Positive Real Parts for a

Polynomial … 219

7.3 Hurwitz Determinants of a Polynomial … 220

7.4 Routh-Hurwitz Criterion … 221

7.5 Solved Examples : Routh-Hurwitz Criterion … 222

7.6 Nyquist Criterion … 229

7.6.1 Procedure for Mapping from s-plane to G(s) H(s)-plane … 229

7.6.2 Determination from the Nyquist Plot the Number of Zeros of

G(s) H(s) which are located inside a Specified Region in s-plane … 231

7.6.3 Application of Nyquist Criterion to Determine Stability of a

Closed-loop Control System … 231

7.7 Gain Margin and Phase Margin … 242

7.8 Relative Stability from Nyquist Plot … 244

7.9 Gain Phase Plot … 245

7.10 Closed-loop Frequency Response of a Unity Feedback Control System from

Nyquist Plot … 246

7.11 Constant Magnitude Loci : M-Circles … 247

7.12 Constant Phase Angles Loci : N-Circles … 249

7.13 Closed-Loop Frequency Response of Control System from M and N-Circles … 250

7.14 Gain Adjustment using M-Circle … 251

7.15 Nichols Chart … 254

7.16 Cutoff Frequency and Bandwidth … 257

7.17 Solved Examples : Nyquist Criterion … 259

7.17.1 Inverse Nyquist Plot … 284

7.17.2 1/M-Circles (Inverse M-Circles) and Constant Phase Angle Loci … 287

7.17.3 Gain Adjustment Using Inverse Polar Plot … 288

7.18 Bode Plot … 289

7.18.1 Bode Plot (Logarithmic Plot) for Transfer Functions … 289

7.18.2 Graphs for the Gain Term K … 290

7.18.3 Graphs for the Term 1( jw)N … 290

7.18.4 Graphs for the Term (1 + jwT) … 291

7.18.5 Graphs for the Term 1 (1 + jwT) … 292

7.18.6 Initial Slope of Bode Plot … 295

7.18.7 Determination of Static Error Coefficients from Initial Slope of

Bode Plot … 297

7.18.8 Graphs for Quadratic Term … 298

7.18.9 Procedure for Drawing Bode Plot and Determination of

Gain Margin, Phase Margin and Stability … 301

7.18.10 Bode Plot for Time Delay Element : e sT … 304

7.18.11 Minimum Phase, Non-minimum Phase and all

Pass Transfer Function … 306

7.19 Solved Examples : Bode Plot … 308

7.20 Correlation between Transient Response and Frequency Response … 315

7.21 Root Locus … 319

7.22 Salient Features of Root Locus Plot … 323

7.23 The Procedure for Plotting Root Locus … 323

7.24 Solved Examples : Root Locus … 324

7.25 Root Contours … 354

Problems … 360

8. COMPENSATION OF CONTROL SYSTEMS 366416

8.1 Phase-Lead Compensation … 367

8.2 Phase-Lag Compensation … 369

8.3 Phase-Lag-Lead Compensation … 371

8.4 Concluding Remarks … 372

8.5 Feedback Compensation … 372

8.6 Solved Examples … 375

8.7 Compensation Network Design: Root Locus Approach … 380

8.7.1 Phase Lead Compensator Design … 381

8.7.2 Phase Lag Compensator Design … 394

8.7.3 Lag-Lead Compensator Design … 404

Problems … 414

9. INTRODUCTION TO STATE SPACE ANALYSIS OF CONTROL SYSTEMS 417-498

9.1 State Space Representation … 418

9.2 The Concept of State … 419

9.3 State Space Representation of Systems … 420

9.4 Block Diagram for State Equation … 427

9.5 Transfer Function Decomposition … 428

9.5.1 Direct Decomposition … 429

9.5.2 Cascade Decomposition … 431

9.5.3 Parallel Decomposition … 432

9.5.4 Parallel Decomposition of a Transfer Function having

Repeated Roots of its Characteristic Equation … 433

9.5.5 Transfer Function Decomposition Using State Signal Flow Graph … 434

9.6 Solution of State Equation … 438

9.6.1 Determination of State Transition Matrix … 440

9.6.2 Properties of State Transition Matrix … 450

9.7 Transfer Matrix … 450

9.8 Controllability … 451

9.9 Observability … 454

9.10 Solved Examples … 456

9.11 State Variable Feedback … 490

Problems … 494

10. SAMPLED DATA CONTROL SYSTEMS 499545

10.1 Sampler … 501

10.2 Sampling Process … 502

10.3 Laplace Transform of Sampled Function … 503

10.4 z-Transform … 504

10.5 z-transform of Some Useful Functions … 505

10.6 Inverse z-transform … 508

10.7 Hold Circuit … 515

10.8 Reconstruction of Signal : Minimum Sampling Frequency … 518

10.9 Pulse Transfer Function (z-transfer Function) … 519

10.10 Stability Analysis of Sampled-data Control Systems … 525

10.11 Solved Examples … 532

Problems … 544

11. SOLUTION OF PROBLEMS USING COMPUTER 546-600

11.1 Introduction to MATLAB … 546

11.2 Running MATLAB … 549

Solved Examples … 552

12. CLASSIFIED SOLVED EXAMPLES 601689

Contains highly graded solved problems selected from question papers of various

Technical Universities, Competitive Examinations and self developed variety of

questions for clearly and deeper understanding of matter/topics covered in text.

Appendix-I : Answers to Selected Problems of Text 690-694

Appendix-II : Objective Type of Questions with Answers 695-736

Appendix-III : Short Answer Questions 734-759

Appendix-IV : Key Formulae, Tables and Charts 760-768

References 769

Index 770-772

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