Design of a Port-Hamiltonian Control for an Alt-Azimuth Liquid–Mirror Telescope

Authors

Juan Cristobal Alcaraz Tapia, Carlos E. Castañeda, Héctor Vargas Rodriguez, P. Esquivel

Abstract

In this work, we design a control strategy to be applied in a port-Hamilton representation of a liquid-mirror telescope for an alt-azimuth configuration. Starting from a dynamical model for an alt-azimuth liquid-mirror telescope based on Lagrange mechanics, a transformation to the port-Hamilton form is made. Such a dynamical model is obtained by computing the kinetic and potential energy of the telescope and substituting them in the Euler–Lagrange equation of motion. Then, for the transformation to the port-Hamiltonian form, we obtain the relation between the Hamiltonian and the Lagrangian. The resulting open-loop model based on the Hamiltonian function is controlled using an extension of the interconnection and damping-assignment passivity-based control aiming for a robust and accurate steady behavior in the closed loop while tracking a star’s position. For comparison purposes, two different control strategies are applied to the Lagrangian model, inverse-dynamics control and sliding mode super-twisting control. Since the light is collected by the principal mirror of the telescope while tracking a star, we make a description of the liquid mirror’s behavior. The tracking star’s position is described as a function of the observer’s position and the star’s coordinates as well as the date of observation. The simulations’ results show that the port-Hamilton control has a good transitory and steady response as well as great accuracy competing with that of inverse-dynamics control but with greater robustness and no chattering drawback.

Citation

• Journal: Mathematics
• Year: 2023
• Volume: 11
• Issue: 16
• Pages: 3443
• Publisher: MDPI AG
• DOI: 10.3390/math11163443

BibTeX

@article{Alcaraz_Tapia_2023,
  title={{Design of a Port-Hamiltonian Control for an Alt-Azimuth Liquid–Mirror Telescope}},
  volume={11},
  ISSN={2227-7390},
  DOI={10.3390/math11163443},
  number={16},
  journal={Mathematics},
  publisher={MDPI AG},
  author={Alcaraz Tapia, Juan Cristobal and Castañeda, Carlos E. and Vargas Rodriguez, Héctor and Esquivel, P.},
  year={2023},
  pages={3443}
}

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