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

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.

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.

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

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.

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.