Control Systems Engineering, 6th Edition

CONTENTS
Preface
	Icons Identifying Major Topics
1. INTRODUCTION
	1.1 Introduction
		Control System Definition
		Advantages of Control Systems
	1.2 A History of Control Systems
		Liquid-Level Control
		Steam Pressure and Temperature Controls
		Speed Control
		Stability, Stabilization, and Steering
		Twentieth-Century Developments
		Contemporary Applications
	1.3 System Configurations
		Open-Loop Systems
		Closed-Loop (Feedback Control) Systems
		Computer-Controlled Systems
	1.4 Analysis and Design Objectives
		Transient Response
		Steady-State Response
		Stability
		Other Considerations
		Case Study
	1.5 The Design Process
		Step 1: Transform Requirements Into a Physical System
		Step 2: Draw a Functional Block Diagram
		Step 3: Create a Schematic
		Step 4: Develop a Mathematical Model (Block Diagram)
		Step 5: Reduce the Block Diagram
		Step 6: Analyze and Design
	1.6 Computer-Aided Design
		MATLAB
		LabVIEW
	1.7 The Control Systems Engineer
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
2. MODELING IN THE FREQUENCY DOMAIN
	2.1 Introduction
	2.2 Laplace Transform Review
		Partial-Fraction Expansion
	2.3 The Transfer Function
	2.4 Electrical Network Transfer Functions
		Simple Circuits via Mesh Analysis
		Simple Circuits via Nodal Analysis
		Simple Circuits via Voltage Division
		Complex Circuits via Mesh Analysis
		Complex Circuits via Nodal Analysis
		A Problem-Solving Technique
		Operational Amplifiers
		Inverting Operational Amplifier
		Noninverting Operational Amplifier
	2.5 Translational Mechanical System Transfer Functions
	2.6 Rotational Mechanical System Transfer Functions
	2.7 Transfer Functions for Systems with Gears
	2.8 Electromechanical System Transfer Functions
	2.9 Electric Circuit Analogs
		Series Analog
		Parallel Analog
	2.10 Nonlinearities
	2.11 Linearization
	Case Studies
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
3. MODELING IN THE TIME DOMAIN
	3.1 Introduction
	3.2 Some Observations
	3.3 The General State-Space Representation
	3.4 Applying the State-Space Representation
		Minimum Number of State Variables
	3.5 Converting a Transfer Function to State Space
	3.6 Converting from State Space to a Transfer Function
	3.7 Linearization
	Case Studies
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
4. TIME RESPONSE
	4.1 Introduction
	4.2 Poles, Zeros, and System Response
		Poles of a Transfer Function
		Zeros of a Transfer Function
		Poles and Zeros of a First-Order System: An Example
	4.3 First-Order Systems
		Time Constant
		Rise Time, Tr
		Settling Time, Ts
		First-Order Transfer Functions via Testing
	4.4 Second-Order Systems: Introduction
		Overdamped Response, Figure 4.7(b)
		Underdamped Response, Figure 4.7 (c)
		Undamped Response, Figure 4.7(d)
		Critically Damped Response, Figure 4.7 (e)
	4.5 The General Second-Order System
		Natural Frequency, ωn
		Damping Ratio, ζ
	4.6 Underdamped Second-Order Systems
		Evaluation of Tp
		Evaluation of Ts
		Evaluation of Tr
		Second-Order Transfer Functions via Testing
	4.7 System Response with Additional Poles
	4.8 System Response With Zeros
	4.9 Effects of Nonlinearities Upon Time Response
	4.10 Laplace Transform Solution of State Equations
		Eigenvalues and Transfer Function Poles
	4.11 Time Domain Solution of State Equations
	Case Studies
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
5. REDUCTION OF MULTIPLE SUBSYSTEMS
	5.1 Introduction
	5.2 Block Diagrams
		Cascade Form
		Parallel Form
		Feedback Form
		Moving Blocks to Create Familiar Forms
	5.3 Analysis and Design of Feedback Systems
	5.4 Signal-Flow Graphs
	5.5 Mason’s Rule
		Definitions
		Mason’s Rule
	5.6 Signal-Flow Graphs of State Equations
	5.7 Alternative Representations in State Space
		Cascade Form
		Parallel Form
		Controller Canonical Form
		Observer Canonical Form
	5.8 Similarity Transformations
		Diagonalizing a System Matrix
		Definitions
	Case Studies
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
6. STABILITY
	6.1 Introduction
	6.2 Routh-Hurwitz Criterion
		Generating a Basic Routh Table
		Interpreting the Basic Routh Table
	6.3 Routh-Hurwitz Criterion: Special Cases
		Zero Only in the First Column
		Entire Row is Zero
	6.4 Routh-Hurwitz Criterion: Additional Examples
	6.5 Stability in State Space
	Case Studies
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
7. STEADY-STATE ERRORS
	7.1 Introduction
		Definition and Test Inputs
		Application to Stable Systems
		Evaluating Steady-State Errors
		Sources of Steady-State Error
	7.2 Steady-State Error for Unity Feedback Systems
		Steady-State Error in Terms of T(s)
		Steady-State Error in Terms of G(s)
	7.3 Static Error Constants and System Type
		System Type
	7.4 Steady-State Error Specifications
	7.5 Steady-State Error for Disturbances
	7.6 Steady-State Error for Nonunity Feedback Systems
	7.7 Sensitivity
	7.8 Steady-State Error for Systems in State Space
		Analysis via Final Value Theorem
		Analysis via Input Substitution
	Case Studies
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
8. ROOT LOCUS TECHNIQUES
	8.1 Introduction
		The Control System Problem
		Vector Representation of Complex Numbers
	8.2 Defining the Root Locus
	8.3 Properties of the Root Locus
	8.4 Sketching the Root Locus
	8.5 Refining the Sketch
		The jω-Axis Crossings
		Angles of Departure and Arrival
		Plotting and Calibrating the Root Locus
	8.6 An Example
		Basic Rules for Sketching the Root Locus
		Additional Rules for Refining the Sketch
	8.7 Transient Response Design via Gain Adjustment
	8.8 Generalized Root Locus
	8.9 Root Locus for Positive-Feedback Systems
	8.10 Pole Sensitivity
	Case Studies
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
9. DESIGN VIA ROOT LOCUS
	9.1 Introduction
		Improving Transient Response
		Improving Steady-State Error
		Configurations
		Compensators
	9.2 Improving Steady-State Error via Cascade Compensation
		Ideal Integral Compensation (PI)
		Lag Compensation
	9.3 Improving Transient Response via Cascade Compensation
		Ideal Derivative Compensation (PD)
		Lead Compensation
	9.4 Improving Steady-State Error and Transient Response
		PID Controller Design
		Lag-Lead Compensator Design
		Notch Filter
	9.5 Feedback Compensation
		Approach 1
		Approach 2
	9.6 Physical Realization of Compensation
		Active-Circuit Realization
		Passive-Circuit Realization
	Case Studies
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
10. FREQUENCY RESPONSE TECHNIQUES
	10.1 Introduction
		The Concept of Frequency Response
		Analytical Expressions for Frequency Response
		Plotting Frequency Response
	10.2 Asymptotic Approximations: Bode Plots
		Bode Plots for G(s) = (s + a)
		Bode Plots for G(s) =1/(s+a)
		Bode Plots for G(s)=s
		Bode Plots for G(s)=1/s
		Bode Plots for G(s)= s² + 2ζωnS + ωn²
		Corrections to Second-Order Bode Plots
		Bode Plots for G(s) = 1/(s²+ + 2ζωnS + ωn²)
		Bode Plots for Ratio of First- and Second-Order Factors
	10.3 Introduction to the Nyquist Criterion
		Derivation of the Nyquist Criterion
		Applying the Nyquist Criterion to Determine Stability
	10.4 Sketching the Nyquist Diagram
	10.5 Stability via the Nyquist Diagram
		Stability via Mapping Only the Positive jω-Axis
	10.6 Gain Margin and Phase Margin via the Nyquist Diagram
	10.7 Stability, Gain Margin, and Phase Margin via Bode Plots
		Determining Stability
		Evaluating Gain and Phase Margins
	10.8 Relation Between Closed-Loop Transient and Closed-Loop Frequency Responses
		Damping Ratio and Closed-Loop Frequency Response
		Response Speed and Closed-Loop Frequency Response
	10.9 Relation Between Closed-and Open-Loop Frequency Responses
		Constant M Circles and Constant N Circles
		Nichols Charts
	10.10 Relation Between Closed-Loop Transient and Open-Loop Frequency Responses
		Damping Ratio From M Circles
		Damping Ratio from Phase Margin
		Response Speed from Open-Loop Frequency Response
	10.11 Steady-State Error Characteristics from Frequency Response
		Position Constant
		Velocity Constant
		Acceleration Constant
	10.12 Systems with Time Delay
		Modeling Time Delay
	10.13 Obtaining Transfer Functions Experimentally
	Case Study
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
11. DESIGN VIA FREQUENCY RESPONSE
	11.1 Introduction
	11.2 Transient Response via Gain Adjustment
		Design Procedure
	11.3 Lag Compensation
		Visualizing Lag Compensation
		Design Procedure
	11.4 Lead Compensation
		Visualizing Lead Compensation
		Lead Compensator Frequency Response
		Design Procedure
	11.5 Lag-Lead Compensation
		Design Procedure
	Case Studies
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
12. DESIGN VIA STATE SPACE
	12.1 Introduction
	12.2 Controller Design
		Topology for Pole Placement
		Pole Placement for Plants in Phase-Variable Form
	12.3 Controllability
		Controllability by Inspection
		The Controllability Matrix
	12.4 Alternative Approaches to Controller Design
	12.5 Observer Design
	12.6 Observability
		Observability by Inspection
		The Observability Matrix
	12.7 Alternative Approaches to Observer Design
	12.8 Steady-State Error Design Via Integral Control
	Case Study
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
13. DIGITAL CONTROL SYSTEMS
	13.1 Introduction
		Advantages of Digital Computers
		Digital-to-Analog Conversion
		Analog-to-Digital Conversion
	13.2 Modeling the Digital Computer
		Modeling the Sampler
		Modeling the Zero-Order Hold
	13.3 The z-Transform
		The Inverse z-Transform
	13.4 Transfer Functions
		Derivation of the Pulse Transfer Function
	13.5 Block Diagram Reduction
	13.6 Stability
		Digital System Stability via the z-Plane
		Bilinear Transformations
		Digital System Stability via the s-Plane
	13.7 Steady-State Errors
		Unit Step Input
		Unit Ramp Input
		Unit Parabolic Input
		Summary of Steady-State Errors
	13.8 Transient Response on the z-Plane
	13.9 Gain Design on the z-Plane
	13.10 Cascade Compensation via the s-Plane
		Cascade Compensation
	13.11 Implementing the Digital Compensator
	Case Studies
	Summary
	Review Questions
	Problems
	Cyber Exploration Laboratory
	Bibliography
APPENDICES
	A: List of Symbols
	B: MATLAB Tutorial
		B.1 Introduction
		B.2 MATLAB Examples
		B.3 Command Summary
		Bibliography
	C: MATLAB’s Simulink Tutorial
		C.1 Introduction
		C.2 Using Simulink
		C.3 Examples
		Summary
		Bibliography
	D: LabVIEW™¹ Tutorial
		D.1 Introduction
		D.2 Control Systems Analysis, Design, and Simulation
		D.3 Using LabVIEW
		D.4 Analysis and Design Examples
		D.5 Simulation Examples
		Summary
		Bibliography
Glossary
Answers to Selected Problems
Credits (Figures & Photos)
INDEX
Key Equations
Solutions to Skill-Assessment Exercises