Digital Control Engineering : Analysis and Design

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.Content: Front Matter • Preface • Table of Contents 1. Introduction to Digital Control 2. Discrete-Time Systems 3. Modeling of Digital Control Systems 4. Stability of Digital Control Systems 5. Analog Control System Design 6. Digital Control System Design 7. State - Space Representation 8. Properties of State - Space Models 9. State Feedback Control 10. Optimal Control 11. Elements of Nonlinear Digital Control Systems 12. Practical Issues Appendices Index Front Cover Digital Control Engineering: Analysis and Design Copyright page Contents Preface Approach Features Numerous examples Extensive use of CAD packages Coverage of background material Inclusion of advanced topics Standard mathematics prerequisites Senior system theory prerequisites Coverage of theory and applications New to this edition Organization of text Supporting material 1 Introduction to Digital Control 1.1 Why digital control? 1.2 The structure of a digital control system 1.3 Examples of digital control systems 1.3.1 Closed-loop drug delivery system 1.3.2 Computer control of an aircraft turbojet engine 1.3.3 Control of a robotic manipulator Resources 2 Discrete-Time Systems 2.1 Analog systems with piecewise constant inputs 2.2 Difference equations 2.3 The z-transform 2.3.1 z-Transforms of standard discrete-time signals 2.3.2 Properties of the z-transform Linearity Time delay Time advance Multiplication by exponential Complex differentiation 2.3.3 Inversion of the z-transform Long division Partial fraction expansion 2.3.4 The final value theorem 2.4 Computer-aided design 2.5 z-Transform solution of difference equations 2.6 The time response of a discrete-time system 2.6.1 Convolution summation 2.6.2 The convolution theorem 2.7 The modified z-transform 2.8 Frequency response of discrete-time systems 2.8.1 Properties of the frequency response of discrete-time systems 2.8.2 MATLAB commands for the discrete-time frequency response 2.9 The sampling theorem 2.9.1 Selection of the sampling frequency Resources Problems Computer exercises 3 Modeling of Digital Control Systems 3.1 ADC model 3.2 DAC model 3.3 The transfer function of the ZOH 3.4 Effect of the sampler on the transfer function of a cascade 3.5 DAC, analog subsystem, and ADC combination transfer function 3.6 Systems with transport lag 3.7 The closed-loop transfer function 3.8 Analog disturbances in a digital system 3.9 Steady-state error and error constants 3.9.1 Sampled step input 3.9.2 Sampled ramp input 3.10 MATLAB commands 3.10.1 MATLAB 3.10.2 Simulink Resources Problems Computer exercises 4 Stability of Digital Control Systems 4.1 Definitions of stability 4.2 Stable z-domain pole locations 4.3 Stability conditions 4.3.1 Asymptotic stability 4.3.2 BIBO stability 4.3.3 Internal stability 4.4 Stability determination 4.4.1 MATLAB 4.4.2 Routh-Hurwitz criterion 4.5 Jury test 4.6 Nyquist criterion 4.6.1 Phase margin and gain margin Resources Problems Computer exercises 5 Analog Control System Design 5.1 Root locus 5.2 Root locus using MATLAB 5.3 Design specifications and the effect of gain variation 5.4 Root locus design 5.4.1 Proportional control 5.4.2 PD control 5.4.3 PI control 5.4.4 PID control 5.5 Empirical tuning of PID controllers Resources Problems Computer exercises 6 Digital Control System Design 6.1 z-Domain root locus 6.2 z-Domain digital control system design Observation 6.2.1 z-Domain contours 6.2.2 Proportional control design in the z-domain 6.3 Digital implementation of analog controller design 6.3.1 Differencing methods Forward differencing Backward differencing 6.3.2 Pole-zero matching 6.3.3 Bilinear transformation 6.3.4 Empirical digital PID controller tuning 6.4 Direct z-domain digital controller design 6.5 Frequency response design 6.6 Direct control design 6.7 Finite settling time design Resources Problems Computer exercises 7 State–Space Representation 7.1 State variables 7.2 State–space representation 7.2.1 State–space representation in MATLAB 7.2.2 Linear versus nonlinear state–space equations 7.3 Linearization of nonlinear state equations 7.4 The solution of linear state–space equations 7.4.1 The Leverrier algorithm Leverrier algorithm 7.4.2 Sylvester’s expansion 7.4.3 The state-transition matrix for a diagonal state matrix Properties of constituent matrices 7.4.4 Real form for complex conjugate eigenvalues 7.5 The transfer function matrix 7.5.1 MATLAB commands 7.6 Discrete-time state–space equations 7.6.1 MATLAB commands for discrete-time state–space equations 7.6.2 Complex conjugate eigenvalues 7.7 Solution of discrete-time state–space equations 7.7.1 z-Transform solution of discrete-time state equations 7.8 z-Transfer function from state–space equations 7.8.1 z-Transfer function in MATLAB 7.9 Similarity transformation 7.9.1 Invariance of transfer functions and characteristic equations Resources Problems Computer exercises 8 Properties of State–Space Models 8.1 Stability of state–space realizations 8.1.1 Asymptotic stability 8.1.2 BIBO stability 8.2 Controllability and stabilizability 8.2.1 MATLAB commands for controllability testing 8.2.2 Controllability of systems in normal form 8.2.3 Stabilizability 8.3 Observability and detectability 8.3.1 MATLAB commands 8.3.2 Observability of systems in normal form 8.3.3 Detectability 8.4 Poles and zeros of multivariable systems 8.4.1 Poles and zeros from the transfer function matrix 8.4.2 Zeros from state–space models 8.5 State–space realizations 8.5.1 Controllable canonical realization Systems with no input differencing Systems with input differencing 8.5.2 Controllable form in MATLAB 8.5.3 Parallel realization Parallel realization for MIMO systems 8.5.4 Observable form 8.6 Duality 8.7 Hankel realization Resources Problems Computer exercises 9 State Feedback Control 9.1 State and output feedback 9.2 Pole placement 9.2.1 Pole placement by transformation to controllable form 9.2.2 Pole placement using a matrix polynomial 9.2.3 Choice of the closed-loop eigenvalues 9.2.4 MATLAB commands for pole placement 9.2.5 Pole placement for multi-input systems 9.2.6 Pole placement by output feedback 9.3 Servo problem 9.4 Invariance of system zeros 9.5 State estimation 9.5.1 Full-order observer 9.5.2 Reduced-order observer 9.6 Observer state feedback 9.6.1 Choice of observer eigenvalues 9.7 Pole assignment using transfer functions Resources Problems Computer exercises 10 Optimal Control 10.1 Optimization 10.1.1 Unconstrained optimization 10.1.2 Constrained optimization 10.2 Optimal control 10.3 The linear quadratic regulator 10.3.1 Free final state 10.4 Steady-state quadratic regulator 10.4.1 Output quadratic regulator 10.4.2 MATLAB solution of the steady-state regulator problem 10.4.3 Linear quadratic tracking controller 10.5 Hamiltonian system 10.5.1 Eigenstructure of the Hamiltonian matrix Resources Problems Computer exercises 11 Elements of Nonlinear Digital Control Systems 11.1 Discretization of nonlinear systems 11.1.1 Extended linearization by input redefinition 11.1.2 Extended linearization by input and state redefinition 11.1.3 Extended linearization by output differentiation 11.1.4 Extended linearization using matching conditions 11.2 Nonlinear difference equations 11.2.1 Logarithmic transformation 11.3 Equilibrium of nonlinear discrete-time systems 11.4 Lyapunov stability theory 11.4.1 Lyapunov functions 11.4.2 Stability theorems 11.4.3 Rate of convergence 11.4.4 Lyapunov stability of linear systems 11.4.5 MATLAB 11.4.6 Lyapunov’s linearization method 11.4.7 Instability theorems 11.4.8 Estimation of the domain of attraction 11.5 Stability of analog systems with digital control 11.6 State plane analysis 11.7 Discrete-time nonlinear controller design 11.7.1 Controller design using extended linearization 11.7.2 Controller design based on Lyapunov stability theory 11.8 Input-output stability and the small gain theorem 11.8.1 Absolute stability Resources Problems Computer exercises 12 Practical Issues 12.1 Design of the hardware and software architecture 12.1.1 Software requirements 12.1.2 Selection of ADC and DAC 12.2 Choice of the sampling period 12.2.1 Antialiasing filters 12.2.2 Effects of quantization errors 12.2.3 Phase delay introduced by the ZOH 12.3 Controller structure 12.4 PID control 12.4.1 Filtering the derivative action 12.4.2 Integrator windup 12.4.3 Bumpless transfer between manual and automatic mode 12.4.4 Incremental form 12.5 Sampling period switching 12.5.1 MATLAB commands 12.5.2 Dual-rate control Resources Problems Computer exercises APPENDIX I: Table of Laplace and z-Transforms APPENDIX II: Properties of the z-Transform APPENDIX III: Review of Linear Algebra A.1 Matrices A.2 Equality of matrices A.3 Matrix arithmetic A.3.1 Addition and subtraction A.3.2 Transposition A.3.3 Matrix multiplication Multiplication by a scalar Multiplication by a matrix A.4 Determinant of a matrix Determinant Properties of determinants A.5 Inverse of a matrix A.6 Trace of a matrix A.7 Rank of a matrix Linearly independent vectors A.8 Eigenvalues and eigenvectors Upper triangular matrix Lower triangular matrix A.9 Partitioned matrix A.10 Norm of a vector Norm axioms lp norms Equivalent norms A.11 Matrix norms Induced matrix norms Submultiplicative property Frobenius norm A.12 Quadratic forms A.13 Singular value decomposition and pseudoinverses A.14 Matrix differentiation/integration A.15 Kronecker product Resources Index 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 . A reference library at your fingertips! This convenient summary of current, pertinent, practical information for OEHS professionals covers such topics as ventilation, noise, heat stress, ionizing and nonionizing radiation, respiratory protection, ergonomics, illumination, and more. The manual also provides general conversion tables, rules of thumb, and a variety of formulas, figures, and charts.