基於順滑模態理論之串接式倒立雙擺系統控制器設計

Abstract

本論文主要在設計順滑模態理論之串接式倒立雙擺系統控制器，並且與極點配置法作平衡控制比較以驗證其穩健性。全文共分為四部份，第一部份依據台車帶動之串接式倒立雙擺結構，推導受控系統之動態方程式，接著針對方程式於平衡點附近作線性化處理。第二部份為平衡控制器設計，所依據之理論包括順滑模態和極點配置法。第三部份為數值模擬，分別用順滑模態控制器和極點配置控制器對串接式倒立雙擺作直立位置平衡控制，並從模擬中得到順滑模態控制器有較佳的穩健性。第四部份以能量控制法與李亞譜諾夫函式的穩定理論為基礎設計上甩控制器，利用雙擺上甩至直立位置，符合平衡控制器切換條件時，切換至平衡控制器，由模擬數據中再次驗證順滑模態控制器確實有較佳的穩健性。

The purpose of this thesis is to design the controller of Series-Type Double Inverted Pendulum based on sliding mode theory and compared with the pole placement method to verify its robustness. The thesis is divided into four parts. First, according to the structure of the Series-Type Double Inverted Pendulum system, its dynamic equations are derived and then the linearized model around the balance position is obtained. The second part is the design of the balance control based on the sliding mode theory and the pole placement method. The third part includes the simulation results of balance control to verify the sliding mode controller is more robust than the pole placement method in the parameter variation of system structure. Finally, the fourth part adopts an energy function to design the swing-up controller based on the Lyapunov stability theory. When the double pendulums are swung up to reach the switching conditions, the controller is switched to the balance controller at once. The feasibility of swing-up control is also demonstrated by numerical simulation.