Sliding mode control framework for reconstruction and rejection of mismatched and matched disturbances

This study proposes a sliding mode control (SMC) framework for the reconstruction and rejection of mismatched and matched unknown disturbances. First, a robust proportional-integral (PI) type controller is designed for dealing with an uncertain scalar system subject to matched disturbance. Then, a 2^nd order uncertain system subjected to both matched and mismatched disturbances is discussed. By incorporating the idea of backstepping design, the mismatched disturbance can be transformed into a matched one with respect to a virtual control input. Therefore, the matching condition can be extended. Finally, the developed method for multivariable systems is further addressed and some formulas for disturbance reconstruction are provided. Simulations evidently illustrate that the proposed control framework can successfully stabilize control plants as well as recover the external faults.