On Multi-Input Chattering-Free Second-Order Sliding Mode Control

A solution to the problem of eliminating the chattering effect, which is always associated with practical implementations of variable structure control, is presented in this paper with reference to a class of uncertain multi-input nonlinear systems. The solution procedure relies on the application of an original control approach capable of enforcing a second-order sliding mode (i.e., a sliding regime on a surface s[x(t)] = 0 in the system state space, with s[x(t)] identically equal to zero, a regime enforced by a control signal depending on s[x(t)], but directly acting only on s[x(t)]). Such an approach, in its original formulation, only applies to single-input nonlinear systems with particular types of uncertainties, in the present paper, its validity is extended to multi-input nonlinear systems characterized by uncertainties of more general nature, covering a wide class of real processes. Index Terms--MIMO systems, nonlinear systems, uncertainty, variable structure systems.