非線性雙軸倒單擺系統之穩定平衡及循軌控制

Stabilizing and Tracking Control of nonlinear Dual-Axis Inverted Pendulum System

張立忠(Li-Chung Chang)

指導教授 ： 魏榮宗

元智大學/工程學院/電機工程學系/碩士(2002年)

摘要

本論文之目的在於發展適應性滑動模式控制系統以及強健型模糊類神經網路控制系統，並應用於具有高度非線性以及時變特性之雙軸倒單擺系統的穩定平衡與循軌控制上。首先，根據能量守恆定律、牛頓運動定律以及座標轉換技巧，分析經由永磁同步馬達所致動之雙軸倒單擺機構動態。為了消除內部動態響應以及方便控制系統設計，進一步推導包含系統不確定量的角度動態模型以及位置動態模型。本論文根據所推導的模型提出適應型滑動模式控制系統，藉由適應性邊界估測法則針對存在於傳統滑動模式控制中之不確定量邊界進行估測，以提高系統對於擾動發生時的適應性。此外，為了降低對於系統參數的依靠程度，本論文進一步提出結合具非線性函數近似能力的模糊類神經網路以及設計用來補償神經網路近似誤差的強健控制器，發展成為強健型模糊類神經網路控制系統。兩控制系統之控制法則皆由里亞普諾穩定分析的推導中獲得，因此即使馬達-機構耦合系統中存在不確定量時，整個閉迴路控制系統依然可保證漸進穩定之特性。最後本論文以數值模擬來驗證所提出控制系統之可行性與強健性。

關鍵字

雙軸倒單擺系統

並列摘要

The purpose of this thesis is to develop an adaptive sliding-mode control (ASMC) system and a robust fuzzy-neural-network control (RFNNC) system for real time stabilization and accurate tracking control of a dual-axis inverted-pendulum system with highly nonlinear and time-varying dynamic characteristics. The energy conservation principle, coordinate transformation technique and Newton's law of motion are adopted initially to build a mathematical model of a dual-axis inverted-pendulum mechanism that is driven by permanent magnet (PM) synchronous motors. In order to take away the internal dynamic for the convenient design of control system, the dynamic motion equation can be divided into angle and position dynamic models according to stick angel and cart position coordinates. In this study, the ASMC system is investigated to control the nonlinear dual-axis inverted-pendulum system, where a simple adaptive algorithm is utilized to estimate the bound of lumped uncertainty. Moreover, in order to relax the requirement of system parameters, the RFNNC system is implemented as an alternative way to control a nonlinear dual-axis inverted-pendulum system. In this control system, the FNN controller is used to learn an equivalent control law in the traditional sliding-mode control, and a robust controller is designed to compensate the residual approximation error. The overall control laws of both ASMC and RFNNC systems are derived in sense of Lyapunov stability analysis, so that system stabilization and accurate tracking control can be guaranteed in the closed-loop system even when the uncertainties occur. In addition, the effectiveness of the proposed control strategies can be verified by numerical simulation results.

並列關鍵字

Dual-Axis Inverted-Pendulum System

參考文獻

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