磁流變阻尼器(Magnetorheological damper, MR damper)，是一種利用磁流變液(Magnetorheological Fluid, MRF)的流變效應製成的阻尼裝置，並廣泛的應用在基底隔震、土木工程以及機械工程上，和一般被動式阻尼器不同的地方在於其內部流體充滿著磁性懸浮顆粒，沒有外加磁場時就維持一般阻尼器被動式減震較果，通入外加磁場時，內部的磁性顆粒就開始排列並增加流體的阻力，改變阻尼器的力輸出，通過外加磁場大小使阻尼器成為可控制可調變的智能阻尼裝置，相較於一般被動式阻尼器，多了可控制性的性質。然而，磁流變阻尼器是一種高度非線性的裝置，阻尼器的力輸出跟活塞的位移、速度以及外加磁場的大小有關，相較於一般被動式阻尼器力輸出的型式還要複雜得多，多數文獻對於磁流變阻尼器的系統識別方法主要可分為高度非線性函數的 Bouc-Wen 模型以及分段連續函數的Bingham 模型，此種識別方法因為函數的不連續性與高度的非線性性質，因此不適用於線性化迴授控制或參考模型適應型控制等典型非線性控制器。
本論文提出以 Duffing equation 方法進行系統識別，Duffing equation 是一種非線性二階常微分方程式，藉由調整一階項的係數觀察整個非線性系統相位圖由收斂到發散的分歧點(bifurcation)，本論文將使用 Duffing equation 藉由調整係數的方式分析各個參數對於磁滯曲線的影響，並歸納出參數調變的步驟，最後使用阻尼器實驗機台測試所獲得的磁滯曲線，利用Duffing equation 方程式所畫出的磁滯曲線，藉由參數調變讓模擬曲線與真實數據曲線重合，以達成系統識別的目的。

Magnetorheological damper (MR damper) is the vibration reduction equipment which is filled with MR fluid in the cylinder and it is used for the purpose of reducing the vibration effects in structural, civil, and mechanical engineering systems. MR damper is different from the ormal passive damper because of the tiny magnetic particles in the cylinder. Therefore, when the applied magnetic field is increased, the suspended magnetic particles become the chain structure, and the effective stiffness of MR damper becomes large. In the absence of magnetic field, the MR fluid behaves like a normal passive damping component. In order to modulate the MR damper force and adjust the associated parameters, various modelling techniques are proposed to identify the MR damper behaviour from researches. The most well-known techniques are Bouc-Wen and Bingham models. These two existing mathematical models of MR damper, including discontinuous and piecewise functions, are non-ideal for numerical computation, stability analysis, and control design. This thesis proposes the Duffing equation for the modelling of MR damper system. Duffing equation is a well-known, continuous, second-order nonlinear differential equation and it has been used to analyse the behaviour of chaotic dynamics, a hardening spring, and structural systems under excitations. By adjusting each parameter of equation analyse the influence of the hysteresis curve and fit the hysteresis curve in order to find the dynamic equation of the MR damper.

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