Design of a Modified Tracking Differentiator

A modified tracking differentiator is proposed. Firstly, a nonlinear odd exponent continuous function is adopted which is only stable at one equilibrium point and proved the global asymptotic stability of the modified tracking differentiator by select a Lyapunov function. Through combining of the nonlinear and linear function properly, it can be sure that the state converges to the equilibrium point with high speed automatically no matter that the state was far away from the equilibrium point or near to it, and it can prevent the chattering. Simulation results show that the modified tracking differentiator tracking results are superior to the classical nonlinear tracking differentiator, and the response of state variables tracking differentiator estimated is almost coincide with the real state of the variables of the given system.