Relay Feedback

by Wang, Qing-Guo; Lee, Tong Heng; Chong, Lin

• ISBN13: 9781852336509
• ISBN10: 1852336501
• Format: Hardcover
• Copyright: 2002-12-01
• Publisher: Springer Nature

Summary

Relay feedback has attracted considerable research attention for more than a century but there has been no recent summary of the many newly-developed tools and results now available for this important area as a whole, those that have been published tending to focus on one process or controller type only. Relay Feedback is divided into three parts, the first of which is devoted to the analysis of relay feedback systems within a general setting with information on: existence of solutions; existence of limit cycles; local and global stability of limit cycles; limit cycles with more than two switchings per period; plants with time delay; relays with asymmetric hysteresis. The second part, on the improvement of process identification shows the reader how to: modify a standard relay to provide better excitation of a process at a number of important frequencies; devise new algorithms designed to make better use of information from relay feedback tests. The book's third part is a presentation of recent developments in control design providing: a unified framework for the design of internal-model, proportional-integral-derivative or general-single-loop controllers for SISO or MIMO systems with or without time delays; characterisation of time delays and non-minimum phase zeros for closed-loop systems. Relay Feedback presents a comprehensive, up-to-date and detailed treatment of relay feedback theory, the use of relay feedback for process identification and the use of identified models for general control design in a single volume. The work assumes only knowledge of linear system theory on the part of the reader and should therefore be of use to graduate students and practising engineers as well as to researchers.

Table of Contents

Part I. Analysis of Relay Feedback Systems
Existence of Solutions	5	(16)
Introduction	5	(1)
System Formulation	6	(2)
Existence of Solutions	8	(3)
Delay-free Case	11	(10)
Existence of Limit Cycles	21	(18)
Introduction	21	(1)
Sufficient Condition	22	(9)
Supporting Lemmas	22	(7)
Existence of Limit Cycles	29	(2)
A Simple Existence Condition	31	(5)
Limit Cycle Location	36	(3)
Local Stability of Limit Cycles	39	(18)
Introduction	39	(1)
Problem Formulation and Preliminaries	40	(1)
Local Stability of Limit Cycles	41	(12)
Extension	53	(4)
Global Stability of Limit Cycles	57	(32)
Introduction	57	(1)
Problem Formulation	58	(1)
Supporting Lemmas	59	(5)
Global Stability of Limit Cycles	64	(9)
Extensions	73	(4)
Existence of Globally Stable Limit Cycles	77	(12)
Preliminaries	77	(1)
Sufficient Conditions	78	(11)
Part II. Process Identification from Relay Feedback Test
Relay Feedback and its Variations	89	(46)
Fundamentals	89	(6)
First-order Modelling	95	(8)
Robustness Enhancement	103	(5)
Parasitic Relay	108	(7)
Cascade Relay	115	(11)
Extension to MIMO Case	126	(9)
Use of Relay Transient Responses	135	(34)
Signal Analysis	135	(5)
Decomposition Method	140	(6)
Weighting Method	146	(3)
Testing on Pilot Plants	149	(11)
Extension to the MIMO case	160	(9)
Transfer Function Modelling	169	(38)
From Frequency Response	170	(4)
From Step Response	174	(28)
Second-order Modelling	175	(5)
nth-order Modelling	180	(12)
Implementation Issues	192	(4)
Simulation and Real-time Test	196	(6)
A Hybrid Approach	202	(5)
A General Identification Approach	207	(32)
SISO Systems	208	(8)
The Method	208	(3)
Simulation	211	(5)
MIMO Systems	216	(14)
The Method	217	(8)
Simulation	225	(5)
Unstable Processes	230	(9)
Part III. Controller Design
Single-variable Systems	239	(34)
Design Methodology	240	(4)
PID Controller	244	(9)
High-order Controller	253	(2)
Stability Analysis	255	(6)
Unstable Processes	261	(12)
PID Controller	266	(3)
High-order Controller	269	(4)
Multivariable Systems	273	(46)
IMC Scheme	274	(22)
Decoupling	275	(5)
Analysis	280	(6)
Design	286	(3)
Simulation	289	(7)
Unity Feedback System	296	(23)
Design Methodology	296	(3)
PID Controller	299	(4)
High-order Controller	303	(8)
Stability Analysis	311	(8)
Partial Internal Model Control	319	(28)
Review of the IMC	320	(2)
The Proposed PIMC Scheme	322	(2)
Internal Stability Analysis	324	(2)
Asymptotic Tracking and Regulation	326	(3)
Primary Control Design	329	(2)
PIMC Primary Controller Design	329	(1)
MPIMC Primary Controller Design	330	(1)
Robustness Analysis	331	(2)
Robust Stability	331	(1)
Practical Stability	332	(1)
Practical Aspects	333	(3)
Pre-filter Design	333	(2)
Determination of G-	335	(1)
Dead Time	336	(1)
Simulation Results	336	(5)
Real-time Implementation	341	(6)
Appendix A: Controller Design for Processes with Two Unstable Poles	343	(2)
Appendix B: Formulas for Decomposition of some Typical Unstable Processes	345	(2)
Decentralized Control	347	(28)
The Proposed Independent Design Strategy	348	(3)
Choice of Solutions to Controller Gain Equations	351	(4)
Rational Approximation of the Irrational Solutions	355	(6)
Controller Reduction and Performance Trade-off	361	(5)
Stability Analysis	366	(3)
Extension to the m x m Case	369	(6)
References	375	(10)
Index	385