六自由度史都沃特平台之力與位移強健控制系統於奈米定位之研究

A Robust Position/Force Control System Design of 6DOF Stewart Platform for Nanoscale Positioning

10.6840/cycu201700122

阮文壽

六自由度史都沃特型平台 ； 磁滯前饋控制器 ； 指數加權移動平均(EWMA)方法 ； 預測校正控制器(PCC)方法 ； 力回饋控制器 ； 6DOF Stewart-type platform ； feedforward hysteresis controller ； Exponentially Weighted Moving Average (EWMA) ； Predictor Corrector Control (PCC) ； force feedback controller

中原大學機械工程學系學位論文

2017年

博士

丁鏞

英文

本研究的重點是針對使用壓電致動器驅動的六自由度史都沃特型平台設計適當之控制方法，在受到外力影響時仍能保持很好的定位精度。首先藉由運動學分析模型與實驗測量終端位置之校正，以提高系統參數的精度。非線性的磁滯、潛變效應、漂移干擾、或溫升效應是使用壓電致動器常見之負面因素，會直接影響系統的精度以及穩定性，故設計控制方法須特別考量。本論文利用Preisach方法推導出壓電致動器的磁滯模型，以建立磁滯前饋控制器來解決磁滯問題。另利用已廣泛用於統計製程控制並能克服系統變化和漂移干擾之指數加權移動平均(Exponentially Weighted Moving Average, EWMA)方法，嘗試將EWMA方法轉移至兩次運轉對比(Run-to-Run)之數位模型參考適應系統(MRAS)，並將磁滯前饋控制器整合於內，完成一套定位控制系統。除了單級演算之EWMA方法，具有兩級演算之EWMA進階型預測校正控制器(Predictor Corrector Control, PCC)，亦將設計與驗證功能之優劣。 除了位移控制器，亦結合非線性PID控制器與常見之計算扭矩方法來設計力回饋控制器，以克服未知且隨環境變化之外力影響。配合選擇之表面研磨範例實驗，於系統中裝設力傳感器和電容式位移傳感器以即時量測工件之受力及形變。本論文進行了幾個加工案例研究，以評估所設計之複合式控制器的效能，亦與單獨使用前饋或力反饋控制器就無負載自由空間運動以及遭遇外力負載操作比較性能，證實其效果優異，無負載運行可以達到平移均方根誤差(x: 95.436 nm, y: 172.513 nm, z: 1111.581 nm)及旋轉均方根誤差(θx: 1.112 nrad, θy: 1.009 nrad, θz: 0.689 nrad)，遭遇外力負載可以達到平移均方根均方根誤差(x: 257.442 nm, y: 182.306 nm, z: 1187.987 nm)及旋轉誤差(θx: 3.35 nrad, θy: 7.015 nrad, θz: 0.687 nrad)的奈米級定位精度。

This study focuses on the development of appropriate control method for a 6DOF Stewart-type platform driven by piezoelectric actuators. It is aimed to preserve good positioning accuracy while encountered with external forces in particular. Kinematic calibration is firstly carried out by using pose measurement to improve the accuracy of kinematic parameters. Negative factors of using piezoelectric actuators such as nonlinear hysteresis, creep, drifting disturbance, and temperature rise that directly affect the accuracy and steadiness of the system are concerned. In this article, modeling of the hysteresis of a piezoelectric actuator is derived to build a hysteresis feedforward controller by means of Preisach method that is able to deal with the rate-independent nonlinear hysteresis. Exponentially Weighted Moving Average (EWMA) method has been widely used in statistical process control and verified its capability of overcoming systematic change and drift disturbance. An attempt is to map the EWMA method into a run-to-run (RtR) Model Reference Adaptive System (MRAS) and combine with the hysteresis feedforward controller for position control. Similarly, a Predictor Corrector Control (PCC) with two stages of EWMA formulas is also used and verified its capability of overcoming the drifting disturbance due to creep and temperature dependence of piezoelectric actuators. Besides the position controller, an improved robust force feedback controller that is based on the idea of combining a nonlinear PID controller with the computed torque method is also investigated. The algorithm provides an essential way of dealing with unacknowledged interacting forces and variations of the environment characteristics. An example of surface grinding on different materials is investigated. Force sensor and capacitive displacement sensors are used to measure the interacting forces and the deformation respectively on the surface where the indentor tool is attached. Several case studies are performed to evaluate its effectiveness and robustness of the proposed controller. Comparison of the proposed controller with other controllers for free-space motion as well as for manipulation encountered with external load is carried out. The experiment results show that using the proposed composite controller is much better than using the feedforward or force feedback controller alone. The position accuracy can achieve root mean square error RMSE (x:95.436nm, y:172.513nm, z:1111.581nm) in translation and (θx:1.112nrad, θy:1.009 nrad, θz:0.689nrad) in orientation for free-space manipulation and RMSE (x:257.442nm, y:182.306nm, and z:1187.987nm) in translation and (θx:3.35nrad, θy:7.015 nrad, θz:0.687nrad) in orientation while encountered with external load.

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