Nonminimum phase tracking in MIMO systems with square input–output dynamics via dynamic sliding manifolds

Abstract

The approximate causal output tracking problem in nonlinear multi-input/multi-output (MIMO) nonminimum phase systems is addressed via sliding mode control. A class of MIMO nonlinear systems with matched nonlinearities as well as matched and unmatched disturbances, where the number of inputs, outputs, and the total relative degree are equal, is considered. The output tracking problem is solved using dynamic sliding manifold technique. The linear bounded error dynamics with desired eigenvalue placement forced by unmatched disturbance and causal reference output profile are provided. Addressing nonminimum phase condition, the sliding mode controller (SMC) joins features of a conventional SMC (insensitivity to matched nonlinearities and disturbances) and a conventional dynamic compensator (accomodation to unmatched disturbances). Theoretical results are demonstrated on a numerical example.