[Aleksei]

Dear Sandip,

You are effectively bounding the parameter search space by fixing some parameters. Obviously, you will arrive at different results, because some fractional-order controller parameters yielding particular control performance will not be accessible.

• This reply was modified 11 years, 2 months ago by Aleksei.

[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.

[Aleksei]

Dear Kapil,

In case of the FOPDT model it will not be possible to obtain the feedback system comprised of the plant and FOPID controller in fotf form due to different delay terms. Only approximations are applicable. This should be taken care of automatically in fpid_optim tool.

[Aleksei]

You are welcome. Should you have a feature request for the toolbox feel free to file it. I will then take it into consideration for the next release.

[Aleksei]

The choice of options depends on the identification problem. Kindly consider this excerpt from the old documentation: https://fomcon.net/pub/temp_docs/fotfid_tool.pdf

In short: What type of model would you like to obtain? You can try obtaining a model with a commensurate order, in which case the model generation panel and “fix exponents” option may be useful. You can also identify integer-order models by fixing exponents with $\alpha_k, \beta_k\in\mathbb{Z}^{+}$.

The identification process involves constrained optimization, where the objective function is based on the model’s output error (see MATLAB’s Optimization toolbox documentation for lsqnonlin). That is, the output error is minimized in the least squares sense.

• This reply was modified 11 years, 5 months ago by Aleksei.
• This reply was modified 11 years, 5 months ago by Aleksei.
• This reply was modified 11 years, 5 months ago by Aleksei.

[Aleksei]

Hi.

This is indeed a valid concern. Roughly speaking, the difference is due to some constraints of the current implementation of the Grünwald-Letnikov algorithm, which is a fixed-step method. For instance, try lowering simulation step size choosing a time range of about 10-20 seconds—you can easily do this in fotf_gui, i.e. compare results with t=[0:0.01:10] and t=[0:0.001:10]. You will see that the damping ratio of the fractional-order system obtained from the undamped integer-order one will decrease with computation step size.

I will look into this problem soon.

[Aleksei]

Hello,
Currently the functionality that you are looking for is not yet implemented. I have, however, added this feature request to my to-do list, and will provide the implementation as soon as possible. This will probably be included in the next release of the toolbox due September.

[Aleksei]

Hello Pritesh,

This feature is not implemented yet.

[Aleksei]

Hello,
This is the FOMCON toolbox support forum. I have no idea about the “FALCON” toolbox.

[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.

[Aleksei]

To consider initial conditions for a fractional-order operator means to reconstruct, in terms of limited memory, the so called “past” of the operator. This feature is yet to be implemented in FOMCON.

[Aleksei]

Hello Pritesh,

1. The choice of approximation parameters ultimately depends on the application. The wider the frequency range and order, the more accurate the results. But it may become difficult to implement the system (or controller) as, e.g., an active filter or a digital IIR filter.

2. Could you provide an example?

[Aleksei]

Any proper LTI model can be used: (fractional-order) transfer function, zero-pole-gain, or state-space.

[Aleksei]

Type fpid_optim in MATLAB command line to launch the tool. If you are still getting errors, please elaborate, i.e. provide the exact steps needed to reproduce the error.

[Aleksei]

You may use the guide tool, integrated into MATLAB, to make modifications to the GUI’s. Since FOMCON code is freely accessible, you can study the existing code.

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