A multi power reaching law of sliding mode control design and analysis

A multi power reaching law of sliding mode control is proposed in this paper, which aims at reducing chattering phenomenon, fastening convergence speed and making dynamic process smoothly. The proposed reaching law has three exponential terms to adjust the convergence process, so that the system has a faster convergence speed obviously and no chattering phenomenon. It is indicated through theoretical analysis that the system under the proposed reaching law has existence, accessibility and stability. The convergence speed and interference stability boundary are deduced in detail. Simulation results show that the dynamic process is improved and the chattering is reduced, as compared with the exponential reaching law, single power reaching law and double power reaching law. Further-more, when there exists interference or uncertainty, the system can converge to a neighborhood of the origin quickly