Why am I getting imaginary values with ode45 ??
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%This is my program R=1;
L=10^-2;
C=400/62505000010;
Is=10^-12;
Vdo=25*10^-3;
f=@(t,y) [(-R*y(1)/L-(y(2)/(C*L)-(Vdo/L)*log(1+(y(1)/Is))));y(1)];
close all;
tic
options = odeset('RelTol',10^-12,'AbsTol',10^-8);
[t,y]=ode45(f,0:10^-3:0.01,[10^-6 -10^-6],options);
toc
plot(t,y)
xlabel('time "t"')
ylabel('output "y"')
figure(2)
plot(y(:,2),y(:,1),'r')
xlabel('current I');
ylabel('charge Q')
I am simulating a simple circuit, which is governed by two differential equations
differential (Q)=I;
differential(I)=(-R/L)*I-(Vdo/L)*log(1+(I/Is))-Q/(C*L);
I,Q are my variables. I am getting the simulated output but the problem is I am getting imaginary values
for y.
As the only possible cause could be 'log' term in the second differential equation,
from that 1+I/Is>0 ==> I>-Is 'to get real values'
so I used odeset to put obsolute tolerence limit as 10^-8.
But I am still getting imaginary values for 'y'!! Why??
Please let me know what I am doing wrong !!
0 Comments
Answers (3)
Shoaibur Rahman
on 29 Dec 2014
Your I has both negative and positive values, which are in the range of 10^(-7), but Is is in 10^(-12). So, I/Is gives high negatives for some negative values of I. In that case, log is getting a negative input, and thus resulting imaginary parts.
I is the current, and negative indicates the direction. So, when using inside log, you can use both I and Is in same direction, hence same signs. This is also equivalent to making I as abs(I) inside the log.
0 Comments
Sai charan Bandi
on 29 Dec 2014
3 Comments
Jan
on 30 Dec 2014
@Sai charan Bandi: Please use the section for comments and not the one for answers, if you post a comment. Thanks.
Jan
on 30 Dec 2014
If you create a function instead of using an anonymous function, you can add a short test for imaginary values:
function dy = fun(t,y)
dy = [(-R*y(1)/L-(y(2)/(C*L)-(Vdo/L)*log(1+(y(1)/Is)))); ...
y(1)];
if any(~isreal(dy))
keyboard
end
4 Comments
Shoaibur Rahman
on 31 Dec 2014
Edited: Shoaibur Rahman
on 31 Dec 2014
You can have a look at the ode45 function itself to see how the function is written. Type edit ode45 on your command window, and see that. It is a complex algorithm though.
Regarding the ignoring of imaginary values, the plot function ignores those, not the ode45. This is the way how plot function works. If you are interested to plot the imaginary part then use imag function. However, in RLC circuit analysis, the most effective way will be to see the magnitude and phase, which can be computed using abs and angle functions, respectively.
Two columns in output have some values; none of them is entirely zero, but one is very small comparing to another. This is not surprising since, I = dQ/dt, your first equation. So, the relation between I and Q vastly depends on the time step.
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