Analysis and synthesis of control systems

The synthesis of stabilization systems under one-sided restrictions on control actions

A. V. Utkin, V. A. Utkin

V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

Abstract: In practical applications of automatic control theory, situations are often encountered where control actions are limited to a certain range of values, in particular, they can only take non-negative values. In this case, such popular synthesis methods as modal and optimal control are not applicable. In this paper, the methods are proposed for stabilizing output (controlled) variables in linear stationary SISO systems under non-negative (unipolar) control constraints. The main idea is to implement control actions in the form of linear functions with saturation, constant values of which coincide with the restrictions on the controls. As an illustration of the developed algorithms, a pulsed DC/DC voltage converter is considered, in which the control has a switching nature with the «on–off» states. The simulation results in Matlab Simulink are presented.

Keywords: stabilization problem, one-sided control restrictions, invariance, DC/DC voltage converter.

UDC: 62-501.2

Received: 18.07.2019
Revised: 13.02.2020
Accepted: 04.03.2020

DOI: 10.25728/pu.2020.3.1

 English version: Control Sciences, 2021, 82:8, 1442–1455