倒單擺系統在學術研究與控制教育實驗上為常見之機電系統，因為其機械結構簡單，同時又具有非線性及欠致動性之特點，因此常被用來驗證許多先進的控制理論；全向移動機器人為一種特殊之輪式機器人，具有可在平面上任意方向移動而不需改變其姿態的優點，在控制上具有較佳之機動性與靈活性。本論文旨在將倒單擺系統結合全向移動機器人，以建構二維倒單擺平衡控制系統。論文中將以Euler-Lagrange方法建立倒單擺系統之動態數學模型，並針對此模型利用LQR控制法則與順滑模態控制法則設計平衡控制器。在實作上，本系統使用德州儀器公司(Texas Instruments, TI)所生產的數位訊號處理器TMS320F2812做為控制核心以實現所有控制法則，並配合周邊介面電路，進而完成倒單擺平衡控制之目的。

The inverted pendulum system is a common electromechanical system for academic researches and control-education experiments. Because of its simplicity of the mechanical structure with the underactuated and nonlinear characteristics, it is often used to verify the advanced control schemes. The omnidirectional mobile robot is a special type of wheeled robots, which can arbitrarily move on a plane without changing its pose and has good mobility and flexibility in control. The objective of this thesis is to combine the inverted pendulum system with the omnidirectional mobile robot to construct a two-dimensional inverted pendulum control system. In this thesis, the Euler-Lagrange method is used to derive the dynamic model of the system. Then, the LQR control law and the sliding mode control law are designed for balance control of this system. In the experiments, the designed controllers are implemented on a digital signal processor (TMS320F2812) produced by Texas Instruments. Then, combining the digital signal processor with the relevant peripheral interface circuits, balance control of the two-dimensional inverted pendulum system actuated by an omnidirectional mobile robot is achieved.

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