Research of K∞-Robust Systems with Constrained Control

Abstract

At the present, there are no satisfactory engineering solutions related to the synthesis of robust regulators taking into account the constraints on control. In this connection, it is important to study the influence of saturation effect of the controller on the robust properties of systems. In this paper, this problem is considered in connection with K∞-robust control systems with a high gain. It is shown that in control limit systems, in particular, K∞-robust systems at the initial instant of time, the control assumes an excessively large value. This ensures the robustness of the dynamic mode. The reason for this feature is related to the fact that at the initial instant of time the initial conditions has a great importance. The main reason for the deterioration of robust properties is due to the tight control in the initial time interval. Provision of robustness of the static mode does not require great control efforts. For the first time, using computer graphics in a three-dimensional coordinate system, taking into account the time, a visual representation of the sections of phase trajectories pertaining to different types of movements is given: rapid motion from an arbitrary initial state that ensures hitting the imaging point into the degenerate trajectory; slow motion along this trajectory; steady-state motion within the specified accuracy. For the limit control systems, an integral robustness estimate is proposed, which consists in calculating the integral of the absolute value of the slow motion trajectory. This indicator characterizes the discrepancy (dispersion) of the real trajectory with respect to the limiting trajectory. The reliability of theoretical reasoning is confirmed by solving a model problem in the block-vision environment of Matlab/Simulink.