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AlekseiKeymaster
Dear Sandip,
You are effectively bounding the parameter search space by fixing some parameters. Obviously, you will arrive at different results, because some fractionalorder controller parameters yielding particular control performance will not be accessible.
 This reply was modified 8 years, 7 months ago by Aleksei.
AlekseiKeymasterIn general, the MittagLeffler 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 fractionalorder differential equations. However, direct use of this function for realtime problems is limited. Therefore, it is not used in FOMCON for FOPID related computations.
AlekseiKeymasterDear 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.AlekseiKeymasterYou 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.
AlekseiKeymasterThe 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 integerorder 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.AlekseiKeymasterHi.
This is indeed a valid concern. Roughly speaking, the difference is due to some constraints of the current implementation of the GrünwaldLetnikov algorithm, which is a fixedstep method. For instance, try lowering simulation step size choosing a time range of about 1020 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 fractionalorder system obtained from the undamped integerorder one will decrease with computation step size.
I will look into this problem soon.
AlekseiKeymasterHello,
Currently the functionality that you are looking for is not yet implemented. I have, however, added this feature request to my todo list, and will provide the implementation as soon as possible. This will probably be included in the next release of the toolbox due September.AlekseiKeymasterHello Pritesh,
This feature is not implemented yet.
AlekseiKeymasterHello,
This is the FOMCON toolbox support forum. I have no idea about the “FALCON” toolbox.AlekseiKeymasterTo an extent, yes; since approximations are used, we may consider a particular fractionalorder PID controller approximation to belong to a set of all possible highorder integerorder controllers for a given control problem.
AlekseiKeymasterTo consider initial conditions for a fractionalorder 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.
AlekseiKeymasterHello 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?
AlekseiKeymasterAny proper LTI model can be used: (fractionalorder) transfer function, zeropolegain, or statespace.
AlekseiKeymasterType
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.AlekseiKeymasterYou 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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