Synthesis of a Controller for a System with a Delay

Abstract

The task of controlling some systems is complicated due to the fact that real technical plants may contain delay links. That is, there is a certain time period when there is no reaction from the regulated plant to the control action. Usually, the delay link presence negatively affects the quality of such system management. There are various ways to synthesize a control system for such systems. These include: Smith predictors, specialized control tuning algorithms, the use of self-adjusting systems with active adaptation. However, they impose additional requirements on the system dynamics or are complex in technical implementation and configuration. Within the framework of this article, an attempt is made to calculate the controller by the polynomial method for a plant with a delay. The delay mathematical model is obtained by approximating the delay link by Pade series. To ensure the necessary dynamics of the transition process, we will require the system to preserve the poles of the delay link. Then the controller, calculated for a system with a delay link in the form of a Pade series, is applied to a system with an “ideal” delay. For clarity of the calculations carried out, an plant in the form of a aperiodic combination and integrating links connected in different ways is taken as an example. The integrating link is necessary to give the system astatic properties. As a delay, we will use the approximation of a number of Pads of different orders. The lag link gives the system an unstable character.