Advanced Control Theory 2nd Nagoor Kani

CONTENTS Chapter 1

Linear system design

1.1

Introduction to design using compensators

1

1.2

Lag compensator

5

1.3

Lead compensator

34

1.4

Lag-Lead compensator

63

1.5

PI, PD and PID controllers

83

1.6

Feedback compensation

109

1.7

Short questions and answers

127

1.8

Exercise

137

Chapter 2

Nonlinear systems

2.1

Introduction to nonlinear sytems

141

2.2

Describing function

150

2.3

Describing function of dead-zone and saturation non-linearity

151

2.4

Describing function of saturation nonlinearity

156

2.5

Describing function of dead-zone nonlinearity

159

2.6

Describing function of relay with dead-zone and hysteresis

162

2.7

Describing function of backlash nonlinearity

167

2.8

Describing function analysis of nonlinear systems

172

2.9

Review of polar plot and Nichols plot

175

2.10

Phase plane and phase trajectories

193

2.11

Short questions and answers

215

2.12

Exercise

225

Chapter 3

Sampled data control systems

3.1

Introduction

229

3.2

Sampling process

231

3.3

Analysis of sampling process in frequency domain

232

3.4

Reconstruction of sampled signals using hold circuits

234

3.5

Discrete sequence (Discrete time signal)

235

3.6

z-Transform

240

3.7

Linear discrete time systems

268

3.8

Transfer function of LDS system (Pulse Transfer Function)

271

3.9

Analysis of sampler and zero-order hold

277

3.10

Analysis of system with impulse sampling

278

3.11

Analysis of sampled data control system using z-transform

284

3.12

The z and s-domain relationship

295

3.13

Stability analysis of sampled data control systems

296

3.14

Short question and answers

305

3.15

Exercises

315

Chapter 4

State space analysis

4.1

Introduction

319

4.2

State space formulation

320

4.3

State model of linear system

321

4.4

State diagram

323

4.5

State space representation using physical variables

325

4.6

State space representation using phase variables

346

4.7

State space representation using canonical variables

360

4.8

Short questions and answers

403

4.9

Exercises

417

Chapter 5

Analysis and design of control system in state space

5.1

Definitions involving matrices

421

5.2

Eigenvalues and eigenvectors

422

5.3

Similarity transformation

424

5.4

Cayley-Hamilton theorem

426

5.5

Transformation of state model

436

5.6

Concepts of controllability and observability

449

5.7

Controllable phase variable form of state model

460

5.8

Control system design via pole placement by state feedback

470

5.9

Obervable phase variable form of state model

489

5.10

State observers

494

5.11

Short questions and answers

504

5.12

Exercises

515