Discrete-time predictive control with overparameterized delay-plant models and an identified cancellation order

Zdzisław Kowalczuk; Piotr Suchomski

International Journal of Applied Mathematics and Computer Science (2005)

  • Volume: 15, Issue: 1, page 5-34
  • ISSN: 1641-876X

Abstract

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The paper presents several solutions to the discrete-time generalized predictive (GPC) controller problem, including an anticipative filtration mechanism, which are suitable for plants with nonzero transportation delays. Necessary modifications of the GPC design procedure required for controlling plants based on their non-minimal models are discussed in detail. Although inevitably invoking the troublesome pole-zero cancellation problem, such models can be used in adaptive systems as a remedy for the uncertainty or variability of the model order. The purpose of this paper is to present a complete GPC controller design for delay plants that is robust to the overparameterization of the plant model. Refined conditions for the existence and stability of GPC control solutions in terms of pertinent design parameters are given, and explicit forms of closed-loop characteristic polynomials are provided. The issue of identifying the model cancellation order is also considered, and practical solutions are proposed. The presented ideas are illustrated numerically.

How to cite

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Kowalczuk, Zdzisław, and Suchomski, Piotr. "Discrete-time predictive control with overparameterized delay-plant models and an identified cancellation order." International Journal of Applied Mathematics and Computer Science 15.1 (2005): 5-34. <http://eudml.org/doc/207728>.

@article{Kowalczuk2005,
abstract = {The paper presents several solutions to the discrete-time generalized predictive (GPC) controller problem, including an anticipative filtration mechanism, which are suitable for plants with nonzero transportation delays. Necessary modifications of the GPC design procedure required for controlling plants based on their non-minimal models are discussed in detail. Although inevitably invoking the troublesome pole-zero cancellation problem, such models can be used in adaptive systems as a remedy for the uncertainty or variability of the model order. The purpose of this paper is to present a complete GPC controller design for delay plants that is robust to the overparameterization of the plant model. Refined conditions for the existence and stability of GPC control solutions in terms of pertinent design parameters are given, and explicit forms of closed-loop characteristic polynomials are provided. The issue of identifying the model cancellation order is also considered, and practical solutions are proposed. The presented ideas are illustrated numerically.},
author = {Kowalczuk, Zdzisław, Suchomski, Piotr},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {delay plants; robust control synthesis; system design; adaptive control; overparameterization; predictive control; overparametrization; anticipative filtering; pole-zero cancellation},
language = {eng},
number = {1},
pages = {5-34},
title = {Discrete-time predictive control with overparameterized delay-plant models and an identified cancellation order},
url = {http://eudml.org/doc/207728},
volume = {15},
year = {2005},
}

TY - JOUR
AU - Kowalczuk, Zdzisław
AU - Suchomski, Piotr
TI - Discrete-time predictive control with overparameterized delay-plant models and an identified cancellation order
JO - International Journal of Applied Mathematics and Computer Science
PY - 2005
VL - 15
IS - 1
SP - 5
EP - 34
AB - The paper presents several solutions to the discrete-time generalized predictive (GPC) controller problem, including an anticipative filtration mechanism, which are suitable for plants with nonzero transportation delays. Necessary modifications of the GPC design procedure required for controlling plants based on their non-minimal models are discussed in detail. Although inevitably invoking the troublesome pole-zero cancellation problem, such models can be used in adaptive systems as a remedy for the uncertainty or variability of the model order. The purpose of this paper is to present a complete GPC controller design for delay plants that is robust to the overparameterization of the plant model. Refined conditions for the existence and stability of GPC control solutions in terms of pertinent design parameters are given, and explicit forms of closed-loop characteristic polynomials are provided. The issue of identifying the model cancellation order is also considered, and practical solutions are proposed. The presented ideas are illustrated numerically.
LA - eng
KW - delay plants; robust control synthesis; system design; adaptive control; overparameterization; predictive control; overparametrization; anticipative filtering; pole-zero cancellation
UR - http://eudml.org/doc/207728
ER -

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