Preface
1 Introduction
1.1 Introduction
1.2 Introduction to ControlSystems
1.3 Definitions
1.4 HistoricalBackground
1.5 DigitalControlDevelopment
1.6 MathematicalBackground
1.7 GeneralNature of the Engineering ControlProblem
1.8 Computer Literacy
1.9 Outline of Text
2 Writing System Equations
2.1Introduction
2.2 Electric Circuits and ComPOnents
2.3 Basic Linear Matrix Algebra
2.4 State Concepts
2.5 Transfer Function and Block Diagram
2.6 MechanicalTranslation Systems
2.7 Analogous Circuits
2.8 MechanicalRotationalSystems
2.9 ThermalSystems
2.10 Hydraulic Linear Actuator
2.ll Liquid-LevelSystem
2.12 Rotating Power Amplifiers
2.13 DC Servomotor
2.14 AC Servomotor
2.15 Lagranges Equation
2.16 Summary
3 Solution of DifferentialEquations
3.1Introduction
3.2 Standard Inputs to ControlSystems
3.3 Steady-State Response f SinusoidalInput
3.4 Steady-State Response: PolynomialInput
3.5 Transient Response f ClassicalMethod
3.6 Definition of Time Constant
3.7 Example f Second-Order System--Mechanical
3.8 Example: Second-Order System--Electrical
3.9 Second-Order Transients
3.10 Time-Response Specifications
3.1l CAD Accuracy Checks (CADAC)
3.12 State-Variable Equations
3.13 Characteristic Values
3.14 Evaluating the State Transition Matrix
3.15 Complete Solution of the State Equation
3.16 Summary
4 Laplace TransfOrm
4.1 Introduction
4.2 Definition of the Laplace TransfOrm
4.3 Derivation of Laplace Transforms of Simple Functions
4.4 LapIace TransfOrm Theorems
4.5 CAD Accuracy Checkst CADAC
4.6 Application of the Laplace Transform to DiffereptialEquations
4.7 Inverse TransfOrmation
4.8 Heaviside Partial-Fraction Expansion Theorems
4.9 MATLAB Partial-Fraction Example
4.10 Partial-Fraction Shortcuts
4.11 GraphicaI Interpretation of Partial-Fraction Coefficients
4.12 Frequency Response from the Pole-Zero Diagram
4.13 Location of Poles and Stability
4.14 Laplace TransfOrm of the Impulse Function
4.15 Second-Order System with Impulse Excitation
4.16 AdditionalMatrix Operations and ProPerties
4.17 SoIution of State Equati()n
4.18 Evaluation of the Transttr-Function Matrix
4.19 Summary
5 System Representation
5.1 Introduction
5.2 Block Diagrams
5.3 Determination of the OverallTransfer Function
5.4 Standard Block Diagram Terminology
5.5 Position ControlSystem
5.6 Simulation Diagrams
5.7 SignalFlow Graphs
5.8 State Transition SignalFlow Graph
5.9 ParallelState Diagrams from Transfer Functions
5.10 Diagonalizing the A Matrix
5.1l Use of State TransfOrmation fOr the State Equation Solution
5.12 Transforming a Matrix with Complex Eigenvalues
5.13 Transforming an A Matrix into Companion FOrm
5.14 Summary
6 Control-System Characteristics
6.l Introduction
6.2 Routh.s Stability Criterion
6.3 Mathematicaland PhysicalForms
6.4 Feedback System TyPes
6.5 Analysis of System Types
6.6 Example f TyPe 2 System
6.7 Steady-State Error Coefficients
6.8 CAD Accuracy Checkst CADAC
6.9 Use of Steady-State Ermr Coefficients
6.10 Nonunity-Feedback System
6.llSummary
7 Root Locus
7.lIntroduction
7.2 Plotting Roots of a Characteristic Equation
7.3 Qualitative Analysis of the Root Locus
7.4 Procedure Outline
7.5 OPen-Loop Transfer Function
7.6 Poles of the ControlRatio C(syR(s)
7.7 Application Qf the Magnitude and Angle Conditions
7.8 GeometricaI ProPerties (Construction Rules)
7.9 CAD Accuracy Checks (CADAC)
7.10 Examples
7.11 Example l:MATLAB Root Locus
7.12 PerfOrmance Characteristics
7.13 Transport Lag
7.14 Synthesis
7.15 Summary of Root-Locus Construction Rules fOr Negative Feedback
7.16 Summary
8 Frequency Response
8.l Introduction
8.2 Co1.reIation of the SinusoidaI and Time ResPOnses
8.3 Frequency-ResPOnse Curves
8.4 Bode Plots (Logarithmic Plots)
8.5 GeneralFrequency-Transfer-Function Relationships
8.6 Drawing the Bode Plots
8.7 Example of Drawing a Bode Plot
8.8 System TyPe and Gain as Related to Log Magnitude Curves
8.9 CAD Accuracy Check (CADAC)
8.10 ExperimentalDetermination of Transfer Functions
8.11 Direct Polar Plots
8.12 Summary: Direct Polar Plots
8.13 Nyquist.s Stability Criterion
8.14 Examples of Nyquist.s Criterion Using Direct Polar Plot
8.15 Nyquist.s Stability Criterion Applied to Systems Having DeadTime
8.16 Definitions of Phase Margin and Gain Margin and Their Relatonto stability
8.17 Stability Characteristics of the Log Magnitude and Phase Diagram
8.18 Stability from the Nichols Plot (Log Magnitude--Angle Diagrarn)
8.19 Sununary
9 Closed-Loop Tracking Performance Based on the Frequency ResPOnse
9.1 Introduction
9.2 Direct Polar Plot
9.3 Determination of M.and com fOr a Simple Second-Order System
9.4 Correlation of Sinusoidaland Time ResPOnses
9.5 Constant M(co) and a(to) Contours of C(jo,yR(jco) on theComplex Plane (Direct Plot)
9.6 Constant 1M and a Contours (Unity Feedback) in the InversePolar Plane
9.7 Gain Adjustment for a Desired M.of a Unity-Feedback System:Direct Polar Plot
9.8 Constant M and a Curves on the Log Magnitude--Angle Diagram(Nichols Chart)
9.9 Generation of MATLAB (1992 Student Version) Bode and NyquistPlots
9.10 Adjustment of Gain by Use of the Log Magnitude--Angle Diagram
9.11 Correlahon of Pole-Zero Diagrarn with Frequency and TimeResPOnses
9.12 sununary
10 Root-Locus Compensation: Design
10.1 Introduction to Design
10.2 Transient ResPOnse: Dominant Complex POles
10.3 AdditionalSignificant Poles
10.4 Root-tocus Design Considerations
10.5 Reshaping the Root Locus
10.6 CAD Accuracy Checks (CADAC)
10.7 IdealIntegralCascade ComPensation (PI ContrOller)
10.8 Cascade Lag ComPensation Design Using Passive Elements
10.9 IdealDerivative Cascade ComPensation (PD ContrOller)
10.10 Lead ComPensation Design Using Passive Elements
10.11 Generalbead-ComPensator Design
10.12 Lag-Lead Cascade ComPensation Design
10.13 Comparison of Cascade ComPensators
10.14 PID ContrOller
10.15 Introduction to Feedback ComPensation
10.16 Feedback Compensation: Design Procedures
10.17 Simplified Rate Feedback ComPensation: A Design Approach
10.18 Design of Rate Feedback
10.19 Design f Feedback of Second Derivative of Output
10.20 Results of Feedback ComPensation Design
10.21 Rate Feedback f Plants with Dominant Complex Poles
10.22 Summary
11 Frequency-Response Compensation Design
11.1 Introduction to Feedback ComPensation Design
11.2 Selection of a Cascade ComPensator
11.3 Cascade Lag ComPensator
11.4 Design Example f Cascade Lag Compensation
11.5 Lead Compensator
11.6 Design Example: Cascade Lead ComPensation
11.7 Lag-Lead ComPensator
11.8 Design Example f Cascade Lag-Lead ComPensation
11.9 Feedback Compensation Design Using Log Plots
11.10 Design Exarnple f Feedback Compensation (Log Plots)
11.11 Application Guidelines f Basic MinorLoop Feedback ComPensators
11.12 Summary
12 Control-Ratio Modeling
12.1 Introduction
12.2 Modeling a Desired Tracking ControlRatio.
12.3 Guillemin-TruxalDesign Procedure
12.4 Introduction to Disturbance Rejection.
12.5 A Second-Order Disturbance-Rejection Model
12.6 Disturbance-Rejection Design Princinles for SISO Systems
12.7 Disturbance-Rejection Design Example
12.8 Disturbance-Rejection Models
12.9 Summary
13 Design: Closed-Loop Pole-Zero Assignment(State-Variable Feedback)
13.l Introduction
13.2 Controllability and Observability
13.3 State Feedback for SISO Systems
13.4 State-Fecdback Design for SISO Systems Using the ContrOlCanonical(Phase-Vdriables) Form
13.5 State-Variable Feedback (PhysicalVariables)
13.6 GeneralProperties of State Feedback (Using Phase Variables)
13.7 State-Variable Feedback: Steady-State Ermr Analysis
13.8 Use of Steady-State Ermr Coefficients
13.9 State-Variable Feedback: All-Pole Plant
13.10 Plants with Complex Poles
13.11 ComPensator Containing a Zero
13.12 State.Variable Feedback: Pole-Zero Plant
13.13 Summary
14 Parameter Sensitivity and State Space Trajectories
14.1 Introduction
14.2 Sensitivity
14.3 Sensitivity Analysis
14.4 Parameter Sensitivity Examples
14.5 Inaccessible States
14.6 State-SpaceTrajectories -
14.7 Linearization (Jacobian Matrix)
14.8 Summary
15 DigitalControlSystems
15.1 Introduction
15.2 Sampling
15.3 IdealSampling
15.4 z-Transform Theorems
15.5 Synthesis in the z Domain (Direct Method)
15.6 The Inverse z Transform
15.7 Zero-Order Hold
15.8 Limitations
15.9 Tustin Transformation
15.10 Tustin Transformation ProPerties
15.11 Pseudo-Continuous-Tme (PCT) ControlSystem (DIG Method)
15.12 Analysis of a Basic (UncomPensated) System
15.13 Design of DigitalControlSystems
15.14 Direct (DIR) Design Technique
15.15 Lead Controller (ComPensator)f DIR Design Method
15.16 Lag and Lag-Lead Controllers f DIR Design Method
15.17 Digitization (DIG) Design Technique
15.18 Summary
16 Entire Eigenstructure Assignment for MultivariableSystems
16.1 Introduction
16.2 Effect of Eigenstructure on Time Response
16.3 Entire Eigenstructure Assignment
16.4 Examples of Entire Eigenstructure Assignment fOr Re.gulators
16.5 MATLAB Eigenvectors
16.6 UncontrolIable Systems
16.7 Tracking Systems
16.8 Tracking-System Design Example
16.9 MATLAB Example of Tracker Design in Sec.16.8
16.10 Summary
17 Design of Tracking Systems Using Output Feedback
17.1 Introduction
17.2 Output.Feedback Tracking System
17.3 Block Diagonalization
17.4 Analysis of Closed-Loop System Performance
17.5 Design Procedure for Regular Plants
17.6 Regular System Design Example
17.7 Irregular Plant Characteristics
17.8 Irregular System Performance
17.9 Design of the Measurement Matrix M
17.10 Irregular System Design ExaInple
17.11 Tracker Simulation
17.12 Summary
18 Quantitative Feedback Theory (QFT) Technique
18.1 Introduction
18.2 Frequency Responses with Parameter Variations
18.3 Introduction to the QFT Method (Single-Loop System)
18.4 Minimum-Phase System Performance SPecifications
18.5 Multiple-Inght Multiple-Output (MIMO) Uncertain Plants
18.6 Plant Templates of P(s), JP(jωi)
18.7 U-Contour
18.8 Tracking Bounds Lm BR(jω) on the NC
18.9 Disturbance Bounds BD(jωi)f Case l[d2(t) = D.u--1(t),d1(t) = 0]
18.10 Disturbance Bounds BD(jωi): Case 2 [d1(t) = D.u-- l(t),d2(t) = 0]
18.1lThe Composite Boundary B.(jωi)
18.12 ShaPing of 1.(jω)
18.13 Guidelines tbr Shaping 1.(jω)
18.14 Design of the Prefilter F(s)
18.15 Basic Design Procedure for a MISO System
18.16 Design Example l
18.17 Design Example 2
18.18 Template Generation for Unstable Plants
18.19 Summary
Appendixes
A Table of Laplace Transform Pairs
B Interactive Computer Aided Design Programs for Digital and Continuous Control-System Analysis and Synthesis
B.1 Introduction
B.2 Overview of lCECAP-PC and TOTAL-PC
B.3 Overview of MATLAB
B.4 QFT CAD Packages
B.5 ComputerAided Design Accuracy Checks (CADAC)
B.6 Other Computer-Aided Design Packages
Problems
Answers to Selected Problems
Index
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