Projects per year

### 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.

Original language | English |
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Pages (from-to) | 411-424 |

Number of pages | 14 |

Journal | IET Control Theory and Applications |

Volume | 4 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Mar 2010 |

### Keywords

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

## Fingerprint Dive into the research topics of 'Polynomial approach to nonlinear predictive generalized minimum variance control'. Together they form a unique fingerprint.

## Projects

- 2 Finished

## INDUSTRIAL NON-LINEAR CONTROL AND REALTIME APPLICATIONS

Grimble, M., Katebi, R. & Ordys, A.

EPSRC (Engineering and Physical Sciences Research Council)

1/05/05 → 30/04/10

Project: Research

## Impacts

## Practical Nonlinear Controllers for Industrial Applications

Michael Grimble (Participant) & M Katebi (Participant)

Impact: Impact - for External Portal › Economic and commerce, Professional practice, training and standards, Environment and sustainability - natural world and built environment

## Cite this

Grimble, M. J., & Majecki, P. M. (2010). Polynomial approach to nonlinear predictive generalized minimum variance control.

*IET Control Theory and Applications*,*4*(3), 411-424. https://doi.org/10.1049/iet-cta.2009.0043