MATHEMATICAL MODEL OF RANDOM PROCESSES OF AUTOMATIC CONTROL SYSTEMS

Abstract

The probabilistic-statistical description operates with the concepts and terms of probability theory and mathematical statistics, such as the mean value, variance or standard deviation, probability density, standard error. The purpose of the research is to build a mathematical model of random processes in automatic control systems. When modeling noise impacts, it is advisable to simulate noise as the normal white noise, which has a constant spectral density. The values of this spectral density can be obtained in practice from the spectrum of the random component of the control error and the complex transmission coefficients of the automatic control systems through the control and disturbance channels. As a result, the automatic control systems developer and the technologist are interested in the value of the root-mean-square control error. But to determine it, it is more convenient to use the spectral-temporal description of the automatic control systems. The peculiarity of noise (random processes) is that it is impossible to explicitly write down the dependence of their magnitude as a function of time, since the noise values change in different ways at each time interval. But you can specify some average values, named above, which give a fairly detailed idea of the noise as a whole. The noises often encountered in engineering practice are ergodic, such that the ensemble averaging coincides with the time averaging. Therefore, the statistical characteristics of such noises can be obtained by averaging their observed values over time.