Driving Straight With Encoders

[microbuns]

How do you drive straight with a tank style drivetrain using encoders (no gyro)? Our bot has 2 wheels which each have identical encoders on them, but unfortunately one side has more friction than the other side.

Our best solution we have right now (which isn't amazing) is to have a speed PID controller on both sides, which ensures they are both going the correct speed relative to the floor. However, this doesn't always guarantee the wheels get up to speed in time - meaning one side may get as much as 2-3 inches ahead of the other while they are speeding up - this difference will be maintained as they stay at speed.

I was thinking about somehow trying to minimize the difference between the two sides' encoders, but I'm not exactly sure what/how to go about that. Do you just have some speed factor you add to one side and subtract to the other that scales off the difference of the two sides?