模糊理論於倒單擺/移載平台/翹翹板系統之原理與實現

本研究在翹翹板平台上乘載兩組無桿氣壓缸移載平台，並配置倒單擺於移載平台上，當倒單擺角度晃動時，移載平台作直線運動以維持倒單擺穩定。本平台使用拉格朗日方程式(Lagrange’s equation)分析系統平台的動態方程式。控制系統使用模糊控制器進行驅動，配合美商國家儀器所開發的LabVIEW 圖控程式進行控制器的設計。實驗利用移載平台作交叉運動保持翹翹板及倒單擺平衡，將系統輸入值設定為擷取倒單擺角度的旋轉電位計，藉由角度控制移載平台運動使倒單擺平衡，並在此實驗中改變倒單擺起使角度及倒單擺長度，針對單擺不同長度配合不同角度時，觀察倒單擺及翹翹板平台的變化量，並與LQR 控制及模糊理論之歸屬函數採平均分配方式控制的結果作對照與比較，最後改變兩邊移載平台重量，為移載平台配置未知負重(unknown payload)，並利用模糊理論控制使倒單擺平衡，以及使倒單擺完成平衡控制時，放置鋼珠於滑軌上滑落至翹翹板平台作未知衝擊(unknown impact)實驗，觀察倒單擺再次平衡的狀況及變化量。本研究是由清雲科技大學量測與感測實驗室自行研發設計的實驗教材，且已獲得國家專利認證，對於相關研究可提供資訊探討或類似系統平台使用。

關鍵字

拉格朗日方程式；模糊控制； LQR ； LabVIEW ；未知負重；未知衝擊

並列摘要

The objectives of the research are to develop a novel model which is called inverted pendulum-cart-seesaw system. The system consists of two mobile carts, which are coupled via rack and pinion mechanics to two parallel tracks mounted on pneumatic rodless cylinders. One cart carries an inverted pendulum, and the other carts acts as a counterbalance to keep the inverted pendulum and seesaw on the dynamic balance. The dynamic equation by using Lagrange’s formulation is the first proposed for control purposes of such new model. Moreover, linear quadratic regulator (LQR) and fuzzy Logic scheme are utilized to investigate the dynamic balancing control for such system. Liner potentiometers were utilized to determine the position of the sliding carts, and rotary potentiometers were adopted to determine the inverted pendulum angle and seesaw angle. Membership function is using by the method of equally spaced at the beginning of experiment, and then adjusts the parameters of the membership function by try and error. Consequently, it is shown that the membership function after adjustment is better and fast convergent rate than before adjustment. Finally, the control law is implemented using fuzzy logic control at experiment with one cart carries an unknown payload and seesaw affected by unknown impact loading. The experimental results are demonstrated the effectiveness of the control system. The complete system is developed at the Sensor and Control laboratory of the Department of Mechanical Engineering of Ching Yun University. The proposed software/hardware platform can be also profitable for the standardization of laboratory test-bed, as well as for the development of entertainment tools. Keyword：Lagrange’s equation, Fuzzy control, LQR control, Unknown payload, Unknown impact.