於本論文中，製作了一套以數位訊號處理器(Digital Signal Processor, DSP)為基礎之球與板系統。整體系統架構包含了機械結構、馬達致動器、感測器、控制器部份，以及配合自行設計之週邊介面電路與軟體結合而完成。球與板系統是一個高度非線性系統，由於系統存在離心力項，所以相對階數(relative degree)沒有被適當的定義。然而此項提供強烈的正回授量，易使系統產生跳動而呈現不穩定狀態，造成系統控制上的困難。在本論文中，將介紹如何建立系統之數學模型與架設機械結構，並使用倒階(backstepping)控制方法設計控制器，其為利用遞迴程序重複選用Lyapunov function來判定穩定性的一種回授控制方法，能在限制的條件下解決穩定性(stabilization)、追蹤(tracking)以及強健性(robustness)的問題。其所設計出的倒階控制器，可減少離心力項對系統的影響，並可使系統達到全域漸進穩定(global asymptotic stability) 。

In this thesis, a digital signal processor based (DSP-based) ball and plate control system is built. This system consists of a mechanism, two motor actuators, a touch panel sensor , a DSP-based control card and the relevant peripheral interface circuits. The ball and plate system is a highly nonlinear system. Due to existence of the centrifugal force, the system relative degree id not well defined. Moreover , the centrifugal force provides a strong positive feedback and easily leads to the peaking phenomenon . In this thesis , it is shown how to build a ball and plate system . Then the mathematical model of this system is derived. The backstepping control design approach is used to design the controller for the ball and plate system . It is a recursive procedure that interlaces the choice of a Lyapunov function to discriminate stability with design of feedback control , and backstepping control often solves stabilization , tracking and robust control , problems under restrictive conditions . In this thesis , the backstepping controller can reduce the effect of centrifugal force on the system , and make the system reach globally asymptotic stability .

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