Fast higher-order sliding mode differentiator

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.