Sliding mode control with closed-loop filtering architecture for a class of nonlinear systems

It is well known by equivalent control theory, that in the sliding mode a low-pass filter, working as an average operator, can capture the desired control fairly well from the switching control signals. However, directly adding the filtered signals in parallel with the switching control does not warrant any improvement in the control system performance. In this work, we make clear the underlying reason why the sliding mode control (SMC) system does not function properly with such a simple closed-loop filtering structure. The correct way of incorporating the closed-loop filtering into SMC requires a second low-pass filter, which works concurrently with the first low pass filter to scale down the gain of the switching control. The SMC system with the new closed-loop filtering is able to realize the acquisition of equivalent control or estimate the disturbance, effectively reduce the switching gain to the minimum level, and as a result to eliminate chattering. Complementary to existing SMC, the proposed control system can easily incorporate feed-forward control into the closed-loop for bounded system perturbations. In addition, the frequency-domain knowledge can be easily used to construct the two filters.