Extended State Observer-Based Discrete-Time Sliding-Mode Control With Mismatched Disturbances Attenuation

This paper proposed an extended state observer (ESO)-based discrete-time sliding-mode controller (DSMCer) to improve the steady-state output tracking accuracy of the systems with unmeasurable states and unknown mismatched disturbances. First, an ESO is designed based on disturbance decomposition, which decomposes the lumped disturbances into the matched part and the mismatched part. Instead of regarding all the elements of the lumped disturbance as new states, the proposed ESO regards the first several elements, i.e., the nonzero elements, of the mismatched part of the disturbances as new states. This will result in a smaller dimension and make it easier to guarantee the existence of the ESO. Then, based on the states of the proposed ESO, a new sliding surface is constructed, a new reaching law is designed, and subsequently, a desirable DSMCer is organized, which can solve the problems of unmeasurable states and unknown disturbances and can effectively attenuate the effect of the mismatched part of the disturbances on the output tracking performance. The system stability is analyzed, and the effectiveness of the proposed method is verified through numerical simulations.