Just to clarify one thing first: I'm not trying to smooth the output voltage from a PWM signal - I would just use an appropriate capacitor for that purpose.
So, I have made some heated insoles for my wife (she struggles with chilblains, and nothing on the market kept her toes sufficiently warm). The insoles generate heat using Nichrome wire and are powered by a USB battery pack. Each insole draws about 1.2A at 5V, which the battery pack is quite happy with and lasts a few hours.
The insoles work great but sometimes needed to be turned down a little bit, so I used a cheap PWM LED dimmer to control the heat output. This works great except when reducing the heat output, the battery pack shuts off after a while.
My USB battery pack shows a 2.1 amp mode and a 1 amp mode on its display. When on full power, it automatically switches to 2.1 amp mode. When on a lower power, it automatically switches to 1 amp mode. My current theory is that the battery pack has a resettable fuse inside, which breaks the circuit because I am actually still drawing 1.2 amps during the PWM cycle.
My question is: How can I "smooth" the current that I am drawing from the battery pack so I don't draw more than 1 amp on the lower PWM settings?