压电微夹钳的位移自感知反馈复合控制

Displacement compound control of piezoelectric micro-gripper using self-sensing feedback

采用自感知方法获取压电微夹钳钳指位移,构成自感知反馈复合控制系统。根据反映钳指位移、表面电荷、夹持力、驱动电压之间关系的压电悬臂梁Smits方程,提出了基于电流积分的钳指位移自感知方法;引入死区算子对传统PI模型进行改进,建立了压电微夹钳钳指位移的迟滞模型;以对偏差的抛物线积分、对输出的先行微分分别代替常规PID控制器中的积分项和微分项,设计出了压电微夹钳的改进PID反馈控制器;将前馈控制器与PID反馈控制器相结合,并采用自感知反馈方式,设计出了压电微夹钳的闭环控制系统。实验结果表明：在自感知反馈复合控制作用下,压电微夹钳对5μm阶跃参考位移的响应时间为0.24 s,若不考虑噪声影响,稳态误差几乎为零;在最大位移为14.7μm的变幅值三角波参考位移以及最大位移为14.1μm的任意波形参考位移作用下,压电微夹钳的自感知反馈复合控制亦可取得良好的控制效果,其稳态误差中线在-0.02-0.04μm之间变化。自感知反馈控制的实验结果与传感器反馈控制基本相同,从而表明压电微夹钳的自感知反馈控制是有效的。

A self-sensing method is adopted to obtain the displacement of piezoelectric micro-gripper,and a compound control system based on self-sensing feedback is developed in this paper. According to the Smits equations of piezoelectric cantilever beam that reveal the relationships among the displacement,surface charge,gripping force and driving voltage of the micro-gripper fingers,the self-sensing method for the gripper finger displacement based on current integration is proposed. The dead zone operator is introduced to improve the traditional PI model,and the hysteresis model of the gripper finger displacement of the piezoelectric micro-gripper is established. The integral and differential terms in conventional PID controller are replaced by the parabolic integral of the deviation and the differential of the output,respectively,and an improved PID feedback controller for the piezoelectric micro-gripper is designed. Through combining the feed-forward controller and PID feedback controller,the closed-loop control system for piezoelectric micro-gripper is designed by means of self-sensing. Experiment results show that under the compound control based on self-sensing feedback,the response time of the microgripper for a step reference displacement of 5 μm is 0. 24 s; without considering noise,the steady state error almost can be regarded as zero. Meanwhile,under the reference displacements for the amplitude-variable triangle wave with maximum displacement of 14. 7 μm and the arbitrary wave with maximum displacement of 14. 1 μm,outstanding control performances of the piezoelectric micro-gripper can be obtained with the compound control based on self-sensing feedback; and the midline value of the steady state error is within- 0. 02μm - 0. 04 μm. The experiment results for self-sensing feedback control are almost the same as those for the sensor feedback control. As a conclusion,the self-sensing feedback control of the piezoelectric micro-gripper is effective and feasible.