Firstly, discontinuous function in higher-order differentiator is substituted by Terminal attractor function to
eliminate chattering. Then, fast convergence term is inserted into each sliding mode of higher-order differentiator to speed up
convergence. The system is stable under different conditions and the estimation error expression is given. A method for noise
restrain is proposed. The difference of the convergence time and the estimation error between fast higher-order differentiator
and normal higher-order differentiator are analyzed. The universal design method for fast higher-order differentiator is
generalized. Finally, simulation results show the correctness and effectiveness of all conclusions.