动态迟滞Hammerstein系统的改进卡尔曼状态估计

Modified Kalman filtering for Hammerstein systems with dynamic hysteresis

迟滞特性具有非光滑、多值映射等复杂特性.而在实际的工程中,当输入电压变化频率超过一定的范围时,迟滞的特性是随着输入频率的改变发生变化,使得整个系统的状态估计工作更复杂.本文首先提出一种新的描述动态迟滞的方法,进而描述了动态迟滞Hammerstein系统的状态空间方程,根据此系统在传统卡尔曼滤波器的基础上进行改进得到一种新的非光滑卡尔曼滤波器.最后通过仿真和实验,比较了在输入信号变化频率比较大时,用动态迟滞Hammerstein系统来描述压电陶瓷和采用静态迟滞Hammerstein系统来描述压电陶瓷的特性,非光滑卡尔曼滤波器对这两种含有噪声的模型进行滤波,结果表明由于静态迟滞Hammerstein系统的建模不能很好的描述压电陶瓷的特性,模型存在着误差,因此对系统状态估计的结果也没有用动态Hammerstein系统的误差小,从而说明当输入电压频率变化比较大时研究动态的迟滞Hammerstein模型是很有意义的.

As the hysteresis inherent in the piezoceramic actuator is a nonsmooth nonlinear with multivalued mapping.In the working process of the system,the hysteresis phenomena are often rate-dependent when excited by voltage excitation with frequency content covering a wide range.It makes the state estimation of the whole system more complicated.In this paper,a new method to describe dynamic hysteresis is proposed,a non-smooth state space model for the dynamic Hammerstein system with hysteresis is constructed,then a non-smooth Kalman filter is proposed.Finally,simulation and experimental example are presented.The dynamic hysteresis Hammerstein system and the static hysteresis Hammerstein system was used to describe the characteristics of the piezoelectric actuators as the frequency increase,the hammerstein system with static hysteresis can not accurately describe the characteristics of piezoelectric actuators,non-smooth Kalman filter can not accurately estimate the state of the hammerstein system with dynamic hysteresis.Therefore,it is meaningful to study the rate-dependent hammerstein system.