Fractional Control Basic

[Pritesh]

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?

sorry for asking stupid question?

Thanking You,

[Aleksei]

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.

[Pritesh Shah]

Hi Alekesi,

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

or In general.

Thanks,

[Aleksei]

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.

[Pritesh Shah]

Hi Alekesi,

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

What is the basics difference between these?

Thanking You,

Pritesh

[Aleksei]

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.

• This reply was modified 11 years ago by Aleksei.
• This reply was modified 11 years ago by Aleksei.

[Pritesh Shah]

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

[Aleksei]

You can use the fotfid tool for this purpose.

[Pritesh Shah]

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.

[Aleksei]

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

[Smita]

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

Please suggest.Thanks

Regards
Smita

[Aleksei]

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

[Pritesh Shah]

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.

[Aleksei]

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 10 years, 3 months ago by Aleksei.
• This reply was modified 10 years, 3 months ago by Aleksei.
• This reply was modified 10 years, 3 months ago by Aleksei.
• This reply was modified 10 years, 3 months ago by Aleksei.

[Pritesh Shah]

Thank You for your kind reply.

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