一类不确定广义系统故障估计的有限时间鲁棒观测器设计

Finite-time robust observer design for fault estimation of a class of descriptor uncertain systems

针对一类具有不确定性的广义系统,提出一种故障估计观测器设计方案。该观测器具有非奇异结构,不仅保证增广误差系统动态方程满足有限时间有界性条件,而且保证故障估计误差对于扰动在有限时间内具有鲁棒性。首先,视故障为系统部分状态变量,建立增广广义系统模型。之后,从有限时间分析增广误差系统的有界性,讨论故障估计误差对于扰动的有限时间鲁棒性;然后,给出观测器增益限制矩阵存在的充分条件,并给出该限制矩阵的线性矩阵不等式形式。最后,基于具有不确定性广义系统的卫星姿态控制系统,针对系统发生的执行器及传感器故障进行仿真,以验证设计方案的有效性。仿真结果表明,设计的有限时间鲁棒观测器不仅能够精确估计系统的故障值,而且能够有效估计耦合于故障的系统状态值:相较于指数稳定观测器,所提出的观测器对于状态变量的估计均方根误差降低了25%以上;对于故障估计的均方根误差降低了50%以上。仿真验证了该方法的有效性。

A fault estimation observer is proposed for a class of descriptor systems with uncertainties.The proposed observer has a non-singular structure,which not only ensures that the dynamic model of the augmented error system is finite time boundedness,but also the fault estimation error is robust to the disturbance in finite time.Firstly,the faults are seen as partial state variables of the descriptor systems,and an augmented descriptor model is established.Then,the finite time boundedness of the augmented error system is analyzed,and the finite time robustness of the fault against the disturbance is discussed;The sufficient conditions of the existence of the observer gain constrained matrices are given and are formulated as the linear matrix inequalities.Finally,a simulation example of attitude control systems of satellite based on the uncertain descriptor systems with actuator and sensor faults is given to show the effectiveness of the method.The simulation results show that the designed finite time robust observer not only estimates the faults of the system accurately,but also estimates the system state values coupled to the faults effectively-compared with the exponential stable observer,all of the root mean square errors of the state variables estimation by the proposed observer are decreased more than 25%.The faults estimation are decreased more than 50%.The simulation results verifies the effectiveness of the proposed method.