Estimate error analysis of the nonlinear third order extended state observer

Nonlinear extended state observer not only estimate all the state of uncertain plant, but also the real-time inner and outer disturbance, independent to plant model and having better robust capability. However, the estimate error analysis of more than second order observer hasn´t been depth researched. Based on the estimate error theory of second order observer and some proper hypothesis, this paper firstly decoupled the third order observer into two second order observers, then the performance of estimate error is analyzed using continuous piece-wise smooth Lyapunov function theory and a tuning rule is put forward. And, based on the analysis of effect of observer parameters, an optimization rule is used with the tuning process. Theoretic analysis and simulation results indicate that the proposed estimate error analysis method is proper, and the tuning law and optimization rule of observer parameter are feasible.