Qualitative Distribution of Modes in the Systems with Distributed Parameters

Abstract

There are many continuous technological processes of high power, with huge material and energy flows. Their parameters can change not only in time, but also in space. The hydrolithospheric processes, the processes connected with heat treatment, diffusion, etc. (in the control theory this class of processes is called objects with the distributed parameters), can serve as an example. Mathematical models of such processes either are not known, or described by the equations in private derivatives. The main approaches, used for analysis of the linear objects with the distributed parameters [6-14] are based on the theory of differential equations in private derivatives and frequency methods. Without a loss of the linear objects with the distributed parameters we will set the task of application of the qualitative theory [15-19] for a synthesis of the control systems with the distributed parameters. We should note that for the distributed objects a decomposition of their mathematical models on the own vector - functions of the operators of objects, the own movement of which is described by large dimensional differential equations, takes place. The technique of synthesis of the distributed regulators using the qualitative theory is considered on the example of construction of the closed control systems of the heat distribution process in a plate of the final sizes.