| Popis: |
The purpose of the research is to create a discrete-time drive tracking control system. A special form is proposed - digital sliding mode. Time-optimal control law shows high accuracy results. Under certain conditions, it provides ideal tracking of signals from a given class. On the other hand, the time-optimal control law turns out to be relay, the control signal u is bounded in absolute value (|u| ≤ A) and takes only marginal values + A or –A. Its current value is determined by the position of the image point with respect to some surface (hypersurface) called the switching surface. Tracking in such a system is possible only in the sliding mode, when the image point moves along the switching surface. The sliding mode, regardless of whether the switching surface is time-optimal, has a number of advantages, including invariance under certain conditions in relation to the parameters of the model of the control object. Under real conditions, a sliding mode is not possible, since it involves the instantaneous switching of the value of the control signal from + A to –A. In addition, in modern practice, the use of digital microcontrollers that operate in discrete time to control follower actuators is becoming more widespread, which eliminates the possibility of instant switching. However, in this case, it is possible to form a control that has all the properties of both a sliding mode and optimal control. In this article, we consider one of the ways to form such a digital algorithm for controlling a follower actuator, which provides the main property of the sliding mode - the movement almost over the switching surface. This movement mode is called digital sliding mode. Several options for the implementation of such an algorithm are proposed and compared, using different information about the control object and its current state. Conclusions are made about the appropriateness of using the digital sliding mode and outlines areas for further research in this direction. |
