Analytical design of optimal control systems of the linear object movement along a given trajectory under stochastic effects influence

This article is devoted to the development of a new method of calculating transfer functions matrices of optimal multivariable regulator's control paths. The regulator is designed to maximize the accuracy of the linear multivarible control object transition from one steady state to another. It is assumed that control object acting disturbances and sensors measuring data have inertia and noise. Both disturbances and noises are an additive combination of regular and random components. Random components belong to a class of interconnected stationary processes with rational spectral density matrices. New method development is based on formulation of a synthesis problem with the help of a new control system block diagram, which is obtained as a result of taking into account sensors dynamics certification data. Synthesis of the regulator is carried out in the frequency domain by the Wiener-Kolmogorov method. A new algorithm, which is obtained as a result of synthesis problem solution, allows you to find the matrix of regulator transfer functions , which provide a minimum of corresponding quadratic quality criteria. The first of them is equal to the sum of certain way weighted squared deviations regular repetition errors of the object path and control signals. The second criterion is equal to the sum of the weighted variance of the random error components and the control signals. To execute the proposed algorithm it is necessary to perform the operations of Wiener factorization and separation of rational matrices. The corresponding functions are contained in the freely distributed software package SciLab.