於本論文中，吾人製作了一套以數位訊號處理器DSP (Digital Signal Processor)為基礎之球與桿系統，整個系統主要分為機械結構、馬達致動器、感測器和控制器部份。機械結構包括機台、鐵桿、鋼球及齒輪組；馬達是採用電樞控制直流馬達(armature controlled DC motor)來做系統致動器；感測器部份有位置及角度感測器，位置是採用接觸式鎳鉻合金電阻線(nichrome resistance)來做感測器，角度是以光學式編碼器(photo encoder)來做感測器。控制器部份是以德州儀器(Texas Instruments, TI)之浮點式(floating-point)數位訊號處理器TMS320VC33為控制核心，並與吾人自行設計的週邊介面互相配合完成。
　　球與桿系統是一個高度非線性系統，由於系統存在有離心力項，所以相對階數(relative degree)沒有被適當的定義(not well defined)，在控制上造成相當高的難度。本論文中，首先介紹如何建立此系統之機構，然後推導出系統之數學模型，再使用倒階(backstepping)控制方法來設計控制器，其為利用遞迴程序重複選用Lyapunov function來判斷穩定性的一種回授控制設計方法，能在限制條件下解決穩定性(stabilization)、追蹤(tracking)和強健(robust)控制上的問題。文中所得之倒階控制器，可以減小離心力項對系統的影響，且使系統達到全域漸進穩定(global asymptotic stability)。最後，吾人以數位訊號處理器為基礎，及利用C語言與組合語言撰寫控制器程式來實現整個控制系統，使球在桿子上達到平衡與追蹤控制。

　　In this thesis, a digital signal processor based (DSP-based) ball and beam control system has been built. This system consists of a mechanism, a motor actuator, sensors and the controller. The mechanism consists of a platform, a beam, a ball and a gear module. An armature controlled DC motor is used. The position-sensor is made up of nichrome resistance and the angular sensor is a photo encoder. A digital controller is realized through floating-point DSP (TMS320VC33, TI), and the peripheral interfaces are designed to accomplish the control operation.
　　Ball and beam is a highly nonlinear system. Due to existence of the centrifugal force, the system relative degree is not well defined. In this thesis, it is shown how to build up a ball and beam 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 beam system. It is a recursive procedure that interlaces the choice of a Lyapunov function to discriminate stability with design of the 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. Finally, the control law is implemented using a digital signal processor with programs coded in C language and assembly. It achieves balancing and tracking control of the ball on the beam.

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