無感測器之多軸壓電平台的精密運動控制

Sensorless Precision Motion Control of a Multi-axis Piezo-actuated Stage

陳聯聖(Lien-Sheng Chen)

指導教授 ： 顏家鈺

國立臺灣大學/工學院/機械工程學研究所/博士(2013年)

https://doi.org/10.6342/NTU.2013.01420

摘要

本論文提出了一種不需要位移感測器的新方法，能夠達成壓電致動的撓性結構載台之精密運動控制。高精度的位移感測器通常價值不斐，在實際應用上也會受到架設空間的限制。此外，致動器及位移感測器常形成非同位(Non-collocated)的架構，可能會造成控制演算法的複雜度大幅提升。
壓電致動器擁有高位移解析度以及優秀的動態響應性能，但卻因遲滯等非線性現象，使其能達成的定位精確度受限。然而，在文獻中所提出壓電致動器的機電模型裡，可以觀察到流經並儲存於壓電致動器中的電荷，與致動器本身的位移量之間有直接關係，並且可以用一個線性非時變系統來表達。因此在本研究中，壓電致動平台的定位以及運動控制，是透過量測儲存於致動器中的電荷，並設計適當控制演算法，使電荷數量對時間的關係遵循一個預先設計好的軌跡來達成。
本論文中提出的新方法與過去文獻中採用的消除遲滯之方法不同。它既不需要針對不同壓電致動器、不同載台而設計獨特且複雜的電荷放大器電路，也不需要針對遲滯現象建立精確的非線性模型。此方法只需要在系統識別階段使用位移感測器的資料，配合量得的電荷量，得到動態模型的描述，並針對此識別出的模型進行數位控制器的設計。由於此電荷迴授控制器是針對致動器及平台的整體動態性能來設計的，因此可以避免因使用高增益的電荷放大電路而導致的系統不穩定現象。完整的模型推導、系統識別流程、控制器設計以及不確定因素對系統性能的分析都會包含於本論文中，而實際的運動控制性能則會呈現於最後的實驗結果。

關鍵字

壓電致動器 ； 撓性結構載台 ； 電荷迴授 ； 運動控制 ； 遲滯現象

並列摘要

This dissertation presents a novel approach for precisely controlling the motion of a piezo actuator embedded in a mechanical stage without using a displacement sensor. Displacement sensors are often costly and space-consuming, resulting in difficulties of designing compact positioning systems. On the other hand, complicated control algorithms might be required if the sensors are not collocated with the actuators.
A piezo actuator has high displacement resolution and high dynamics response, but the positioning performance is degraded by nonlinearities such as the hysteresis between the applied voltage and resultant displacement. However, an electromechanical model of a piezo actuator suggests that the charge flowing into the actuator is directly related to the dynamic response of the piezo displacement, and the interaction can be described by a linear time-invariant dynamic system. Therefore in this study, the charge stored in piezo actuators are directly measured, and dynamic reference tracking of the stage’s displacement is achieved by regulating the charge flowing through the actuator to follow a predefined trajectory.
This novel approach requires neither specially designed charge amplifier circuits nor implementation of an inverse hysteresis model. Complete model identification and digital controller design procedure for a piezo-driven mechanical stage are presented. The charge feedback controller is designed according to the dynamic characteristics of both the actuator and the stage, so that instability problem can be avoided comparing to using a high gain charge amplifier. The experimental results confirm satisfactory tracking performance, and reveal the influence of model uncertainties on the system performance.

並列關鍵字

Piezo actuators ； flexure-hinge stage ； charge feedback ； motion control ； hysteresis

參考文獻

[2] J. Minase, T.-F. Lu, B. Cazzolato and S. Grainger, “A review, supported by experimental results, of voltage, charge and capacitor insertion method for driving piezoelectric actuators,” Precision Engineering, Vol. 34, Issue 4, pp.692-700, 2010.

[3] Qing Yao, Jingyan Dong and Placid M. Ferreira, " A novel parallel-kinematics mechanisms for integrated, multi-axis nanopositioning: Part 1. Kinematics and design for fabrication," Precision Engineering, Vol. 32, Issue 1, pp.7-19, 2008.

[4] Jong-Lick Lin and Jer-Nan Juang, " Sufficient Conditions for Minimum-Phase Second-Order Linear Systems," Journal of Vibration and Control, Vol. 1, No. 2, pp.183-199, 1995.

[5] J.L. Lin, K.C. Chan and S.J. Chen, " Minimum phase robustness margin for second-order systems with multidirectional perturbations," Journal of the Franklin Institute, Vol. 341, Issue 3, pp.255-265, 2004.

[6] Kuo-Jung Lan, Active Vibration Isolation Technologies for Scanning Probe Microscope, Doctorial Dissertation, Department of Mechanical Engineering, National Taiwan University, 2004.