# How to solve an integral equation in simulink?

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Leon Rinke on 9 Mar 2021
Commented: Leon Rinke on 17 Mar 2021
Hi,
I need to solve the following equation in simulink:
I have ξ (= xi) as an input and need iav as an output to forward it to other blocks. I tried to use the MATLAB function block, but the code I've written doesn't work.
function iav = fcn(xi)
syms xi phi iav
fun = 1/(sqrt(1-(1-phi^(3/2))*((1-iav)*xi)^(3/2)));
eqn = (1-iav)*int(fun,phi,0,1)==1;
iav = solve(eqn,iav);
end
Any help would be much appreciated. Thanks in advance.
Leon

Deepak Meena on 17 Mar 2021
Hi,
Please let us know what error exactly you are getting while using Function block in Simulink.
My Initial guess is that error might be coming because iav is returning as empty symbolic variable . I tried to run the your function on your end and the value you passing to the function is not getting assigned to the symbolic Variable xi.
Also it is advised to convert the iav to double before returning.
function t = fcn(txi)
syms xi phi iav
xi = txi;
fun = 1/(sqrt(1-(1-phi^(3/2))*((1-iav)*xi)^(3/2)));
eqn = (1-iav)*int(fun,phi,0,1)==1;
iav = vpasolve(eqn,iav);
t = double(iav);
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Deepak Meena on 17 Mar 2021
Hi ,
It seems to be known issue with using syms in MATLAB function block. There is one workaround though, that is using the sym and vpassolve in another function and call that file as extrinsic.
Using that example I created a separate .m file 'fcn.m':
function y = fcn(u)
syms xi phi iav
xi = u;
fun = 1/(sqrt(1-(1-phi^(3/2))*((1-iav)*xi)^(3/2)));
eqn = (1-iav)*int(fun,phi,0,1)==1;
iav = vpasolve(eqn,iav);
y = double(iav);
and then I call this file as extrinsic:
MATLAB function block call:
function y = fcn1(u)
coder.extrinsic('fcn');
y = 0;
y = fcn(u);
Using this I am able to remove the errors .
On another note the simulation will be very slow because the symbolic integration takes a lot of time
Thanks
Leon Rinke on 17 Mar 2021
Hi,
Thanks a lot. I was able to remove the errors too. But, your right. The simulation now just takes forever because of that.
Can you think of any other solution to solve this problem? Maybe an entirely different approach which would be quicker?

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