Authority-on-demand: Adaptive suspension control for the Gravity Probe B gyroscopes

The Gravity Probe B (GP-B) experiment will test Einstein's General Theory of Relativity by measuring non-Newtonian drifts in the angular-momentum vectors of four ultra-precise electrostatically-suspended gyroscopes. The extremely-small relativistic drifts are difficult to measure, because they can be masked by larger Newtonian drifts caused by (amongst others) the gyroscope-suspension forces and torques.; GP-B will reduce the nominal support forces and torques by suspending the gyroscopes within a dragfree earth-orbiting spacecraft. However, the spacecraft will also be subject to a number of unpredictable micrometeoroid strikes with sufficient momentum to cause significant motion and vibration of the spacecraft. Subsequent to such strikes, it is crucial that the gyroscope rotors be prevented from colliding with their housings. Linear controllers with sufficient authority to do so produce excessive forces in response to the nominal disturbances. With such controllers, the Newtonian drifts would exceed GP-B error margins.; The Authority-on-Demand (AOD) concept was developed to address this problem. Specifically, AOD is a self-tuning adaptive controller which uses some or all of the system states which it is controlling to: (1) detect the need for higher authority, (2) smoothly increase its authority, but only as necessary to meet specifications, and (3) stably reduce its authority back to a low nominal authority as the disturbance is brought under control.; The first part of the dissertation develops the AOD concept in general and by example of its application to a 1/ms2 plant—a simplified form of the GP-B problem. It is shown that AOD performs as desired: it adapts quickly to control large meteoroid strikes, and then smoothly reduces its authority back to nominal. The dynamic range of the AOD controller is limited only by sampling rate and actuator saturation. General conditions for the exponential stability of an AOD controller are developed, and various implementation issues such as computational delay are discussed.; The second part of the dissertation extends the AOD controller to the full 3-axis GP-B system. The resulting controller has been implemented in C-code and will fly on the GP-B spacecraft. Simulations show that the gyroscope drift-rates will be several orders of magnitude lower than with a linear controller.