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Moreover, the reference acceleration signal is easily available.
The reference acceleration is then employed to give the acceleration at the other positions.
When using a force actuator, the feedforward needs to generate a force proportional to the reference acceleration, which can be measured by means of an accelerometer or can be created by double differentiation of the reference position.
A procedure has been developed to measure dynamic strain in a beam by the use of two accelerometers placed on the beam and frequency response functions between them which relate measured accelerations at different positions to the fixed reference acceleration position.
Based on these inputs, the CACC/ACC controller can calculate a reference acceleration "a ref".
The reference acceleration is derived from the nominal thrust force and satellite mass.
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Since the reference accelerations obtained from GPS tracking do not contain the influence of these accelerations, we have to remove them beforehand.
We calculated the scale factor by the ratio of the peak-to-peak reference accelerations and the peak-to-peak measured accelerations.
During the maneuver the thrusters are repeatedly activated for 10 seconds, which creates a sequence of large, sharp signals that serve as reference accelerations.
We expect that the reference accelerations have an error of 5 10%% due to small deviations of the real thrust force and direction from the nominal ones and uncertainties in the satellite mass due to the calculation of the remaining fuel from pressure sensors.
A tracking control law is then designed to track the reference drag acceleration profile.
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