Hi,
I'm trying to simulate a second order system (see the picture and simulink file attached). It´s a system where each equation has a different time scale. "I1" is in function of "mi", and "I2" is in function of "t", where mi=t*beta, and, for instance, beta=5.
The different "mi" and "t" are irrelevances in terms of stability analysis. But the problem is to get a numerical solution.
I tried Mathematica (Wolfram) and it failed. Now I'm trying Simulink Matlab, but I have no idea how to put the different time scales.
Important 1: Note, I think the system has not a kind of delay. When I think about delay, the left side of all equations are in function of "t", and in the right side we have something like "t - z" , where z is the delay. I think that is not the case.
Important 2: It's possible to do a transformation, where we divide the right side part of I1 equation by beta. But I think it´s not a good choice. I tried it and I had a numeral solution with no oscillation, and I was expecting some.
Thanks.
Hi, can you be more precise? If t is an integer (from equations) then these are not differential equations. Could they be difference/recurrence equations? If this is the case you could try to use RSolve[] instead of DSolve[].
Hi, Fabio,
Sorry. They are Ordinary Differential Equations (ODE). Acctualy, time is "continuous".
Have you tried making an exponential substitution for the time variable? In that setting this does become a delay equation.
Sorry, Thomas. Sincerely, I didn't understand what you mean. Can you elaborate? Thank you very much.
Suppose one sets t=e^s for a new variable s. Then \mu=\beta t= e^[s-h] with -h=\ln(\beta) so I_1 and I_2 become functions of s and s-h. This is a delay for \beta
Thomas is right, do the substitution carefully and you can solve the system with \beta1 I do not think it is possible to integrate the system and if it has physical sense
If you can find a change of variables that result in an equivalent differential-delay equation, there are packages in the in the file exchange area on the Matlab site address these problems. I don't know if you exact problem is there but it is a place to start looking for ideas.
http://www.mathworks.com/matlabcentral/fileexchange/?utf8=✓&term=differential-delay+equations
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