Optimal rejection of nonstationary narrowband disturbances for flexible systems

Abstract

Optimal performance and optimal allocation of resources, such as pointing accuracy and onboard fuel utilization, are of primary concern in the design and operation of precision pointing spacecraft. Ironically, internal spacecraft instruments and reaction control actuators often act as sources of narrowband disturbances and impede the optimal performance of these precision systems. The fundamental objective of this work is the development of an active control methodology capable of rejecting disturbances with narrowband nonstationary spectral distributions with particular focus on spacecraft reaction wheel induced disturbances. A closed-form symbolically parameterized optimal feed-forward disturbance rejection methodology for flexible systems has been developed. The methodology combines disturbance modeling for narrowband disturbances together with quasi-stationary optimal control to yield a parameterized feed-forward control architecture. In the case of the reaction wheel disturbance rejection problem, the symbolic optimal control gains are parameterized in terms of wheel spin rate, enabling continuous and analytically exact gain adjustments as a function of the measurable scheduling parameter. The methodology was shown to be compatible with loop-shaping control design methods such as frequency-weighted optimal control. This quasi-stationary disturbance rejection methodology has been generalized and applied to the nonstationary reaction wheel imbalance problem. The nonstationary formulation involves expanding the reaction wheel's angular states in terms of a general series representation. Bessel functions and their properties are employed to define an equivalent finite-dimensional quasi-stationary disturbance signal.

(cont.) The effectiveness of the methodology has been experimentally demonstrated on a highly compliant system with non-collocated sensors and actuators. Experimental results show peak performance yielding nearly a 40 dB improvement over conventional broadband control with improved performance across a wide range of frequencies.