基于鲁棒二次稳定性理论的状态观测器增益矩阵求法

Solution of Gain Matrix for Status Observer Based on Robust Secondary Stability Theory

针对具有定子电阻不确定参数的电机模型,设计了全阶自适应状态观测器,运用具有定子电阻参数不确定系统的二次稳定性理论,推导出转子速度的自适应辨识率,同时将定子电阻和速度视作不确定参数,利用LMI工具箱中求解不确定参数系统二次稳定性的方法,得到状态观测器的增益矩阵来保证整个系统在全速度范围内的稳定运行。此方法计算量小,易满足实时性控制要求。仿真结果表明,基于鲁棒二次稳定性理论求出状态观测器增益矩阵能保证系统在全速度范围内的稳定运行,并且可抑制定子电阻不确定性对速度辨识的影响,具有很好的鲁棒性能。

According to the induction motor model with uncertain parameter of stator resistance, a full-step adaptive status observer is designed. The secondary stability theory of system which has uncertain parameter of stator resistance is used, and rotor speed adaptive law is deduced. Stator resistance and speed will be regarded as the uncertain parameters, and the gain matrix of status observer is obtained by using the linear matrix inequality to solve the secondary stability of uncertain parameter system, so that the stability of the whole system can be guaranteed in full-speed range. Less calculation is demanded and requirement of real-time control could be easily satisfied. Simulation results show that the gain matrix of status observer can ensure the stability of the adaptive observer, and the speed identification is hardly affected by the stator resistance uncertainty and features high robustness.