Stages and main tasks of the century-long control theory and system identification development. Part VII. Multirate sampling control systems

The article provides a review and generalization of the main approaches and methods of designing discrete controllers with multirate sampling for multidimensional and multi-connected control objects described by models in the state space, which have the property of functioning in two time scales. At the same time, the initial model of the object is decomposed into slow- and fast-acting subsystems based on the assumption of a quasi-steady state of rapidly changing processes in the control object. In the introduction, an analysis of the well-known methods of synthesis of composite multirate discrete regulators based on linear-quadratic optimality criteria is carried out. The method of different multirate sampling of singularly perturbed continuous systems, which functioning in a stochastic environment and two time scales under the action of disturbances of the white noise type, is considered. Method for the synthesis of a composite multirate state regulator for multidimensional objects with a delay under the action of slow-acting disturbances with an average value other than zero has been developed. On the basis of this method, discrete slow- and fast-acting models are formed with a delay and different multirate sampling in the state spaces and measurement variables, which made it possible to compensate for slow-acting disturbances. At the same time, the measurability of slow- and fast-acting subsystems with different multirate sampling does not depend on the value of the delay. This article solves the problem of stabilization and coordination at a given level of non-measurable slow- and fast-changing components of the vector of initial measured coordinates in systems that implicitly operate in two time scales.