Some Feasibility Problems in the Exact Solution of Сontrol Exercises

Abstract

There is studied the mathematical foundations of the synthesis methodology in the engineering interpretation of a number of popular feedback control systems and the reasons for the impracticability of the results due to the appearance in the synthesis equations of pure differentiation operators and sources of various types of roughness violation. The global reason for the increasingly accelerated divergence of control theory from practice is associated with the impact on creative thinking such as mutation, incompatibility, randomness, fuzziness, asymmetry which underlies the evolution of synergetic systems. Both the "methodological crisis" and a number of seemingly insignificant engineering inconsistencies lead to a decrease in the planned efficiency of the developed control systems. There is a tendency to solve this practical problem through its excessive mathematization. As a result, there is nonsense — "the more mathematics, the worse", which leads to a "mathematical labyrinth", to exit from which the mathematical apparatus becomes more and more complicated until the creation of a new theory. It is shown that the use of even "correct" mathematical relations, which are the basis of the synthesis method, often leads to a violation of feasibility and rudeness. It is cited that the neglect of important poorly formalized technical indicators and the conditions of rudeness (robustness) when setting the problem does not allow us to obtain a constructive solution and is one of the main reasons for the discrepancy between theoretical results and practice. A number of popular directions of the classical theory of feedback control are considered: an inverse approach-compensation method, which forms the basis for constructing astatic, invariant, robust and other compensation systems; synthesis methods for systems with a finite settling time; assessment and control methods based on the concept of " inverse dynamics problems"; high gain limit systems. Violation of various types of feasibility and rudeness is demonstrated by specific examples tested on Matlab / Simulink. Computer research has made it possible to draw a number of positive conclusions that have important applied value.