It may from time to time necessary to damp nutation with thrusters on a momentum bias spacecraft. For example, nutation can happen when you transition from stationkeeping mode, which uses thrusters, to normal mode, in which you use low control authority actuators, such as magnetic torquers, for control.
We’ve written a script that simulation a momentum bias spacecraft. Let’s show the results.
The spacecraft body rate is 0.01 rad/s. This is much greater than you will ever see on your own spacecraft. The peak roll angle is about 18 degrees! The last plot shows the thruster control. In this simulation we don’t apply any control so the line is flat.
All you need is one thruster pulse, properly timed, to drive the x angular rate to zero. You must time it properly so as not to not leave a roll error. What we do is measure the peak angular rate, compute the pulsewidth needed to drive the rate to zero, and turn on the thruster when the roll angle is zero and the nutation rate is at its peak with the appropriate sign. The following plot shows the results.
The results aren’t perfect, as they would not be operationally. We did both simulations with the same Spacecraft Control Toolbox http://www.psatellite.com/products/sct/ script. This is a link to the m-file, saved as a zip file.
You won’t be able to run this without our toolboxes but you can see how we implemented “manual” nutation control. This script, and the new function RHSGyrostat.m will be available in SCT 2020.1 coming soon!