1. HAM-SAS fabrication weekly CALTECH, 4/26/06 V. Boschi, V. Sannibale HAM-SAS Mechanical Model Present Status

2. HAM-SAS fabrication weekly CALTECH, 4/26/06 HAM-SAS Mechanical Model We have developed a state-space model model of HAM-SAS mechanical structure using Maple Let’s summarize the approximations used in the model: Lumped system, i.e. rigid body approximation Elastic elements are approximated using quadratic potentials, i.e. small oscillation regime Dissipation mechanisms are accounted using viscous damping which approximate structural/hysteretic damping in the small oscillation regime The system is considered symmetric enough to separate horizontal displacements x, y, and yaw from pitch, roll and vertical displacement z Internal modes of the mechanical structures are not accounted Approximations

3. HAM-SAS fabrication weekly CALTECH, 4/26/06 HAM-SAS Mechanical Model GAS filter representationIP representation Horizontal and Vertical stages

4. HAM-SAS fabrication weekly CALTECH, 4/26/06 Horizontal stage Model Results: Trasmissibilities HAM-SAS Mechanical Model Transmissibility for the horizontal (blue) and yaw (red) degrees of freedom 30 mHz IP frequency 1.2 Hz Horizontal GAS frequency 110 Hz Resonance frequency due to the little pendulum 30 Hz Horizontal GAS notch frequency

5. HAM-SAS fabrication weekly CALTECH, 4/26/06 Vertical stage Model Results: Trasmissibilities HAM-SAS Mechanical Model Transmissibility for the vertical (blue), pitch (red) and roll (green) degrees of freedom 30 mHz GAS resonance frequency 2 Hz GAS notch frequency

6. HAM-SAS fabrication weekly CALTECH, 4/26/06 Triple pendulum Model HAM-SAS Mechanical Model Upper mass Intermediate mass Test mass

7. HAM-SAS fabrication weekly CALTECH, 4/26/06 Triple pendulum model Results: x Trasmissibility HAM-SAS Mechanical Model

8. HAM-SAS fabrication weekly CALTECH, 4/26/06 Triple pendulum model Results:  z Trasmissibility HAM-SAS Mechanical Model

9. HAM-SAS fabrication weekly CALTECH, 4/26/06 Triple pendulum model Results: comparison HAM-SAS Mechanical Model We can compare our results with a previous (2003) Mathematica model made by M. Burton Test massIntermediate massUpper mass

10. HAM-SAS fabrication weekly CALTECH, 4/26/06 HAM-SAS Mechanical Model Triple pendulum + Horizontal stage model Results: Trasmissibilities

11. HAM-SAS fabrication weekly CALTECH, 4/26/06 HAM-SAS Mechanical Model The next steps are Introduce structural damping in the Triple pendulum models Connect the Vertical stage model to the Triple pendulum model Rerun our control simulations with the new models in order to optimize the feedback loops Further developments