倒單擺系統為一種構造簡單、響應快速、不穩定之非線性系統，故學術領域常用來驗證各種先進的控制理論。在本論文中探討以線性馬達為致動器，並以不同之控制器法則，達到倒單擺之平衡控制。本論文先以Euler-Lagrange方法對倒單擺系統建立動態數學模型，再依此模型設計LQR (Linear Quadratic Regulator)控制器、傳統順滑模態控制器以及二階順滑模態控制器，接著利用MATLAB/Simulink軟體進行模擬，最後將各自模擬結果互相比較。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TMS320F28335做為控制核心以實現倒單擺之平衡控制的目的。藉由模擬與實作結果得知，二階順滑模態控制具有較佳的性能及強健性。

The inverted pendulum system is a simple, fast, unstable and nonlinear system. It is commonly used as a testbed for studying many advanced control theory. This thesis considers the problems of controlling an inverted pendulum actuated by a linear motor. Different control schemes are used to design the stabilizing controllers. In this thesis, the Euler-Lagrange method is used to derive the dynamic model of the inverted pendulum system. The LQR (Linear Quadratic Regulator) control law, first-order sliding mode control law and second order sliding mode control law are then designed to achieve balance control of this system. The MATLAB/Simulink software is used to conduct the simulation. In the experiments, control laws are implemented through a digital signal processor (TMS320F28335) produced by Texas Instruments. The effectiveness of the control schemes are verified and validated through experimental and simulation studies. It is shown that second-order sliding mode control has better performance and robustness.

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