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High‐precision state feedback control systems for linear and non‐linear plants

Adam Łozowicki (Maritime University of Szczecin, Szczecin, Poland)
Teresa Łozowicka Stupnicka (Cracow University of Technology, Kraków, Poland)
Dorota Łozowicka (Maritime University of Szczecin, Szczecin, Poland)

Kybernetes

ISSN: 0368-492X

Article publication date: 17 June 2008

Abstract

Purpose

The purpose of this paper is to provide the high‐precision robust control method for plants given by a high order of differential equations. This method is useful for linear and non‐linear plants. Considering the problem of minimization of energy consumed in the world is very important and very actual.

Design/methodology/approach

For theoretical solving of the problem, the functional analysis and methods of the Banach spaces H2 and H are used. Next the conditions for controllability with ε‐accuracy are given. For the non‐linear plants additionally two methods are used – method based on van der Schaft inequality and harmonically linearization.

Findings

Provides state feedback control systems with sufficiently large gain (called Tytus feedback). Such systems can perform a high‐degree accuracy (called there ε‐accuracy).

Practical implications

The considerations have many practical applications. For example, solving the problem of a high‐precision robust control for a ship track‐keeping and designing of a robust controller for a non‐linear two‐benchmark problem.

Originality/value

This is an original theoretical method of obtaining a high‐precision performance for feedback control systems. System presented in the paper enables controlling with ε‐accuracy the stable or unstable plants P described by high‐degree differential equations. Paper regards a robust control of stable as well as unstable plants with uncertainty.

Keywords

Citation

Łozowicki, A., Łozowicka Stupnicka, T. and Łozowicka, D. (2008), "High‐precision state feedback control systems for linear and non‐linear plants", Kybernetes, Vol. 37 No. 5, pp. 608-622. https://doi.org/10.1108/03684920810873254

Publisher

:

Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited