Quantitative Feedback Design of Linear and Nonlinear Control Systems

by Yaniv, Oded

• ISBN13: 9780792385295
• ISBN10: 0792385292
• Format: Hardcover
• Copyright: 1999-06-01
• Publisher: Kluwer Academic Pub

Summary

Quantitative Feedback Design of Linear and Nonlinear Control Systems is a self-contained book dealing with the theory and practice of Quantitative Feedback Theory (QFT). The author presents feedback synthesis techniques for single-input single-output, multi-input multi-output linear time-invariant and nonlinear plants based on the QFT method. Included are design details and graphs which do not appear in the literature, which will enable engineers and researchers to understand QFT in greater depth. Engineers will be able to apply QFT and the design techniques to many applications, such as flight and chemical plant control, robotics, space, vehicle and military industries, and numerous other uses. All of the examples were implemented using Matlab® Version 5.3; the script file can be found at the author's Web site. QFT results in efficient designs because it synthesizes a controller for the exact amount of plant uncertainty, disturbances and required specifications. Quantitative Feedback Design of Linear and Nonlinear Control Systems is a pioneering work that illuminates QFT, making the theory - and practice - come alive.

Table of Contents

Foreword	xv	(2)
Preface	xvii	(2)
Acknowledgments	xix	(2)
Abbreviations Notation and Symbols	xxi
1. INTRODUCTION	1	(14)
1. Basic Components of Feedback Controlled Systems	1	(1)
2. Why Embed a Plant in a Feedback System?	2	(2)
3. The Design Process of Feedback Control Systems	4	(5)
4. Book Outline	9	(6)
Part I LINEAR SYSTEMS	15	(232)
2. BASICS OF SISO FEEDBACK CONTROLLED SYSTEMS	15	(44)
1. Introduction	15	(1)
2. Basic Frequency Domain Characteristics	15	(10)
2.1 Relative Stability, Cross-Over Frequency and Bandwidth	16	(1)
2.2 Conditionally Stable Systems	17	(1)
2.3 High Frequency Gain	18	(2)
2.4 Stability Analysis Using Nichols Charts	20	(1)
2.4.1 Continuous Systems	21	(1)
2.4.2 Discrete Time Systems	22	(3)
2.4.3 Some Remarks About the Nyquist Plot	25	(1)
3. Closed Loop Specifications	25	(9)
3.1 t-Domain Specification	26	(1)
3.2 Omega-Domain Specification	27	(2)
3.3 Translation of Specifications From t-Domain to Omega-Domain	29	(1)
3.3.1 Model Based Technique	30	(3)
3.3.2 Krishnan and Cruickshanks' Technique	33	(1)
4. Performance Limitations of NMP or Unstable Systems	34	(15)
4.1 Stable Plants	35	(2)
4.1.1 Extension to Several RHP Zeros and/or Delay	37	(3)
4.1.2 Comparison to Loop Transmissions Which Violate Assumption 2.1	40	(2)
4.2 Unstable Plants	42	(1)
4.2.1 Unstable Plants With a Single RHP Pole	43	(3)
4.2.2 An Example and Limitations	46	(1)
4.2.3 Extension to Several RHP Poles	47	(2)
5. Loop Shaping	49	(6)
6. Summary	55	(1)
7. Exercises	56	(1)
8. Notes and References	57	(2)
3. SYNTHESIS OF LTI CONTROLLERS FOR MISO LTI PLANTS	59	(34)
1. Introduction	59	(1)
2. One DOF System	59	(14)
2.1 Sensitivity Reduction Problem	61	(1)
2.2 Bound Calculations	62	(2)
2.3 Control Effort Problem	64	(1)
2.4 Examples	65	(8)
3. Two DOF Systems	73	(8)
3.1 Bound Calculations	75	(1)
3.1.1 Bound Calculations With The Aid of Plant Templates	75	(3)
3.1.2 Bound Calculations Using a Closed Form Algorithm	78	(2)
3.2 An Example	80	(1)
4. Extension to NMP Plants	81	(4)
5. Extension to Sampled Data Systems	85	(3)
6. Summary	88	(1)
7. Exercises	88	(2)
8. Notes and References	90	(3)
4. SYNTHESIS OF LTI CONTROLLERS FOR MIMO LTI PLANTS	93	(154)
1. Synthesis of One DOF Feedback Systems	94	(43)
1.1 2 X 2 Plants and Disturbances at the Plant's Inputs	95	(18)
1.2 2 X 2 Plants and Disturbances at the Plant's Outputs	113	(12)
1.3 n X n Plants and Disturbances at the Plant's Inputs	125	(9)
1.4 n X n Plants and Disturbances at the Plants' Outputs	134	(1)
1.5 Design Improvements by Iteration	135	(2)
1.6 Shortcuts in Low Frequency Bound Calculations	137	(1)
2. Synthesis of Two DOF Feedback Systems	137	(23)
2.1 2 X 2 Plants	139	(9)
2.2 n X n Plants	148	(9)
2.3 Model Matching Specifications	157	(1)
2.4 Shortcuts in Low Frequency Bound Calculations	158	(2)
3. Synthesis for Margins at the Plants' Outputs	160	(20)
3.1 2 x 2 Plants and Diagonal Controllers	163	(7)
3.2 n X n Plants and Diagonal Controllers	170	(10)
4. Synthesis for Margins at the Plants' Inputs	180	(6)
5. Synthesis of Non-diagonal Controllers for n X m Plants	186	(8)
6. Synthesis for Minimum Phase Diagonal Elements	194	(11)
6.1 2 X 2 Plants	196	(5)
6.2 n X n Plants	201	(4)
7. Synthesis for the General Control Problem Using LFT Notation	205	(7)
7.1 Some Special Cases	206	(2)
7.2 Statement of the Problem	208	(1)
7.3 Development of the Design Equations	209	(1)
7.3.1 Special Cases	210	(1)
7.4 A Design Procedure For The Stated Problems	211	(1)
8. Sensitivity Reduction Limitations and Tradeoffs in NMP Feedback Systems	212	(18)
8.1 SISO Plants	214	(3)
8.2 MIMO Plants	217	(1)
8.3 Sensitivity Reduction Limitations For a Single Row of S	217	(5)
8.4 Sensitivity Reduction Limitations For Several Rows of S	222	(3)
8.5 Necessary Conditions	225	(2)
8.6 A Design Example	227	(3)
9. Exercises	230	(7)
10. Appendix A	237	(1)
11. Appendix B	238	(1)
12. Appendix C	239	(1)
13. Appendix D	239	(1)
14. Appendix E	239	(1)
15. Summary	240	(1)
16. Notes and References	241	(6)
Part II NONLINEAR SYSTEMS	247	(120)
5. SYNTHESIS OF LTI CONTROLLERS FOR NONLINEAR SISO PLANTS	247	(34)
1. Synthesis for Tracking Specifications	247	(17)
1.1 The Schauder Technique	250	(3)
1.2 Guidelines for the Choice of P(N,y),d(N,y) and Theoretical Limitations	253	(1)
1.2.1 How to choose the pairs P(N,y),d(N,y)	253	(3)
1.2.2 Some Theoretical Limitations	256	(2)
1.3 The Homotopic Invariance Technique	258	(3)
1.4 An Example	261	(1)
1.4.1 Implementation of the Design Procedure -- A Four-Step Process	261	(3)
2. Synthesis for Zeroing the Plant Output	264	(14)
2.1 The Schauder Technique	267	(3)
2.2 Guidelines for the Choice of P(N,y),d(N,y) and Theoretical Limitations	270	(1)
2.2.1 How to choose the pairs P(N,y),d(N,y)	270	(4)
2.2.2 Some Theoretical Limitations	274	(1)
2.3 The Homotopic Invariance Technique	275	(1)
2.4 An Example	276	(1)
2.4.1 Implementation of the Design Procedure -- a Two-Step Process	276	(2)
3. Appendix A	278	(2)
4. Summary	280	(1)
5. Notes and References	280	(1)
6. SYNTHESIS OF LTV CONTROLLERS FOR NONLINEAR SISO PLANTS	281	(14)
1. Statement of the Problem	281	(2)
2. The Design Procedure	283	(3)
2.1 Guidelines for the Choice of P(N,y),d(N,y) and the Time Slices	284	(2)
3. An Example	286	(8)
3.1 Statement of the Problem	286	(2)
3.2 Single Time Slice Design	288	(2)
3.3 The Two Consecutive Time Slices Design	290	(1)
3.3.1 Design on the First Time Slice	290	(2)
3.3.2 Design on the Second Time Slice	292	(1)
3.4 Comparisons and Discussion	293	(1)
4. Summary	294	(1)
7. SYNTHESIS OF LTI CONTROLLERS FOR NONLINEAR MIMO PLANTS	295	(48)
1. Synthesis for Tracking Specifications	295	(19)
1.1 The Schauder Technique	299	(6)
1.2 Guidelines for Choosing of P(N,y),d(N,y) and Remarks	305	(3)
1.3 The Homotopic Invariance Technique	308	(2)
1.4 An Example	310	(4)
2. Synthesis for Zeroing the Plant Outputs	314	(12)
2.1 The Schauder Technique	317	(2)
2.2 Guidelines for Choosing P(N,y),d(N,y) and Remarks	319	(3)
2.3 The Homotopic Invariance Technique	322	(1)
2.4 An example	323	(3)
3. Synthesis of the MIMO LTI Problem	326	(11)
3.1 2 X 2 plants	328	(3)
3.1.1 A design Procedure With Less Stringent High Frequency Conditions	331	(1)
3.1.2 A Third Design Procedure	332	(1)
3.2 n X n Plants	332	(2)
3.2.1 A Design Procedure With Less Stringent High Frequency Conditions	334	(2)
3.2.2 A Third Design Procedure	336	(1)
4. Rational TF Approximations From Input Output Data	337	(4)
4.1 SISO Systems	338	(1)
4.2 MIMO systems	339	(2)
5. Summary	341	(1)
6. Notes and References	341	(2)
8. SYNTHESIS OF LTV CONTROLLERS FOR NONLINEAR MIMO PLANTS	343	(24)
1. Statement of the Problem	343	(1)
2. The Design Procedure	344	(3)
2.1 Guidelines for the Choice of P(N,y),d(N,y) and Time Slices	346	(1)
3. An Example	347	(7)
4. Notes	354	(13)
Index	367