慣性輪單擺系統(inertia wheel pendulum system)是一個不穩定的非線性系統，其機械結構並不複雜，故適用於驗證各種控制理論。本論文中首先介紹如何建立慣性輪單擺系統。本系統主要包括了電樞控制直流馬達(armature controlled DC motor)、輪盤、單擺、感測器則使用光學式旋轉型編碼器。然後推導出慣性輪單擺系統機械部份數學模型，並且建立直流馬達模型，利用識別方法求出馬達參數，最後並將機械部份與電氣部份合一。

　　控制目的為由直流馬達驅動輪盤帶動單擺做甩上運動與倒立平衡控制，在平衡控制的設計我們考慮兩個方法，一個是先在平衡點處作線性化再利用極點配置法，一個是全域的非線性回授線性化。在甩上的問題我們討論以能量為基礎之部分回授線性化。控制器透過運動控制軸卡來實現，控制介面部份是利用Visual C++撰寫，利於控制器參數調設，此Visual C++介面，分成三個部份-顯示部份、設定部份、控制部份。並從實驗結果證實慣性輪單擺均能夠確實達到準確且有效的垂直平衡及甩上的控制目標。

　　The inertia wheel pendulum system is an unstable nonlinear system. The mechanism of this system is not complicated. Because of this, this system provides a platform for verifying the effectiveness of different control schemes. In this thesis, it is first shown how to build up an inertia wheel pendulum system. This system includes an armature controlled DC motor, a wheel, a pendulum, and an optical rotary encoder. Then the mathematical model of the inertia wheel pendulum system is derived and also the DC motor model is built. The system identification method is then used to determine DC motor parameters.

　　The control objective is to swing up and then keep the pendulum at upright position through rotation of the wheel driven by a DC motor. For the design of the balance controller we consider two approaches; a pole placement design based on linearized approximation of the nonlinear dynamics about the inverted equilibrium, and a full state feedback linearization controller. For the swing up problem we use an energy-based approach with the collocated partial feedback linearization system. The control law is then implemented through a motion control card. A control panel interface is coded in Visual C++ for controller parameter setting. The Visual C++ interface contains three units: display, setting, and control scheme selection. The experimental results show that the proposed control laws are effective in controlling the inverted pendulum to accomplish balancing and swing-up control.

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