Non-linear generalised minimum variance control using unstable state-dependent multivariable models

Michael Grimble, Pawel Majeckie

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A non-linear generalised minimum variance (NGMV) control law is derived for systems represented by an input–output state dependent non-linear (NL) subsystem that may be open-loop unstable. The solution is obtained using a model for the multivariable discrete-time process that includes a state-dependent (NL and possibly unstable) model that links the output and any ‘unstructured’ NL input subsystem. The input subsystem can involve an operator of a very general NL form, but this has to be assumed to be stable. This is the first NGMV control solution that is suitable for systems containing an unstable NL sub-system which is contained in the state-dependent model. The process is also assumed to include explicit common delays in input or output channels. The generalised minimum variance cost index to be minimised involves both error and control Q1 signal costing terms but to increase generality weighted states are also included in the cost index. The controller derived is simple to implement considering the complexity of the system represented. If the plant is stable the controller structure can be manipulated into an internal model control form. This form of the controller is like an NL version of the Smith Predictor which is valuable for providing confidence in the solution.
LanguageEnglish
JournalIET Control Theory and Applications
DOIs
Publication statusAccepted/In press - 2013

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Generalized Variance
Minimum Variance
Unstable
Dependent
Controllers
Subsystem
Controller
Model
Costs
Output
Smith Predictor
Internal Model Control
Signal Control
Confidence
Discrete-time

Keywords

  • minimum variance control
  • multivariable models

Cite this

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N2 - A non-linear generalised minimum variance (NGMV) control law is derived for systems represented by an input–output state dependent non-linear (NL) subsystem that may be open-loop unstable. The solution is obtained using a model for the multivariable discrete-time process that includes a state-dependent (NL and possibly unstable) model that links the output and any ‘unstructured’ NL input subsystem. The input subsystem can involve an operator of a very general NL form, but this has to be assumed to be stable. This is the first NGMV control solution that is suitable for systems containing an unstable NL sub-system which is contained in the state-dependent model. The process is also assumed to include explicit common delays in input or output channels. The generalised minimum variance cost index to be minimised involves both error and control Q1 signal costing terms but to increase generality weighted states are also included in the cost index. The controller derived is simple to implement considering the complexity of the system represented. If the plant is stable the controller structure can be manipulated into an internal model control form. This form of the controller is like an NL version of the Smith Predictor which is valuable for providing confidence in the solution.

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