Doesnt feedback control disturb the measurement?
In fact feedback control, properly done, will usually improve the measurement, although it may add a small amount of noise. Consider an accelerometer with a very nonlinear spring which is well calibrated only in a small range. If the test mass moves very much, the spring constant (and calibration of the acceleration) changes, resulting in an error . Feedback keeps the mass in its linear range, resulting in a net improvement in performance. The concern here is that noise added by all the amplifiers and stuff in the feedback loop will be much greater than the natural noise the system would have if the feedback were not present. Formally, we can represent the accelerometers by a linear differential operator H which converts force to position: x = Hf. (Laplace transformed, H = 1/(Ms2 ) for a free mass. This is equivalent to the statement that the force has to be integrated twice with respect to time, to get the position.). The feedback is a gain operator G which takes the measured position
