2. the position of the cart formula_22 relative to track center is stabilized by slightly modulating the null angle (the angle error that the control system tries to null) by the position of the cart, that is, null angle formula_23 where formula_24 is small. this makes the pole want to lean slightly toward track center and stabilize at track center where the tilt angle is exactly vertical. any offset in the tilt sensor or track slope that would otherwise cause instability translates into a stable position offset. a further added offset gives position control.