Optimal Auto-tuning of Satellite Attitude Control using the Two Relay Feedback Test under Modeling Uncertainties

This paper proposes a non-parametric automatic tuning method for satellite attitude control that accounts for modeling uncertainties in the inertia and actuator dynamics. The method utilizes a two-relay feedback test, which induces self-sustained periodic oscillations in the system's output. The existence of the periodic oscillations is analyzed using the describing function method. The profile of these oscillations is used to optimally tune the control parameters through the proposed optimal tuning rules (tuning formulas), with a guarantee on a specific phase margin. The tuning rules are found through numerical optimization for a class of satellites ranging from nanosatellites to large scale satellites, where the attitude dynamics vary depending on the satellite sample. The tuning rules map the oscillations' amplitude and frequency to the optimal controller gains. The tuning of the controllers happens online in real-time using these tuning rules. The effectiveness of the proposed tuning procedure is evaluated through nonlinear three-axis satellite simulations and validated experimentally using a magnetic-levitation testbed simulating a frictionless space environment.