Abstract:To address the chattering problem of the traditional power reaching law and the slow global convergence, a new compound reaching law is proposed. By introducing the tangent function and improving the traditional power reaching law, the fast convergence and chattering free property of the reaching law are realized. Firstly, the tangent function is introduced, which can make the system converge faster when the initial state is known. Secondly, the proposed approach law improves the chattering problem caused by the product term of the signed function in the traditional power approach law. In this paper, it is proved theoretically that the new compound reaching law can converge quickly without chattering, and the reaching rate and steady-state error bound are derived. Finally, the effectiveness of the new compound reaching law is further verified by the magnetic levitation system simulation of Linear Magnetic Levitation Synchronous Motor.