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.