Abstract:

By combining the sliding mode control for mismatched uncertainties with the linear matrix inequality（LMI）approach，a novel robust sliding mode observer for a class of uncertain dynamic system with mismatched uncertainties was designed. The necessary and sufficient condition of stabilizing the sliding mode observer and the LMI existence theorem were presented and strict verification was done to guarantee robustness to uncertainties of systems and disturbances. The Lyapunov function was used as the judgement condition for stabilizing observers，and the convergence rate between observer and system was changed by regulating the sliding-mode strategy so as to attain the desired performance of state estimation. Simultaneously，without the canonical transformation of the dynamic systems，the linear feedback matrix and nonlinear feedback matrix of the robust sliding mode observer were solved by LMI that has advantages in computation. The problems of actuator fault detection and reconstruction for a class of uncertain dynamic system with mismatched uncertainties were discussed. By applying the equivalence output error concept and LMI approach，the optimizing strategy of reconstructing actuator fault can be designed，and a new actuator fault detection and reconstruction design method based on the designed sliding mode observer was proposed to obtain the fault information on-line. The design procedure was described and nonlinear simulation results were presented to demonstrate the approach.

摘要：

针对一类不匹配不确定性动态系统，将不匹配不确定性的滑模控制方法与线性矩阵不等式（LMI）方法结合，设计一种新的鲁棒滑模观测器，提出了不匹配不确定动态系统滑模观测器稳定的充分必要条件以及LMI的存在定理，并证明了对系统不确定性以及外界干扰具有鲁棒性。无须对动态系统进行规范化处理，直接利用LMI方法求解鲁棒观测器增益矩阵，简化了滑模观测器设计过程。根据上述设计的鲁棒滑模观测器，应用等价输出误差介入原理和LMI方法，设计重构执行器故障的优化策略，提出在线获取故障信息的鲁棒执行器故障检测与重构方法，实现执行器故障的检测与重构。数字仿真验证了执行器故障重构方法的可靠性。