ავტომატური მართვის სისტემის წრფივი მაკორექტირებელი მოწყობილობის პარამეტრების ოპტიმალური მნიშვნელობების განსაზღვრა ინტეგრალური კვადრატული კრიტერიუმის მიხედვით

Abstract

When designing an automatic control system (ACS), it is important to determine the optimal values of the parameters of the correcting device according to any of the criteria. Recently, more and more publications have appeared on the use of the method of nonlinear mathematical programming for solving problems of synthesis of an automated control system. The article discusses a method for determining the optimal parameters of linear correcting devices according to the quadratic integral criterion. The novelty is the presentation of the above mentioned problem in the form of a nonlinear mathematical programming problem. To find a multiparametric, multiextremal, i.e. complex, objective function, a random search method is used. Also, a class of automatic control systems having one extreme objective function is highlighted. For this case, the theorems are proved, and the formula for determining extreme points is given in an analytical form. Numerical examples are also considered. Programs have been developed for implementing the corresponding algorithms on a computer in VBA language. The graphs of the corresponding transients are given.