Digital Control Engineering: Analysis and Design

✍ Scribed by M. Sami Fadali, Antonio Visioli

• Publisher: Academic Press
• Year: 2012
• Tongue: English
• Leaves: 601
• Edition: 2
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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