基於T-S模糊模型之智慧型順滑模態追蹤與同步控制於龍門平台

本文提出一基於T-S模糊模型之智慧型順滑模態控制器於H型龍門式三軸平台。由不均勻的質量和摩擦力等干擾所造成的同步誤差，是此類型平台最需解決的問題。使用Lagrangian方程式，所有的控制目標可以被整理成狀態方程式，接著將此非線性的系統使用T-S模糊模型線性化，再針對T-S模糊模型設計追蹤控制器。透過控制器內部轉換，可以對速度和位置設計控制增益矩陣。再透過求解加入參數不確定性的線性矩陣不等式，可以得到對應的速度和位置增益矩陣。為了進一步克服未知的外部擾動，本文提出基於T-S模糊模型之順滑模態控制器，當系統狀態進入順滑平面時，具有對抗外擾的強健性，但順滑模態控制中不連續的切換控制力會造成抖動的現象，使得控制精度下降。為此，本文再提出基於T-S模糊模型之智慧型順滑模態控制器，此架構具有六組倒傳遞式柴比雪夫神經網路估測器，可以線上估測外部干擾。因此，可有效減少順滑模態控制器的抖動問題，並且增加強建性與控制精度。穩定度問題也在本文中以Lyapunov函數的型式證明。最後，由模擬和實驗結果可以看出T-S 模糊智慧型順滑模態控制器最能有效的減少龍門平台的追蹤和同步誤差。

關鍵字

T-S模糊模型； Lagrangian方程式；線性矩陣不等式；順滑模態控制；類神經網路；適應性學習；龍門平台

並列摘要

In this paper, we propose a T-S fuzzy model based controller for the H-type gantry stage. The synchronous error, which is caused by mismatch quality and friction, is an important control problem for the H-type gantry stage. Utilizing a Lagrangian equation, all states can be formulated as a state equation. Furthermore, the T-S fuzzy model based controller (TSFC) is designed to reduce velocity error. And the position control gains can be also designed through internal transformation to achieve velocity and position tracking control. By solving LMIs, we can obtain corresponding control gain matrices for system existing parametric uncertainties. In addition, the T-S fuzzy model based sliding mode controller (TSFSMC) is proposed to enhance performance of the system with unknown external disturbance. But the hitting control law of the TSFSMC makes the chattering and will reduce system precision. To this end, a T-S fuzzy model based intelligent sliding mode controller (TSFISMC) structure with six recurrent Chebyshev neural networks (RCNNs) is proposed to estimate the disturbance online, can effectively avoid chattering and increase the robustness of the control system. Moreover, by utilizing additional transformations, the stabilization problem can be transformed into a linear matrix inequalities (LMIs) problem. Finally, numerical simulation and experimental results are illustrated to demonstrate that the TSFISMC control scheme can most effectively reduce tracking error and synchronous error of gantry stage.

並列關鍵字

T-S fuzzy model ； Lagrangian equation ； Linear Matrix Inequalities (LMIs) ； Sliding mode control ； Adaptive law ； Neural network ； Gantry stage

參考文獻

[30] 李柏勳，以T-S模糊模型為基礎之適應性T-S模糊順滑追蹤控制器於非線性系統，碩士論文，國立臺北科技大學自動化科技研究所，台北，2010。

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基於T-S模糊模型之智慧型順滑模態追蹤與同步控制於龍門平台

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