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. Using fractional calculus 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 power-law tail. The effect is that the effects of all time are computed for each iteration of the control algorithm, creating a "distribution of time constants," the upshot of which is that there is no particular time constant, or resonance frequency for the system.

In fact, the fractional integral operator ${\displaystyle {\frac {1}{s^{\lambda }}}}$ is different from any integer-order rational transfer function ${\displaystyle {G_{I}}(s)}$. It is a non-local operator that possesses an infinite memory and considers 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, resonance and time-diffuse applications such as thermal dissipation and chemical mixing. Fractional-order control has also been demonstrated to suppress chaotic behaviors in mathematical models of, for example, muscular blood vessels^[3] and robotics.^[4]

Initiated in the 1980s by the Pr. Oustaloup's group, the CRONE approach,^{[clarification needed]} is one of the most developed control-system design methodologies that uses fractional-order operator properties.^{[citation needed]}

• Differintegral
• Fractional calculus
• Fractional-order system

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

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