Fractional PID Controller Design

[kapil dhama]

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

[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.

[Pritesh Shah]

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

[Smita]

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

[Shefali]

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

[Aleksei]

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 10 years, 4 months ago by Aleksei.

[Aleksei]

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

[Smita]

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

Thanks
Smita

[Smita]

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

[Shefali]

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

[Aleksei]

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.

[Shefali]

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

[Aleksei]

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 10 years, 4 months ago by Aleksei.

[Shefali]

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

[Aleksei]

The function is named oustafod, not ousta_fod.

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