针对传统的Bouc-Wen模型不能准确表征压电陶瓷执行器固有的迟滞非对称特征，导致控制精度受限问题，该文提出一种基于传统的Bouc-Wen模型与Hammerstein 模型结合的迟滞建模方法，基于利用卡曼状态预估的滑模控制的控制策略来提高控制精度。首先，利用粒子群算法对传统的Bouc-Wen模型与Hammerstein结构结合迟滞模型的参数进行辨识，然后根据二阶系统的状态空间矩阵建立卡尔曼观测器，并根据卡尔曼观测器的状态预估利用滑模规律进行反馈补偿和建立逆模型进行前馈补偿，形成前馈-反馈复合补偿。通过数值仿真表明，在0~100 V峰值与0~100 Hz激励频率内，所建立的非线性模型能很好地描述与预测压电陶瓷执行器的动态输出。执行器位移在0~6 μｍ时，传统的Bouc-Wen模型开环、基于传统的Bouc-Wen模型与Hammerstein 结构结合迟滞模型的平均迟滞误差分别为0.654 95 μm、0.186 39 μm; 在50 Hz下，基于传统的Bouc-Wen模型与Hammerstein 结构的前馈PID补偿均方根误差为0.088 5 μm，其前馈滑模复合控制补偿均方根误差为0.047 μm，仅为最大输出位移的0.78%，最大跟踪误差仅为0.153 μm，精度提高了78%，说明该文所提出的基于传统的Bouc-Wen模型与Hammerstein 结构结合迟滞模型及其补偿控制算法，有助于实现压电陶瓷执行器的高速、宽频超精密定位控制。

Aiming at the problem that the traditional Bouc-Wen model cannot accurately characterize the intrinsic hysteresis asymmetry of piezoelectric actuators thus caused the limited control precision, in this paper, a hysteresis modeling method based on the combination of traditional Bouc-Wen model and Hammerstein model is proposed. The control strategy based on the sliding mode control using Kalman state estimation is used to improve the control accuracy. First, the parameters of the hysteresis model combined with the traditional Bouc-Wen model and the Hammerstein structure are identified by using particle swarm optimization (PSO). Then, the Kalman observer is built based on the state space matrix of the second-order system. According to the state prediction of Kakman observer, the feedback compensation is made by using sliding mode law and the feedforward compensation is made by establishing the inverse model, forming a feedforwar-feedback composite compensation. The numerical simulation shows that the nonlinear model can well describe and predict the dynamic output of piezoelectric ceramic actuator in the range of 0-100 V peak value and 0-100 Hz excitation frequency. The displacement of the actuator is between 0 and 6 μm, the average hysteresis error of the traditional Bouc-Wen model is 0.654 95 μm and 0.186 39 μm, respectively, at 50 Hz, based on the traditional Bouc-Wen model and Hammerstein structure, the room mean square (RMS) error of feedforward proportion integration differentiation (PID) compensation is 0.088 5 μm, and the RMS error of feedforward sliding mode composite control compensation is 0.047μm, which is only 0.78% of the maximum output displacement, the maximum tracking error is only 0.153 μm, and the precision is improved by 78%, indicating that the proposed hysteresis model based on traditional Bouc-Wen model and Hammerstein structure and its compensation control algorithm are helpful to realize high-speed and wide-frequency ultra-precision positioning control of piezoelectric ceramic actuator.