Synthesis of robust control algorithms for linear interval dynamic systems in the electric power industry

Abstract

When studying the objects of management in the field of electric power, we meet with various inaccuracies in determining their parameters. One of the methods of dealing with uncertainties is the use of various estimates of the parameters of the control object. modern science has developed various methods for assessing the uncertain parameters of the control object in the electric power industry. parameter uncertainty occurs when the set of parameters of the control object is more than one point. If this set is defined using probabilistic characteristics, then this is the so-called probabilistic uncertainty of the object parameters. If the boundaries of the intervals in which they are enclosed are known for the object parameters, then such uncertainty is called interval uncertainty. if the object parameters are set using the membership function, then the theory of fuzzy logic is used. Interval determination of parameters of the control object is used when working with values for which only the boundaries of the intervals within which their values are enclosed are known. The interval approach in the description of object parameters is used to account for rounding and errors that occur during calculations on a computer and is a strong method in the representation of objects with uncertain parameters, which are very common in the electric power industry. The reason why interval systems are used is the incompleteness of information about the control object, errors in measuring the parameters of the object, linearization errors, and so on. Various problems of the classical theory of automatic control allow us to replace the concentrated parameters with their interval analogues. Many interval problems are adequate for practical applications. The synthesis of linear quadratic regulators refers to the classical method, which allows us to obtain regulators that minimize the integral quality criterion with respect to the resource of regulated and regulatory quantities. In this paper, we study the possibility of synthesizing linear quadratic regulators for electric power facilities specified in intervals. This application of two well-known methods makes it possible to work with nonlinear objects using the classical linear control theory.