# Fractional Control Basic

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• #794 Pritesh
Guest

Hi,

I have some basic understanding problem. Whenever we take fractional transfer function. Inside calculation, they use approximation method and convert to higher order control system.

Then, if we use higher order PID (some different form), is it the same?

Thanking You,

#796

To an extent, yes; since approximations are used, we may consider a particular fractional-order PID controller approximation to belong to a set of all possible high-order integer-order controllers for a given control problem.

#881 Pritesh Shah
Guest

Hi Alekesi,

One more question. What is use of Mittage Leffer function in FPID?

or In general.

Thanks,

#883

In general, the Mittag-Leffler function in two parameters is a powerful generalization. It may be used to compute the (roughly speaking) fractional exponential function and thus may be employed for solving fractional-order differential equations. However, direct use of this function for real-time problems is limited. Therefore, it is not used in FOMCON for FOPID related computations.

#893 Pritesh Shah
Guest

Hi Alekesi,

I am little bit confuse between CRONE controller and fractional PID Controller.

What is the basics difference between these?

Thanking You,

Pritesh

#895

The underlying principles are the same. However, different approaches are used: the fractional-order PID may be seen as a generalization of the classical PID, while the CRONE controller is based on a novel control strategy specifically developed by leveraging the flexibility of fractional-order operators. In both cases frequency domain analysis plays an important role, in case of CRONE controllers even more so.

#932 Pritesh Shah
Guest

Hi Alekesi,

Once again, I am troubling you.

I am trying to identify model of fractional order structure.

Say I want to identify , k/(s^a+b); a is non integer.

How can I use FOMCON for the same?

Could you please give some small example if possible?

Thanking You,

Pritesh

#935

You can use the fotfid tool for this purpose.

#958 Pritesh Shah
Guest

Hi Alekesi,

I have some basic understanding problem. We have a process control in our lab. We want to implement in real time.

By your toolbox, we got controller in Z Transform.

Now, we get error in time domain. How do we find out controller output? (Controller in z Transform)

Thanking You, once again.

#960

Please elaborate. If you use Simulink then you can use the fractional PID block from the FOMCON library.

#965 Smita
Guest

Hi Aleksei,
I am finding error while testing the stability of a FOPDT(First Order Plus Delay) plant in fotf viewer(FOMCON command).The plant is K.(e^0.2s)/20s+1.

The error is : Cannot assess the stability of a system with internal delays.
How can I solve it???

Also I want to know which is the updated version of FOMCON : 0.41-beta or 0.42-beta

Regards
Smita

#969

At the moment, it is not possible to assess the stability of systems with delays.
The latest version is 0.41-beta, for which a patch has been released in April. See this post: https://fomcon.net/forums/topic/preliminary-releases-and-patches/#post-914

#1012 Pritesh Shah
Guest

Hi Alekesi,

Difference between crone and fractional order controller ?

I know that both of them use kind of fractional calculus only. They have a different structure of controller.

Any comparison or any paper which you can suggest.

Thanking You, once again.

#1014

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).

#1019 Pritesh Shah
Guest