The research of transients of the fourth-order automatic control systems by the quadrature method

Abstract

Modern transient analysis methods are approximate, which leads to significant control errors. It is shown that improving the accuracy and speed of automatic control systems, and providing optimal operation is possible using the quadrature method for the transient analysis. The fourth-order automatic control system, which is described by a linear differential equation with real and compatible complex roots was investigated. The influence of these roots on the first-quadrature time constants is shown. The methods for determining the first-quadrature time constants and transient analysis accuracy were described. The time constant, which is a multiplier at the first derivative of the first quadrature can be determined by the minimum space between the real RFR of the system and RFR of the first quadrature. The second quadrature can be determined by the difference between the real RFR and RFR, identified by the first quadrature. It is shown that for the fourth-order ACS, transition frequency of the second quadrature RFR is equal to the first quadrature frequency. Since the second quadrature is negligible, it can be neglected in many practical tasks. The main advantage of the quadrature method is the transient analysis using analytical formulas, used for second-order differential equations. Using the quadrature method is especially valuable for the software support of modern computer-integrated process control systems, in which close and complex method of inverse Laplace transform is typically used. Investigating the high-order control systems with delay and using the method for calculating the optimal regulator settings are practically important.