Fractional PID Controller Design

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    I came across FOMCON toolbox and found that it is very interesting and useful for the control system design. After trying several things, I have the following questions:

    1. In order to find the parameters of FOPID and optimization, does the plant to be controlled need to be stable first?

    2. When trying to do the optimization of the FOPID, by selecting Noise and disturbance rejection box, the program give an error: ” Undefined function ‘csens’ for input argument of type ‘zpk’  “.

    3. Lastly, is there any example of the usage of FOMCON?


    Thanks for your time and help.




    Hello, and thank you for your feedback!

    1. In order to run the optimization procedure, the plant does not need to be stable per se; however, you will most likely run into problems with unstable plants. Careful initial inspection of unstable systems is advised.

    2. Please check that your path is correctly set. Which version of MATLAB are you using? There is a backwards compatibility issue that appeared somewhere between R2010 and R2012 which is related to particular class methods and overloading thereof. This issue may need to be reported via the bug tracker.

    3. Yes, there are several upcoming conference papers illustrating the use of the toolbox. Unfortunately, I cannot publish these on the site. I am, however, planning on creating several tutorials covering some basics of using the toolbox. A complete user manual is also planned.


    Thank you for your answer Aleksei. I’m looking forward for the upcoming development. You did a very good job.


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    Hi, first of all thank you for your great job !!

    i have a question : is there any command in FOMCON same az the command ” stepinfo” ?

    thank you so much.


    No, there is no overloading function `stepinfo()` for the fractional-order transfer function object yet, but the CST version can be employed as well. Consider an example:


    Here, I first load the example systems provided with FOMCON, then approximate a fractional-order system G2 by an integer-order one in the form of a refined Oustaloup recursive filter and obtain y and t vectors explicitly.

    Note, however, that approximation parameters for a particular system need to be thoroughly selected to obtain a feasible result.


    Dear Aleksei,
    Im trying to run the fpid_optim .fig file fpid_optim .m file, which is used to find out the fractional order PID parameters through FPID Optimum tool. but wen im trying to fix the gain parameters in the table it getting the errors listed below

    Attempt to reference field of non-structure array.

    Error in fpid_optim>menuFix_Callback (line 957)
    set(handles.txtLam, ‘Enable’, expEnable);

    Error in gui_mainfcn (line 96)

    Error in fpid_optim (line 24)
    gui_mainfcn(gui_State, varargin{:});

    Error in

    Error while evaluating uicontrol Callback.

    if there is any example program regarding this problem please send me….
    thank you in advance………..


    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.


    Dear Aleksei,
    hi, Regarding FPID Optimum tool,if i entering lti plant model as a transfer function model in FPID Optimum tool its showing the below errors

    Undefined function or variable “Z_p”.

    Error in fpid_optimfun (line 105)
    e = 1 – step(feedback(Z_p*Z_c,1), t);

    Error in fpid_optimize>@(x)fpid_optimfun(x,G,opt) (line 267)
    x_opt = optimize(@(x) fpid_optimfun(x,G,opt), …

    Error in optimize/funfncP (line 613)
    obj_fval = funfcn(x_new, varargin{:});

    Error in optimize>@(x)funfncP(X(x),varargin{:}) (line 393)
    funfncT = @(x) funfncP(X(x), varargin{:});

    is these tool is not supported to transfer function model(instead if i entering fotf model im getting the results)……please refer to it
    Thanks in advance


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


    im doing the same procedure as you replied to me ,sorry to say this sir,but for fractional order transfer function as plant model it is working fine but when it comes to integer order transfer function as plant model its showing the above mentioned error……..


    Hi Aleksei,

    I am using FOMCON from last couple of months. It is really nice toolbox for beginners in fractional calculus to understand and implement.

    Some Questions:

    1. How do we select minimum and maximum frequency and order of Approximation?

    2. Sometime, Frictional PID Optimization gives good result but When I implement same result into simulation, it gives error.

    Could you please help me in above issues?


    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?



    Do we have a function for root locus in FOMCON?

    If yes, could you please give some small example?

    Thanking You,



    Hello Pritesh,

    This feature is not implemented yet.

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