Digital Control Engineering

by Fadali; Visioli

• ISBN13: 9780123744982
• ISBN10: 0123744989
• Format: Hardcover
• Copyright: 2009-02-02
• Publisher: Elsevier Science

Summary

Digital controllers are part of nearly all modern personal, industrial, and transportation sytems. Every senior or graduate student of electrical, chemical or mechanical engineering should therefore be familiar with the basic theory of digital controllers. This new text covers the fundamental principles and applications of digital control engineering, with emphasis on engineering design. Extensive Use of computational tools: Matlab sections at end of each chapter show how to implement concepts from the chapter. Frees the student from the drudgery of mundane calculations and allows him to consider more subtle aspects of control system analysis and design. An engineering approach to digital controls: emphasis throughout the book is on design of control systems. Mathematics is used to help explain concepts, but throughout the text discussion is tied to design and implementation. For example coverage of analog controls in chapter 5 is not simply a review, but is used to show how analog control systems map to digital control systems. Review of Background Material: contains review material to aid understanding of digital control analysis and design. Examples include discussion of discrete-time systems in time domain and frequency domain (reviewed from linear systems course) and root locus design in s-domain and z-domain (reviewed from feedback control course). Inclusion of Advanced Topics In addition to the basic topics required for a one semester senior/graduate class, the text includes some advanced material to make it suitable for an introductory graduate level class or for two quarters at the senior/graduate level. Examples of optional topics are state-space methods, which may receive brief coverage in a one semester course, and nonlinear discrete-time systems. Minimal Mathematics Prerequisites The mathematics background required for understanding most of the book is based on what can be reasonably expected from the average electrical, chemical or mechanical engineering senior. This background includes three semesters of calculus, differential equations and basic linear algebra. Some texts on digital control require more mathematical maturity and are therefore beyond the reach of the typical senior.

Author Biography

M. Sami Fadali holds a BS in electrical engineering from Cairo University in Egypt, an MS in automatic control from UMIST in Manchester, England, and a Ph.D. in biomedical engineering from the University of Wyoming. He is currently a professor of electrical and biomedical engineering at the University of Nevada Reno. He has taught many courses in the control systems area including nonlinear control, linear control, and robust control. He has also taught an undergraduate course in digital control for more than twenty years. His research interests are in fault detection, fuzzy logic, and the mathematical modeling of cellular processes. He is a Senior Member of the IEEE. Antonio Visioli earned a Laurea degree from the University of Parma in Italy in electronic engineering and a Ph.D. degree in applied mechanics from the University of Brescia, Italy. He is currently an associate professor of automatic control with the Department of Electronics for Automation at the University of Brescia. He has taught many courses in the control systems area. His research interests are in robotics, industrial controllers, and input-output inversion-based control. He is a Senior Member of the IEEE.

Table of Contents

Introduction to Digital Control	p. 1
Why Digital Control?	p. 2
The Structure of a Digital Control System	p. 2
Examples of Digital Control Systems	p. 3
Resources	p. 6
Problems	p. 7
Discrete-Time Systems	p. 9
Analog Systems with Piecewise Constant Inputs	p. 9
Difference Equations	p. 11
The z-Transform	p. 12
Computer-Aided Design	p. 31
z-Transform Solution of Difference Equations	p. 32
The Time Response of a Discrete-Time System	p. 33
The Modified z-Transform	p. 38
Frequency Response of Discrete-Time Systems	p. 40
The Sampling Theorem	p. 46
Resources	p. 50
Problems	p. 51
Computer Exercises	p. 53
Modeling of Digital Control Systems	p. 55
ADC Model	p. 55
DAC Model	p. 56
The Transfer Function of the ZOH	p. 57
Effect of Sampler on Transfer Function of a Cascade	p. 58
Transfer Function for the DAC, Analog Subsystem, ADC Combination	p. 62
Systems with Transport Lag	p. 70
The Closed-Loop Transport Function	p. 72
Analog Disturbances in a Digital System	p. 75
Steady-State Error and Error Constants	p. 77
MATLAB Commands	p. 80
Resources	p. 81
Problems	p. 82
Computer Exercises	p. 85
Stability of Digital Control Systems	p. 87
Definitions of Stability	p. 87
Stable z-Domain Pole Locations	p. 89
Stability Conditions	p. 89
Stability Determination	p. 97
Jury Test	p. 100
Nyquist Criterion	p. 104
Resources	p. 118
Problems	p. 118
Computer Exercises	p. 120
Analog Control System Design	p. 123
The Root Locus	p. 123
Root Locus Using MATLAB	p. 128
Design Specifications and the Effect of Gain Variation	p. 128
Root Locus Design	p. 131
Empirical Tuning of PID Controllers	p. 154
Resources	p. 158
Problems	p. 158
Computer Exercises	p. 159
Digital Control System Design	p. 161
z-Domain Root Locus	p. 161
z-Domain Digital Control System Design	p. 164
Digital Implementation of Analog Controller Design	p. 176
Direct z-Domain Digital Controller Design	p. 196
Frequency Response Design	p. 202
Direct Control Design	p. 210
Finite Settling Time Design	p. 215
Resources	p. 225
Problems	p. 225
Computer Exercises	p. 227
State-Space Representation	p. 229
State Variables	p. 229
State-Space Representation	p. 232
Linearization of Nonlinear State Equations	p. 237
The Solution of Linear State-Space Equations	p. 240
The Transfer Function Matrix	p. 256
Discrete-Time State-Space Equations	p. 258
Solution of Discrete-Time State-Space Equations	p. 261
z-Transfer Function from State-Space Equations	p. 268
Similarity Transformation	p. 270
Resources	p. 274
Problems	p. 275
Computer Exercises	p. 279
Properties of State-Space Models	p. 281
Stability of State-Space Realizations	p. 282
Controllability and Stabilizability	p. 290
Observability and Detectability	p. 301
Poles and Zeros of Multivariable Systems	p. 307
State-Space Realizations	p. 313
Duality	p. 326
Resources	p. 327
Problems	p. 328
Computer Exercises	p. 333
State Feedback Control	p. 335
On State and Output Feedback	p. 335
Pole Placement	p. 337
Servo Problem	p. 349
Invariance of System Zeros	p. 353
State Estimation	p. 355
Observer State Feedback	p. 362
Pole Assignment Using Transfer Functions	p. 370
Resources	p. 374
Problems	p. 374
Computer Exercises	p. 378
Optimal Control	p. 379
Optimization	p. 379
Optimal Control	p. 384
The Linear Quadratic Regulator	p. 389
Steady-State Quadratic Regulator	p. 399
Hamiltonian System	p. 406
Resources	p. 409
Problems	p. 410
Computer Exercises	p. 413
Elements of Nonlinear Digital Control Systems	p. 415
Discretization of Nonlinear Systems	p. 415
Nonlinear Difference Equations	p. 424
Equilibrium of Nonlinear Discrete-Time System	p. 425
Lyapunov Stability Theory	p. 426
Stability of Analog Systems with Digital Control	p. 439
State Plane Analysis	p. 442
Discrete-Time Nonlinear Controller Design	p. 447
Resources	p. 452
Problems	p. 452
Computer Exercises	p. 455
Practical Issues	p. 457
Design of the Hardware and Software Architecture	p. 457
Choice of the Sampling Period	p. 461
Controller Structure	p. 468
PID Control	p. 471
Sampling Period Switching	p. 481
Resources	p. 494
Problems	p. 494
Computer Exercises	p. 495
Table of Laplace and Z-Transforms	p. 497
Properties of the Z-Transform	p. 499
Review of Linear Algebra	p. 501
Matrices	p. 501
Equality of Matrices	p. 502
Matrix Arithmetic	p. 502
Determinant of a Matrix	p. 508
Inverse of a Matrix	p. 509
Eigenvalues	p. 512
Eigenvectors	p. 513
Norm of a Vector	p. 516
Matrix Norms	p. 517
Quadratic Forms	p. 518
Matrix Differentiation/Integration	p. 520
Kronecker Product	p. 522
Resources	p. 523
Index	p. 525
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