Vst Telescope Dynamic Analisys and Position Control Algorithms

The VST (VLT Survey Telescope) is a 2.6 m class Alt-Az telescope to be installed on Cerro Paranal in the Atacama desert, Northern Chile, in the European Southern Observatory (ESO) site. The VST is a widefield imaging facility planned to supply databases for the ESO Very Large Telescope (VLT) science and carry out stand-alone observations in the UltraViolet to Infrared spectral range. So far no telescope has been dedicated entirely to surveys; the VST will be the first survey telescope to start the operation, as a powerful survey facility for the VLT observatory. This paper will focus on the axes motion control system. The dynamic model of the telescope will be analyzed, as well as the effect of the wind disturbance on the telescope performance. Some algorithms for the telescope position control will be briefly discussed. 1 VST TELESCOPE DYNAMIC MODEL The telescope coupling dynamic is so slow that it is possible to study independently the two main axis behaviors. The coupling of the two axes is usually negligible in a telescope, especially in the most important operating condition, i.e. the tracking phase, in which the axes trajectory is most of the time regular and not interested by strong accelerations. Both axes structures are modeled by a number of inertias joined by stiffnesses and structural dampings (Figure 1 shows the altitude axis simplified model, the meaning of the symbols is reported in table 1). The axis gear is represented by the motor and teeth contact stiffness and by the damping. The inertia of the motor itself is taken into account, properly scaled by the transmission ratio. The structural data are derived from a Finite Element Analysis of the mechanical structure of the telescope. The dynamic of the mechanical system can be described by second order differential equations in matrix form as: J F K T Θ Θ Θ .. . + + = where J, F, K, T are the inertia, viscous damping, stiffness and torque matrix respectively, and Θ is the angular position vector. Figure 3 shows the open loop response of the altitude axis electromechanical model. Figure 4 shows the open loop transfer function of the azimuth axis. The first notch in the bode gain plots represents the Locked Rotor eigenfrequency (~10 Hz for both axes). Table 1: Altitude axis structural parameters Parameter Symbol Center Piece inertia [kg·m] J2a M1 (Primary Mirror) inertia [kg·m] J2b Top Ring Inertia [kg·m] J3a M2 (Secondary Mirror) box Inertia [kg·m] J3b M2 Inertia [kg·m] J3c Motors inertia [kg·m] J1 Motors viscous friction [Nm/(rad/s)] F1 Viscous friction [Nm/(rad/s)] F2 Transmission damping [Nm/(rad/s)] F12 M1 pad damping [Nm/(rad/s)] F2ab Structural damping [Nm/(rad/s)] F23 Top Ring M2 box damping [Nm/(rad/s)] F3ab M2 box Mirror damping [Nm/(rad/s)] F3bc Transmission stiffness [Nm/rad] K12 M1 pad stiffness [Nm/rad] K2ab Structural stiffness [Nm/rad] K23 Top Ring M2 box stiffness [Nm/rad] K3ab M2 box Mirror stiffness [Nm/rad] K3bc Transmission ratio R J1 J2b J2a J3a J3c J3b K12 K2ab K23