Causal nonminimum phase output tracking in MIMO nonlinear systems in sliding mode: stable system center technique

Abstract

The problem of approximate output tracking of an arbitrary reference profile in nonlinear multi-input/multi-output (MIMO) nonminimum phase systems is considered. The causal nonminimum phase output tracking is provided via sliding mode control using an extension of the method of system center for nonminimum phase systems and a dynamic sliding manifold technique. Linear bounded closed-loop error dynamics with desired eigenvalue placement are enforced in sliding mode. The smooth profile with finite number of non-zero time derivatives under presence of unmatched disturbance of the same property will be asymptotically followed. Addressing nonminimum phase output tracking, the sliding mode controller (SMC) joins features of a conventional SMC (insensitivity to matched uncertain nonlinearities and disturbances) and a conventional dynamic compensator (accommodation to unmatched disturbances). Theoretical results are demonstrated on a numerical example.