Double Hyperbolic Reaching Law With Chattering-Free and Fast Convergence

This paper proposes a novel continuous reaching law for chattering-free sliding mode control by using two hyperbolic functions with similar changing rate and opposite amplitude characteristics. The first function is an inverse hyperbolic sine function, which can guarantee the fast convergence as the initial value of the sliding mode variable is far away from the equilibrium. When the sliding mode variable is approaching to zero, the second hyperbolic tangent function can ensure the sliding mode variable be infinitely close to zero rather than cross the zero. With the proposed reaching law, the fast convergence and chattering-free property can be both guaranteed, and the satisfactory convergence performance of the reaching phase is achieved with an approximation method. Moreover, the steady state error bound is analyzed in details when considering external disturbances. A simple example is provided to demonstrate the effectiveness of the proposed method.