A COMPARATIVE STUDY OF THIRD-ORDER SLIDING MODE CONTROL SYSTEMS WITH OPTIMAL AND MODAL REGULATORS SYNTHESIZED BY THE N-i SWITCHING METHOD

Electric servo drives are characterized by the restriction of intermediate coordinates in transient modes. Such restrictions are implemented by a system with cascade controllers. The N-i switching method, which has a relatively simple mathematical apparatus, provides optimization for the speed of cascade sliding mode control systems. At the same time, the N-i switching method makes it possible to justify such pole placement of relay-modal control systems, which ensures a minimum deviation of their transition trajectories from the optimal ones in terms of speed. In this paper, a comparative study of typical dynamic regimes of sliding mode control systems with optimal and modal settings, synthesized on a single methodological basis, is performed. In this case, as an ideal control object, a cascade of integrators was considered, and a servo drive was used as the real one. The study revealed a number of advantages of modal regulators over optimal ones. Modal settings of the sliding mode control system of point-to-point control provide an aperiodic nature of the final stages of positioning without increasing the total duration of the process and less oscillation in the modes of compensation of disturbances compared with the optimal settings. This conclusion extends both to a system with ideal, and with real dynamic objects. The results obtained in the work are supported by specific numerical examples. Due to the simplicity of the computational procedures, the N-i switching method provides real-time adaptation of the control system settings to the shape of the optimal transient trajectory. The results of the research open the prospect of integrating modal settings into adaptive algorithms for the synthesis of cascade sliding mode control systems based on the N-i switching method.