Fractional Control Basic

[Pritesh Shah]

Hi,

I want to use stepinfo for fractional order system.

It is giving error.

Could you please give one example?

Thanking You,

[Aleksei]

You may use stepinfo() on an approximated system. This function is not yet available for fotf systems.

[Pritesh Shah]

Regarding FInding Norm 2.
———————

Dear Alekesi,

I want to find norm 2 of fractional order controller.

G2=fotf(tf([0.5 -0.1 0.01],[1 2 1 0]))
Fractional-order transfer function:
0.5s^{2}-0.1s+0.01
——————
s^{3}+2s^{2}+s
norm(G2)
Error::
Attempt to reference field of non-structure array.

Error in fotf/freqresp (line 14)
a = G.a;

Error in fotf/norm>@(x)freqresp(x,G).*freqresp(-x,G) (line 25)
f = @(x)freqresp(x, G).*freqresp(-x,G);

Error in quadgk/evalFun (line 331)
fx = FUN(x);

Error in quadgk/vadapt (line 250)
[fx,too_close] = f(x);

Error in quadgk (line 149)
[q,errbnd] = vadapt(@evalFun,tinterval);

Error in fotf/norm (line 27)
n = quadgk(f, -dx*1i, dx*1i) / (2*pi*1i);
—————————————————–

Please help me for this also.
Also, if you can help me out to explain important of norm 2, it will be useful to me.

Thanking You,

[Aleksei]

This is a bug. Consider the following patch: https://fomcon.net/forums/topic/preliminary-releases-and-patches/#post-1037
Towards your second request, see the following PDF: http://www.abo.fi/~htoivone/courses/robust/rob2.pdf

[syed naeem haider]

Hi,

i am trying to use fractional integrator in simulink with physical model,, but the problem i am facing is that physical ball and beam system is attached with pc and matlab version used in that system is Matlab2008a ,,,, so when i load fomcon toolbox i do not get ant fractional blocks in simulink library of fomcon… ” FOTF_gui ” is working fine ….. in matlab ,,, but i cannot use fractional blocks in simulink…..

is there any way possible to use fractional integrator in simulink model by using fractional transfer function from work space to simulink…..

or any way to make fractional transfer function in simulink without blocks …..

[Aleksei]

Please see this comment: https://fomcon.net/fomcon-toolbox/download/#comment-1921

[pritesh shah]

Hi Aleksei,

Hope you are fine. Once again, thanks for nice toolbox.

I have some basic

1. If order of fractional parameters between, 1 to 2, than what is the effect on stability?

2. If more then 2, than what is the effect on stability?

There is some concept q*pi/2, but I am not able to understand properly.

[Nitish Katal]

Dear Sir,

I’ve been using the FOMCON toolbox and its working great.

I have some issue regarding the check of stability of the Fractional Order System;

Say I’ve a FO plant G and a FO PID Controller, how can I check for the stability of this system directly,

Like is the system is STABLE return 1 if NOT-STABLE return 0.

[pritesh shah]

Hi Alekesi,

I want to find out output of system using lsim function.

If it is same time interval (T), then we are able to get correct results.

But, in one of the problem, time interval is not the same. I am getting different answer.

Could you please suggest something.

Thanking You in advance,

Say example,

G=fotf(‘1′,’s^0.5+1’);
u=ones(1, 1001);
t=0:0.01:10;
y=lsim(G,u,t);
% I will get correct result as time vector has same interval.

% if t has variable time values, I am not getting correct answer.
% U have checked code of lsim, h=t(2)-t(1)

[Aleksei]

Dear Nitish,
The function you are looking for is called isstable(). Therefore, just do isstable(feedback(G_PLANT*G_FOPID,1)).

• This reply was modified 9 years, 4 months ago by Aleksei.

[Aleksei]

Dear pritesh,
This is a known problem with fixed-step solvers. The suggested method is to decrease step size until the results are the same.

[pritesh shah]

Hi Nitish,

I think, You can make system closed loop transfer function using feedback function.

Check for stability of closed loop system.
Say Example,
G is fO plant, C is FPID.

G=fotf(‘1′,’s^0.5+1’);
C=fracpid(1,1,0.5,1,0.5)
G_C=feedback(G*C,1);
isstable(G_C)

[pritesh]

Dear Alekesi,

I want to define fractional transfer function k/(s+a)^alpha.
where, alpha is fractional order between 0 to 1.

Could you please help for the same?

[pritesh]

Dear Alekesi,

Any idea about inverse Laplace of fractional order system?

Y(s)= (k1*s^(lam+mu)+k2*s^lam+k3)/(k1*s^(lam+mu+1)+(1+k2)*s^(lam+1)+T*s^(lam+2)+k3*s);

I want to find out inverse Laplace of Y(s)?

Any idea or comments??

[Aleksei]

You may want to check this out: http://www.tuke.sk/petras/foc_laplace.pdf

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