Classical Control Using H

by Helton, J. William; Merino, Orlando; Society for Industrial and Applied Mathematics

• ISBN13: 9780898714241
• ISBN10: 0898714249
• Format: Paperback
• Copyright: 1998-07-01
• Publisher: Society for Industrial & Applied

Summary

One of the main accomplishments of control in the 1980s was the development of H8 techniques. This book teaches control system design using H8 methods. Students will find this book easy to use because it is conceptually simple. They will find it useful because of the widespread appeal of classical frequency domain methods. Classical control has always been presented as trial and error applied to specific cases; Helton and Merino provide a much more precise approach. This has the tremendous advantage of converting an engineering problem to one that can be put directly into a mathematical optimization package. After completing this course, students will be familiar with how engineering specs are coded as precise mathematical constraints.

Table of Contents

Preface	ix
I Short Design Course	1	(62)
A Method for Solving System Design Problems	3	(8)
Rational functions	3	(1)
The closed-loop system S	4	(2)
Designable transfer function	6	(1)
A system design problem	6	(1)
The method	7	(2)
Exercises	9	(2)
Internal Stability	11	(6)
Control and stability	11	(2)
Interpolation	13	(2)
Systems with a stable plant	15	(1)
Exercise	16	(1)
Frequency Domain Performance Requirements	17	(18)
Introduction	17	(2)
The closed-loop system S	17	(1)
Frequency domain performance requirements	18	(1)
Disk inequalities	18	(1)
Measures of performance	19	(6)
Gain-phase margin	19	(2)
Tracking error	21	(1)
Bandwidth	22	(1)
Closed-loop roll-off	23	(1)
Fundamental trade-offs	24	(1)
Choosing sets of performance requirements	24	(1)
Piecing together disk inequalities	25	(2)
More performance measures	27	(5)
Peak magnitude	27	(1)
Compensator bound	27	(1)
Plant bound	28	(1)
Disturbance rejection	29	(1)
More on tracking error	30	(1)
Tracking and type n plants	31	(1)
A fully constrained problem	32	(3)
Optimization	35	(12)
Review of concepts	35	(1)
Generating a performance function	36	(2)
Finding T with best performance	38	(2)
Example	39	(1)
Acceptable performance functions	40	(3)
Performance not of the circular type	43	(1)
Optimization	44	(1)
The optimization problem OPTI	44	(1)
Internal stability and optimization	45	(1)
The optimization problem OPT	45	(1)
OPT with circular Λ	45	(1)
Exercises	46	(1)
A Design Example with OPTDesign	47	(16)
Introduction	47	(1)
The problem	47	(3)
Optimization with OPTDesign	50	(2)
Producing a rational compensator	52	(2)
How good is the answer?	54	(4)
More on plots and functions	56	(2)
Optimality diagnostics	58	(1)
Specifying compensator roll-off	58	(1)
Reducing the numerical error	59	(1)
Rational Fits	60	(1)
Exercises	61	(2)
II More on Design	63	(50)
Examples	65	(36)
Numerical practicalities	65	(4)
Sampling functions on the j axis	66	(1)
Discontinuous functions	67	(1)
Vanishing radius function	68	(1)
Performance function incorrectly defined	69	(1)
Design example 1	69	(12)
Electro-mechanical and electrical models	69	(2)
Mathematical model	71	(2)
Statement of the problem	73	(1)
Reformulation of requirements	73	(1)
Optimization	74	(4)
Second modification of the envelope and optimization	78	(3)
Time domain performance requirements	81	(4)
Two common time domain requirements	83	(1)
A native method	83	(2)
A refinement of the native method	85	(1)
Design example 2	85	(8)
Statement of the problem	86	(1)
Translation of time domain requirements	86	(7)
Performance for competing constraints	93	(8)
Rounding corners of performance functions	94	(3)
Constrained optimization with a barrier method	97	(4)
Internal Stability II	101	(12)
Calculating interpolants	101	(4)
Calculating one interpolant	102	(1)
Parameterization of all interpolants	103	(1)
Interpolation with a relative degree condition	104	(1)
Plants with simple RHP zeros and poles	105	(2)
Parameterization: The general case	107	(3)
Higher-order interpolation	107	(2)
Plants with high-multiplicity RHP zeros and poles	109	(1)
Exercises	110	(3)
III Appendices	113	(46)
A History and Perspective	115	(4)
B Downloading OPTDesign and Anopt	119	(2)
C Computer Code for Example in Chapter 6	121	(6)
C.1 Computer code for design example 1	121	(3)
C.2 Computer code for design example 2	124	(3)
D Anopt Notebook	127	(10)
D.1 Foreword	127	(1)
D.2 Optimizing in the sup norm: The problem OPT	128	(1)
D.3 Example 1: First run	128	(3)
D.4 Example 2: Vector-valued analytic functions	131	(1)
D.5 Example 3: Specification of more input	132	(3)
D.6 Quick reference for Anopt	135	(2)
E NewtonInterpolant Notebook	137	(6)
E.1 First calculation of an interpolant	138	(1)
E.2 Specifying the pole location	138	(1)
E.3 Specifying of the relative degree	139	(1)
E.4 Complex numbers as data	139	(1)
E.5 Higher-order interpolation	140	(3)
F NewtonFit Notebook	143	(8)
F.1 First example	144	(3)
F.2 Template for many runs	147	(1)
F.3 Using a weight	147	(1)
F.4 Stable zeros and poles	148	(3)
G OPTDesign Plots, Data, and Functions	151	(8)
G.1 Functions and grids	151	(2)
G.2 Plots	153	(3)
G.3 Rational approximation and model reduction	156	(3)
References	159	(10)
Index	169