Ralph E. Bach

Linearization of attitude-control error dynamics

Some useful properties of direction-cosine and quaternion attitude formulations that include specification of attitude error and the inversion of rigid-body rotational dynamics are reviewed. The inversion procedure is then applied to a measure of attitude error to realize a new model-follower control system that exhibits linear attitude-error dynamics. Error analyses and simulation results for spacecraft attitude-control systems are presented to demonstrate the more robust performance obtainable from an exact linear-error formulation over that obtained from either direction-cosine or quaternion formulations with simple linear feedback control laws. >

Recursive inversion of externally defined linear systems by FIR filters

The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least-squares procedure is shown to have an exact initialization based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problem of system identification and compensation. >