含有迟滞Hammerstein系统的非光滑卡尔曼状态估计
Non-smooth Kalman filter based state estimation for Hammerstein systems with hysteresis

迟滞特性具有非光滑、多值映射等复杂特性. 如果迟滞环节的末端还存在一个线性子系统, 导致迟滞的输 出信号不可测, 使得整个系统的状态估计工作成为很大的难题, 常规的估计方法无法直接应用到这类系统中. 本文 提出一种新的非光滑卡尔曼滤波器, 描述了Hammerstein系统的状态空间方程. 据此构造了能够随系统工作区间变 化而自动切换的非光滑滤波器. 最后通过仿真和实验, 比较了非光滑卡尔曼滤波器和传统的卡尔曼滤波器的状态 估计效果, 比较结果表明非光滑卡尔曼滤波器对于带迟滞的Hammerstein系统状态变量的估计的准确性要优于传统 的卡尔曼滤波器.
As the hysteresis inherent in the piezoceramic actuator is a nonsmooth nonlinear with multivalued mapping, the hysteresis subsystem is preceded in series with a linear subsystem and the output of the hysteresis cannot be measured directly, it is very difficult to use the traditional filter to estimate the states of system. In this paper, a non-smooth Kalman filter is proposed, a non-smooth state space model for the Hammerstein system with hysteresis is constructed, firstly, the filter is switched among different operating zones automatically according to the operating conditions. Finally, simulation and experimental example are presented. The comparison between the proposed non-smooth scheme and the conventional Kalman filter shows that the former has resulted in better estimation performance.