# Reply To: Fractional Control Basic

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#1014
Aleksei
Keymaster

CRONE has several generations of controllers. Kindly see the book in https://fomcon.net/fo/overview-of-literature/ for details.

For instance, the first generation CRONE controller has the following form
$C(s)=C_0 s^{\alpha}\tag{1},$
with $\alpha, C_0\in\mathbb{R}$. This can be seen as one of the dynamical components of a fractional-order PID controller, e.g., the integral component
$C_I(s)=K_i s^{-\lambda},$
where $C_0=K_i$ and $\alpha=-\lambda$ in (1).

• This reply was modified 7 years, 1 month ago by Aleksei.
• This reply was modified 7 years, 1 month ago by Aleksei.
• This reply was modified 7 years, 1 month ago by Aleksei.
• This reply was modified 7 years, 1 month ago by Aleksei.