Model predictive star tracking control for ground-based telescopes: the Telescopio Nazionale Galileo case

With the aim of improving the star tracking performance of ground-based telescopes, we deal with the design of model predictive control architecture so as to properly lead their axes while mitigating possible external disturbances affecting the control task. The proposed architecture is composed of two layers, namely, (i) a trajectory generator that determines, based on the astronomic computation, the telescope position and speed references to be tracked while ensuring that all the telescope physical constraints, in terms of speed and acceleration, are never violated; (ii) an model predictive control (MPC) controller that guarantees the optimal tracking of the desired reference behavior by providing the torque inputs for telescope axes for the achievement of star observation task. The control architecture is tailored for the tracking control problem of Telescopio Nazionale Galileo (TNG), located at La Palma (Spain). To this end, by leveraging real data measurements in specific operative scenarios, a 12-order linear system describing the TNG dynamics is identified, via the non-iterative subspace method, for the design of the second layer. Validation results confirm the goodness of the dynamical model in predicting the TNG behavior within the operative range of (80 and 90 deg) altitude position. The effectiveness of the proposed MPC-based control architecture is proven via an ad-hoc virtual testing simulation platform implemented in MATLAB and Simulink and tailored for the identified TNG model. Virtual testing results, involving the real scientific target TYC 1731-916-1, confirm the capability of the proposed solution in ensuring optimal star tracking while mitigating the wind external disturbances forces. Finally, a comparison analysis w.r.t. the state-of-the-art control approaches, i.e., Linear-Quadratic-Gaussian and Proportional-Integrator-Derivative controller, and a robustness analysis w.r.t. the model mismatch between the MPC prediction model and the simulated TNG dynamics are provided to disclose the improved tracking performance achievable via the proposed MPC-based control architecture.