STABILITY OF THE PROGRAM MANIFOLD OF DIFFERENT AUTOMATIC INDIRECT CONTROL SYSTEMS

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Özet

This article discusses the problems of constructing different automatic systems of indirect control. It is known that a given program is not always exactly performed, since there are always initial, constantly acting perturbations. Therefore, it is also advisable to require the stability of the program manifold itself with respect to some function. In the first part, the stability of automatic indirect control systems is investigated taking into account external load. The equations of the hydraulic actuating mechanism taking into account the action of an external load are presented for a convenient type of study. Then it comes down to studying a system of equations for a given manifold. By constructing the Lyapunov functions for the system in canonical form, sufficient conditions for the absolute stability of the program manifold are obtained in the form of some equality. In the second part, a tough feedback indirect control system is considered. Different Lyapunov functions are constructed. Algebraic sufficient conditions for absolute stability are obtained. They are compared with frequency conditions like Popov, Yakubovich. The necessary conditions for absolute stability are also indicated. In the simplest case, necessary and sufficient conditions for absolute stability are obtained. The results obtained can be used to construct stable automatic systems of indirect control.