Global sliding-mode control with generalized sliding dynamics

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 T AE, 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, (he 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.