摘要
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 Prandtl-Ishlinskii)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(Prandtl-Ishlinskii)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10 Hz,40 Hz,80 Hz和复合频率10~90 Hz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(auto regressive model with exogenous input)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试验平台,对单频率1 Hz,40 Hz,80 Hz和复合频率10~90 Hz的正弦输入电压信号进行了微位移实时跟踪控制试验,试验中的相对误差在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。
Piezoelectric ceramics are intelligent materials with hysteresis nonlinearity.In order to realize precise tracking control of a system,a Hammerstein dynamic hysteresis model based on MPI was proposed,and a sliding mode tracking control scheme for the system was designed based on the model.The delay coefficients were introduced at the rising edge and falling edge thresholds of the play operator,and the dead zone operator was 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 sinusoidal input voltage signals of single frequency 10 Hz,40 Hz,80 Hz and compound frequency in the band of 10-90 Hz 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 was verified.Compared with the classical PI-based Hammerstein dynamic hysteresis model,the model error is reduced by 37%,42%,35%and 24%,respectively.Finally,a hysteresis compensator was constructed,and a sliding mode control scheme was proposed to realize the dynamic tracking control of the system.A sliding mode control piezoelectric system experimental platform was built,and the micro-displacement real-time tracking control experiments were carried out under the excitation of the sinusoidal input voltage signals of single frequency 1 Hz,40 Hz,80 Hz and a group of compound frequencies in the band of 10-90 Hz.The relative errors in the experiments are within 7.62%,and the maximum root mean square error is 1.8573μm,indicating that the proposed sliding mode controller has strong tracking performance.
作者
周子希
王贞艳
ZHOU Zixi;WANG Zhenyan(School of Electronic Information Engineering,Taiyuan University of Science and Technology,Taiyuan 030024,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2024年第18期131-136,共6页
Journal of Vibration and Shock
基金
山西省重点研发计划项目(202102020101013)
山西省基础研究计划项目(202103021224271)
太原科技大学博士科研启动基金项目(20202070)。
