Global sliding-mode control with generalized sliding dynamics

Abstract

A global sliding-mode control (GSMC) scheme is proposed to provide a framework for ensuring the existence of a sliding mode throughout an entire response. Based on this framework, robust eigenvalue-assignment GSMC (REA-GSMC) is proposed to robustly assign closed-loop eigenvalues that must be real. The eigenvalues being all real, however, leads to sluggish responses. According to most error criteria such as IAE, ISE, and ITAE, the optimum system should have complex eigenvalues. This paper proposes a GSMC scheme with generalized sliding dynamics, referred to as Generalized GSMC, in order to release the previous constraint on the REA-GSMC. Thus, the Generalized GSMC can be designed to achieve a system that is both robust and optimum in the sense that it minimizes certain error performance indices in spite of the presence of system uncertainties. Experiments were conducted on a two-link direct-drive manipulator to demonstrate the effectiveness of the proposed scheme.