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Control Systems Engineering 6th(Norman S. Nise).pdf
Front Cover
Inside Front Cover
Title Page
Dedication Page
Copyright Page
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
Antenna Azimuth Position
Control System
Layout
Antenna
Potentiometer
θ
i(t)
Desired
azimuth angle
input
Differential amplifier
and power amplifier
o(t)θ
Azimuth
angle
output
Motor
Potentiometer
Schematic
+V
n-turn potentiometer
–V
Differential
preamplifier
vi(t)
vo(t)
+
–
K
vp(t)
Power
amplifier
K1
s + a
Motor
Fixed
field
Ra
ea(t)
Ja kg-m2
Da N-m s/rad
Kb V-s/rad
Kt N-m/A
n-turn potentiometer
N1
Gear
N3
Gear
Armature
N2
Gear
–V
+V
JL kg-m2
DL N-m-s/rad
Block Diagram
Desired
azimuth
angle
qi(s)
Potentiometer
Preamplifier
Vi(s)
+
Ve(s)
Vp(s)
K
Kpot
–
Power
amplifier
Ea(s)
K1
s + a
Motor
and load
K1
s(s+am)
Azimuth
angle
qo(s)
Gears
Kg
qm(s)
Potentiometer
Kpot
Schematic Parameters
Parameter
Configuration 1
Configuration 2
Configuration 3
V
n
K
K1
a
Ra
Ja
Da
Kb
Kt
N1
N2
N3
JL
DL
10
10
—
100
100
8
0.02
0.01
0.5
0.5
25
250
250
1
1
10
1
—
150
150
5
0.05
0.01
1
1
50
250
250
5
3
10
1
—
100
100
5
0.05
0.01
1
1
50
250
250
5
3
Block Diagram Parameters
Parameter
Configuration 1
Configuration 2
Configuration 3
Kpot
K
K1
a
Km
am
Kg
0.318
—
100
100
2.083
1.71
0.1
Note: reader may fill in Configuration 2 and Configuration 3 columns after completing
the antenna control Case Study challenge problems in Chapters 2 and 10, respectively.
Unmanned Free-Swimming
Submersible Vehicle
Pitch Control System
Pitch
command
θc(s)
+
–
Pitch gain
–K1
+
–
Commanded
elevator
deflection
δ
(s)
ec
Elevator
actuator
Elevator
deflection
δ
e(s)
2
s + 2
Vehicle
dynamics
–0.125(s + 0.435)
(s + 1.23)(s2 + 0.226s +0.0169)
Pitch
θ (s)
Pitch rate
sensor
–K2s
Heading Control System
Heading
command
ψ
c(s)
+
–
Commanded
rudder
deflection
δ
rc
(s)
Heading
gain
–K1
+
–
Rudder
actuator
Rudder
deflection
Vehicle
dynamics
δr(s)
2
s + 2
–0.125(s + 0.437)
(s + 1.29)(s + 0.193)
Heading
(yaw)
rate
ψ(s)
Heading
ψ(s)
1
s
Yaw
rate
sensor
–K2s
CONTROL SYSTEMS ENGINEERING
Sixth Edition
Norman S. Nise
California State Polytechnic University, Pomona
John Wiley & Sons, Inc.
E1FTOC
10/27/2010
16:47:4
Page 5
Contents
PREFACE,
ix
1.
INTRODUCTION, 1
2
Introduction,
1.1
1.2 A History of Control Systems,
1.3
1.4 Analysis and Design Objectives,
System Configurations,
7
4
1.5
1.6
1.7
12
Case Study,
The Design Process,
15
Computer-Aided Design,
20
The Control Systems Engineer,
Summary,
Review Questions,
Problems,
Cyber Exploration Laboratory,
Bibliography,
23
23
24
31
10
21
30
2. MODELING IN THE FREQUENCY
DOMAIN, 33
2.1
2.2
2.3
2.4
2.5
34
Introduction,
Laplace Transform Review,
The Transfer Function,
44
Electrical Network Transfer Functions,
Translational Mechanical System
Transfer Functions,
35
61
2.6 Rotational Mechanical System
98
Problems,
Cyber Exploration Laboratory,
Bibliography,
115
112
3. MODELING IN THE TIME
DOMAIN, 117
3.1
3.2
3.3
Introduction,
118
Some Observations,
The General State-Space
Representation,
123
119
3.4 Applying the State-Space
3.5
3.6
3.7
47
139
132
124
Representation,
Converting a Transfer Function
to State Space,
Converting from State Space to a
Transfer Function,
Linearization,
Case Studies,
Summary,
Review Questions,
Problems,
Cyber Exploration Laboratory,
Bibliography,
141
144
148
149
149
159
157
4. TIME RESPONSE, 161
2.7
2.8
69
Transfer Functions,
Transfer Functions for Systems
with Gears,
Electromechanical System
Transfer Functions,
79
Electric Circuit Analogs,
84
74
2.9
2.10 Nonlinearities,
2.11 Linearization,
Case Studies,
Summary,
Review Questions,
88
89
94
97
97
4.8
4.9
162
Introduction,
Poles, Zeros, and System Response,
First-Order Systems,
Second-Order Systems: Introduction,
The General Second-Order System,
4.1
4.2
4.3
4.4
4.5
4.6 Underdamped Second-Order Systems,
4.7
166
162
168
173
System Response with
Additional Poles,
186
System Response With Zeros,
Effects of Nonlinearities Upon
Time Response,
196
191
177
v
Cyber Exploration Laboratory,
Bibliography,
336
335
7. STEADY-STATE ERRORS, 339
228
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
353
356
349
343
340
Introduction,
Steady-State Error for Unity
Feedback Systems,
Static Error Constants
and System Type,
Steady-State Error Specifications,
Steady-State Error for Disturbances,
Steady-State Error for Nonunity
Feedback Systems,
Sensitivity,
Steady-State Error for Systems in
State Space,
Case Studies,
Summary,
Review Questions,
Problems,
Cyber Exploration Laboratory,
Bibliography,
364
368
386
371
372
373
358
362
384
E1FTOC
10/27/2010
16:47:4
Page 6
vi
Contents
4.10 Laplace Transform Solution
of State Equations,
199
4.11 Time Domain Solution of
207
203
213
State Equations,
Case Studies,
Summary,
Review Questions,
Problems,
Cyber Exploration Laboratory,
Bibliography,
215
232
214
5. REDUCTION OF
MULTIPLE SUBSYSTEMS, 235
Introduction,
5.1
5.2 Block Diagrams,
236
5.3 Analysis and Design of
236
245
248
Feedback Systems,
Signal-Flow Graphs,
251
5.4
5.5 Mason’s Rule,
5.6
Signal-Flow Graphs of
State Equations,
254
5.7 Alternative Representations in State
5.8
272
256
Space,
Similarity Transformations,
Case Studies,
Summary,
Review Questions,
Problems,
Cyber Exploration Laboratory,
Bibliography,
278
280
299
279
266
297
6. STABILITY, 301
Introduction,
6.1
6.2 Routh-Hurwitz Criterion,
6.3 Routh-Hurwitz Criterion:
302
Special Cases,
308
6.4 Routh-Hurwitz Criterion:
8. ROOT LOCUS TECHNIQUES, 387
392
388
Introduction,
8.1
8.2 Defining the Root Locus,
8.3
8.4
8.5 Refining the Sketch,
8.6 An Example,
8.7
Properties of the Root Locus,
Sketching the Root Locus,
402
Transient Response Design
415
via Gain Adjustment,
411
394
397
305
8.8 Generalized Root Locus,
8.9 Root Locus for Positive-Feedback
419
Systems,
421
8.10 Pole Sensitivity,
424
6.5
314
320
Additional Examples,
Stability in State Space,
Case Studies,
Summary,
Review Questions,
Problems,
325
323
326
325
431
426
Case Studies,
Summary,
Review Questions,
Problems,
Cyber Exploration Laboratory,
Bibliography,
452
432
432
450
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