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E-raamat: Mathematical Introduction To Control Theory, A (Second Edition)

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(Jerusalem College Of Technology, Israel)
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Mathematical Introduction To Control Theory, A (Second Edition)Suurem pilt
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Striking a nice balance between mathematical rigor and engineering-oriented applications, this second edition covers the bedrock parts of classical control theory — the Routh-Hurwitz theorem and applications, Nyquist diagrams, Bode plots, root locus plots, and the design of controllers (phase-lag, phase-lead, lag-lead, and PID). It also covers three more advanced topics — non-linear control, modern control, and discrete-time control.This invaluable book makes effective use of MATLAB® as a tool in design and analysis. Containing 75 solved problems and 200 figures, this edition will be useful for junior and senior level university students in engineering who have a good knowledge of complex variables and linear algebra.
Preface to the Second Edition vii
Preface to the First Edition ix
1 Mathematical Preliminaries 1(36)
1.1 An Introduction to the Laplace Transform
1(1)
1.2 Properties of the Laplace Transform
2(10)
1.3 A Second Proof of the Initial Value Theorem
12(3)
1.3.1 The Intuition Behind the Proof
13(1)
1.3.2 The Proof
13(2)
1.4 Finding the Inverse Laplace Transform
15(4)
1.4.1 Some Simple Inverse Transforms
16(2)
1.4.2 The Quadratic Denominator
18(1)
1.5 Integro-Differential Equations
19(5)
1.6 An Introduction to Stability
24(5)
1.6.1 Some Preliminary Manipulations
24(2)
1.6.2 Stability
26(2)
1.6.3 Why We Obsess about Stability
28(1)
1.6.4 The Tacoma Narrows Bridge-A Brief Case History
29(1)
1.7 MATLAB®
29(3)
1.7.1 Assignments
29(1)
1.7.2 Commands
30(2)
1.8 Exercises
32(5)
2 Transfer Functions 37(30)
2.1 Transfer Functions
37(2)
2.2 The Frequency Response of a System
39(3)
2.3 Bode Plots
42(3)
2.4 The Time Response of Certain "Typical" Systems
45(3)
2.4.1 First Order Systems
45(1)
2.4.2 Second Order Systems
46(2)
2.5 Three Important Devices and Their Transfer Functions
48(6)
2.5.1 The Operational Amplifier (op amp)
48(3)
2.5.2 The DC Motor
51(1)
2.5.3 The "Simple Satellite"
52(2)
2.6 Zeros in the Right Half-Plane
54(1)
2.7 Block Diagrams and How to Manipulate Them
55(3)
2.8 A Final Example
58(3)
2.9 Exercises
61(6)
3 Feedback-An Introduction 67(20)
3.1 Why Feedback-A First View
67(1)
3.2 Sensitivity
68(2)
3.3 More about Sensitivity
70(1)
3.4 A Simple Example
71(1)
3.5 System Behavior at DC
72(4)
3.6 Tracking Inputs of the Form tnu(t)
76(2)
3.7 Internal Stability
78(2)
3.8 Disturbance Rejection
80(1)
3.9 Exercises
81(6)
4 The Routh-Hurwitz Criterion 87(18)
4.1 Roots of Polynomials-A Little History
87(1)
4.2 Theorem, Proof, and Applications
88(9)
4.3 A Design Example
97(4)
4.4 Exercises
101(4)
5 The Principle of the Argument and Its Consequences 105(46)
5.1 More about Poles in the Right Half Plane
105(1)
5.2 The Principle of the Argument
106(1)
5.3 The Proof of the Principle of the Argument
107(2)
5.4 How are Encirclements Measured?
109(3)
5.5 First Applications to Control Theory
112(2)
5.6 Systems with Low-Pass Open-Loop Transfer Functions
114(6)
5.7 MATLAB® and Nyquist Plots
120(1)
5.8 The Nyquist Plot and Delays
121(4)
5.9 Delays and the Routh-Hurwitz Criterion
125(2)
5.10 Relative Stability
127(5)
5.11 The Bode Plots
132(1)
5.12 An (Approximate) Connection between Frequency Specifications and Time Specification
133(3)
5.13 Some More Examples
136(7)
5.14 Exercises
143(8)
6 The Root Locus Diagram 151(42)
6.1 The Root Locus-An Introduction
151(2)
6.2 Rules for Plotting the Root Locus
153(15)
6.2.1 The Symmetry of the Root Locus
153(1)
6.2.2 Branches on the Real Axis
154(1)
6.2.3 The Asymptotic Behavior of the Branches
155(3)
6.2.4 Departure of Branches from the Real Axis
158(5)
6.2.5 A "Conservation Law"
163(1)
6.2.6 The Behavior of Branches as They Leave Finite Poles or Enter Finite Zeros
164(2)
6.2.7 A Group of Poles and Zeros Near the Origin
166(2)
6.3 Some (Semi-)Practical Examples
168(16)
6.3.1 The Effect of Zeros in the Right Half-Plane
168(1)
6.3.2 The Effect of Three Poles at the Origin
169(1)
6.3.3 The Effect of Two Poles at the Origin
169(2)
6.3.4 A System that Tracks t sin(t)
171(3)
6.3.5 Variations on Our Theme
174(2)
6.3.6 The Effect of a Delay on the Root Locus Plot
176(3)
6.3.7 The Phase-lock Loop
179(3)
6.3.8 Sounding a Cautionary Note-Pole-Zero Cancellation
182(2)
6.4 More on the Behavior of the Roots of Q (s) I K + P(s) = 0
184(2)
6.5 Exercises
186(7)
7 Compensation 193(54)
7.1 Compensation-An Introduction
193(1)
7.2 The Attenuator
193(1)
7.3 Phase-Lag Compensation
194(7)
7.4 Phase-Lead Compensation
201(5)
7.5 Lag-Lead Compensation
206(1)
7.6 The PID Controller
207(7)
7.7 An Extended Example
214(8)
7.7.1 The Attenuator
215(1)
7.7.2 The Phase-Lag Compensator
215(2)
7.7.3 The Phase-Lead Compensator
217(2)
7.7.4 The Lag-Lead Compensator
219(2)
7.7.5 The PD Controller
221(1)
7.8 The Ziegler-Nichols Rules
222(8)
7.8.1 Introduction
222(1)
7.8.2 The Assumption
223(1)
7.8.3 Characterizing the Plant
224(2)
7.8.4 A Partial Verification
226(2)
7.8.5 Estimating the System's Phase Margin
228(1)
7.8.6 Estimating the System's Gain Margin
228(1)
7.8.7 Estimating the System's Settling Time
229(1)
7.9 Bode's Sensitivity Integrals
230(11)
7.9.1 Introduction
230(1)
7.9.2 The Sensitivity Function
230(1)
7.9.3 Bode's Sensitivity Integrals
230(1)
7.9.4 Case I
231(2)
7.9.5 Case II
233(1)
7.9.6 Case III
234(2)
7.9.7 Case IV
236(3)
7.9.8 Available Bandwidth
239(1)
7.9.9 Open-Loop Unstable Systems with Limited Available Bandwidth
240(1)
7.10 Exercises
241(6)
8 Some Nonlinear Control Theory 247(24)
8.1 Introduction
247(1)
8.2 The Describing Function Technique
248(12)
8.2.1 The Describing Function Concept
248(3)
8.2.2 Predicting Limit Cycles
251(1)
8.2.3 The Stability of Limit Cycles
252(3)
8.2.4 More Examples
255(3)
8.2.4.1 A Nonlinear Oscillator
255(1)
8.2.4.2 A Comparator with a Dead Zone
256(1)
8.2.4.3 A Simple Quantizer
257(1)
8.2.5 Graphical Method
258(2)
8.3 Tsypkin's Method
260(5)
8.4 The Tsypkin Locus and the Describing Function Technique
265(2)
8.5 Exercises
267(4)
9 An Introduction to Modern Control 271(32)
9.1 Introduction
271(1)
9.2 The State Variables Formalism
271(2)
9.3 Solving Matrix Differential Equations
273(1)
9.4 The Significance of the Eigenvalues of the Matrix
274(2)
9.5 Poles and Eigenvalues
276(1)
9.6 Inhomogeneous Matrix Differential Equations
277(1)
9.7 The Cayley-Hamilton Theorem
278(1)
9.8 Controllability
279(1)
9.9 Pole Placement
280(1)
9.10 Observability
281(2)
9.11 Observer Design
283(2)
9.12 Choosing States When a System is Characterized by an ODE
285(1)
9.13 Converting Transfer Functions to State Equations
286(3)
9.14 Examples
289(8)
9.14.1 Pole Placement
289(1)
9.14.2 Adding an Integrator
290(2)
9.14.3 Modern Control Using MATLAB®
292(1)
9.14.4 A System that is not Observable
293(1)
9.14.5 A Second System that is not Observable
294(1)
9.14.6 A System that is neither Observable nor Controllable
295(1)
9.14.7 Designing an Observer
296(1)
9.15 Some Technical Results about Series of Matrices
297(2)
9.16 Exercises
299(4)
10 Control of Hybrid Systems 303(44)
10.1 Introduction
303(1)
10.2 The Definition of the Z-Transform
303(1)
10.3 Some Examples
304(1)
10.4 Properties of the Z-Transform
305(4)
10.5 Sampled-data Systems
309(1)
10.6 The Sample-and-Hold Element
310(2)
10.7 The Delta Function and its Laplace Transform
312(1)
10.8 The Ideal Sampler
313(1)
10.9 The Zero-Order Hold
313(1)
10.10 Calculating the Pulse Transfer Function
314(4)
10.11 Using MATLAB® to Perform the Calculations
318(2)
10.12 The Transfer Function of a Discrete-Time System
320(1)
10.13 Adding a Digital Compensator
321(2)
10.14 Stability of Discrete-Time Systems
323(2)
10.15 A Condition for Stability
325(3)
10.16 The Frequency Response
328(2)
10.17 A Bit about Aliasing
330(1)
10.18 The Behavior of the System in the Steady-State
330(1)
10.19 The Bilinear Transform
331(5)
10.20 The Behavior of the Bilinear Transform as T -> 0
336(1)
10.21 Digital Compensators
337(3)
10.22 When Is There No Pulse Transfer Function?
340(1)
10.23 An Introduction to The Modified Z-Transform
341(2)
10.24 Exercises
343(4)
11 Answers to Selected Exercises 347(80)
11.1
Chapter 1
347(5)
11.1.1 Exercise 1
347(1)
11.1.2 Exercise 3
348(1)
11.1.3 Exercise 5
349(1)
11.1.4 Exercise 7
350(1)
11.1.5 Exercise 9
350(1)
11.1.6 Exercise 11
351(1)
11.2
Chapter 2
352(5)
11.2.1 Exercise 1
352(1)
11.2.2 Exercise 3
352(2)
11.2.3 Exercise 5
354(1)
11.2.4 Exercise 7
355(1)
11.2.5 Exercise 9
356(1)
11.2.6 Exercise 11
356(1)
11.3
Chapter 3
357(4)
11.3.1 Exercise 1
357(1)
11.3.2 Exercise 3
358(1)
11.3.3 Exercise 5
359(1)
11.3.4 Exercise 7
359(1)
11.3.5 Exercise 9
360(1)
11.3.6 Exercise 11
360(1)
11.3.7 Exercise 13
360(1)
11.4
Chapter 4
361(5)
11.4.1 Exercise 1
361(1)
11.4.2 Exercise 3
362(1)
11.4.3 Exercise 5
363(1)
11.4.4 Exercise 7
363(1)
11.4.5 Exercise 9
364(1)
11.4.6 Exercise 11
365(1)
11.4.7 Exercise 13
366(1)
11.5
Chapter 5
366(19)
11.5.1 Exercise 1
366(3)
11.5.2 Exercise 3
369(1)
11.5.3 Exercise 5
370(1)
11.5.4 Exercise 7
371(1)
11.5.5 Exercise 9
371(1)
11.5.6 Exercise 11
372(1)
11.5.7 Exercise 13
373(1)
11.5.8 Exercise 15
374(1)
11.5.9 Exercise 17
375(4)
11.5.10 Exercise 19
379(2)
11.5.11 Exercise 21
381(2)
11.5.12 Exercise 23
383(2)
11.6
Chapter 6
385(13)
11.6.1 Exercise 1
385(1)
11.6.2 Exercise 3
386(1)
11.6.3 Exercise 5
387(2)
11.6.4 Exercise 7
389(1)
11.6.5 Exercise 9
390(2)
11.6.6 Exercise 11
392(3)
11.6.7 Exercise 13
395(1)
11.6.8 Exercise 15
395(2)
11.6.9 Exercise 17
397(1)
11.7
Chapter 7
398(13)
11.7.1 Exercise 1
398(2)
11.7.2 Exercise 3
400(2)
11.7.3 Exercise 5
402(1)
11.7.4 Exercise 7
403(3)
11.7.5 Exercise 9
406(1)
11.7.6 Exercise 11
407(1)
11.7.7 Exercise 13
408(1)
11.7.8 Exercise 15
409(1)
11.7.9 Exercise 17
410(1)
11.8
Chapter 8
411(5)
11.8.1 Exercise 1
411(3)
11.8.2 Exercise 3
414(1)
11.8.3 Exercise 5
415(1)
11.8.4 Exercise 7
415(1)
11.9
Chapter 9
416(5)
11.9.1 Exercise 1
416(1)
11.9.2 Exercise 3
416(1)
11.9.3 Exercise 4
417(1)
11.9.4 Exercise 5
417(1)
11.9.5 Exercise 6
418(1)
11.9.6 Exercise 7
419(1)
11.9.7 Exercise 11
419(1)
11.9.8 Exercise 13
420(1)
11.9.9 Exercise 15
420(1)
11.10
Chapter 10
421(6)
11.10.1 Exercise 4
421(1)
11.10.2 Exercise 10
421(1)
11.10.3 Exercise 13
422(1)
11.10.4 Exercise 16
423(1)
11.10.5 Exercise 17
424(1)
11.10.6 Exercise 19
425(2)
Bibliography 427(2)
Index 429
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