مهندسی کنترل دیجیتال، ویرایش دوم: تحلیل و طراحی

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. * 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. * 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. * 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). Front Cover......Page 1 Digital Control Engineering: Analysis and Design......Page 2 Copyright page......Page 3 Contents......Page 4 Numerous examples......Page 12 Standard mathematics prerequisites......Page 13 New to this edition......Page 14 Organization of text......Page 15 Supporting material......Page 18 1 Introduction to Digital Control......Page 20 1.2 The structure of a digital control system......Page 21 1.3.1 Closed-loop drug delivery system......Page 22 1.3.3 Control of a robotic manipulator......Page 23 Resources......Page 25 2.1 Analog systems with piecewise constant inputs......Page 28 2.2 Difference equations......Page 30 2.3 The z-transform......Page 31 2.3.1 z-Transforms of standard discrete-time signals......Page 32 2.3.2 Properties of the z-transform......Page 34 Time advance......Page 35 Multiplication by exponential......Page 36 Complex differentiation......Page 37 Long division......Page 38 Partial fraction expansion......Page 39 2.3.4 The final value theorem......Page 47 2.4 Computer-aided design......Page 48 2.5 z-Transform solution of difference equations......Page 50 2.6.1 Convolution summation......Page 51 2.6.2 The convolution theorem......Page 53 2.7 The modified z-transform......Page 56 2.8 Frequency response of discrete-time systems......Page 58 2.8.1 Properties of the frequency response of discrete-time systems......Page 61 2.8.2 MATLAB commands for the discrete-time frequency response......Page 63 2.9 The sampling theorem......Page 64 2.9.1 Selection of the sampling frequency......Page 65 Problems......Page 68 Computer exercises......Page 71 3.1 ADC model......Page 74 3.2 DAC model......Page 75 3.3 The transfer function of the ZOH......Page 76 3.4 Effect of the sampler on the transfer function of a cascade......Page 77 3.5 DAC, analog subsystem, and ADC combination transfer function......Page 80 3.6 Systems with transport lag......Page 88 3.7 The closed-loop transfer function......Page 90 3.8 Analog disturbances in a digital system......Page 93 3.9 Steady-state error and error constants......Page 94 3.9.2 Sampled ramp input......Page 96 3.10.1 MATLAB......Page 98 3.10.2 Simulink......Page 99 Problems......Page 104 Computer exercises......Page 108 4.1 Definitions of stability......Page 110 4.2 Stable z-domain pole locations......Page 112 4.3.1 Asymptotic stability......Page 113 4.3.2 BIBO stability......Page 114 4.3.3 Internal stability......Page 117 4.4.1 MATLAB......Page 120 4.4.2 Routh-Hurwitz criterion......Page 121 4.5 Jury test......Page 123 4.6 Nyquist criterion......Page 128 4.6.1 Phase margin and gain margin......Page 133 Problems......Page 142 Computer exercises......Page 144 5.1 Root locus......Page 146 5.3 Design specifications and the effect of gain variation......Page 151 5.4 Root locus design......Page 154 5.4.1 Proportional control......Page 156 5.4.2 PD control......Page 157 5.4.3 PI control......Page 166 5.4.4 PID control......Page 172 5.5 Empirical tuning of PID controllers......Page 175 Problems......Page 180 Computer exercises......Page 182 6.1 z-Domain root locus......Page 184 6.2 z-Domain digital control system design......Page 187 Observation......Page 189 6.2.1 z-Domain contours......Page 190 6.2.2 Proportional control design in the z-domain......Page 194 6.3 Digital implementation of analog controller design......Page 199 Forward differencing......Page 200 Backward differencing......Page 201 6.3.2 Pole-zero matching......Page 202 6.3.3 Bilinear transformation......Page 205 6.3.4 Empirical digital PID controller tuning......Page 218 6.4 Direct z-domain digital controller design......Page 219 6.5 Frequency response design......Page 224 6.6 Direct control design......Page 232 6.7 Finite settling time design......Page 237 Problems......Page 249 Computer exercises......Page 252 7.1 State variables......Page 254 7.2 State–space representation......Page 257 7.2.2 Linear versus nonlinear state–space equations......Page 259 7.3 Linearization of nonlinear state equations......Page 262 7.4 The solution of linear state–space equations......Page 265 7.4.1 The Leverrier algorithm......Page 270 Leverrier algorithm......Page 271 7.4.2 Sylvester’s expansion......Page 274 7.4.3 The state-transition matrix for a diagonal state matrix......Page 276 Properties of constituent matrices......Page 279 7.4.4 Real form for complex conjugate eigenvalues......Page 281 7.5 The transfer function matrix......Page 283 7.5.1 MATLAB commands......Page 284 7.6 Discrete-time state–space equations......Page 285 7.6.2 Complex conjugate eigenvalues......Page 288 7.7 Solution of discrete-time state–space equations......Page 290 7.7.1 z-Transform solution of discrete-time state equations......Page 291 7.8 z-Transfer function from state–space equations......Page 296 7.9 Similarity transformation......Page 298 7.9.1 Invariance of transfer functions and characteristic equations......Page 301 Problems......Page 302 Computer exercises......Page 308 8 Properties of State–Space Models......Page 312 8.1.1 Asymptotic stability......Page 313 8.1.2 BIBO stability......Page 316 8.2 Controllability and stabilizability......Page 320 8.2.1 MATLAB commands for controllability testing......Page 326 8.2.2 Controllability of systems in normal form......Page 327 8.2.3 Stabilizability......Page 328 8.3 Observability and detectability......Page 332 8.3.1 MATLAB commands......Page 335 8.3.3 Detectability......Page 336 8.4 Poles and zeros of multivariable systems......Page 338 8.4.1 Poles and zeros from the transfer function matrix......Page 339 8.4.2 Zeros from state–space models......Page 342 8.5 State–space realizations......Page 344 Systems with no input differencing......Page 345 Systems with input differencing......Page 347 8.5.2 Controllable form in MATLAB......Page 349 8.5.3 Parallel realization......Page 350 Parallel realization for MIMO systems......Page 353 8.5.4 Observable form......Page 355 8.6 Duality......Page 357 8.7 Hankel realization......Page 358 Resources......Page 362 Problems......Page 363 Computer exercises......Page 368 9.1 State and output feedback......Page 370 9.2 Pole placement......Page 372 9.2.1 Pole placement by transformation to controllable form......Page 375 9.2.2 Pole placement using a matrix polynomial......Page 376 9.2.3 Choice of the closed-loop eigenvalues......Page 378 9.2.5 Pole placement for multi-input systems......Page 383 9.3 Servo problem......Page 386 9.4 Invariance of system zeros......Page 391 9.5.1 Full-order observer......Page 393 9.5.2 Reduced-order observer......Page 396 9.6 Observer state feedback......Page 399 9.6.1 Choice of observer eigenvalues......Page 402 9.7 Pole assignment using transfer functions......Page 408 Problems......Page 412 Computer exercises......Page 416 10.1 Optimization......Page 418 10.1.1 Unconstrained optimization......Page 419 10.1.2 Constrained optimization......Page 421 10.2 Optimal control......Page 423 10.3 The linear quadratic regulator......Page 428 10.3.1 Free final state......Page 429 10.4 Steady-state quadratic regulator......Page 438 10.4.1 Output quadratic regulator......Page 439 10.4.2 MATLAB solution of the steady-state regulator problem......Page 440 10.4.3 Linear quadratic tracking controller......Page 442 10.5 Hamiltonian system......Page 445 10.5.1 Eigenstructure of the Hamiltonian matrix......Page 448 Problems......Page 452 Computer exercises......Page 455 11.1 Discretization of nonlinear systems......Page 458 11.1.1 Extended linearization by input redefinition......Page 459 11.1.2 Extended linearization by input and state redefinition......Page 461 11.1.3 Extended linearization by output differentiation......Page 462 11.1.4 Extended linearization using matching conditions......Page 464 11.2 Nonlinear difference equations......Page 466 11.3 Equilibrium of nonlinear discrete-time systems......Page 467 11.4.1 Lyapunov functions......Page 469 11.4.2 Stability theorems......Page 471 11.4.4 Lyapunov stability of linear systems......Page 473 11.4.5 MATLAB......Page 476 11.4.6 Lyapunov’s linearization method......Page 477 11.4.7 Instability theorems......Page 478 11.4.8 Estimation of the domain of attraction......Page 480 11.5 Stability of analog systems with digital control......Page 482 11.6 State plane analysis......Page 484 11.7.1 Controller design using extended linearization......Page 489 11.7.2 Controller design based on Lyapunov stability theory......Page 492 11.8 Input-output stability and the small gain theorem......Page 493 11.8.1 Absolute stability......Page 500 Problems......Page 504 Computer exercises......Page 508 12.1.1 Software requirements......Page 510 12.1.2 Selection of ADC and DAC......Page 513 12.2.1 Antialiasing filters......Page 514 12.2.2 Effects of quantization errors......Page 517 12.2.3 Phase delay introduced by the ZOH......Page 522 12.3 Controller structure......Page 523 12.4.1 Filtering the derivative action......Page 526 12.4.2 Integrator windup......Page 528 12.4.3 Bumpless transfer between manual and automatic mode......Page 531 12.4.4 Incremental form......Page 534 12.5 Sampling period switching......Page 535 12.5.1 MATLAB commands......Page 538 12.5.2 Dual-rate control......Page 545 Resources......Page 547 Problems......Page 548 Computer exercises......Page 549 APPENDIX I: Table of Laplace and z-Transforms......Page 552 APPENDIX II: Properties of the z-Transform......Page 554 A.1 Matrices......Page 556 A.3.2 Transposition......Page 557 Multiplication by a matrix......Page 559 Properties of determinants......Page 563 A.5 Inverse of a matrix......Page 564 A.6 Trace of a matrix......Page 565 Linearly independent vectors......Page 566 A.8 Eigenvalues and eigenvectors......Page 567 Lower triangular matrix......Page 568 A.9 Partitioned matrix......Page 570 Equivalent norms......Page 572 Frobenius norm......Page 573 A.12 Quadratic forms......Page 574 A.13 Singular value decomposition and pseudoinverses......Page 576 A.14 Matrix differentiation/integration......Page 580 A.15 Kronecker product......Page 582 Resources......Page 583 Index......Page 584 Digital controllers are part of nearly all modern personal, industrial, and transportation systems. 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.

Fadali and Visioli cover analysis and design of digitally controlled systems and describe applications of digital controls in a wide range of fields. With worked examples and Matlab applications in every chapter and many end-of-chapter assignments, this text provides both theory and practice for those coming to digital control engineering for the first time, whether as a student or practicing engineer.

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.
Digital controllers are part of nearly all modern personal, industrial, and transportation systems. 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. Fadali and Visioli cover analysis and design of digitally controlled systems and describe applications of digital controls in a wide range of fields. With worked examples and Matlab applications in every chapter and many end-of-chapter assignments, this text provides both theory and practice for those coming to digital control engineering for the first time, whether as a student or practicing engineer. 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 Machine generated contents note: Table of Contents Chapter 1. Introduction to Digital Control Chapter 2. Discrete-Time systems Chapter 3. Modeling of Digital Control Systems Chapter 4. Stability of Digital Control Systems Chapter 5. Analog Control System Design Chapter 6. Digital Control System Design Chapter 7. State-Space Representation Chapter 8. Properties of State-Space Models Chapter 9. State Feedback Control Chapter 10. Elements of Nonlinear Digital Control Systems Chapter 11. Practical Issues Appendix I: Table of Laplace and Z-Transforms Appendix II: Properties of the Z-Transform Appendix III: Review of Linear Algebra .