An Adaptive Sliding Mode Controller with The Exponential and Power Reaching Law for Discrete Systems

With the development of aeronautics and astronautics, the response speed of servo system need be faster. First, In order to improve the dynamic quality of servo system, the exponential and power reaching law, which combines the advantages of the exponential reaching law and the power reaching law, is introduced. Second, the chattering of the sliding mode controller (SMC) with the exponential and power reaching law for discrete systems is investigated. Finally, the adaptive sliding mode controller (ASMC) with the exponential and power reaching law is introduced. The stability of the ASMC with the exponential and power reaching law for discrete systems is analyzed, and the simulation of this approach on one joint of a six degrees of freedom robot is carried out. The experimental results indicate that the ASMC with the exponential and power reaching law is effective in reducing the time of arriving the sliding mode surface. The experimental results also indicate that the ASMC with the exponential and power reaching law may make output error reach zero in a shorter time.