H/spl infin/ Control of Nonlinear Systems with Common Multi-channel Delays

A generalized Hinfin controller is derived for the control of nonlinear, possibly time-varying, multivariable systems with common output or input channel delays. A nonlinear generalized minimum variance (NGMV) controller has recently been proposed for plants modelled by a combination of linear and nonlinear subsystems, where the disturbance and reference models are linear. The aim in the following is to obtain a related controller but one which minimizes an Hinfin norm, to enable sensitivity functions to be shaped. The cost-function to be minimized involves both error and control signal costing terms, which are related to sensitivity and control sensitivity costing terms

[1]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[2]  Michael J. Grimble,et al.  H∞ robust controller for self-tuning control applications Part 2. Self-tuning and robustness , 1987 .

[3]  Michael J. Grimble.  H ∞ robust controller for self-tuning control applications Part 1. Controller design , 1987 .

[4]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[5]  H. Kwakernaak.  Minimax frequency domain performance and robustness optimization of linear feedback systems , 1985 .

[6]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[7]  D. W. Clarke,et al.  Design of digital controllers for randomly disturbed systems , 1971 .

[8]  H. Kwakernaak.  A polynomial approach to minimax frequency domain optimization of multivariable feedback systems , 1986 .

[9]  Michael J. Grimble,et al.  Optimal H∞ robustness and the relationship to LQG design problems , 1986 .

[10]  M. Grimble.  Non-linear generalized minimum variance feedback, feedforward and tracking control , 2005, Autom..

[11]  M. J. Grimble,et al.  A note on a compatriot of the real Marcinkiewicz space , 1981 .

[12]  A. Isidori.  Nonlinear Control Systems , 1985 .

[13]  H. Kwakernaak.  Minimax Frequency Domain Optimization of Multivariable Linear Feedback Systems , 1984 .

[14]  D. P. Goodall,et al.  Nonlinear Filters and Operators and the Constant-Gain Extended Kalman Filter , 1984 .

[15]  G. Siouris,et al.  Nonlinear Control Engineering , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  Michael J. Grimble,et al.  Generalized minimum variance control law revisited , 2007 .

[17]  Pawel Majecki,et al.  NONLINEAR GENERALIZED MINIMUM VARIANCE CONTROL UNDER ACTUATOR SATURATION , 2005 .

[18]  M. Grimble.  A control weighted minimum-variance controller for non-minimum phase systems , 1981 .

[19]  M. Safonov,et al.  SIMPLIFYING THE H" THEORY VIA LOOP SHIFTING* , 1988 .

[20]  Michael J. Grimble,et al.  Industrial Control Systems Design , 1994 .

[21]  Michael J. Grimble.  GMV control of nonlinear multivariable systems , 2004 .

[22]  M. J. Grimble.  H∞ multivariable-control-law synthesis , 1993 .