Mathematical model of the automatic control system in the problem of guaranteed accuracy

The formulation and solution of the mathematical problem of the synthesis of an automatic control system (ACS) of guaranteed accuracy under uncertain disturbances using the inverse dynamic system approach is considered. No restrictions are imposed on uncertain perturbations, and the perturbations themselves can be arbitrary. The procedure for forming the structure of the ACS with guaranteed accuracy, which ensures the preservation of the quality (stability and quality of the transient process) of the ACS during compensation of disturbances, and the features of this structure are shown. The proposed method of forming a corrective influence to compensate for the effects of disturbances as a function of the approximation of the ACS state variable to the limit of the permissible value. For the first time, it is shown that such a structure of ACS with guaranteed accuracy corresponds to a new mathematical structure - an algebraic differential equation (for a system with one degree of freedom) or a system of such equations (for a system with several degrees of freedom).