|Abstract: ||近來，基於T-S模糊建模的控制設計已被廣泛的研究。然而當這些理論實際應用於差速驅動二輪式移動機器人(two-wheeled mobile robot; TWMR)控制時則仍有些許問題待克服。例如：雖然區段非線性(sector nonlinearity)方法可將TWMR的運動學模型轉成T-S模糊模型，但此T-S模型卻是不可控。為避免不可控的問題，有文獻改以切換式T-S模型建模(switching T-S fuzzy model)，並依照李亞普諾夫定理(Lyapunov Theorem)設計出切換式T-S模糊控制器。控制設計條件可轉成線性矩陣不等式(LMI)表示，並以軟體求解。但實作中常出現求解出的控制訊號大於TWMR驅動電路限制的情況。因此有文獻提出在求解LMI時加入輸入限制(input constraint)條件，但此文獻提供的方法常會過度限制，反而導致控制訊號太小。因此本計畫將考慮以不同形式的LMI或頂點表示法(vertex expression)來放寬目前的輸入限制條件。此外，現有模糊模型只考慮TWMR的y軸位置與轉向角( )控制，我們將同時考慮三個維度(x, y, )，並考慮以分散式控制技巧避免切換式T-S模型維度增加時規則擴增太多的問題。最後將自製TWMR驗證所提出的控制設計理論。|
Recently, based on the T-S fuzzy model and Lyapunov theorem, T-S fuzzy model-based control design issues have been extensively investigated. However, while the T-S fuzzy model-based control is employed to the differential drive two-wheeled mobile robot (TWMR), some additional practical issues are induced. For example, by using the sector nonlinearity method, the kinematic model of a TWMR can be converted into a T-S fuzzy model. However, the derived model leads to an uncontrollable problem. In some previous studies, to avoid the uncontrollable issue of the derived T-S fuzzy model, the switching T-S fuzzy model is employed instead of the traditional T-S fuzzy model. Then the Lyapunov stability criterion is utilized to design the switching T-S fuzzy controller. The derived Lyapunov inequalities can be converted into linear matrix inequalities (LMIs), and be solved by existing LMI tools. Still, the previous studies show that the control gains are often too large and unsuitable for the driver circuit of a practical TWMR system. The so-called input constraint conditions in LMI forms were proposed to bound control gains. But, the input constraint conditions often overly limit the control gains and induce some too small control signals. Therefore, in this project, we will try to relax the input constraint conditions by some equivalent/similar LMIs and/or vertex expression. Besides, only two states (position in y-direction and orientation of a TWMR) are considered in present switching T-S fuzzy model for the TWMR. We will try to extend the present model to a three-dimension (x, y, and ) model by the decentralized control techniques, which may suppress the coupling terms and fuzzy rules of a derived switching T-S fuzzy model. Then, a more suitable controller for the TWMR could be designed by directly solving the derived LMIs. Finally, the proposed control law will be implemented on a (developed) TWMR to perform the effectiveness of the control design.