Introduction to Digital Control: An Integrated Approach

Preface
Acknowledgments
Contents
About the Author
Chapter 1: Introduction
	1.1 Basic Control Systems
	1.2 Digital Control Systems
	1.3 Organization of Book Chapters
	Further Reading
Chapter 2: Discrete-Time Systems and z-Transform
	2.1 Introduction
	2.2 Discrete-Time Systems
	2.3 Ideal Sampler and z-Transform
	2.4 Examples of z-transform of Commonly Used Functions
		2.4.1 Unit Impulse
		2.4.2 Unit Step
		2.4.3 Unit Ramp
		2.4.4 Exponentially Decaying Function
	2.5 z-Transform Using Matlab
		2.5.1 Unit Step
		2.5.2 Unit Ramp
		2.5.3 Exponentially Decaying Function
	2.6 z-Transform from s-Domain Functions
	2.7 Properties of z-Transform
		2.7.1 Addition and Subtraction
		2.7.2 Multiplication by a Constant
		2.7.3 Linear Translation
		2.7.4 Complex Translation
		2.7.5 Initial Value Theorem
		2.7.6 Final Value Theorem
	2.8 Inverse z-Transform
	2.9 Difference Equation
	2.10 Simulation Diagrams and Signal Flow Diagrams
	Exercises
	Further Reading
Chapter 3: Data Sampling and Reconstruction
	3.1 Introduction
	3.2 Sampling Theorem
	3.3 Ideal Sampler
		3.3.1 Laplace Transform of Sampled Signals
		3.3.2 Laplace Transform of Sampled Signals Represented in s-Domain
	3.4 Data Reconstruction
		3.4.1 Zero-Order Hold (ZOH)
		3.4.2 First-Order Hold (FOH)
		3.4.3 Fractional-Order Hold (FrOH)
	Exercises
	Further Reading
Chapter 4: Open-Loop Discrete-Time Systems
	4.1 Introduction
	4.2 Relationship Between Sampled Signal s-Transform F*(s) and z-Transform F(z)
	4.3 Open-Loop Discrete-Time System Transfer Function
		4.3.1 Zero-Order Hold (ZOH)
		4.3.2 First-Order Hold (FOH)
		4.3.3 Fractional-Order Hold (FrOH)
	4.4 Open-Loop Discrete-Time Systems of Different Configurations
	4.5 Open-Loop Discrete-Time Systems with Digital Filters
	4.6 Modified z-Transform
	4.7 Discrete-Time Systems with Time Delays
	4.8 Simulation Using Matlab/Simulink
	4.9 Systems with Nonsynchronous Sampling
	Exercises
	Further Reading
Chapter 5: Closed-Loop Discrete-Time Systems
	5.1 Introduction
	5.2 Closed-Loop Discrete-Time System Transfer Function
	5.3 Discrete-Time Systems with Disturbance Inputs
	5.4 Estimation of Model Parameters and Validation for Discrete-Time Systems
	Exercises
	Further Reading
Chapter 6: Discrete-Time System Characteristics
	6.1 Introduction
	6.2 Discrete-Time System Time Response
	6.3 Discrete-Time System Characteristic Equation
	6.4 Mapping of the s-Plane in the z-Plane
	6.5 Discrete Equivalents
		6.5.1 Discrete Equivalents via Numerical Integration
		6.5.2 Zero-Pole Matching Equivalents
		6.5.3 Hold Equivalents
	6.6 Discrete-Time System Steady-State Accuracy
	Exercises
	Further Reading
Chapter 7: Stability Analysis of Discrete-Time Systems
	7.1 Introduction
	7.2 Stability of Discrete-Time Systems
	7.3 Jury´s Stability Test
	7.4 Nyquist Criterion for Stability Analysis
	7.5 Bilinear Transformation
	7.6 Routh-Hurwitz Criterion for Discrete-Time Systems
	Exercises
	Further Reading
Chapter 8: Root Locus for Discrete-Time Systems
	8.1 Introduction
	8.2 Root Locus in z-Plane
	8.3 Stability Analysis Using Root Locus in z-Plane
	8.4 Generalized Root Locus in z-Plane
	8.5 Laboratory Experiment for Stability Analysis of Discrete-Time Systems Using z-Domain Techniques
	Exercises
	Further Reading
Chapter 9: Frequency Domain Analysis of Discrete-Time Systems
	9.1 Introduction
	9.2 Frequency Domain Analysis of Discrete-Time Systems
	9.3 Bode Plots for Discrete-Time Systems
	9.4 Stability Analysis of Discrete-Time Systems Using Bode Plots
	9.5 Stability Analysis of Discrete-Time Systems Using Nyquist Diagrams
	9.6 Generalized Bode Plots for Discrete-Time Systems
	9.7 Laboratory Experiment for Stability Analysis of Discrete-Time Systems Using Frequency Domain Techniques
	Exercises
	Further Reading
Chapter 10: Discrete-Time System Performance Specifications for Controller Design
	10.1 Introduction
	10.2 Steady-State Accuracy
	10.3 Time Domain Specifications
	10.4 Frequency Domain Specifications
	10.5 Relationship Between Specifications in Time and Frequency Domains
	Exercises
	Further Reading
Chapter 11: Controller Design for Discrete-Time Systems Using Time Domain Specifications
	11.1 Introduction
	11.2 Types of Controllers for Discrete-Time Systems
		11.2.1 PI, PD, and PID Controllers
		11.2.2 Phase-Lag, Phase-Lead, and Phase-Lag-Lead Controllers
	11.3 Design of PI, PD, and PID Controllers for Discrete-Time Systems
		11.3.1 PID Controllers
		11.3.2 PI Controllers
		11.3.3 PD Controllers
	11.4 Design of Phase-Lag, Phase-Lead, and Phase-Lag-Lead Controllers for Discrete-Time Systems
		11.4.1 Design of Phase-Lag Controllers
		11.4.2 Design of Phase-Lead Controllers
		11.4.3 Design of Phase-Lag-Lead Controllers
	11.5 Implementation of Controllers
		11.5.1 Laboratory Experiment for Analysis, Design, Simulation, and Implementation of PI, PD, and PID Controllers for Discrete-...
		11.5.2 Lab Experiment for Analysis, Design, Simulation, and Implementation of Phase-Lag, Phase-Lead, and Phase-Lag-Lead Contro...
	Exercises
	Further Reading
Chapter 12: Controller Design for Discrete-Time Systems Using Frequency-Domain Specifications
	12.1 Introduction
	12.2 Design of PI, PD, and PID Controllers for Discrete-Time Systems
		12.2.1 PID Controller Transfer Function in w-Domain
		12.2.2 Design of PID Controllers
		12.2.3 PI Controllers
		12.2.4 PD Controllers
	12.3 Design of Phase-Lag, Phase-Lead, and Phase-Lag-Lead Controllers for Discrete-Time Systems Using Analytical Approach
		12.3.1 Design of Phase-Lag Controllers
		12.3.2 Design of Phase-Lead Controllers
		12.3.3 Design of Phase-Lag-Lead Controllers
	12.4 Design of Phase-Lag, Phase-Lead, and Phase-Lag-Lead Controllers for Discrete-Time Systems Using Bode Plots
		12.4.1 Magnitude and Phase Angle Relations for Phase-Lag and Phase-Lead Controllers
		12.4.2 Design of Phase-Lag Controllers
		12.4.3 Design of Phase-Lead Controllers
		12.4.4 Design of Phase-Lag-Lead Controllers
	12.5 Implementation of Controllers
		12.5.1 Lab Experiment for Analysis, Design, Simulation, and Implementation of PI, PD, and PID Controllers for Discrete-Time Sy...
		12.5.2 Lab Experiment for Analysis, Design, Simulation, and Implementation of Phase-Lag, Phase-Lead, and Phase-Lag-Lead Contro...
	Exercises
	Further Reading
Chapter 13: State Space Representation of Discrete-Time Systems
	13.1 Introduction
	13.2 State-Space Representation of Continuous-Time Systems
		13.2.1 State-Space Equations in Continuous Time
		13.2.2 Conversion from Continuous-Time to Discrete-Time Systems
		13.2.3 From s-Domain Transfer Functions to State-Space Representation
	13.3 Controllability and Observability of Discrete-Time Systems
	13.4 Transfer Function Representation from State-Space
	Exercises
	Further Reading
Chapter 14: Design of Controllers for Discrete-Time Systems in State Space
	14.1 Introduction
	14.2 Full State Feedback Pole Placement Control
	14.3 Design of Full-Order Prediction Observers
	14.4 Reduced-Order Observers
	14.5 Design of Current Observers
	14.6 Laboratory Experiment for Analysis, Design, Simulation, and Implementation of State-Space Controllers for Discrete-Time S...
	Exercises
	Further Reading
Chapter 15: Discrete-Time System Identification
	15.1 Introduction
	15.2 Least-Squares System Identification
	15.3 Weighted Least-Squares System Identification
	15.4 Recursive Least-Squares System Identification
	15.5 Laboratory Experiment for Identification of Discrete-Time Systems
	Exercises
	Further Reading
Chapter 16: Design of Optimal Controllers for Discrete-Time Systems in State Space
	16.1 Introduction
	16.2 Design of Linear Quadratic Optimal Controllers
	16.3 Design of Linear Quadratic Optimal Estimators (Kalman Filters)
	16.4 Laboratory Experiment for Analysis, Design, Simulation, and Implementation of Optimal Controllers for Discrete-Time Syste...
	Exercises
	Further Reading
Chapter 17: Case Studies
	17.1 Introduction
	17.2 A Hybrid Electric Vehicle (HEV) Model
	17.3 Rotary Inverted Pendulum Model
	Further Reading
Appendix A: z-Transform Table of Commonly Used Functions
Appendix B: Answers to Selected Exercises
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 7
	Chapter 8
	Chapter 9
	Chapter 10
	Chapter 11
	Chapter 12
	Chapter 13
	Chapter 14
	Chapter 15
	Chapter 16
Index