Firstly, the discontinuous function is substituted by Terminal attractor function to eliminate chattering. To solve the problem that it is difficult to choose proper design parameters for higher-order differentiator, the range of design parameters is relaxed and the stability of higher-order differentiator in different conditions is proved. By analyzing design parameters and system structure, a design method which is more suitable for engineering application to reduce estimation error is proposed and the conditions needed are given. Finally, the simulation results show the effectiveness and correctness of these conclusions.