Design and Analysis of Control Systems

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ISBN: 9780849318986 | 084931898X
Cover: Hardcover
Copyright: 6/23/1999

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Written to inspire and cultivate the ability to design and analyze feasible control algorithms for a wide range of engineering applications, this comprehensive text covers the theoretical and practical principles involved in the design and analysis of control systems. From the development of the mathematical models for dynamic systems, the author shows how they are used to obtain system response and facilitate control, then addresses advanced topics, such as digital control systems, adaptive and robust control, and nonlinear control systems.

An Introduction to Control Systems

(48)

Introduction

(1)

Background

(1)

A Recent History of Control Systems

(3)

Automatic Control

(1)

Multivariable Control

(1)

The Basic Components of a Control System

(1)

Open-Loop Control vs. Closed-Loop Control

(3)

Open-Loop Control

(1)

Closed-Loop Control

(1)

Advantages of Closed-Loop Systems

(1)

Disadvantages of Closed-Loop Systems

(1)

Examples of Control Systems

(8)

Manual Car Direction of Travel Control

(2)

Cruise Control for a Car

(1)

Automatic Water Level Control

(1)

Manual Water Level Control

(1)

Turntable Speed Control

(2)

Blood Glucose Control

(1)

Manual Control of a Sound Amplifier

(1)

Feedback in Social, Economic, and Political Systems

(1)

Classification of Control Systems

(3)

Linear vs. Nonlinear Control Systems

(1)

Time-Invariant vs. Time-Variant Control Systems

(1)

Continuous-Data vs. Discrete-Data Control Systems

(1)

Regulator vs. Tracking Control Systems

(1)

Control System Design

(3)

Advanced Applications of Control Systems

(10)

A Modular and Scalable Wheeled Mobile Robot

(2)

The Mars Sojourner Rover

(1)

Mars Surveyor 2001 Orbiter and Lander

(3)

Deep Space 1

(1)

The Experimental Unmanned Vehicle (XUV)

(2)

Magnetic Levitation

(1)

Process Control: Metal Rolling Mill

(1)

Examples of Control System Experiments

(9)

Inverted Pendulum

(2)

2-DOF Helicopter Experiment

(2)

3-DOF Helicopter Experiment

(1)

2-DOF Robot Experiment

(1)

Magnetic Levitation Experiment

(1)

The Pendubot

(3)

Book Outline

(3)

Problems

(4)

Modeling of Dynamic Systems

(100)

Introduction

(2)

Chapter Objectives

(1)

Dynamic Systems

(1)

Dynamic System Models

(1)

Modeling Concepts

(1)

Summary of the Model Derivation Procedure

(1)

Forms of the Dynamic System Model

(1)

Overview of Different Dynamic Systems

(32)

Translational Mechanical Systems

(8)

Rotational Mechanical Systems

(4)

Electrical Systems

(12)

Electromechanical Systems

(1)

Pneumatic, Hydraulic and Fluid Systems

(6)

Thermal Systems

(2)

State-Variable Matrix Form

(6)

Choice of State Variables

(3)

State-Variable Form for Nonlinear Systems

(1)

Characteristics of State-Variable Models

(1)

Summary of the State-Variable Form Modeling

(1)

Input-Output Differential Equation Form

(1)

Comparison with the State-Variable Form

(1)

Transfer Function Form

(9)

Obtaining the Transfer Function

(1)

Directly Taking Laplace Transforms

(2)

The s-Operator Method

(3)

The Component Transfer Function Method

(3)

The Transfer Function in Pole-Zero Factored Form

101

(1)

Switching Between Different Model Forms

101

(3)

Examples of Dynamic System Modeling

104

(25)

An Electromechanical System

124

(5)

Linearization of Nonlinear Models

129

(5)

Small Signal Linearization

130

(1)

Linearization of Element Laws

130

(1)

Linearization of Models

131

(1)

Linearization Concepts

132

(2)

Experimental Data Approach

134

(3)

Transient Response

135

(1)

Frequency Response

136

(1)

Stochastic Steady State

136

(1)

Pseudo-Random Noise (PRBS)

136

(1)

Models from Transient-Response Data

137

(1)

Models from Other Data

137

(1)

Pure Time Delay

137

(1)

Problems

137

(12)

Dynamic System Response

149

(112)

Introduction

149

(2)

Chapter Objectives

150

(1)

Time Domain Solution of System Models

151

(22)

Homogeneous Input-Output Equations

151

(2)

Nonhomogeneous Input-Output Equations

153

(3)

First-Order Systems

156

(7)

Second-Order Systems

163

(2)

Analogous Mechanical and Electrical Systems

165

(2)

Solution of State-Variable Matrix Equations

167

(6)

Frequency Domain Solution of Models

173

(20)

The Laplace Transform

173

(1)

Properties of Laplace Transforms

174

(2)

Laplace Transform of Some Key Functions

176

(6)

Partial Fractions

182

(11)

Determination of the System Response

193

(8)

Using the Input-Output Equation

193

(8)

Using the System Transfer Function

201

(8)

The Impulse Response (Natural Response)

204

(1)

The Unit Step Response

205

(1)

The Impulse and Unit Step Responses: The Relationship

205

(1)

Final Value Theorem (FVT)

206

(1)

Initial Value Theorem (IVT)

207

(1)

DC Gain

208

(1)

First-Order Systems

209

(1)

Second-Order Systems

210

(11)

Impulse and Step Responses

211

(3)

Stability for Second-Order System

214

(3)

Characteristics of a Step Response

217

(1)

Effects of Pole-Zero Location on the Response

218

(3)

Examples: System Response (Laplace Transforms)

221

(11)

Block Diagrams

232

(3)

Networks of Blocks

232

(3)

Simplifying Block Diagrams

235

(8)

Direct Block Diagram Reduction

235

(3)

The Signal Flow Graph

238

(1)

Properties of Signal Flow Graphs

239

(1)

Mason's Transfer Function Rule

240

(3)

Examples: Simplifying Block Diagrams

243

(7)

Problems

250

(11)

Characteristics of Feedback Control Systems

261

(86)

Introduction

261

(1)

Open-Loop Control vs. Closed-Loop Control

262

(3)

Open-Loop Control

262

(1)

Closed-Loop Control

263

(1)

Advantages of Closed-Loop Systems

263

(1)

Disadvantages of Closed-Loop Systems

264

(1)

Examples of Open- and Closed-Loop Systems

265

(1)

Car Cruise Control System (Open-Loop)

265

(5)

Input-Output Form

266

(1)

Transfer Function Form

266

(1)

Block Diagram Form

267

(1)

State-Variable Form

268

(2)

Car Cruise Control System (Closed-Loop)

270

(5)

Input-Output Form

271

(1)

Transfer Function Form

271

(1)

Block Diagram Form

271

(2)

State-Variable Form

273

(2)

DC Motor Speed Control (Open-Loop)

275

(6)

Input-Output Form

276

(2)

Transfer Function Form

278

(2)

Block Diagram Form (Open-Loop)

280

(1)

State-Variable Form

280

(1)

DC Motor Position Control (Open-Loop)

281

(3)

Input-Output Form

282

(1)

Transfer Function

282

(1)

State-Variable Form

283

(1)

DC Motor Speed Control (Closed-Loop)

284

(7)

Input-Output Form

284

(1)

Transfer Function Form

285

(1)

Block Diagram Form (Closed-Loop)

286

(2)

State-Variable Form

288

(3)

Modeling of PID Controllers

291

(9)

Proportional Controller (P)

292

(1)

Proportional and Integral Controller (PI)

292

(2)

Proportional and Derivative Controller (PD)

294

(1)

Proportional, Integral & Derivative Controller (PID)

294

(4)

Summary of PID Controller Characteristics

298

(2)

MATLAB Implementation

300

(2)

State-Variable Form

300

(1)

Transfer Function

300

(1)

Sample MATLAB Code: Motor Speed PID Control

301

(1)

Tuning of PID Controllers

302

(2)

Quarter Decay Ratio Method

302

(1)

Stability Limit Method

303

(1)

Steady State Tracking and System Type

304

(10)

Sensitivity

314

(7)

Definition of Sensitivity

314

(1)

Open- and Closed-Loop Sensitivity

315

(6)

Stability

321

(11)

Bounded Input-Bounded Output Stability

322

(1)

Asymptotic Internal Stability

323

(1)

Routh-Hurwitz Stability Criterion

323

(9)

Problems

332

(15)

Root Locus Design Methods

347

(46)

Introduction

347

(1)

Root Locus

348

(3)

Background

348

(1)

The Root Locus: Definition

348

(2)

Magnitude and Angle Criteria

350

(1)

Breakpoint, Departure and Arrival Angles

351

(1)

Constructing the Root Locus

351

(9)

Summary of the Root Locus Steps

352

(1)

Details of the Root Locus Steps

352

(6)

Determining the Control Gain (Root Locus Gain)

358

(1)

Root Locus for Second-Order Systems

359

(1)

Examples of Root Locus Design

360

(22)

Dynamic Compensation: Lead and Lag

382

(2)

Extensions of Root Locus Method

384

(2)

Time Delay

384

(2)

Nonlinear Systems

386

(1)

Computer-Aided Determination of the Root Locus

386

(3)

MATLAB

388

(1)

Problems

389

(4)

Frequency-Response Design Methods

393

(82)

Introduction

393

(7)

Magnitude and Phase Angle

394

(2)

Combining Magnitudes and Phase Angles

396

(4)

Bode Plots: The Principles

400

(6)

Background

400

(1)

Advantages of Bode Plots

401

(2)

Bode Plot Techniques

403

(3)

Constant Factors (Gain)

406

(2)

Magnitude

406

(1)

Phase Angle

407

(1)

A Simple Zero Factor

408

(3)

Magnitude

409

(1)

Phase Angle

410

(1)

A Simple Pole Factor

411

(3)

Magnitude

412

(1)

Phase Angle

413

(1)

An Integrator Factor

414

(2)

Magnitude

414

(1)

Phase Angle

415

(1)

A Derivative Factor

416

(2)

Magnitude

416

(1)

Phase Angle

417

(1)

A Complex Pole Factor

418

(2)

Magnitude

418

(2)

Phase Angle

420

(1)

A Complex Zero Factor

420

(1)

Magnitude

421

(1)

Phase Angle

421

(1)

Drawing Bode Plots

421

(13)

Nonminimum Phase Systems

434

(2)

Magnitude and Phase

434

(2)

Time Delay (Transport Lag)

436

(2)

Magnitude

436

(1)

Phase Angle

437

(1)

Bode Plots Using MATLAB

438

(1)

Sample Algorithms

438

(1)

System Models From Experiment Frequency Data

439

(1)

Nyquist Analysis

440

(1)

Advantages of Nyquist Method

440

(1)

Polar Plots

441

(1)

Four Classes of Basic Factors

442

(11)

Properties of Polar Plots

447

(1)

Nyquist Path

448

(1)

Nyquist Diagram

448

(1)

Plotting and Analyzing the Nyquist Plot

448

(1)

Nyquist Stability Criterion

449

(1)

Nyquist Diagrams Using MATLAB

450

(3)

Argument and Rouche's Theorem

453

(1)

Examples of Nyquist Analysis

453

(10)

Stability margins

463

(1)

Gain Margin (GM)

463

(1)

Phase Margin (PM)

464

(1)

Relative Stability

464

(1)

Gain and Phase Relationship

464

(1)

Compensation

465

(3)

PD Compensation

466

(1)

Lead Compensation

466

(1)

PI Compensation

466

(1)

Lag Compensation

466

(1)

PID Compensation (Lead-Lag Compensator)

467

(1)

Summary of Compensation Characteristics

467

(1)

Problems

468

(7)

State-Space Design Methods

475

(96)

Introduction

475

(1)

The Block Diagram and the Transfer Function

476

(7)

State-Space Description and the Block Diagram

476

(3)

Transfer Function, Poles, and Zeros

479

(4)

System Response: The State-Transition Matrix

483

(14)

Direct Solution of the Differential Equation

483

(9)

System Response by Laplace Transform Method

492

(5)

System Controllability and Observability

497

(12)

Controllability

497

(5)

Observability

502

(7)

Similarity Transformations: Canonical Forms

509

(12)

Similarity Transformation

509

(1)

Controllable Canonical Form

510

(4)

Observable Canonical Form

514

(4)

Diagonal Canonical Form

518

(2)

Jordan Canonical Form

520

(1)

Transfer Function Decomposition

521

(2)

Direct Decomposition

521

(2)

Full State Feedback Control

523

(13)

Pole Placement Design Method

525

(6)

Pole Placement Using Ackermann's Formula

531

(5)

Introduction to Optimal Control

536

(11)

Overview of Optimization Theory

537

(3)

The Basic Optimal Control Problem

540

(7)

Estimator Design

547

(17)

Full State Estimator

548

(3)

Duality of Estimation and Control

551

(1)

Reduced-Order Estimator

552

(9)

Compensator Design: Control Law and Estimator

561

(3)

Problems

564

(7)

Digital Control Systems

571

(98)

Introduction

571

(1)

Sampled Data Systems

572

(15)

General Structure

572

(1)

Data Sampling

572

(6)

Characteristics of Discrete Time Signals

578

(9)

Analysis of the Discrete Time Systems

587

(64)

Difference Equations

587

(11)

The Difference Operator (Δ) and Shift Operator (q)

598

(4)

Discrete Approximation of Continuous Processes

602

(4)

The Z-Transforms

606

(15)

Dynamic System Response and Stability Analysis

621

(7)

Discretization in the Frequency Domain

628

(4)

The State-Space Analysis

632

(8)

The Root Locus in the Z-Plane

640

(2)

The Frequency-Response Analysis

642

(9)

Design of Discrete Time Controllers

651

(11)

Controller Feasibility: the Concept of Causality

651

(1)

Pole-Zero Matching Control Technique

652

(2)

The Pole Placement Methods in the z-Domain

654

(1)

The Frequency-Response Design Methods

655

(1)

The Discrete Time PID Controller

655

(6)

Implementation of Digital Control Systems

661

(1)

Problems

662

(7)

Advanced Control Systems

669

(96)

Introduction

669

(1)

State-Space Estimation

670

(3)

System Description

670

(1)

Kalman Filter Algorithm

671

(2)

The Information Filter

673

(11)

Information Space

673

(3)

Information Filter Derivation

676

(3)

Filter Characteristics

679

(1)

An Example of Linear Estimation

679

(3)

Comparison of the Kalman and Information Filters

682

(2)

The Extended Kalman Filter (EKF)

684

(7)

Nonlinear State-Space

685

(1)

EKF Derivation

686

(4)

Summary of the EKF Algorithm

690

(1)

The Extended Information Filter (EIF)

691

(4)

Nonlinear Information Space

691

(1)

EIF Derivation

692

(2)

Summary of the EIF Algorithm

694

(1)

Filter Characteristics

695

(1)

Examples of Estimation in Nonlinear Systems

695

(12)

Nonlinear State Evolution and Linear Observations

696

(2)

Linear State Evolution with Nonlinear Observations

698

(3)

Both Nonlinear State Evolution and Observations

701

(2)

Comparison of the EKF and EIF

703

(2)

Decentralized Estimation

705

(2)

Optimal Stochastic Control

707

(7)

Stochastic Control Problem

708

(1)

Optimal Stochastic Solution

709

(3)

Nonlinear Stochastic Control

712

(2)

Centralized Control

714

(1)

An Extended Example

714

(5)

Unscaled Individual States

715

(1)

Continuous Time Models

716

(2)

Discrete Time Models

718

(1)

Nonlinear Control Systems

719

(38)

Nonlinear Dynamic Systems

719

(2)

Describing Function Analysis

721

(1)

Phase Plane Methods

722

(18)

Lyapunov's Theory

740

(17)

Design of Nonlinear Control Systems

757

(4)

Feedback Linearization Methods

757

(1)

Introduction to Adaptive Control

758

(1)

Introduction to Neural Control

758

(1)

Introduction to Robust Control

758

(3)

Problems

761

(4)

A Laplace and Z-Transforms

765

(6)

A.1 Properties of Laplace Transforms

765

(1)

A.2 Table of Laplace Transforms

766

(1)

A.3 Properties of Z-Transforms

767

(1)

A.4 Table of Z-Transforms

768

(1)

A.5 Table of Z-Transforms (contd.)

769

(2)

B MATLAB: Basics and Exercises

771

(24)

B.1 Getting Started

771

(1)

B.2 Creating MATLAB Files

772

(1)

B.3 Commands

772

(6)

B.3.1 Vectors

772

(1)

B.3.2 Functions

773

(1)

B.3.3 Plotting

774

(1)

B.3.4 Polynomials

775

(1)

B.3.5 Matrices

776

(2)

B.4 Printing

778

(1)

B.5 Using M-files in MATLAB

778

(1)

B.6 Saving Workspace

779

(1)

B.7 Getting Help in MATLAB

780

(1)

B.8 Control Functions

780

(3)

B.9 More Commands

783

(1)

B.10 Labwork I

784

(2)

B.11 Labwork II

786

(1)

B.12 Labwork III

786

(3)

B.13 Labwork IV

789

(2)

B.14 Labwork V

791

(1)

B.15 Labwork VI

792

(3)

Bibliography

795

(2)

Index

797

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Design and Analysis of Control Systems

Summary

Table of Contents

Supplemental Materials