Modified PI dynamic hysteresis modeling and control of piezoelectric ceramic actuators

ZHOU Zixi, WANG Zhenyan

Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (18) : 131-136.

PDF(1707 KB)
PDF(1707 KB)
Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (18) : 131-136.

Modified PI dynamic hysteresis modeling and control of piezoelectric ceramic actuators

  • ZHOU Zixi,WANG Zhenyan
Author information +
History +

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.

Key words

Piezoelectric ceramic actuators / Hysteresis nonlinearity / Hammerstein dynamic hysteresis model / MPI model / Sliding mode tracking control

Cite this article

Download Citations
ZHOU Zixi, WANG Zhenyan. Modified PI dynamic hysteresis modeling and control of piezoelectric ceramic actuators[J]. Journal of Vibration and Shock, 2024, 43(18): 131-136

References

[1] 范伟,傅雨晨,于欣妍.压电陶瓷驱动器的迟滞非线性规律[J].光学精密工程,2019, 27(8): 1793-1799.
FAN Wei, FU Yuchen, YU Xinyan. The hysteresis and nonlinear law of piezoelectric ceramic driver[J]. Optics and Precision Engineering, 2019, 27(8): 1793-1799.
[2] 贺一丹,王贞艳,何延昭等.压电陶瓷作动器的改进Duhem迟滞建模[J].压电与声光, 2021, 43(03): 431-434.
He Yidan, Wang Zhenyan, He Yanzhao et al. Improved Duhem hysteresis Modeling of piezoelectric ceramic Actuators[J]. Piezoelectrics and Acoustooptics, 2021, 43(03): 431-434.
[3] Kim S Y, Lee C H. Description of asymmetric hysteretic behavior based on the Bouc-Wen model and piecewise linear strength-degradation functions[J]. Engineering Structures, 2019, 181(FEB.15): 181-191.
[4] BERMUDEZ A, DUPRE L, GOMEZ D, et al. Electromagnetic computations with Preisach hysteresis model[J]. Finite Elements in Analysis and Design, 2017, 126(4): 65-74.
[5] KUHNEN K, JANOCHA H. Inverse feedforward controller for complex hysteretic nonlinearities in smart-material systems[J]. Control and Intelligent Systems, 2001, V29(3): 74–83.
[6] 尚爱鹏,王贞艳,贺一丹.基于H-like模型的压电陶瓷作动器内模控制[J]. 压电与声光,2020, 42(5): 708-712.
SHANG Aipeng, WANG Zhenyan, HE Yidan. Internal mode control of piezoelectric ceramic actuator based on H-like model[J]. Piezoelectrics and Acoustooptics, 2020, 42(5) : 708-712.
[7] 陈圣鑫,赵新龙,苏强等.基于区间二型T-S模糊系统的压电迟滞特性建模[J].压电与声光,2020,42(06):843-847+853.
CHEN Shengxin, ZHAO Xinlong, SU Qiang et al. Modeling of piezoelectric hysteresis characteristics based on interval II T-S fuzzy system[J].Piezoelectrics and Acoustooptics, 2020, 42(06): 843-847+853.
[8] 张臻,辛峰,周克敏.压电舵机动态迟滞建模与带有鲁棒干扰观测器的两自由度控制[J].控制理论与应用, 2019, 36(6): 841-849.
ZHANG Zhen, XIN Feng, ZHOU Kemin. Dynamic hysteresis modeling of piezoelectric servos and two-degree-of-freedom control with robust disturbance observer[J]. Control Theory and Applications, 2019, 36(6): 841-849.
[9] SHI Beichao, SHI Rui, WANG Fujun. Design of an adaptive feedforward/feedback combined control for piezoelectric actuated micro positioning stage[J].Precision Engineering, 2022, 78(2022): 199-205.
[10] 李亮,喻俊,温盛军.基于Hammerstein模型的动态率相关迟滞特性建模及分析[J].组合机床与自动化加工技术,2022,(06):31-35.
LI Liang, YU Jun, WEN Shengjun. Modeling and analysis of dynamic rate-dependent hysteresis characteristics based on Hammerstein model[J].Modular Machine Tool&Automatic Manufacturing Technique,2022,(06):31-35.
[11] WANG Wen, WANG Jian, CHEN Zhanfeng, et al. Research on Asymmetric Hysteresis Modeling and Compensation of Piezoelectric Actuators with PMPI Model[J].Micromachines, 2020, 11(4): 357.
PDF(1707 KB)

Accesses

Citation

Detail

Sections
Recommended

/