兩輪機器人之自我平衡控制

機器人已被廣泛應用於各種領域中，有關於機器人的研究也越來越受到重視。本文提出利用T-S模糊控制和多項式模糊控制來實現兩輪機器人自我平衡控制。在多項式模型中，矩陣可存在狀態的形式，相對於T-S 模糊模型裡，所能容許的狀態矩陣都是常數，能求出的增益範圍更大，這意味著更有機會找到最佳控制增益的機會也跟著變大。多項式模糊系統不僅解決了T-S模糊系統的缺點，更使得控制器有效率，也更一般性。因此，本論文將使用多項式控制系統，來改善並兩輪機器人所遇到的問題，進行討論自我平衡研究。接著，在所得出的機器人模型中，分別利用線性矩陣不等式及平方和形式的穩定條件，求出平行分布補償法中的控制增益。並在最後的電腦模擬中，來呈現出T-S模糊控制和多項式模糊控制結果，以及利用穩定條件所得出的控制器。更可清楚的看到多項式模糊控制系統的優異性大於T-S模糊的控制系統。

關鍵字

多項式模糊控制；平行分佈補償； T-S模糊控制；兩輪機器人；線性矩陣不等式；平方和

並列摘要

This thesis proposes a Takagi-Sugeno (T-S) fuzzy control and a polynomial fuzzy control to achieve the self-balance control of a two-wheeled robot. In the polynomial fuzzy model, the state can exist in the matrix, whereas the T-S fuzzy model can only support the constant in the state matrix. Thus, the polynomial fuzzy system has a greater control gain range than the T-S fuzzy system does. This means that the polynomial fuzzy system has a greater chance of finding the optimal control gain. The polynomial fuzzy system is therefore not only capable of addressing the shortcomings of the T-S fuzzy system, but also of increasing the efficiency of the fuzzy controller. The thesis then uses linear matrix inequality (LMI) stability conditions and the sum of square (SOS) approach in the robot model to obtain the parallel distributed compensation (PDC) control gain. Finally, computer simulations show the results of the T-S fuzzy system and polynomial fuzzy system. These clearly show that the performance of the polynomial fuzzy system is much better than that of the T-S fuzzy system.

並列關鍵字

Polynomial fuzzy control ； Parallel distributed compensation ； T-S fuzzy control ； Two-wheeled robot ； Linear matrix inequality ； Sum of square

參考文獻

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[3] M. S. Park, and D. K. Chwa, “Swing-up and stabilization control of inverted-pendulum systems via coupled sliding-mode control method,” IEEE Trans. Ind. Electron., vol. 53, no. 2, pp.631-639, Sep. 2006.

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兩輪機器人之自我平衡控制

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