### Abstract

Language | English |
---|---|

Journal | IET Control Theory and Applications |

DOIs | |

Publication status | Accepted/In press - 2013 |

### Fingerprint

### Keywords

- minimum variance control
- multivariable models

### Cite this

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**Non-linear generalised minimum variance control using unstable state-dependent multivariable models.** / Grimble, Michael; Majeckie, Pawel.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Non-linear generalised minimum variance control using unstable state-dependent multivariable models

AU - Grimble, Michael

AU - Majeckie, Pawel

N1 - DOI not working

PY - 2013

Y1 - 2013

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.

AB - 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.

KW - minimum variance control

KW - multivariable models

UR - http://www.scopus.com/inward/record.url?scp=84879493960&partnerID=8YFLogxK

U2 - 10.1049/iet-cta.2011.0706

DO - 10.1049/iet-cta.2011.0706

M3 - Article

JO - IET Control Theory and Applications

T2 - IET Control Theory and Applications

JF - IET Control Theory and Applications

SN - 1751-8644

ER -