I am working on the response of vibrational energy harvesters to a very abrupt forcing function with many high-frequency components. As you can see the peaks in the attached signal are very narrow and have high-frequency components. To accurately reproduce the forcing signal, ode45 needs to take very small time steps. But limiting the time steps via "MaxStep" option makes the simulation very very slow.
Are there any alternatives ?
Hi Adytia,
if I am not mistaken ode45 uses an adjustable integration interval (internally). Your problem seems to have two very different time scales (kind of a stiff problem) which is always tricky to solve. What if you do not limit the maximum integration step but use an interval sufficiently small (i.e. 1/10 or 1/20 of the fast cycles). So, if you do not limit the maximum step and if ode is adjustable, then it will increase the integration step at lower frequencies.
Cheers
I agree with Antonio, stiff problems are tricky. My experience was representing stick-slip friction with a Coulomb simple model. The solution I found was artificially smoothing the discontinuous functions
You can try separating the simulation in a chain of two kinds of simulation, large step (LS) and short step (SS). Since you know the forcing function you can configure two solver parameter sets. You have to use the final state of one simulation as the initial conditions of the follow one. If you do not ensure state variables continuity, your results wont be realistic.
Dear Aditya, if you simulate some real world structure of harvester you need take into account that the harvesters are always loaded on the resistive/capacitive load. And this electric capacitance will filter all high frequency harmonics. I don't know what program tool do you use to simulate your problem. But using of low pass RC filter (its program implementation) is very efficient way to overcome your difficulty. It's my first advice. Further. ODE45 is not suitable for the stiff problem. ODE23, ODE15 and their variety are useful for these cases. MATLAB provides all such solvers, and you can use them directly or by means of Simulink
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