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Fractional-order control (FOC) is a field of control theory that uses the fractional-order integrator as part of the control system design toolkit. The use of fractional calculus (FC) can improve and generalize well-established control methods and strategies. In fact, the fractional integral operator is different from any integer-order rational transfer function , in the sense that it is a non-local operator that possesses an infinite memory and takes into account the whole history of its input signal.

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  • Fractional-order control (en)
  • 分數階控制 (zh)
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  • 分數階控制（Fractional-order control，簡稱FOC）是利用作為控制系統設計工具的控制理論。 分數階控制主要的好處是分數階的積分器會利用隨時間长尾遞減的函數，針對歷史進行加權。每一次的控制演算法迭代都會計算所有時間下的影響。因此會有「時間常數的分佈」效果，系統沒有特定的時間常數或是共振頻率。 分數階積分算子不同於任何整數階的有理傳遞函數 ，分數階積分算子是非局部算子，有無限長度的記憶，而且會考慮輸入信號的所有歷史資訊。 分數階控制適合用在許多傳統控制會出現過沖及共振的場合，也包括像散热及化學混合等時間擴散應用。分數階控制也可以抑制數學模型（例如肌肉血管模型）中的混沌特性。 (zh)
  • Fractional-order control (FOC) is a field of control theory that uses the fractional-order integrator as part of the control system design toolkit. The use of fractional calculus (FC) can improve and generalize well-established control methods and strategies. In fact, the fractional integral operator is different from any integer-order rational transfer function , in the sense that it is a non-local operator that possesses an infinite memory and takes into account the whole history of its input signal. (en)
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  • Fractional-order control (FOC) is a field of control theory that uses the fractional-order integrator as part of the control system design toolkit. The use of fractional calculus (FC) can improve and generalize well-established control methods and strategies. The fundamental advantage of FOC is that the fractional-order integrator weights history using a function that decays with a power-law tail. The effect is that the effects of all time are computed for each iteration of the control algorithm. This creates a 'distribution of time constants,' the upshot of which is there is no particular time constant, or resonance frequency, for the system. In fact, the fractional integral operator is different from any integer-order rational transfer function , in the sense that it is a non-local operator that possesses an infinite memory and takes into account the whole history of its input signal. Fractional-order control shows promise in many controlled environments that suffer from the classical problems of overshoot and resonance, as well as time diffuse applications such as thermal dissipation and chemical mixing. Fractional-order control has also been demonstrated to be capable of suppressing chaotic behaviors in mathematical models of, for example, muscular blood vessels. Initiated from the 80's by the Pr. Oustaloup's group, the CRONE approach is one of the most developed control-system design methodologies that uses fractional-order operator properties. (en)
  • 分數階控制（Fractional-order control，簡稱FOC）是利用作為控制系統設計工具的控制理論。 分數階控制主要的好處是分數階的積分器會利用隨時間长尾遞減的函數，針對歷史進行加權。每一次的控制演算法迭代都會計算所有時間下的影響。因此會有「時間常數的分佈」效果，系統沒有特定的時間常數或是共振頻率。 分數階積分算子不同於任何整數階的有理傳遞函數 ，分數階積分算子是非局部算子，有無限長度的記憶，而且會考慮輸入信號的所有歷史資訊。 分數階控制適合用在許多傳統控制會出現過沖及共振的場合，也包括像散热及化學混合等時間擴散應用。分數階控制也可以抑制數學模型（例如肌肉血管模型）中的混沌特性。 (zh)
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