Inverse problems of optimal stabilization with scalar control

Introduction. The paper explores inverse problems of optimal stabilization with a full measurement of the control object state vector. Using the so-called optimality relations, the authors propose an algorithm for the numerical determination of the weight matrices of a quadratic quality functional. Materials and Methods. As initial data, mathematical models of linear stationary fully controlled objects are used. The initial stage of the solution is connected with the task of modal control to obtain a proportional regulator - a modal controller - to stabilize the control object by arranging the poles of a closed system. The next approach is the optimal stabilization method by the root-mean-square criterion. At this stage, the basic process of determining the weight matrices of a quadratic functional is carried out using numerical methods for solving algebraic equations and optimality relations. Results. Based on the proposed algorithm for determining the weight matrices of a quadratic functional, the programs were developed to study the results of stabilizing control objects with scalar control up to the 20th order. In a particular case, the problem was considered with the parameter of the quadratic functional weight coefficient that allows the control systems designer to make a decision about the expediency of the stabilization process by secondary indicators of the transient process quality for the optimal system output. Discussions and Conclusions. The results of the numerical experiment showed that the proposed stabilization method, based on the solution of the inverse problem of optimal stabilization, avoids the limitations of modal control. In addition, for designing stabilization systems the authors propose using an iterative algorithm to assess the quality of transients in a closed control system.