On the Influence of Time Discretization of Signals on the Stability of Modern Electromechanical Automatic Control Systems (ACS)

The modern automatic control systems are the systems with pulse semiconductor converters power, digital sensors of mechanical variables – torque and movement speed, and digital control devices – regulators. All these devices “break” the signals in time, that is, they make them discrete. Time discretization significantly affects the stability of processes in ACS. Theoretical analysis of ACS even with one discrete element demands a transfer from continuous frequency characteristics and transfer functions of all links of the ACS structure to the discrete characteristics. That significantly demands the change of engineering approaches to the ACS analysis. In recent years, due to a significant reduction in the sampling time in digital sensors and controllers, the influence of discreteness on the ACS stability has weakened, and little attention has been paid to it in research. However, the mathematical “content” of the problem has not changed since the 80s of the 20th century.Moreover, this problem is very relevant in high-precision high-speed automatic control systems, especially in those using sliding processes.In this paper a new approach is proposed, which consists in interpreting the discretization operation by a link that suppresses input signals with a high variation frequency. This link greatly simplifies the engineering calculations of ACS with discretization and shows new possibilities for the synthesis of such systems. Such possibilities include the efficient distribution of sampling intervals between the channels of widely used PID controllers and the channels of amplification and formation of slip trajectories in systems with a variable structure with sliding processes (SVS with SP) that have been rapidly developing in recent years. It is specifically important that the proposed estimation technique remains effective when the discretization intervals are comparable with the times of transient processes in the ACS under consideration. Theoretical provisions have been verified and confirmed by modeling, the results of which are given in this chapter.