Fractional PID Controller Design

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  • #873
    kapil dhama
    Guest

    Respected sir

    i am currently doing phd work on fractional order pid controller design for drilling machine which has a transfer function
    1958/s^3 + 17.89s^2 + 103.3^s + 190.8
    how i will design the fopid controller for the above transfer function of the order 3
    when the above model should be approximated by a first order lag plus time delay system which is give in the following
    G = (10/1+.387*s)*e^-197*s
    how i will combine the fopid controller and above transfer function to get combined transfer function
    basically i am going to design various controller stratgies for FOPID using soft computing techniques.
    please suggest
    thanking you
    kapil dhama
    Ph.D. scholar
    ymca university of science & technology , haryana , india

    #875
    Aleksei
    Keymaster

    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.

    #937
    Pritesh Shah
    Guest

    Just use fomcon

    Do following things steps by step

    1. Define your plant model in transfer function using tf command in matlab.

    2. Convert same system in fractional transfer function object using fotf command. (Assuming that you have already added FOMCON in set path of your MATLAB)

    3. open fomcon. (Type fomcon in your command window)

    4. Go to Tools and select ‘Fractional PID Design’.

    5. Go to Tuning tab and select ‘optimize’.

    6. Defined constraints and other options as per your requirement.

    7. Say optimize and wait for optimization

    8. After sya, Take Values

    9. Do simulate in Fractional PID design window

    #971
    Smita
    Guest

    Hi Aleksei,
    I have a doubt.I have transfer function K.e^(o.2s)/20s+1.
    I want to control it via IO PID controller first and then with FO PID controller.
    I manually did the calc. as per Zeigler Nichols first rule(based on ‘S’ shaped response) and found Kp=120,Ki=300 and Kd=12.

    My qn is that when I will control the same transfer function via FOPID controller will these 3 value remain same or these will vary?

    As per the tuning rules set by “Duarte Valerio” I got totally different values :
    Kp=0.0815
    Ki=6.6208
    Kd=2.5762
    Lambda=0.6804
    Mu=0.704

    I don’t know which concept is correct? Please explain.

    Thanks
    Smita

    #972
    Shefali
    Guest

    Hi,

    If I have a state space matrix(A,B,C,D) then how can I design a FOPID controller for the same ?

    Thanks
    Shefali

    #975
    Aleksei
    Keymaster

    Dear Smita,
    ZN is an aggressive tuning rule (albeit frequently used).
    I have no idea what you mean by “Duarte Valerio” tuning rules, as these are not implemented in FOMCON.

    • This reply was modified 6 years, 1 month ago by Aleksei.
    #976
    Aleksei
    Keymaster

    Dear Shefali,
    Use the FOMCON FOPID tuning tool, it supports SISO state-space models as well.

    #978
    Smita
    Guest

    Please check the paper.I have sent it you to your email.

    Thanks
    Smita

    #980
    Smita
    Guest

    Hi Alex,
    If I have a plant which is to be controlled via a IO PID controller first.Here I will get Values for Kp,Ki and Kd.

    My qn is :I can use the same gain parameters(of IO PID) for FOPID so that I have only to find out lamda and mu.Is this stmt Correct?

    Another thing : the tuning rule used in FOMCON is the same tuning rule provided by Y.Chen in “Fractional -Order Systems and Controls”.Is it Right??
    Please suggest.

    Thanks
    Smita

    #983
    Shefali
    Guest

    Hi,
    I have have a state matrix which is MIMO(3 inputs and 5 outputs). Then how can I control it by FOPID in FOMCON?Please reply.

    Thanks
    Shefali

    #985
    Aleksei
    Keymaster

    At this time FOMCON supports control of SISO plants only. While MIMO control is possible with cascades of FOPID controllers, this falls out of the current scope of the toolbox, hence I cannot provide support for it.

    #992
    Shefali
    Guest

    Hi,
    I was replicating the design of a FOPID controller for the system 1/(14994s^1.31+6009.5s^0.97+1.69) in page 96 of FOMCON manual.

    When identified with freq range(10^-4 to 10^4),and order 5, I got some different values other than the written.Then I changed the order to 8 and got nearly similar results for K,L,T.

    But when I computeed with Z-N rule totally diff. results came.

    Kp=860.428 where as given is 802.915, Kd=4906.64 whereas the given amt is Kd=6.095.

    Please explain why it happens.

    Thanks
    Shefali

    #994
    Aleksei
    Keymaster

    At some point I discovered an issue in FOMCON code related to classical PID controller tuning.

    What I am currently getting is this. With $K=0.588205$, $L=67.379$, and $T=5054.34$ the tuning is $K_p=153.036$, $K_i=1.13563$, and $K_d=5155.69$.

    • This reply was modified 6 years ago by Aleksei.
    #996
    Shefali
    Guest

    Thank You Very much for your explanation.

    I have a qn.While using oustaloup approximation in MatLAB i am getting below error.

    clc;
    close all;
    clear all;
    N=5;
    w1=1e-3;
    w2=1e3;
    g1=ousta_fod(0.3,N,w1,w2)

    ??? Undefined function or method ‘ousta_fod’ for input arguments of type ‘double’.

    Error in ==> FOoustal at 7
    g1=ousta_fod(0.3,N,w1,w2)

    Why the error is like this?? How can i rectify it??

    Thanks
    Shefali

    #998
    Aleksei
    Keymaster

    The function is named oustafod, not ousta_fod.

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