基于有限时间输出反馈的线性扩张状态观测器

Linear Extended State Observer Based on Finite-time Output Feedback

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.

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.