雙平行倒立單擺系統之積分式順滑模態控制器設計

Abstract

本論文提出台車式雙平行倒立單擺系統之上甩及平衡控制器設計，其中上甩控制利用能量函數來達成，平衡控制則是採用積分式順滑模態控制器。全文共分三大部分，第一部份依據台車式雙平行倒立單擺系統之結構，推導動態方程式及系統平衡點之線性化模式。第二部份為設計系統控制器，先藉由上甩控制器之能量控制函數與自然擺盪頻率的關係驅動台車將雙平行桿同時上甩，待達到切換條件時再利用平衡控制器完成穩定平衡。本文採用積分式順滑模態控制器作為非線性系統的平衡控制器。第三部份主要是控制系統之模擬，除了分析控制器性能外，也與LQR控制器做比較，由模擬數據可知積分式順滑模態控制器確實對系統參數有較佳之穩健性。

This thesis is concerned with the swinging-up and balance controller design of the cart-type parallel double inverted pendulum system, respectively based on the energy function and the integral sliding-mode theory. It is divided into three parts. First, according to the structure of the cart-type parallel double inverted pendulum system, its dynamic equations are derived and then the linearized model around the balance position is obtained. The second part is to drive the cart to swing up both the pendulums simultaneously by choosing an energy function related to the natural swinging frequency. Once both the pendulums reach the switching condition, the integral sliding-mode controller is applied to balance them uprightly. The third part is to analyze the control ability from the simulation results. By comparing the LQR controller, it can be seen that the integral sliding mode controller is indeed more robust to the variation of system structure parameters.