Polynomial approach to nonlinear predictive generalized minimum variance control

M.J. Grimble, P.M. Majecki

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

A relatively simple approach to non-linear predictive generalised minimum variance (NPGMV) control is introduced for non-linear discrete-time multivariable systems. The system is represented by a combination of a stable non-linear subsystem where no structure is assumed and a linear subsystem that may be unstable and modelled in polynomial matrix form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The NPGMV control law involves an assumption on the choice of cost-function weights to ensure the existence of a stable non-linear closed-loop operator. A valuable feature of the control law is that in the asymptotic case, where the plant is linear, the controller reduces to a polynomial matrix version of the well known generalised predictive control (GPC) controller. In the limiting case when the plant is non-linear and the cost-function is single step the controller becomes equal to the polynomial matrix version of the so-called non-linear generalised minimum variance controller. The controller can be implemented in a form related to a non-linear version of the Smith predictor but unlike this compensator a stabilising control law can be obtained for open-loop unstable processes.
LanguageEnglish
Pages411-424
Number of pages14
JournalIET Control Theory and Applications
Volume4
Issue number3
DOIs
Publication statusPublished - 1 Mar 2010

Fingerprint

Generalized Variance
Minimum Variance
Polynomials
Polynomial
Polynomial Matrices
Controller
Controllers
Cost functions
Cost Function
Subsystem
Unstable
Smith Predictor
Generalized Predictive Control
Nonlinear Discrete-time Systems
Multivariable systems
Multivariable Systems
Predictive Control
Signal Control
Compensator
Closed-loop

Keywords

  • polynomial systems
  • optimal
  • predictive
  • nonlinear
  • minimum variance
  • transport delays

Cite this

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Polynomial approach to nonlinear predictive generalized minimum variance control. / Grimble, M.J.; Majecki, P.M.

In: IET Control Theory and Applications , Vol. 4, No. 3, 01.03.2010, p. 411-424.

Research output: Contribution to journalArticle

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