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

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 H 2 and H 1 are used. Next the conditions for controllability with 1-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 1-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 1-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.