﻿ 基于Riccati方程解的高增益未知输入观测器设计
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Design of high-gain unknown input observer based on Riccati equation
ZHU Fanglai , ZHANG Yongjun
College of Electronics and Information Engineering, Tongji University, Shanghai 200092, China
Abstract:For a class of Lipschitz nonlinear system, the reconstruction problems of state estimation, unknown input and measurement noise were studied. Regarding the measurement noise as an extended state, the original system can be transformed into a descriptor system. For the descriptor system, first, a high-gain observer which can estimate the states and the measurement noise of original system simultaneously was developed based on the solution of a Riccati equation. Second, a second-order high gain sliding mode observer was used to exactly estimate the derivatives of the system outputs in a finite time. Third, by using the estimates of the states and the output derivatives, an algebraic unknown input reconstruction method was proposed. It was pointed out that both the unknown input and measurement noise reconstruction methods are suitable for stronger time-varying signals. Finally, a numerical simulation of a practical model was given to illustrate the effectiveness of the proposed methods.
Key words: unknown input observer     measurement noise reconstruction     Riccati equation     unknown input reconstruction     high-gain

1 问题描述

2 观测器设计

,则它为XR=In+w的解,其中YRn×(n+p)可以取为任意矩阵.当计算出X后,就可以得到

3 未知输入重构

4 仿真分析

 图 1 状态1(t)对x1(t)的跟踪Fig. 1 Track of 1(t) to x1(t)
 图 2 状态2(t)对x2(t)的跟踪Fig. 2 Track of 2(t) to x2(t)
 图 3 状态3(t)对x3(t)的跟踪Fig. 3 Track of 3(t) to x3(t)
 图 4 状态4(t)对x4(t)的跟踪Fig. 4 Track of 4(t) to x4(t)
 图 5 估计噪声及实际噪声Fig. 5 Estimation of noise and the actual noise

 图 6 输出微分1,2,3的估计误差Fig. 6 Estimation error of the output differential 1,2,3
 图 7 未知输入及其重构Fig. 7 Unknown input and its reconstruction
5 结 论

1) 提出了状态估计和未知输入和测量噪声同时重构的方法.

2) 本文的方法可以有效地抵消系统未知输入项给观测器带来的影响,即在不知道未知输入的情况下,实现对系统状态任意小邻域收敛估计.

3) 本文还结合二阶高增益滑模观测器,提出了一种未知输入代数重构方法,且方法具有不必用到系统可测输出微分信息的优点.

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#### 文章信息

ZHU Fanglai, ZHANG Yongjun

Design of high-gain unknown input observer based on Riccati equation

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(1): 8-13.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0041