Correction of the optimal regulator based on solving the inverse problem of optimal stabilization with vector control

Abstract

Objective. The problem of designing controllers that implement a given programmed movement of a controlled object and the problem of determining the movement of a dynamic system are two main problems in classical control theory. This article discusses the solution of direct and inverse optimal stabilization problems. The state vector is assumed to be completely available for measurement.Method. Based on the optimality ratio linking the weight coefficients of the quadratic quality functional and the optimal gain matrix, which closes the control object, it is proposed to use a numerical method for determining the functional matrices. Mathematical models of autonomous fully controlled objects were used for the study, the formation of which was carried out randomly, in particular, according to the normal distribution law.Result. The initial stage of the solution is associated with modal synthesis, the result of which is a proportional regulator that provides stabilization of the control object by the location of the poles of the synthesized system. The next step is to determine the weighting coefficients of the functional by numerically solving the optimality ratio. The final stage is the solution of the direct optimal stabilization problem, which is based on the Lagrange variational problem. As a result, the optimal regulator is calculated, which, when switched on in a closed system instead of a modal one, reduces the duration of the transient process.Conclusion. The proposed approach of the authors allows minimizing to a certain extent the transients of the adjusted control system.