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) over dot [x(t)] identically equal to zero, a regime enforced by a control signal depending on s[x(t)], but directly acting only on s[m(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.