Design of a robust controller with guaranteed H∞ criteria for a servo system considering summative and polytopic pncertainty

Abstract

This paper addresses the challenge of robustness against model uncertainties as well as simplicity in controller design for position control in servo systems. More specifically, in this paper, during the modeling of a permanent magnet synchronous motor for a servo system, uncertainties of the model are considered and are introduced as a summative term in its state space equation. But to increase the controller robustness, in addition to this cumulative uncertainty term, a polytopic uncertainty is also considered in the model design for the system state matrix. The system becomes fully robust to uncertainties after modeling. A state feedback controller is then designed based on this model, ensuring that the H∞ performance criterion is satisfied. In this way, and by satisfying the H∞ condition, the controller becomes robust against uncertainties accumulated by the model. On the other hand, the considered polytopic uncertainties also create a resistance to the uncertainties of the system's transient matrix. The advantage of the method presented in this article is that it has a very simple structure and its design is very simple. It also has a low computational burden and, despite its simplicity, has very good resistance to uncertainties. In addition, the proposed method also eliminates the chattering problem that exists in the sliding mode control family. To examine the performance of the proposed method, a series of experiments was conducted in the laboratory, and the results confirmed the effectiveness of this method in the cases mentioned above.