Buck converter worked for 1000+ start/stop cycles with power from regulated DC power supply, failed with li-ion battery
I understand why you see the initial fast droop, because the electrodes in the battery are quite complex electrically:







simulate this circuit &ndash; Schematic created using CircuitLab

At the application of the load, an EDLC forms at the electrodes and the capacitance can be enormous - 60μF to 100μF is not unusual (the effective plates are literally Angstroms apart) with a sub milliohm ESR and that gives you a very effective differentiator at initial transient loading of the battery into a heavy load.

Once the EDLC has formed, it stops conducting and the only resistance is the ESR of the battery electrodes themselves. As the terminals recover to being limited only by load and internal ESR, there can be an inductive effect (after all, self inductance exists anywhere current flows, to a greater or lesser degree).

Your waveform looks like a damped resonance, so an appropriate snubber may work.

You can see how EDLCs form at battery electrodes in this paper.

I have seen this effect a few times and it was quite confusing the first time it appeared (in a seawater activated circuit).