Calculation of the regulator for the object with a delay

The task of managing some systems is complicated due to the fact that real technical objects contain delay links. That is, there is a certain period of time when there is no reaction from the object of regulation to the control action. Usually, the presence of a delay link negatively affects the quality of management of such a system. 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 dynamics of the system or are complex in technical implementation and configuration. Within the framework of this article, an attempt is made to calculate the regulator by the polynomial method for an object with a delay. The mathematical model of the delay is obtained by approximating the delay link next to the Pade. To ensure the necessary dynamics of the transition process from the system, we require the preservation of the poles of the delay link. Then the regulator, calculated for a system with a delay link in the form of a series of Pads, is applied to a system with an "ideal" delay. For clarity of the calculations carried out, an object in the form of a combination of aperiodic 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 the range of different orders. The link of delay gives the system a non-stable character.