Thanks for sharing Andrew. It's something I've never considered in my spreadsheets since it was an unknown assumption. I took my lunch hour and did algebra to come up with a solution for x(t) because the "Battery Voltage Gain Filter" strikes me as wonkish (though that filter is an interesting way to fix the problem). The result was based on some constants that are pre-computed via the motor & robot properties, yet the point is that (luckily) a solution exists for the non-linear differential equation:
Results on Wolfram|Alpha
It's not exactly pretty, and solving that solution for t (so time can be a function of gear ratio) is causing WolframAlpha to blow up... so more work will have to be done. Yet it does allow for more straightforward calculations of pretty much everything (including voltage) without the need for circularly-dependent equations that need several hundred lines at high resolution to get accurate.
Pretty equations for constants A, B, C, D & E to come tonight or early tomorrow.