Influence of Discretization on the Speed Gradient Synchronization Control

Abstract

Increasing the productivity of technological operations is a current task of modern science. The introduction of modern industrial equipment control systems is associated with the digitalization and computerization of enterprises. Vibration technology is one of the common types of industrial equipment used for screening, crushing, vibratory movement, etc. The energy approach for the vibration setups control makes it possible to keep a constant level of total energy of vibration setup oscillations, which makes it possible to develop intelligent control system under conditions of uncertainty in the parameter space. This paper is devoted to the study of the influence of digitalization and discretization on the speed gradient algorithm operation for the multiple synchronization control of vibration setup rotors and evaluation of the critical sensor signals sampling steps. The paper presents the results of numerical simulation based on the system dynamics equations and approximate values of vibration setup parameters. The simulation results present that an increase of the discretization sampling step leads to a disruption of the multiple synchronization mode up to the stability loss. The results of an experimental study on a mechatronic vibration setup SV-2M demonstrate in normal operation mode the low-frequency oscillations of the rotors speeds and the total system energy, which frequency is determined by the control signal limit. When the discretization step increase, the motion with stops is observed, which has a similar nature with the stable relaxation self-oscillations. The practical relevance of the obtained results is a detection of possible effects that occur in the system with significant discretization steps. Further development of adaptive control systems can be aimed to compensating of the discretization effect on the operation of the speed gradient control of the vibration setup rotors synchronization.