匹配条件不满足时线性系统未知输入观测器设计

摘要

This paper discusses unknown input observer design method for a class of linear systems with unknown inputs when the observer matching condition (OMC) is not satisfied. Firstly, in order to break through the restriction of the OMC, a new auxiliary output construction method, which has nothing to do with the concept of relative degree with respect to the unknown input, is proposed. Then, the original system is transformed into an augmented linear descriptor system which contains no unknown inputs. In view of the transformation of the systems, a series of equivalent preconditions are discussed in detail. After this, a Luenberger observer is designed for the augmented linear descriptor system to estimate both the state and the unknown input simultaneously. Besides, a high-order sliding mode differentiator is used to estimate the unknown information of the auxiliary output. Finally, a simulation example of a single-link flexible joint robotic is given to illustrate the effectiveness of the proposed method.%针对一类不满足观测器匹配条件的线性系统,讨论了未知输入观测器设计方法.首先,为了突破观测器匹配条件的限制,提出了一种与未知输入相对阶无关的辅助输出构造方法.然后,把未知输入看作系统状态的一部分,将原系统转化为一个不含未知输入的增维线性描述系统.针对这样的系统转化,对一系列等价前提条件进行了详细的讨论.之后,针对该增维线性描述系统,构造Luenberger观测器来估计原系统的状态和未知输入.同时,借助于高阶滑模微分器,来估计辅助输出中的未知信号.最后,对一个单连杆柔性机械手模型进行了数值仿真,仿真结果表明了方法的有效性.