Fractional-order control

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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. ^[1]

The fundamental advantage of FOC is that the fractional-order integrator weights history using a function that decays with a

In fact, the fractional integral operator ${\displaystyle {\frac {1}{s^{\lambda }}}}$ is different from any integer-order rational transfer function ${\displaystyle {G_{I}}(s)}$, 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.^[2]

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

• Differintegral
• Fractional calculus
• Fractional-order system

External links

• Dr. YangQuan Chen's latest homepage for the applied fractional calculus (AFC)
• Dr. YangQuan Chen's page about fractional calculus on Google Sites

References

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