Choosing appropriate capacitor value from ripple
For similar problems, with 10% V ripple , I let RC= 8T.
If motor equiv R=12V/15A and T= 1/500Hz=2ms then C=8*2ms*15A/12V= 20 mF

(assuming your current is RMS)

This is consistent with your calculation and you can achieve this with a power supply with Zout = &lt;&lt;10% of load or better with a 12V battery and trickle charger.  Batteries have much larger capacitance and low ESR and would perform better but Caps will be cheaper.

However since startup current due to DCR of motor can be up to 10x Imax rated current, soft start is necessary or a much higher capacity such as from a battery.