旋轉式雙倒立單擺積分式順滑控制器設計

Abstract

本論文主要是在設計積分式順滑控制器，將之應用於旋轉式雙倒立單擺系統之平衡控制上。首先依照動力學知識及拉格朗日方程式建立起系統之非線性動態方程式，包括兩條內部方程式及一條外部方程式，接著針對內部方程式於平衡點附近作線性化處理，再使用李亞普諾夫函式的穩定理論設計積分型順滑模態法則，對含有扭力輸入的外部方程式進行線性化，得出非時變之線性狀態方程式，再利用極點配置法完成控制器之設計。接著利用MATLAB/SIMULINK軟體建立系統平台模型及控制器模型，並模擬測試確認了系統平台和控制器是可信賴的。為了探討控制器對系統參數改變的強健性，本論文除了利用積分型順滑模態法則之外，也設計傳統線性控制器，並選擇三種方式比較測試控制器，分別為在不考慮系統參數不定量下改變初值條件測試，加入系統參數不定量測試，以及引入輸入干擾信號測試。經由模擬結果表明積分式順滑控制器相較於狀態回授控制器對不定量或干擾的影響表現得更為強健。

This thesis proposes the controller design of Rotary Double Inverted Pendulum System whose dynamic equations derived by the Lagrange's method are nonlinear and consist of two pendulums' equations and one arm equation. The pendulums' equations are linearized around the equilibrium point, while the arm equation is linearized by the integral sliding-mode algorithm based on the stability theory of Lyapunov function. The total system is finally changed into a linear time-invariant system with an input which is related to the integrand of the integral sliding function and designed by the pole placement. Three cases, including different initial pendulum angles, uncertain mass or length of pendulum and external noise, are simulated to check the robustness of the proposed controller and are compared with traditional linear controller. From the simulation, it is clear that integral sliding mode controller is more robust than the traditional linear controller.