Synthesis of Zonal Controls for a Problem of Heating with Delay Under Nonseparated Boundary Conditions
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SYNTHESIS OF ZONAL CONTROLS FOR A PROBLEM OF HEATING WITH DELAY UNDER NONSEPARATED BOUNDARY CONDITIONS
S. Z. Guliyev
UDC 517.977.56:517.977.58
Abstract. The problem of synthesis of feedback control for objects with distributed parameters using continuous monitoring of the phase state of an object at its definite points is considered and illustrated by the example of control of the process of heating a tubular heat exchanger in its steam jacket. To solve the problem, it is proposed to use first-order numerical methods. Formulas for components of the gradient of an objective functional in the space of the parameters being optimized are derived. The results of the made numerical experiments are presented. Keywords: synthesis of control, zonal control, feedback, distributed system, tubular heat exchanger, gradient of functional. INTRODUCTION One of important sections of the modern theory of automatic control is the theory of control of systems with distributed parameters. In most cases, problems of synthesizing control for distributed systems are more complicated than those for concentrated systems in view of the specifics of distributed objects. Distributed control objects include many chemical-technological, radiation, aerodynamic, and hydrodynamic processes, processes of thermal conductivity and diffusion, processes connected with the motion of elastic constructions, etc. In view of the absence of a formalized methodological approach to solving problems of control of objects with distributed parameters, new problems arise that require the use of nonstandard methods of investigation and decision-making in each concrete case. The main contribution to the development of the theory of control of systems with distributed parameters was made by the fundamental results obtained in [1–7] and others. The modern engineering tools of measuring and computer engineering that make it possible to perform a large amount of work in real time played the key role in the development of feedback control systems and their wide practical implementation. This article considers the problem of synthesizing the control of an object with distributed parameters on special classes of control actions. The specific of the object being investigated is that it includes a retarded argument. For the controls being synthesized, the concept of zonality is introduced, i.e., the constancy of values of the control parameters being synthesized in each of subsets (zones) into which the totality of possible states of an object or the time interval of functioning of a process (an object) is divided in advance. Values of control actions are also determined by the type of feedback and the class of functional dependence of control on the current observed state value or current monitoring period. The case of continuous feedback is analyzed using continuous monitoring of the phase state of an object at its definite points. The constancy of the parameters of zonal control actions (the zonal controls themselves or zonal amplification coefficients when control is l
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