Digital Control Engineering: Analysis and Design

Digital Control Engineering
Copyright
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
Acknowledgments
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
	Problems
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
			2.3.2.1 Linearity
			2.3.2.2 Time delay
			2.3.2.3 Time advance
			2.3.2.4 Multiplication by exponential
			2.3.2.5 Complex differentiation
		2.3.3 Inversion of the z-transform
			2.3.3.1 Long division
			2.3.3.2 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 Analog-to-digital converter (ADC) model
	3.2 Digital-to-analog converter (DAC) model
	3.3 The transfer function of the zero-order hold (ZOH)
	3.4 Effect of the sampler on the transfer function of a cascade
	3.5 DAC, analog subsystem, and analog-to-digital converter (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
	3.11 Sensitivity analysis
		3.11.1 Pole sensitivity
	Further reading
	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 Proportional-derivative (PD) control
		5.4.3 Proportional-integral (PI) control
		5.4.4 Proportional-integral-derivative (PID) control
	5.5 Empirical tuning of PID controllers
	References
	Further reading
	Problems
	Computer exercises
6 - Digital control system design
	6.1 z-domain root locus
	6.2 z-domain digital control system design
		Observation
		Remarks
		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
			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
		6.7.1 Eliminating intersample oscillation
	Further reading
	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
			7.4.1.1 Leverrier algorithm
		7.4.2 Sylvester's expansion
		7.4.3 The state-transition matrix for a diagonal state matrix
			7.4.3.1 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
	Reference
	Further reading
	Problems
	Computer exercises
8 - Properties of state–space models
	8.1 Stability of state–space realizations
		8.1.1 Asymptotic stability
		8.1.2 Bounded-Input–Bounded-Output 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
			8.5.1.1 Systems with no input differencing
			8.5.1.2 Systems with input differencing
		8.5.2 Controllable form in MATLAB
		8.5.3 Parallel realization
			8.5.3.1 Parallel realization for multiinput-multioutput systems
		8.5.4 Observable form
	8.6 Duality
	8.7 Hankel realization
	8.8 Realizations for continuous-time systems
	Further reading
	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
	Further reading
	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
	10.6 Return difference equality and stability margins
	10.7 Model predictive control
		10.7.1 Model
		10.7.2 Cost function
		10.7.3 Computation of the control law
		10.7.4 Constraints
		10.7.5 MATLAB commands
	10.8 Modification of the reference signal
		10.8.1 Dynamic Matrix Control
	Further reading
	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
	Further reading
	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 zero-order hold
	12.3 Controller structure
	12.4 Proportional–integral–derivative 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
	Reference
	Further reading
	Problems
	Computer exercises
13 - Linear matrix inequalities
	13.1 Linear matrix inequalities (LMI) from matrix equation
		13.1.1 From Linear Equations to LMIs
	13.2 The Schur complement
	13.3 Decision variables
	13.4 MATLAB LMI commands
		13.4.1 LMI editor
	Further reading
	Problems
I - Table of Laplace and z-transforms
II Properties of the z-transform
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
	A.4 Determinant of a matrix
	A.5 Inverse of a matrix
	A.6 Trace of a matrix
	A.7 Rank of a matrix
	A.8 Eigenvalues and eigenvectors
	A.9 Partitioned matrix
	A.10 Norm of a vector
	A.11 Matrix norms
	A.12 Quadratic forms
	A.13 Singular value decomposition and pseudoinverses
	A.14 Matrix differentiation/integration
	A.15 Kronecker product
	Further reading
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	W
	Z