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.

In this paper, a speed tracking and synchronization control approach is proposed for a multimotor system based on fuzzy active disturbance rejection control (FADRC) and enhanced adjacent coupling scheme. By employing fuzzy logic rules to adjust the coefficients of the extended state observer (ESO), FADRC is presented to guarantee the speed tracking performance and enhance the system robustness against external disturbance and parametric variations. Moreover, an enhanced adjacent coupling synchronization control strategy is proposed to simplify the structure of the speed synchronization controller through introducing coupling coefficients into the conventional adjacent coupling approach. Based on the proposed synchronization control scheme, an adaptive integral sliding mode control (AISMC) is investigated such that the chattering problem in conventional sliding mode control can be weakened by designing an adaptive estimation law of the control gain. Comparative simulations are carried out to prove the superiorities of the proposed method.