Firstly, a new sliding mode control reaching law with a special power function and an inverse hyperbolic sine function is constructed. Then, an adaptive sliding control law is designed with the reaching law, and the error asymptotic convergence of the sliding control system is proved. The simulation experiments demonstrate that the adaptive sliding control system with the changing rotational inertia and friction torque has higher position and speed tracking precision, and reduces high frequency fluctuation phenomenon of the control input signal effectively. The adaptive law with the inverse hyperbolic sine function can well reduce the estimation value of the rotational inertia and control input signal.