KEYWORDS: Telescopes, Stars, Matrices, Data modeling, Design, Control systems, Signal filtering, Performance modeling, Detection and tracking algorithms, Error analysis
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.
This paper focuses on the designing of tracking control strategies for ground-based telescopes by also comparing model-based solutions with more classical alternatives. Within this framework, we synthesize a double-layer control architecture consisting of: i) a position control layer, which combines a Kalman filter observer and Linear-Quadratic-Gaussian-Proportional-Integral (LQG-PI) controller to compute the appropriate speed profile guaranteeing a reliable tracking of a given telescope position trajectories; ii) a speed control layer, which ensures the optimal tracking of the computed speed profile by driving the torque of the telescope. Moreover, a trapezoidal speed pre-processor is embedded in our control architecture with the aim of computing the appropriate telescope axes position trajectories: this ensures that all the telescope physical constraints, in terms of speed and acceleration, are not always violated. Virtual simulations, carried out via an ad-hoc simulation platform, implemented in Matalb&Simulink and tailored for the specific case study Telescopio Nazionale Galileo (TNG) located at La Palma island, disclose the effectiveness of the hierarchical control architecture for a representative set of star trajectories. Validation phase also considers several realistic conditions and takes into account input disturbance such as the Von-Karman wind disturbance model. Finally, a comparison analysis with a PID-based control architecture is provided to discuss about the advantages and benefits of the proposed optimal control solution.
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