Simple Multi-Rate Adaptive Control on Spacecraft Jitter Rejection for FSO Pointing System

Free space optical communication systems on satellites require precise pointing, but mechanical micro-vibrations in the satellite platform can degrade the pointing. The actuator in the pointing system, a fast steering mirror, limits its effectiveness due to the non-constant velocity of the transient motion. This study proposes a multi-rate adaptive algorithm that utilizes a faster sensor rate to capture the transient behavior. The gradient update equation for the error function is derived that incorporates the multi-rate architecture, and its convergence with the stability condition is thoroughly examined. The analysis provides insights into the least-mean-square algorithm's behavior with sinusoidal inputs. Simulation results validate the effectiveness of the multirate approach over the single-rate method in the complex sinusoidal disturbances. Further validation was obtained from experimental data using an optical testbed, which was consistent with simulations. This study validates a multi-rate adaptive control strategy for precise pointing in satellite free space optical communications, offering a solution for resource-constrained platforms.