Reconstruction and rejection of mismatched and matched disturbances for a class of multivariable systems

This study proposes a synthetic control strategy for the reconstruction and rejection of mismatched and matched unknown disturbances. For a nonlinear scalar system, a nonlinear proportional-integral (PI) control is developed for dealing with matched disturbances. Next, a 2nd order system subjected to both matched and mismatched disturbances is considered. By incorporating the idea of backstepping design and conventional sliding mode control (SMC), the mismatched disturbance can be transformed into a matched one with respect to a virtual control input, and therefore the matching condition is extended. An extension of the proposed control framework for a class of multi-input multi-output (MIMO) systems is further provided.