Optimal tracking conditions for linear extended state observer on uncertain system.

摘要

This thesis describes numerically the optimal tracking condition and the absolute error estimation of the Linear Extended State Observer (LESO) for a class of nonlinear and uncertain motion control problems by finite difference method approach. In current industrial control applications, the Proportional + Integral + Derivative (PID) control is still used as the leading tool. But constructing controller requires the precise mathematical model of plant, and tuning the parameters of controllers is not simple to implement. Motivated by the gap between theory and practice in control problems, Linear Active Disturbance Rejection Control (LADRC) addresses a set of control problems in the absence of precise mathematical models. LADRC depends on the quick convergence of a unique state observer, known as the extended state observer, proposed by Jinqing Han. LADRC has two parameters to be tuned, namely, a closed loop bandwidth and observer bandwidth. Only one of them, observer bandwidth, significantly affects the tracking speed of extended state observer. In this thesis, the optimal fast tracking condition for LESO is found in terms of observer bandwidth and sampling time. And uncertainties of the plant are considered in the case of two possible behaviors: continuous and piecewise continuous.