Mechanical modeling of the Seismic Attenuation System for AdLIGO Candidato: Valerio Boschi Relatore interno: Prof. Virginio Sannibale Relatore esterno: Prof. Diego Passuello 1
Introduction LIGO Observatories LIGO Hanford Observatory (LHO) H1 : 4 km arms H2 : 2 km arms 30 10 00 ms km LIGO Livingston Observatory (LLO) L1 : 4 km arms Graduate School Report Pisa, 11-18-06 2
Introduction LIGO Optical Layout End mirror Input optics stabilize laser frequency & intensity, and select fundamental mode Fabry-Perot arm cavity Main interferometer has three additional semitransparent mirrors to form optical cavities Pre- Stabilized Laser Mode cleaner Recycling mirror Input mirror Beam splitter Nd:YAG ~10 W Reflected photodiode GW signal Antisymmetric photodiode Pick-off photodiode 3
Introduction AdLIGO Optical Layout End mirror High Power Laser Pre- Stabilized Laser Mode cleaner Power Recycling mirror Fabry-Perot arm cavity Signal Recycling Cavity Output Mode Cleaner Cavity Input mirror Beam splitter Nd:YAG 180 W Reflected photodiode GW signal Antisymmetric photodiode Signal Recycling mirror Output Mode cleaner 4
Introduction BSC and HAM vacuum chambers Hanford Observatory 2 km photodiode 2 km laser The Corner Station houses the laser, detector, and all of the optics except the End Test Masses. HAM chamber BSC chamber Each vacuum chamber has an independently supported, seismically isolated table on which the optics are mounted. 4 km laser 4 km photodiode The beam tubes are 1.2 m diameter, low oxygen stainless steel BSCs are approximately 5.5 m high and hold the beam splitter and the main interferometer mirrors. HAMs are smaller chambers used for the Mode Cleaner and the Recycling cavity mirrors. 5
Introduction HAM-SAS Attenuation Stages HAM-SAS is a seismic attenuation system expressly designed to fit in the tight space of the LIGO HAM vacuum chamber. Rigid Bodies Optical Table (OT) and Payload Top Platform 4 MGAS Springs disposed on a 1.1 x 1 m rectangular configuration. Top + Intermediate Platforms + Springs = Spring Box (SB) Intermediate Platform 4 Inverted Pendula Legs (IPs) disposed on a 1.1 x 0.9 m diamond configuration. Base Platform 6
Modeling Modeling Approach (I) A state-space model of HAM-SAS mechanical structure have been developed using an Analytical approach. 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 7
Modeling Modeling Approach (II) Inverted Pendulum - Flexural Joint with Ideal pivot point about the attachment point. -Leg, a rigid body - Hysteretic/structural damping approximated with viscous damping. GAS - Blade stiffness modeled with simple Springs - Hysteretic/structural damping approximated with viscous damping. - Transmissibility saturation modeled using the "magic wand" 8
Modeling The scripts (I) 1. Initialization 2. Loading System Lagrangian, Dissipation Function, Constraints Numeric Parameters 3. Coordinate Selection The way that the code has been written is such that allows to progressively introduce new features to improve the accuracy and remove degrees of freedom to check the consistency of the simulation. 4. State-space generation Small oscillation regime 9
Modeling The scripts (II) (Continued from the previous slide) Mass (M), Stiffness (K) and Damping (L) matrices evaluation: The system is written in the form Mq () t + Lq () t + Kq() t = u() t And then converted in the equivalent A,B,C,D state-space canonical form: ξ = Aξ + Bu y = Cξ + Du The two state-space models generated by the Maple scripts have a total of 13 inputs and 18 outputs: 6 force/torque actuators on a massive shaker 7 force/torque actuators on the system x 6 D.o.f. of OT COM 6 D.o.f. of SB COM 6 D.o.f. of Shaker COM 10
Modeling Parameters Parameter files are text files separated and indipendent from the simulation scripts. The physical parameters used in the model have been in part extracted from production drawings, in part evaluated to match experimental data acquired on several prototypes. Masses and moments of inertia have been calculated using SolidWorks CAD from HAM-SAS threedimensional drawings. Comparison of MGAS model with experimental data 11
Transmissibilities Definition The transmissibility is essentially a measure of how a mechanical system respond, in the frequency domain, to a generic excitation. Mathematically, the Transmissibility T i (s) along the i-th degree of freedom of a mechanical system is defined as the ratio T() s i i Q () s = Q () s between the Laplace transform of the vibration of the system and the Laplace transform of the excitation applied to the system, along the i-th degree of freedom. In our models the transmissibilities have been obtained applying the proper transfer function ratios to remove the dependency on the generalized forces: i 0 Q () s F () s F () s Q () s i i 0 i () = i i 0 0 T s 12
Transmissibilities Horizontal Stage Model 30 mhz IP frequency 1.2 Hz Horizontal GAS frequency 105 Hz Little Pendula Horizontal freq. 13
Transmissibilities Vertical Stage Model 100 mhz MGAS res. frequency 105 Hz Little Pendula Vertical freq. 14
Noise spectra Seismic Noise Model The horizontal and vertical ground noise are considered equal and expressed, in the frequency range 100 mhz< f <40 Hz, as a polynomial expansion in log space: log x ( f) = p (log f) + p (log f) + + p log f + p n n 1 g 1 2 n n+ 1 The LHO and LLO reference spectra have been merged and extrapolated below 100 mhz using the USGS New Low Noise Model developed by J.Peterson The ground tilt noise was generated in the 10 mhz - 40 Hz band using the Rayleigh waves propagation model: ω θg ( ω ) = Sv Vertical Seismic Motion c Seismic waves propagation speed 15
Noise spectra Horizontal Stage Model Region exceeding requirements Possible Solutions: Tune the IP notch at 1.2 Hz to compensate the MGAS resonance. Tune IP at a lower resonance frequency (20 mhz) Use active damping 16
Noise spectra Vertical Stage Model Requirements are not met in a wide region Solution: Vertical Noise Requirements are probably too strict. They can be lowered by 2 or 3 degrees of magnitude without compromising AdLIGO sensitivity (P. Fritschel, 2006) 17
Asymmetric Models Asymmetric IP leg lenghts 30 mhz IP frequency D.o.f. Contamination 1.2 Hz Horizontal GAS frequency 105 mhz Little pendulum The optical table is inclined respect to the ground by an angle theta_x or theta_y 18
Asymmetric Models Asymmetric IP leg lenghts Noise Spectra 19
Asymmetric Models Asymmetric spring elastic constant k (infinite Quality Factors) 60 mhz < f < 140 mhz D.o.f couplingc 60 mhz < f < 140 mhz D.o.f coupling 60 mhz < f < 140 mhz 20
Asymmetric Models Asymmetric spring elastic constant k (expected Quality Factors) Small Effect Small Effect Small Effect 21
MC suspension Triple Pendulum Triple Pendulum is a seismic attenuation device, based on a design developed for GEO600 Top Mass Intermediate Mass Test Mass It is capable of providing 90 db of horizontal attenuation and 50 db of vertical attenuation at 10 Hz. The system is composed by three bodies, called Top, Intermediate, and Test mass that weight approximately 3 kg each and provide three stages of passive horizontal attenuation. The triple pendulum external cage is supported by the optical table, that will be placed on HAM-SAS top platform. In this way the motion of the test will be attenuated by both HAM-SAS and the Triple suspension. 22
MC suspension Triple Pendulum + Horizontal Stage Model Results 30 mhz IP frequency Triple Pendulum Resonances 0.67-1.5Hz Little Pendula 23
LVDT Measurements LVDT Driver VME Board Board is based on AD698 signal conditioner and has 8 channels One single-ended input, for external oscillator operation. Master-slave/asynchronous operation selectable through onboard jumpers. ±15V - ±18V Operating voltage Modulation frequency 12kHz (20kHz max. tuned with capacitor C109) 22 Vpp Primary coil output voltage 24
LVDT Measurements Measurements 25
Future developments Control Traditional Approach Sensors/Actuators Space Diagonalization Classical Filter design Very Low quality factors Position DC control LQG multivariable technique State-space MIMO method Optimal control Quasi-stable oscillators Under Quasi-stable condition a very weak force is necessary to keep a tunable oscillator steady (stable). Just an easy control law is needed Interactions with Triple Pendulum active control have to be studied 26
Future developments Models HAM-SAS Models improvements: Nonlinear models. Several multibody dynamics simulation tools has been tested: SimMechanics Simulink blockset, Maplesoft DynaflexPro. A collaboration with Politecnico di Milano Aerospace Engineering Department started recently for MBDyn simulation tool testing. Complete study of parameters space (Montecarlo method) Experimental data integration using System Identification techniques HAM-SAS Models extensions: Connection with Triple Suspension 3D model developed by M. Barton, study of backreaction effects. A collaboration with the e2e Simulation group started recently. BSC-SAS project BSC-SAS model Connection with Quad Suspension 3D model developed by M.Barton 27