Saturated Time-Varying State Feedback for Fast and Damped Attitude Transient Convergence

Mission performance is often anchored on the fulfillment of tight attitude pointing requirements, which rely on high-precision control. Attitude transients stemming from a wide range of initial conditions or due to unpredictable dynamic events often inhibit nominal operations as pointing requirements are violated, a challenge found in the future gravitational-wave observer Laser Interferometer Space Antenna (LISA) as a consequence of micrometeoroid impacts. A suitable onboard control solution must provide the minimization of the transient peak and a fast fine-pointing recovery for a large range of initial conditions, a combination not satisfactorily achieved by existing methods. This work introduces a saturated state feedback with a time-varying gain adaptation for fast attitude convergence while maintaining a damped response. This simple and intuitive method is proven to achieve a damped response for a bounded actuation authority uncertainty. For multiple degrees of freedom constrained by a bounded actuation authority set and subject to an impulse disturbance, equal settling times are achieved in the sense that all velocity components decay simultaneously. A comparison with three methods in the time-optimality class shows the efficacy of the proposed method. The method is applied to the LISA micrometeoroid impact recovery scenario, demonstrating its performance in the presence of nonlinearities and uncertainties.