基于有限时间输出反馈的线性扩张状态观测器

为快速、准确地观测系统中的未知扰动及状态, 提出一种有限时间线性扩张状态观测器(Finite-time linear extended state observer, FT-LESO), 它具有期望的收敛性能且结构简单、易于设计. 假设系统的状态无法量测, 观测器设计问题转化为扰动下的输出反馈控制问题. 针对该问题, 提出一种扰动下的有限时间线性输出反馈控制方法, 得到控制器参数与闭环系统状态向量2-范数间的解析关系. 在此基础上, 提出有限时间线性扩张状态观测器, 得到观测器参数与观测误差收敛速度及稳态观测误差间的解析关系, 给出一充分条件保证观测误差有限时间有界、且能以不低于指数收敛的速度收敛到给定范围内, 为观测器参数设计提供理论依据. 通过数值仿真验证提出的观测器, 仿真结果与理论分析相符, 提出的观测器是有效的.

Linear Extended State Observer Based on Finite-time Output Feedback

To observe unknown disturbance and states in a system rapidly and exactly, a finite-time linear extended state observer (FT-LESO) is proposed. The observer is with desired observation performance, simple structure, and is easy to design. Suppose the states are unmeasurable, the observer design problem is transformed to an output-feedback control problem of a system with disturbance. To solve the control problem, a linear finite-time output-feedback control method is presented. An analytic relationship between the controller''s parameter and state vector''s 2-norm of the closed-loop system is derived. Based on the control method, an FT-LESO is proposed. An analytic relationship between the FT-LESO''s parameter, observation error''s convergence speed, and steady observation error is obtained. And a sufficient condition is derived to ensure the observation error is finite-time bounded and can converge to a specified range no slower than exponential convergence. This sufficient condition provides a theoretical basis for designing an FT-LESO. The FT-LESO is demonstrated by a numerical simulation. Simulation results are coincident with theoretical analysis. The proposed FT-LESO is effective.