Synthesis of Tracking Algorithms for Linear Objects with a Generative Model of the Reference Signal

Abstract

In the article the class of linear stationary objects with a scalar input is considered. The purpose of control is formulated in the form of tracking the output of the control object for a given input reference. At the same time, the principle of the internal model is used to form a generating model of the input reference. The solution of the representation subtask with a predetermined finite precision of a time-discretized input reference in the form of a linear expansion on the basic functions corresponding to the roots of the desired characteristic polynomial of a discrete linear dynamic system (generator) is considered. By using the continualization, a continuous, linear generating model of the input reference with non-zero initial conditions and input is constructed in the state space, coinciding in dimension with the model of the control object. The generating model makes it possible to formulate the control goal in the form of tracking the state vector of a closed system with the state vector of the generating model. In general, the generating model may not be stable. Therefore, the desired rate of convergence of the tracking error vector is given by the Hurwitz reference model. The developed method of generating the generating model is considered in the context of solving the general problem of the synthesis of the tracking algorithm.