Control Systems: An Introduction

Preface
Contents
Abbreviations
1 Introduction
	1.1 Basics of Control Systems
	1.2 Basic Signals
		1.2.1 The Unit-Step Signal
		1.2.2 The Unit-Impulse Signal
		1.2.3 The Unit-Ramp Signal
		1.2.4 The Unit-Parabolic Signal
	1.3 Sinusoids
		1.3.1 The Polar Form of Sinusoids
		1.3.2 The Rectangular Form of Sinusoids
			Sum of Sinusoids with the Same Frequency
		1.3.3 The Complex Sinusoids
			Real Causal Exponential Signal
			Exponentially Varying Amplitude Sinusoids
	1.4 System Modeling
	1.5 Summary
	Exercises
2 The Laplace Transform
	2.1 Laplace Transform
		2.1.1 Properties of the Laplace Transform
			Linearity
		2.1.2 Time-Shifting
		2.1.3 Frequency-Shifting
		2.1.4 Time-Differentiation
		2.1.5 Integration
		2.1.6 Time-Scaling
		2.1.7 Convolution in Time
		2.1.8 Multiplication by t
		2.1.9 Initial Value
		2.1.10 Final Value
	2.2 Laplace Transform Solution of Differential Equations
		2.2.1 The Transfer Function
		2.2.2 Transfer Function of Feedback Systems
	2.3 Finding the Inverse Laplace Transform
		2.3.1 Inverse Laplace Transform by Partial-FractionExpansion
	2.4 Characterization of a System by Its Poles and Zeros and System Stability
	2.5 Routh–Hurwitz Stability Criterion
	2.6 Summary
	Exercises
3 Mathematical Modeling of Electrical Systems
	3.1 Modeling of Electrical Circuits
		3.1.1 Circuit Analysis
			Basic Elements in Electrical Circuits
		3.1.2 Series Circuits
		3.1.3 Parallel Circuits
		3.1.4 Examples of Circuit Analysis
	3.2 Summary
	Exercises
4 Mathematical Modeling of Mechanical Systems
	4.1 Modeling Electrical Systems
	4.2 Modeling Translational Mechanical Systems
		4.2.1 Theoretical Analysis
	4.3 Modeling Rotational Mechanical Systems
		4.3.1 Simple Pendulum
		4.3.2 A Mechanical Rotational System
		4.3.3 Field Current Controlled DC Motor
		4.3.4 Armature-Controlled DC Motor
	4.4 Summary
	Exercises
5 Block Diagrams and Signal-Flow Graphs
	5.1 Block Diagrams
	5.2 Signal-Flow Graphs
		5.2.1 Mason's Gain Formula
			Conversion of a Block Diagram to the Corresponding SFG
	5.3 Summary
	Exercises
6 Steady-State and Transient Responses
	6.1 Transfer Function of Feedback Systems
	6.2 Steady-State Errors in Control Systems
		6.2.1 Type 0 System
		6.2.2 Type 1 System
		6.2.3 Type 2 System
			Steady-State Errors of Nonunity Feedback Systems
	6.3 Unit-Step Response and Transient Response Specifications
	6.4 Linearization
	6.5 Parameter Sensitivity
	6.6 Summary
	Exercises
7 Root Locus
	7.1 Plotting the Root Locus
		7.1.1 Negative Feedback Systems
			Angle of a Line in the Complex Plane
			Breakaway and Break-in Points
		7.1.2 Nonminimum-Phase Systems
	7.2 Control System Design by Root Locus Method
		7.2.1 Proportional Compensator
		7.2.2 Proportional-Integral Compensator
		7.2.3 Lag Compensator
		7.2.4 Proportional-Derivative Compensator
			Higher-Order Systems
		7.2.5 Lead Compensator
			Alternate Design
		7.2.6 Proportional-Integral-Derivative Compensator
		7.2.7 Lead-Lag Compensator
	7.3 Summary
	Exercises
8 Design of Control Systems in Frequency Domain: Bode Plot
	8.1 Bode Plot
		8.1.1 Bode Plot of a Lag Compensator
		8.1.2 Bode Plot of a Lead Compensator
			Approximation of e-Ts
	8.2 Design of Control Systems
		8.2.1 Relation Between Time-Domain and Frequency-Domain Specifications
		Relation Between Phase Margin and the Damping Ratio ζ
		8.2.2 Lag Compensator
		8.2.3 Lead Compensator
		8.2.4 Lead–Lag Compensator
		8.2.5 Proportional–Integral–Derivative Compensator
			The First Method
			Second Method
	8.3 Summary
	Exercises
9 Nyquist Plot
	9.1 Nyquist Plot
		9.1.1 Nyquist Plots of Simple Transfer Functions
			The Constant
			First-Order Zero
			First-Order Pole
			Poles and Zeros at the Origin
	9.2 Stability Analysis from Bode and Nyquist Plots
		9.2.1 Nyquist Stability Criterion
			Closed-Loop Stability from the Nyquist Plot
		9.2.2 Nonminimum-Phase Systems
		9.2.3 Systems with Delay Units
		9.2.4 Pade Approximation of e-Ts
	9.3 Summary
	Exercises
10 State-Space Analysis of Control Systems
	10.1 The State-Space Model
	10.2 Frequency-Domain Solution of the State Equation
	10.3 Time-Domain Solution of the State Equation
	10.4 Commonly Used Realizations of Systems
	10.5 Linear Transformation of State Vectors and Diagonalization
	10.6 Controllability
	10.7 Observability
	10.8 Summary
	Exercises
11 Design of Control Systems in State Space
	11.1 Design by Pole-Placement
		11.1.1 Direct Comparison Method
		11.1.2 Using Transformation Matrix
		11.1.3 Using Ackermann's Formula
	11.2 State Observers
		11.2.1 Design of Regulator Systems with Observers
			Transfer Function of the Observer-Based Controller
	11.3 Design of Control Systems with Observers
		11.3.1 Quadratic Optimal Regulator Systems
	11.4 Digital Implementation of Continuous-Time Systems
		11.4.1 The Bilinear Transformation
			Frequency Warping
			Application of the Bilinear Transformation
	11.5 Summary
	Exercises
Answers to Selected Exercises
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 7
	Chapter 8
	Chapter 9
	Chapter 10
	Chapter 11
Bibliography
Index