以串接結構及里亞普諾夫理論為基礎之非線性雙軸倒單擺適應性模糊控制系統設計

Adaptive Fuzzy Control Based on Cascade Structure and Lyapunov Theorem for Nonlinear Two-Axis Inverted-Pendulum Servomechanism

郭孟安(Meng-An Kuo)

指導教授 ： 魏榮宗

元智大學/工程學院/電機工程學系/碩士(2007年)

摘要

本論文之目的在於發展以串接結構及里亞普諾夫理論為基礎之適應性模糊滑動控制以及直接型適應性模糊控制，並應用於具有高度非線性以及欠致動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理論，分析經由永磁同步馬達所致動之雙軸倒單擺機構動態模型。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擺桿角度動態模型以及台車位置動態模型，根據本論文所推導的動態模型可驗證此馬達-機構耦合系統實為非線性且欠致動的系統。有鑑於此，本論文設計串接適應性模糊滑動控制架構，其中包含內部及外部控制迴路，並藉由模糊系統之近似能力及串接結構解決系統之非線性和欠致動的問題，雖然此控制法則不需系統參數，此架構屬於間接型模糊控制系統，其較為直接型模糊控制系統複雜。因此，本論文進一步提出串接直接型適應性模糊控制，在此內部控制迴路中使用直接型適應性模糊控制精簡其架構。此外，本論文所提出之控制法則皆由里亞普諾穩定分析的推導中獲得，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。最後本論文利用數值模擬與實作結果佐證所提出控制系統之有效性與強健性。

關鍵字

串接結構 ； 適應性模糊控制 ； 倒單擺系統 ； 雙軸伺服機構 ； 欠致動系統

並列摘要

The purpose of this thesis is to design adaptive fuzzy sliding-mode control (AFSMC) and direct adaptive fuzzy control (DAFC) schemes in the sense of cascade structure and Lyapunov theorem for real time stabilization and accurate tracking control of a two-axis inverted-pendulum servomechanism with highly nonlinear and under-actuated dynamic characteristics. The energy conservation principle, coordinate transformation technique and Newton's law of motion are adopted initially to build a mathematical model of the motor-mechanism coupling system that is driven by permanent magnet synchronous motors (PMSM). In order to take away the internal dynamic for the convenient design of control system, the dynamic motion equation can be divided into the stick-angle and cart-position dynamic models. Because the dynamic characteristic of a two-axis inverted-pendulum servomechanism is a nonlinear under-actuated system, it is difficult to design a suitable control scheme that realizes real time stabilization and accurate tracking control simultaneously. In this thesis, the cascade AFSMC scheme including inner and outer control loops is investigated for solving the problem of an under-actuated system. Although this control scheme is independent of system parameters, the indirect fuzzy control scheme in the inner control loop of the cascade AFSMC scheme seems to be more complicated than the direct one. Therefore, the cascade DAFC system with a DAFC law in the inner control loop is further investigated to overcome this problem in the cascade AFSMC scheme. The overall control laws of both cascade AFSMC and DAFC schemes are derived via Lyapunov stability analysis, so that the system stabilization and accurate tracking control can be guaranteed in the entire closed-loop system despite the existence of uncertainties. Finally, the effectiveness of the proposed control systems is verified by numerical simulations and experimental results under the possible occurrence of uncertainties.

並列關鍵字

Cascade structure ； Adaptive fuzzy control ； Inverted-pendulum system ； Two-axis servomechanism ； Under-actuated system

參考文獻

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