Identification and Control Using Volterra Models

by Doyle, F. J.; Pearson, Ronald K.; Ogunnaike, Babatunde A.

• ISBN13: 9781852331498
• ISBN10: 1852331496
• Format: Hardcover
• Copyright: 2001-12-01
• Publisher: Springer Verlag

Summary

This text covers recent results in the analysis, identification and control of systems described by Volterra models. Topics covered include:- qualitative behavior of finite Volterra models compared and contrasted with other nonlinear model classes- structural restrictions and extensions to Volterra model class - least squares and stochastic identification approaches - model inversion issues - direct synthesis and model predictive control design - guidelines for practical applicationsExamples are drawn from Chemical, Biological and Electrical Engineering. The book is suitable as a text for a graduate control course, or as a reference for both research and practice.

Table of Contents

Introduction	1	(16)
Motivation	3	(1)
Historical background	4	(2)
Continuous-time Volterra models	6	(3)
Discrete-time models	9	(5)
Organization of the rest of the book	14	(3)
Qualitative Behavior	17	(30)
The class V(N, M) of finite Volterra models	17	(4)
Parameterization of Volterra models	18	(2)
Interconnection of Volterra models	20	(1)
Important subclasses of V(N, M)	21	(7)
Hammerstein models	22	(1)
Wiener models	23	(2)
Uryson models	25	(2)
Projection-pursuit models	27	(1)
Qualitative characterization of V(N, M)	28	(7)
Responses to periodic inputs	29	(1)
Steady-state behavior of V(N, M) models	30	(3)
Preservation of asymptotic constancy	33	(1)
BIBO stability of NMAX models	34	(1)
Infinite-dimensional Volterra models	35	(6)
The class V(∞, M)	36	(1)
The class V(N, ∞)	37	(3)
The class V(∞, ∞)	40	(1)
Approximation issues	41	(3)
Summary	44	(3)
Restrictions & Extensions	47	(32)
Second-order Volterra models	49	(6)
Connections with the bispectrum	50	(2)
Some applications of second-order models	52	(3)
Third-order Volterra models	55	(4)
Connections with the trispectrum	56	(2)
Some applications of third-order models	58	(1)
Applications of higher-order models	59	(2)
Hammerstein models	61	(3)
Wiener models	64	(2)
Other related model structures	66	(11)
Pruned Volterra models	66	(2)
Block-oriented models	68	(3)
Volterra-Laguerre models	71	(4)
AR-Volterra models	75	(2)
Summary	77	(2)
Determination of Volterra Model Parameters	79	(26)
Identification of general Volterra models	80	(3)
The problem in the time domain	80	(2)
The problem in the frequency domain	82	(1)
Second-order Volterra models	83	(7)
Third-order Volterra models	90	(1)
Hammerstein models	91	(4)
Wiener models	95	(3)
Other related models	98	(2)
Approximation of nonlinear continuous-time models	100	(3)
Summary	103	(2)
Practical Considerations in Volterra Model Identification	105	(58)
Model structure selection	106	(9)
Structure selection via behavior constraints	107	(3)
Structure selection via screening inputs	110	(5)
Noise and disturbance models	115	(3)
Input sequence design	118	(8)
General considerations	119	(2)
Input sequence design options	121	(5)
Data pretreatment	126	(6)
Model validation and refinement	132	(3)
Four brief case studies	135	(24)
Identification with IID inputs	136	(4)
Identification of simple V(∞, ∞) models	140	(5)
The influence of outliers	145	(5)
Approximate identification of a continuous-time model	150	(9)
Summary	159	(4)
Model-Based Controller Synthesis	163	(16)
Introduction	164	(3)
General concepts of nonlinear model-based control	164	(2)
The partitioned nonlinear model	166	(1)
Volterra model-based controller synthesis	167	(9)
Basic results	167	(1)
The ``standard'' approach	168	(3)
Controller synthesis using generalized inverses	171	(5)
Summary	176	(3)
Advanced Direct Synthesis Controller Design	179	(18)
Motivation	179	(2)
Nomenclature	181	(1)
Controller design	182	(12)
Feedforward compensation for constrained linear synthesis	182	(4)
Feedforward compensation for unconstrained nonlinear synthesis	186	(2)
Feedforward compensation for constrained nonlinear synthesis	188	(4)
Extensions for nonminimum phase synthesis	192	(2)
Summary	194	(3)
Model Predictive Control Using Volterra Series	197	(20)
Introduction	197	(1)
General nonlinear MPC problem	198	(1)
Model predictive controller formulations for Volterra models	199	(6)
Standard impulse response form	199	(1)
Dynamic matrix control	200	(1)
Generalized predictive control	201	(1)
State-space MPC	202	(2)
Impact of model structure on NLP structure	204	(1)
Numerical approaches to problem solution	205	(5)
Successive substitution	206	(3)
Quasi-Newton and related methods	209	(1)
Approximation solution methods	210	(1)
Stability analysis	210	(3)
Nominal stability	210	(3)
Robust stability and performance	213	(1)
Application of Volterra series model predictive control	213	(3)
Customized nonlinear MPC approaches	213	(1)
Volterra series systems	214	(1)
Wiener and Hammerstein systems	215	(1)
Summary	216	(1)
Application Case Studies	217	(70)
Van de Vusse CSTR	217	(5)
Process description	217	(2)
Volterra model-based IMC design	219	(3)
Isothermal polymerization reactor	222	(28)
Process description	222	(2)
Volterra IMC design	224	(6)
Volterra-Laguerre IMC design	230	(6)
Volterra MPC design	236	(5)
AR-Volterra MPC design	241	(9)
Multivariable polymerization reactor	250	(9)
Process description	250	(3)
Volterra MPC design	253	(3)
Remarks	256	(3)
Industrial polymerization reactor	259	(11)
Process description	259	(2)
AR-Volterra MPC controller design	261	(9)
Biochemical reactor	270	(17)
Process description	270	(7)
Volterra-Laguerre IMC and MPC design	277	(10)
Summary	287	(8)
Recap of key results	287	(1)
Promising areas for future research	288	(7)
Constrained Volterra models	288	(2)
Generalized Volterra models	290	(1)
Multivariable Volterra models	291	(1)
Inclusion of disturbance inputs	292	(3)
Bibliography	295	(16)
Index	311