压电陶瓷是一种具有迟滞非线性的智能材料。为了实现系统的精密跟踪控制，提出一种基于MPI（modified proportional-integral）的Hammerstein动态迟滞模型，并基于该模型设计了滑模跟踪控制方案。在play算子的上升边沿和下降边沿阈值处引入了延时系数，并串联死区算子构成改进的非对称PI模型，基于MPI的Hammerstein动态迟滞非线性模型可以描述压电陶瓷作动器的率相关迟滞特性。通过采集在单频率10Hz，40Hz，80Hz和复合频率10~90Hz正弦输入电压信号下的压电陶瓷作动器的位移数据，并采用粒子群算法和最小二乘递推方法辨识MPI模型参数和ARX模型参数，验证了模型的可行性，相较于基于经典PI的Hammerstein动态迟滞模型，模型误差分别降低了37%、42%、35%和24%。最后，构建迟滞补偿器，利用Hammerstein模型的模块化特点，提出一种可以实现对系统动态跟踪控制的滑模控制方案，并搭建了滑模控制压电系统实验平台，对单频率1Hz、40Hz、80Hz和复合频率10~90Hz的正弦输入电压信号进行了微位移实时跟踪控制实验，实验中的相对误差在7.62%以内，均方根最大误差为1.8573μm，表明所提出的滑模控制器有较强的跟踪性能。
Abstract
Piezoelectric ceramics are intelligent materials with hysteresis nonlinearity. In order to realize precise tracking control of the system, a Hammerstein dynamic hysteresis model based on MPI is proposed, and a sliding mode tracking control scheme is designed based on the model. The delay coefficients are introduced at the rising edge and falling edge thresholds of the play operator, and the dead zone operator is connected in series to form an improved asymmetric PI model. The MPI-based Hammerstein dynamic hysteresis nonlinear model can describe the rate-dependent hysteresis characteristics of piezoelectric ceramic actuators. By collecting the displacement data of the piezoelectric ceramic actuator under the single frequency 10Hz, 40Hz, 80Hz and a compound frequency 10~90Hz sinusoidal input voltage signal, and using particle swarm optimization algorithm and least squares recursion method to identify the parameters of the MPI model and the ARX model, the feasibility of the model is verified. Compared with the classical PI-based Hammerstein dynamic hysteresis model, the model error is reduced by 37%, 42%, 35% and 24%, respectively. Finally, the hysteresis compensator is constructed, and a sliding mode control scheme is proposed to realize the dynamic tracking control of the system. Built a sliding mode control piezoelectric system experimental platform, the single frequency 1Hz, 40Hz, 80Hz and a group of compound frequency 10~90Hz sinusoidal input voltage signal is carried out micro-displacement real-time tracking control experiment. The relative error in the experiment is within 7.62%, and the maximum root mean square error is 1.8573μm, indicating that the proposed sliding mode controller has strong tracking performance.
关键词
压电陶瓷作动器 /
迟滞非线性 /
Hammerstein动态迟滞模型 /
MPI模型 /
滑模跟踪控制
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Key words
Piezoelectric ceramic actuators /
Hysteresis nonlinearity /
Hammerstein dynamic hysteresis model /
MPI model /
Sliding mode tracking control
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