系統建模的不精確對控制系統的穩定性有很大的影響。強健控制理論為專門應付系統不確定性的重要方法之一，而順滑模態控制為強健控制理論中重要的一環。在本論文中，吾人考慮一個「球與球系統」的控制問題。此系統透過兩個直流馬達帶動大球做二自由度的滾動，其中以影像感測器感測小球在大球上之位置，而大球之位置則由馬達的旋轉角度推估而得，使小球能立在大球上達到平衡。此為先天非線性、不穩定且欠致動性的系統，而這個控制問題將是一件具挑戰性的任務。於論文中，吾人將球與球系統於平衡點附近解耦合成兩軸獨立的球與輪系統，利用順滑模態控制理論設計控制器達成閉迴路系統穩定之目的，並透過模擬與實驗結果來驗證此控制系統之可行性。

The inaccuracies in modeling of a physical system can lead to poor performance or even instability of the resulting control system. Robust control is one of the most important approaches to deal with model uncertainty, and sliding mode control is one of them. In this thesis, we consider the control design problem of a system, called the ball and sphere system. This system consists of two dc motors and a image sensor. The overhead image sensor is use to measure the displacement of the small ball on the top of the sphere. Two dc motors drive a big sphere to roll in two directions so that the small ball can be kept staying on the top of the sphere. The position of the sphere can be derived by the angle of rotation of the motor. This system is inherently nonlinear, unstable, and underactuated. The control of this system is a challenging task. In this thesis, we show that around the equilibrium point of the system can be decoupled into two independent ball and wheel systems. Based on sliding mode control, a controller is designed to achieve the closed-loop stability of the system. The simulation and experimental results are given to demonstrate and validate the effectiveness of the control scheme.

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