### Abstract

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

Pages | 411-424 |

Number of pages | 14 |

Journal | IET Control Theory and Applications |

Volume | 4 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Mar 2010 |

### Fingerprint

### Keywords

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

### Cite this

*IET Control Theory and Applications*,

*4*(3), 411-424. https://doi.org/10.1049/iet-cta.2009.0043

}

*IET Control Theory and Applications*, vol. 4, no. 3, pp. 411-424. https://doi.org/10.1049/iet-cta.2009.0043

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Polynomial approach to nonlinear predictive generalized minimum variance control

AU - Grimble, M.J.

AU - Majecki, P.M.

PY - 2010/3/1

Y1 - 2010/3/1

N2 - 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.

AB - 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.

KW - polynomial systems

KW - optimal

KW - predictive

KW - nonlinear

KW - minimum variance

KW - transport delays

U2 - 10.1049/iet-cta.2009.0043

DO - 10.1049/iet-cta.2009.0043

M3 - Article

VL - 4

SP - 411

EP - 424

JO - IET Control Theory and Applications

T2 - IET Control Theory and Applications

JF - IET Control Theory and Applications

SN - 1751-8644

IS - 3

ER -