Methods of automatic and optimal control in dynamic measurements

The article reviews the results of solving dynamic measurement problems of two scientific schools of South Ural State University. The dynamic properties of the measurement system are critical factors affecting the dynamic measurement error, while the structures of dynamic measurement system and automatic control system have common principles of construction. Thus, the methods of automatic control theory were implemented in the study of dynamic measuring systems. However, dynamic measuring systems are characterized by the absence of feedback, which required the development of new methods when using the ideas of automatic control theory. These include the method of modal control of dynamic characteristics of measuring systems. It led to the development and application of other methods: iterative principle of measuring systems, method of sliding modes, parametric adaptation of systems, neural network technologies, numerical methods for solving inverse problems. The first section of the article is devoted to these studies. The second section presents the results of the theory of optimal dynamic measurements. The problem of restoring a dynamically distorted signal is solved here using the methods of optimal control theory, and the measuring device is simulated by a Leontief-type system. The reduction of the solution of the inverse problem of dynamic measurements to a direct mathematical problem allowed us to effectively apply the existing mathematical apparatus of the theory of Sobolev equations in the case of taking into account the inertia of the measuring system. Analytical and then numerical studies were initiated to investigate the problem of restoring a dynamically distorted signal in the presence of \flqq noise\frqq , which led to the creation of the theory of stochastic equations of Sobolev and Leontief types and the development of numerical methods. The review focuses on numerical methods based on the idea of extracting a useful output signal from a known noisy observation and then applying a numerical method to recover the input signal. In addition, the algorithm of a new numerical method based on the use of the counting theorem and simple averaging is briefly presented. The bibliographic review is based on the obtained results, though it is far from being exhaustive.