Gyroscopically Coupled Slow Manifolds

Abstract

When doing partial feedback decoupling of computed torques, the neglected elastic dynamics reappears in the expressions for generating the actuator inputs from those computed from the decoupled dynamics. This has motivated considerable research on the use of singular perturbation methods to create controls that force the coupled rotational and vibratory dynamics to evolve in a slow integral manifold. In such a constrained motion regime the elastic dynamics is expressible in terms of the attitude dynamics, thereby reducing slew actuator bandwidth requirements. In particular, it has been shown in previous work how to create "exact" slow manifolds by properly relating slew actuators and structural control actuators, which are polynomial in the chosen singular perturbation parameter, rather than correct only "to first order." That work was done for the fully linear case of small slew rates, for which only symbolic matrix inversions in the Laplace transform domain were needed. In this paper the high slew rates case is similarly treated. Gyroscopic coupling now leads to the presence of time-varying differential operators, so that symbolic operator multiplications and inversions in the time domain must be carried out (instead of simply Laplace transform matrix inversions). Only an outline of the results is given here.