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E-raamat: Robust Control: Youla Parameterization Approach

(University of California, Davis, CA), (University of California, Davis, CA)
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  • Ilmumisaeg: 28-Jan-2022
  • Kirjastus: Wiley-ASME Press
  • Keel: eng
  • ISBN-13: 9781119500308
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Robust Control: Youla Parameterization ApproachSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Wiley-ASME Press Series
  • Ilmumisaeg: 28-Jan-2022
  • Kirjastus: Wiley-ASME Press
  • Keel: eng
  • ISBN-13: 9781119500308
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Discover efficient methods for designing robust control systems 

In Robust Control: Youla Parameterization Approach, accomplished engineers Dr. Farhad Assadian and Kevin R. Mallon deliver an insightful treatment of robust control system design that does not require a theoretical background in controls. The authors connect classical control theory to modern control concepts using the Youla method and offer practical examples from the automotive industry for designing control systems with the Youla method. 

The book demonstrates that feedback control can be elegantly designed in the frequency domain using the Youla parameterization approach. It offers deep insights into the many practical applications from utilizing this technique in both Single Input Single Output (SISO) and Multiple Input Multiple Output (MIMO) design. Finally, the book provides an estimation technique using Youla parameterization and controller output observer for the first time. 

Robust Control offers readers: 

  • A thorough introduction to a review of the Laplace Transform, including singularity functions and transfer functions 
  • Comprehensive explorations of the response of linear, time-invariant, and dynamic systems, as well as feedback principles and feedback design for SISO 
  • Practical discussions of norms and feedback systems, feedback design by the optimization of closed-loop norms, and estimation design for SISO using the parameterization approach 
  • In-depth examinations of MIMO control and multivariable transfer function properties 

Perfect for industrial researchers and engineers working with control systems, Robust Control: Youla Parameterization Approach is also an indispensable resource for graduate students in mechanical, aerospace, electrical, and chemical engineering. 

Preface xv
Acknowledgments xix
Introduction xxi
About the Companion Website xxix
Part I Control Design Using Youla Parameterization: Single Input Single Output (SISO)
1(204)
1 Review of the Laplace Transform
3(22)
1.1 The Laplace Transform Concept
3(1)
1.2 Singularity Functions
3(4)
1.2.1 Definition of the Impulse Function
4(1)
1.2.2 The Impulse Function and the Riemann Integral
5(1)
1.2.3 The General Definition of Singularity Functions
5(1)
1.2.3.1 "Graphs" of Some Singularity Functions
5(2)
1.3 The Laplace Transform
7(6)
1.3.1 Definition of the Laplace Transform
7(1)
1.3.2 Laplace Transform Properties
8(1)
1.3.3 Shifting the Laplace Transform
8(2)
1.3.4 Laplace Transform Derivatives
10(2)
1.3.5 Transforms of Singularity Functions
12(1)
1.4 Inverse Laplace Transform
13(3)
1.4.1 Inverse Laplace Transformation by Heaviside Expansion
13(1)
1.4.1.1 Distinct Poles
13(1)
1.4.1.2 Distinct Poles with G(s) Being Proper
13(1)
1.4.1.3 Repeated Poles
14(2)
1.5 The Transfer Function and the State Space Representations (State Equations)
16(5)
1.5.1 The Transfer Function
16(1)
1.5.2 The State Equations
16(1)
1.5.3 Transfer Function Properties
17(1)
1.5.4 Poles and Zeros of a Transfer Function
18(1)
1.5.5 Physical Readability
19(2)
1.6 Problems
21(4)
2 The Response of Linear, Time-Invariant Dynamic Systems
25(36)
2.1 The Time Response of Dynamic Systems
25(18)
2.1.1 Final Value Theorem
25(1)
2.1.2 Initial Value Theorem
26(1)
2.1.3 Convolution and the Laplace Transform
27(2)
2.1.4 Transmission Blocking Response
29(2)
2.1.5 Stability
31(4)
2.1.6 Initial Values and Reverse Action
35(1)
2.1.7 Final Values and Static Gain
36(2)
2.1.8 Time Response Metrics
38(1)
2.1.8.1 First-Order System (Single-Pole Response)
38(1)
2.1.8.2 Second-Order System (Quadratic Factor)
39(2)
2.1.9 The Effect of Zeros on Transient Response
41(1)
2.1.10 The Butterworth Pattern
42(1)
2.2 Frequency Response of Dynamic Systems
43(12)
2.2.1 Steady-State Frequency Response of LTI systems
43(2)
2.2.2 Frequency Response Representation
45(1)
2.2.3 Frequency Response: The Real Pole
45(2)
2.2.4 Frequency Response: The Real Zero
47(2)
2.2.5 Frequency Response: The Quadratic Factor
49(1)
2.2.6 Frequency Response: Pure Time Delay
50(3)
2.2.7 Frequency Response: Static Gain
53(1)
2.2.8 Frequency Response: The Composite Transfer Function
53(1)
2.2.9 Frequency Response: Asymptote Formulas
54(1)
2.2.10 Physical Readability
54(1)
2.2.11 Non-minimum Phase, All-Pass, and Blaschke Factors
55(1)
2.3 Frequency Response Plotting
55(2)
2.3.1 Matlab Codes for Plotting System Frequency Response
56(1)
2.3.1.1 Bode Plot
56(1)
2.3.1.2 Polar Plot/Nyquist Diagram
56(1)
2.4 Problems
57(4)
3 Feedback Principals
61(34)
3.1 The Value of Feedback Control
62(2)
3.1.1 The Advantages of the Closed Loop
63(1)
3.2 Closed-Loop Transfer Functions
64(6)
3.2.1 The Return Ratio
65(1)
3.2.2 Closed-Loop Transfer Functions and the Return Difference
65(1)
3.2.3 Sensitivity, Complementary Sensitivity, and the Youla Parameter
66(4)
3.3 Well-Posedness and Internal Stability
70(6)
3.3.1 Well-Posedness
70(1)
3.3.2 The Internal Stability of Feedback Control
71(1)
3.3.2.1 The Closed-Loop Characteristic Equation and Closed-Loop Poles
72(1)
3.3.2.2 Closed-Loop Zeros
72(1)
3.3.2.3 Pole-Zero Cancellation and The Internal Stability of Feedback Control
73(3)
3.4 The Youla Parameterization of all Internally Stabilizing Compensators
76(4)
3.5 Interpolation Conditions
80(3)
3.6 Steady-State Error
83(1)
3.7 Feedback Design, and Frequency Methods: Input Attenuation and Robustness
83(7)
3.7.1 The Frequency Paradigm
84(1)
3.7.2 Input Attenuation and Command Following
84(1)
3.7.3 Bode Measures of Performance Robustness
85(3)
3.7.4 Graphical Interpretation of Return, Sensitivity, and Complementary Sensitivity
88(1)
3.7.5 Weighting Factors and Performance Robustness
89(1)
3.8 The Saturation Constraints
90(3)
3.8.1 Bandwidth and Response Time
90(1)
3.8.2 The Youla Parameter and Saturation
91(2)
3.9 Problems
93(2)
4 Feedback Design For SISO: Shaping and Parameterization
95(34)
4.1 Closed-Loop Stability Under Uncertain Conditions
95(8)
4.1.1 Harmonic Consistency
95(1)
4.1.2 Nyquist Stability Criterion: Heuristic Justification
96(2)
4.1.3 Stability Margins and Stability Robustness
98(1)
4.1.4 Margins, T(jω) and S(jω), and Hx Norms (Relationships Between Classical and Neoclassical Approaches)
99(2)
4.1.4.1 Neoclassical Approach
101(2)
4.2 Mathematical Design Constraints
103(1)
4.2.1 Sensitivity/Complementary Sensitivity Point-wise Constraints
103(1)
4.2.2 Sensitivity, Complementary Sensitivity, and Analytic Constraints
104(1)
4.2.2.1 Non-minimum Phase Constraints on Design
104(1)
4.3 The Neoclassical Approach to Internal Stability
104(2)
4.4 Feedback Design And Parameterization: Stable Objects
106(4)
4.4.1 Renormalization of Gains
108(1)
4.4.2 Shaping of the Closed-Loop: Stable SISO
108(1)
4.4.3 Neoclassical Design Principles
109(1)
4.5 Loop Shaping Using Youla Parameterization
110(6)
4.5.1 LHP Zeros of Gp
111(1)
4.5.2 Non-minimum Phase Zeros
112(2)
4.5.3 LHP Poles of Gp
114(1)
4.5.4 Unstable Poles
115(1)
4.6 Design Guidelines
116(1)
4.7 Design Examples
117(8)
4.8 Problems
125(4)
5 Norms of Feedback Systems
129(20)
5.1 The Laplace and Fourier Transform
129(5)
5.1.1 The Inverse Laplace Transform
129(2)
5.1.2 Parseval's Theorem
131(1)
5.1.3 The Fourier Transform
132(1)
5.1.3.1 Properties of the Fourier Transform
133(1)
5.1.3.2 Inverse Fourier Transformation By Heaviside Expansion
133(1)
5.2 Norms of Signals and Systems
134(6)
5.2.1 Signal Norms
134(1)
5.2.1.1 Particular Norms
135(1)
5.2.1.2 Properties of Norms
136(1)
5.2.2 Norms of Dynamic Systems
137(1)
5.2.3 Input-Output Norms
138(1)
5.2.3.1 Transient Inputs (Energy Bounded)
138(1)
5.2.3.2 Persistent Inputs (Energy Unbounded)
139(1)
5.3 Quantifying Uncertainty
140(7)
5.3.1 The Characterization of Uncertainty in Models
140(1)
5.3.2 Weighting Factors and Stability Robustness
141(1)
5.3.3 Robust Stability (Complementary Sensitivity) and Uncertainty
142(3)
5.3.4 Sensitivity and Performance"
145(1)
5.3.5 Performance and Stability
146(1)
5.4 Problems
147(2)
6 Feedback Design By the Optimization of Closed-Loop Norms
149(24)
6.1 Introduction
149(2)
6.1.1 Frequency Domain Control Design Approaches
150(1)
6.2 Optimization Design Objectives and Constraints
151(3)
6.2.1 Algebraic Constraints
151(1)
6.2.2 Analytic Constraints
152(1)
6.2.2.1 Nonminimum Phase Effect
152(1)
6.2.2.2 Bode Sensitivity Integral Theorem
153(1)
6.3 The Linear Fractional Transformation
154(2)
6.4 Setup for Loop-Shaping Optimization
156(4)
6.4.1 Setup for Youla Parameter Loop Shaping
158(2)
6.5 H∞-norm Optimization Problem
160(3)
6.5.1 Solution to a Simple Optimization Problem
161(2)
6.6 H∞ Design
163(1)
6.7 H∞ Solutions Using Matlab Robust Control Toolbox for SISO Systems
164(4)
6.7.1 Defining Frequency Weights
164(4)
6.8 Problems
168(5)
7 Estimation Design for SISO Using Parameterization Approach
173(10)
7.1 Introduction
173(2)
7.2 Youla Controller Output Observer Concept
175(2)
7.3 The SISO Case
177(5)
7.3.1 Output and Feedthrough Matrices
178(1)
7.3.2 SISO Estimator Design
178(4)
7.4 Final Remarks
182(1)
8 Practical Applications
183(22)
8.1 Yaw Stability Control with Active Limited Slip Differential
183(12)
8.1.1 Model and Control Design
183(4)
8.1.2 Youla Control Design Using Hand Computation
187(1)
8.1.3 H∞ Control Design Using Loop-shaping Technique
188(7)
8.2 Vehicle Yaw Rate and Side-Slip Estimation
195(10)
8.2.1 Kalman Filters
195(1)
8.2.2 Vehicle Model - Nonlinear Bicycle Model with Pacejka Tire Model
196(1)
8.2.3 Linearizing the Bicycle Model
197(1)
8.2.4 Uncertainties
197(1)
8.2.5 State Estimation
198(1)
8.2.6 Youla Parameterization Estimator Design
198(2)
8.2.7 Simulation Results
200(1)
8.2.8 Robustness Test
201(1)
8.2.8.1 Vehicle Mass Variation
201(2)
8.2.8.2 Tire-road Coefficient of Friction
203(2)
Part II Control Design Using Youla Parametrization: Multi Input Multi Output (MIMO)
205(182)
9 Introduction to Multivariate Feedback Control
207(10)
9.1 Nonoptimal, Optimal, and Robust Control
207(3)
9.1.1 Nonoptimal Control Methods
208(1)
9.1.2 Optimal Control Methods
208(1)
9.1.3 Optimal Robust Control
209(1)
9.2 Review of the SISO Transfer Function
210(5)
9.2.1 Schur Complement
210(1)
9.2.2 Interpretation of Poles and Zeros of a Transfer Function
211(1)
9.2.2.1 Poles
211(1)
9.2.2.2 Zeros
212(1)
9.2.2.3 Transmission Blocking Zeros
213(2)
9.3 Basic Aspects of Transfer Function Matrices
215(1)
9.4 Problems
215(2)
10 Matrix Fractional Description
217(30)
10.1 Transfer Function Matrices
217(2)
10.1.1 Matrix Fraction Description
218(1)
10.2 Polynomial Matrix Properties
219(2)
10.2.1 Minimum-Degree Factorization
220(1)
10.3 Equivalency of Polynomial Matrices
221(1)
10.4 Smith Canonical Form
222(3)
10.5 Smith-McMillan Form
225(9)
10.5.1 Smith-McMillan Form
225(3)
10.5.2 MFD's and Their Relations to Smith-McMillan Form
228(1)
10.5.3 Computing an Irreducible (Coprime) Matrix Fraction Description
229(5)
10.6 MIMO Controllability and Observability
234(9)
10.6.1 State-Space Realization
235(1)
10.6.1.1 SISO System
235(1)
10.6.1.2 MIMO System
236(2)
10.6.2 Controllable Form of State-Space Realization of MIMO System
238(1)
10.6.2.1 Mathematical Details
239(4)
10.7 Straightforward Computational Procedures
243(2)
10.8 Problems
245(2)
11 Eigenvalues and Singular Values
247(20)
11.1 Eigenvalues and Eigenvectors
247(1)
11.2 Matrix Diagonalization
248(5)
11.2.1 Classes of Diagonalizable Matrices
250(3)
11.3 Singular Value Decomposition
253(4)
11.3.1 What is a Singular Value Decomposition?
254(1)
11.3.2 Orthonormal Vectors
255(2)
11.4 Singular Value Decomposition Properties
257(1)
11.5 Comparison of Eigenvalue and Singular Value Decompositions
258(4)
11.5.1 System Gain
259(3)
11.6 Generalized Singular Value Decomposition
262(3)
11.6.1 The Scalar Case
264(1)
11.6.2 Input and Output Spaces
264(1)
11.7 Norms
265(1)
11.7.1 The Spectral Norm
265(1)
11.8 Problems
266(1)
12 MIMO Feedback Principals
267(18)
12.1 Mutlivariable Closed-Loop Transfer Functions
267(3)
12.1.1 Transfer Function Matrix, From r to y
265(3)
12.1.2 Transfer Function Matrix From dy to y As Shown in Figure 12.1
268(1)
12.1.3 Transfer Function Matrix From r to e
269(1)
12.1.4 Transfer Function From r to u
269(1)
12.1.5 Realization Tricks
270(1)
12.2 Well-Posedness of MIMO Systems
270(1)
12.3 State Variable Compositions
271(2)
12.4 Nyquist Criterion for MIMO Systems
273(3)
12.4.1 Characteristic Gains
273(1)
12.4.2 Poles and Zeros
274(1)
12.4.3 Internal Stability
275(1)
12.5 MIMO Performance and Robustness Criteria
276(2)
12.6 Open-Loop Singular Values
278(3)
12.6.1 Crossover Frequency
279(1)
12.6.2 Bandwidth Constraints
280(1)
12.7 Condition Number and its Role in MIMO Control Design
281(1)
12.7.1 Condition Numbers and Decoupling
281(1)
12.7.2 Role of Tu and Su in MIMO Feedback Design
282(1)
12.8 Summary of Requirements
282(1)
12.8.1 Closed-Loop Requirements
282(1)
12.8.2 Open-Loop Requirements
283(1)
12.9 Problems
283(2)
13 Youla Parameterization for Feedback Systems
285(18)
13.1 Neoclassical Control for MIMO Systems
285(1)
13.1.1 Internal Model Control
285(1)
13.2 MIMO Feedback Control Design for Stable Plants
286(1)
13.2.1 Procedure to Find the MIMO Controller, Gc
287(1)
13.2.2 Interpolation Conditions
287(1)
13.3 MIMO Feedback Control Design Examples
287(7)
13.3.1 Summary of Closed-Loop Requirements
290(1)
13.3.2 Summary of Open-Loop Requirements
290(4)
13.4 MIMO Feedback Control Design: Unstable Plants
294(7)
13.4.1 The Proposed Control Design Method
294(6)
13.4.2 Another Approach for MIMO Controller Design
300(1)
13.5 Problems
301(2)
14 Norms of Feedback Systems
303(16)
14.1 Norms
303(4)
14.1.1 Signal Norms, the Discrete Case
303(1)
14.1.2 System Norms
304(1)
14.1.3 The H2,-Norm
305(1)
14.1.4 The H∞-Norm
306(1)
14.2 Linear Fractional Transformations (LFT)
307(2)
14.3 Linear Fractional Transformation Explained
309(3)
14.3.1 LFTs in Control Design
310(2)
14.4 Modeling Uncertainties
312(11)
14.4.1 Uncertainties
312(1)
14.4.2 Descriptions of Unstructured Uncertainty
312(11)
14.5 General Robust Stability Theorem
323(3)
14.5.1 SVD Properties Applied
314(1)
14.5.2 Robust Performance
315(1)
14.6 Problems
316(3)
15 Optimal Control in MIMO Systems
319(1)
15.1 Output Feedback Control
319(1)
15.1.1 LQG Control
320(2)
15.1.2 Kalman Filter
322(1)
15.1.3 H∞ Control
323(1)
15.1.3.1 Kalman Filter Dynamic Model
324(1)
15.1.3.2 State Feedback
325(1)
15.2 Control Design
325(5)
15.2.1 State Feedback (Full Information) H∞ Control Design
327(2)
15.2.2 Filtering
329(1)
15.3 H∞ Robust Optimal Control
330(2)
15.4 Problems
332(3)
16 Estimation Design for MIMO Using Parameterization Approach
335(10)
16.1 YCOO Concept for MIMO
335(2)
16.2 MIMO Estimator Design
337(1)
16.3 State Estimation
338(1)
16.3.1 First Decoupled System (Gsm1)
338(1)
16.3.2 Second Decoupled System (Gsm2)
338(1)
16.3.3 Coupled System
339(1)
16.4 Applications
339(5)
16.4.1 States Estimation: Four States
340(1)
16.4.2 Input Estimation: Skyhook Based Control
341(1)
16.4.3 Input Estimation: Road Roughness
342(2)
16.5 Final Remarks
344(1)
17 Practical Applications
345(42)
17.1 Active Suspension
345(11)
17.1.1 Model and Control Design
345(3)
17.1.2 MIMO Youla Control Design
348(2)
17.1.3 H∞ Control Design Technique
350(1)
17.1.4 Uncertain Actuator Model
351(1)
17.1.5 Design Setup
351(3)
17.1.6 Simulation Results
354(2)
17.1.7 Robustness Test: Actuator Model Variations
356(1)
17.2 Advanced Engine Speed Control for Hybrid Vehicles
356(8)
17.2.1 Diesel Hybrid Electric Vehicle Model
357(2)
17.2.2 MISO Youla Control Design
359(1)
17.2.3 First Youla Method
359(1)
17.2.4 Second Youla Method
360(1)
17.2.5 H∞ Control Design
360(2)
17.2.6 Simulation Results
362(1)
17.2.7 Robustness Test
363(1)
17.3 Robust Control for the Powered Descent of a Multibody Lunar Landing System
364(10)
17.3.1 Multibody Dynamics Model
365(1)
17.3.2 Trajectory Optimization
366(1)
17.3.3 MIMO Youla Control Design
367(4)
17.3.4 Youla Method for Under-Actuated Systems
371(3)
17.4 Vehicle Yaw Rate and Sideslip Estimation
374(13)
17.4.1 Background
375(1)
17.4.2 Vehicle Modeling
376(1)
17.4.2.1 Nonlinear Bicycle Model With Pacejka Tire Model
376(1)
17.4.2.2 Kinematic Relationship
376(1)
17.4.2.3 Multi-Input Model
377(1)
17.4.2.4 Linearizing the Bicycle Model for SISO and MIMO Cases
378(1)
17.4.3 State Estimation
378(1)
17.4.3.1 Youla Parameterization Control Design
378(1)
17.4.4 Simulation and Estimation Result
379(3)
17.4.5 Robustness Test
382(1)
17.4.5.1 Vehicle mass variation
382(1)
17.4.5.2 Tire-road coefficient of friction
382(1)
17.4.6 Sensor Bias
382(4)
17.4.7 Final Remarks
386(1)
A Cauchy Integral
387(16)
A.1 Contour Definitions
387(1)
A.2 Contour Integrals
388(1)
A.3 Complex Analysis Definitions
389(1)
A.4 Cauchy-Riemann Conditions
390(2)
A.5 Cauchy Integral Theorem
392(2)
A.5.1 Terminology
394(1)
A.6 Maximum Modulus Theorem
394(2)
A.7 Poisson Integral Formula
396(2)
A.8 Cauchy's Argument Principle
398(2)
A.9 Nyquist Stability Criterion
400(3)
B Singular Value Properties
403(4)
B.1 Spectral Norm Proof
403(1)
B.2 Proof of Bounded Eigenvalues
404(1)
B.3 Proof of Matrix Inequality
404(2)
B.3.1 Upper Bound
405(1)
B.3.2 Lower Bound
405(1)
B.3.3 Combined Inequality
406(1)
B.4 Triangle Inequality
406(1)
B.4.1 Upper Bound
406(1)
B.4.2 Lower Bound
406(1)
B.4.3 Combined Inequality
406(1)
C Bandwidth
407(10)
C.1 Introduction
407(1)
C.2 Information as a Precise Measure of Bandwidth
408(2)
C.2.1 Neoclassical Feedback Control
408(1)
C.2.2 Defining a Measure to Characterize the Usefulness of Feedback
408(1)
C.2.3 Computation of New Bandwidth
409(1)
C.3 Examples
410(4)
C.4 Summary
414(3)
D Example Matlab Code
417(8)
D.1 Example 1
417(2)
D.2 Example 2
419(1)
D.3 Example 3
420(2)
D.4 Example 4
422(3)
References 425(2)
Index 427
Farhad Assadian, PhD, is Professor of Dynamic Systems and Control in the Department of Mechanical and Aerospace Engineering at the University of California, Davis. He teaches courses on dynamics, modelling and simulation, and control theory.

Kevin R. Mallon is a PhD student in the Department of Mechanical and Aerospace Engineering at the University of California, Davis. He previously worked as a robotics engineer at Intelligrated Systems.
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