Analysis and application of Fal function filter

Fal function is a kind of special nonlinear structure, which is the key part of extended state observer in auto disturbance rejection controller. Fal function filter was proposed, which has good filtering effect on noises; moreover the filtering characteristics of Fal function filter was analyzed. Then a new type extended state observer (ESO) based on Fal function filter was proposed to deal with nonlinear system with measurement noises. Comparing with the method of extending a rank state to ESO and that of extending filter equation to ESO, this new method did not need extend the rank of ESO. So the tracking error increasing problem and the parameter tuning problem can be avoided. At last, the simulation results show that this new type ESO has good performance of states tracking for system with noises measurement.