Global sliding mode control with chatter alleviation for robust eigenvalue assignment

This paper proposes a global sliding mode control (GSMC) scheme that can guarantee a chattering-free performance for systems without external perturbations and ensure a chattering-alleviated performance under the perturbations of known bounds. The GSMC has been a remarkable control technique and is designed to achieve extremely robust performance. This perfectly robust control, however, suffers from the same problem as the conventional sliding mode control, i.e. the chattering problem due to switching control. In this paper, the GSMC scheme employs a smooth function for the switching device to alleviate the chattering phenomenon. Moreover, the proposed scheme uses an auxiliary compensator not only to establish the sliding condition for an ideal system but also to specify directly the dynamic characteristics of the sliding variable. According to Lyapunov's direct method, an explicit condition to ensure a stable attractor is derived. Experimental studies of designing a positioning system with a permanent magnet a.c. servomotor are conducted to illustrate further the feasibility and effectiveness of the proposed scheme.