Digital automatic control systems in mechatronic systems

Abstract

Morneva M.O., Golubieva S.M., Toropov A.S. Digital automatic control systems in mechatronic systems

The article deals with the issues of digital automatic control systems, which belong to the class of linear impulse systems, but have their own characteristics.Automatic control systems(ACS), as a rule, are equipped with built-in control micro-computers or microprocessors.The advantage of digital automatic control systems is high accuracy of operation, small dimensions of the control part, the ability to quickly change the algorithm of the ACS operation by changing the control program.The computer operates not with differences, but with the absolute values of the variables of the equation in finite differences; therefore, it is unsuitable for use in applied programs and is converted into difference equations.The presence and type of information in the intervals between the moments of measurement depends on the type of extrapolator (in a computer, this is a program that determines the law of information change between the moments of measurement of information). Extrapolators are of zero, first and higher order. The zero-order extrapolator keeps the signal constant after measurement until the next measurement. The first-order extrapolator implements the tendency of the signal to change according to the first derivative, etc.The theory of impulse, and therefore digital systems, is based on difference equations (analogue of differential equations) and z-transfer functions (analogs of transfer functions of continuous systems).Difference equations and Z-transformations of the transfer function were also found in two ways: classical and using bilinear transformations; transient and frequency characteristics were also constructed.Using the "bileniar" procedure of the Matlab package, you can find the coefficients of the Z-transfer function for the correcting link. Using the "bileniar" procedure of the Matlab package, the coefficients of the Z-transfer function for the correcting link are found..By means of mathematical modeling, it was confirmed that when comparing the characteristics of continuous and discrete filters with increasing frequency, the difference in characteristics increases.