1. Thursday, 18 March 2004 Andrea Viceré, Urbino University 1/34 Issues in the Virgo mechanical simulation Why a mechanical simulation How the simulation is set up Comparison with real data, and how these are used to tune the models Examples and problems Andrea Viceré University of Urbino vicere@fis.uniurb.it

2. Thursday, 18 March 2004 Andrea Viceré, Urbino University 2/34 A VIRGO Super Attenuator An inverted pendulum for low frequency control »6 seismic filters (in all DOFs) »1 longitudinal-angular control stage (the marionetta) »1 longitudinal control stage (the reference mass) The system has a double role »Filtering out the seismic noise »Actuate on the mirror position

3. Thursday, 18 March 2004 Andrea Viceré, Urbino University 3/34 Attenuation goals Vertical seism is dominant On paper, above 3÷4 Hz the noise should become dominated by other sources The choice is to achieve this goal only by passive means.

4. Thursday, 18 March 2004 Andrea Viceré, Urbino University 4/34 Price to pay: LF amplification Left: ground motionRight: mirror motion  control requirements

5. Thursday, 18 March 2004 Andrea Viceré, Urbino University 5/34 The SA as a control device Three sensing devices »LVDT sensors on top of the IP »Accelerometers … »The interferometer itself Three actuation stages »Below 5 Hz, coils on the IP »In the range 5, 20 Hz, from the marionette »In the upper range, from the reference mass Hierarchy of forces  hierarchy of noises »Avoid large forces applied directly to the test-mass Y Z X

6. Thursday, 18 March 2004 Andrea Viceré, Urbino University 6/34 Why a mechanical simulation?… In the plot, the vertical TFs of a seismic filter »The two curves correspond to two options for the fundamental frequency. What happens when chaining several such elements? R.Flaminio, S.Braccini

7. Thursday, 18 March 2004 Andrea Viceré, Urbino University 7/34 What one would like to know In the plot, some of the (simulated) TFs which are relevant in controlling mirror position The design of control filters depend on these TFs. A complex system: one needs »A good model, and »direct measurements

8. Thursday, 18 March 2004 Andrea Viceré, Urbino University 8/34 Model scope and requirements Assess attenuation performance in the detection band [ 4Hz – 10 kHz ] »Help in deciding where improvement is needed »Requires modeling of the internal modes of elastic elements »Limit: only the ITF shall be able to fully validate the results! Predict the motion of test masses »Due to noise inputs (seism, thermal noise …) »Under the influence of control forces Provide a time domain model »Needed to integrate with optics and study lock-acquisition »Simple: as few DOF as possible to keep simulation time within reasonable limits »Neglect internal modes as much as possible

9. Thursday, 18 March 2004 Andrea Viceré, Urbino University 9/34 Is this strategy consistent? »Low frequency structure relevant for control studies »High frequency structure important for noise in detection band. »The “gap” in between guarantees that it makes sense to use a simplified model for control.

10. Thursday, 18 March 2004 Andrea Viceré, Urbino University 10/34 Model construction Describe elastic elements »Only those relevant in the frequency band of interest! Keep the model simple »Possibly limit to an effective potential representation »Neglect higher order modes (violins) for control studies, keep them otherwise. Left: VIRGO blades for vertical attenuation

11. Thursday, 18 March 2004 Andrea Viceré, Urbino University 11/34 Example: a simple wire Consider the longitudinal motion of a wire, with a linear density  S and a Young modulus E: one has kinetic and potential energies Attach a mass M at the end L. The resulting lagrangian equations can be solved to get the TF between input x(0,  ) and output x(L,  ) The sin, cos functions tell us that this exact solution displays an infinite number of resonances. Cannot be simulated in time domain with a finite # of DOF !

12. Thursday, 18 March 2004 Andrea Viceré, Urbino University 12/34 Potential approximation To simplify the model, assume that at fixed boundary the wire takes the shape of minimal energy: this leads to an obvious spring Also the kinetic term can be approximated in the same way! One gets Notice the cross-term: it links velocity at input and at output and will be a limiting factor in the “attenuation” of this spring-mass system

13. Thursday, 18 March 2004 Andrea Viceré, Urbino University 13/34 Comparison of the approximations Albeit simple, this example displays all the relevant features »A potential limit is always good at low frequencies »The exact model will display resonances, that cannot be modeled with the few (two!) DOF used »Corrections to the kinetic energy can approximate the “attenuation breakdown” occurring at the frequencies of the resonances

14. Thursday, 18 March 2004 Andrea Viceré, Urbino University 14/34 A suspension wire Write down kinetic and potential energies The order is higher: the solution depends both on y and y’ at the extrema, that is on position and angles: for instance Here W is a 4 x 4 matrix which describes both the coupling due to gravity (the T term) and the coupling due to wire bending elasticity (the EI term)  coupling between y motion and tilt

15. Thursday, 18 March 2004 Andrea Viceré, Urbino University 15/34 Model construction and simulation Given K and U energies, one can assemble a total Lagrangian for a system »One needs also dissipation, actually! It can be written with the same methods assuming it proportional to the work done inside the elastic elements From the Lagrangian, one can obtain a state space model Y is the vector of observables (output of accelerometers, positions of optical elements, for instance. The SSM can be simulated in TD in a variety of ways, with an error only due to the discrete time step

16. Thursday, 18 March 2004 Andrea Viceré, Urbino University 16/34 Simulation parameters and tuning In VIRGO we chose to start from physical parameters »Masses, characteristics of wires and blades, strength of magnets … »Some are better known, other are actually approximate An alternative approach would have been to see the mechanics as a black box »One could define it as a MIMO model and then fit its parameters »Advantage of generality, but total loss of contact with the instrument The tuning is a typical (hard) inverse problem »Physical parameters as a basis »Mode identification to select subsystems »Parameter tuning using mode characteristics and TF measurements

17. Thursday, 18 March 2004 Andrea Viceré, Urbino University 17/34 Example: vertical performance Impossible to measure the entire SA chain TF ! »Only the ITF shall have the sensitivity needed »Possible to measure stage by stage Compose the partial SA TFs to obtain the full one S.Braccini et al

18. Thursday, 18 March 2004 Andrea Viceré, Urbino University 18/34 Seismic noise and sensitivity »Vertical seismic noise dominates over horizontal, in the detection band »The stage-by-stage measurement agrees with simulation  confidence that no effect has been forgotten »Blade resonances come close to the sensitivity curve, in quiet conditions: for safety, in the Cascina suspensions they have been damped.

19. Thursday, 18 March 2004 Andrea Viceré, Urbino University 19/34 Passive isolation is not enough At low frequency the SA is an “amplifier” An array of sensors picks up the motion, where is larger, and feedbacks it. »Below 10÷20 mHz the system is “locked” to the ground »In the [20mHz, 5Hz] it is locked to the inertial frame How this system performs? Courtesy G.Losurdo

20. Thursday, 18 March 2004 Andrea Viceré, Urbino University 20/34 Actuator response On top of the IP the sensors allow to measure the response to control forces The simulation can be tuned to reproduce the main features. Data: courtesy by A.Gennai

21. Thursday, 18 March 2004 Andrea Viceré, Urbino University 21/34 Response to seism: open loop… Assuming a model for the noise, the IP motion can be estimated. The absolute scale is wrong, but the main features are reproduced Data: courtesy by G.Losurdo

22. Thursday, 18 March 2004 Andrea Viceré, Urbino University 22/34 …closed loop »Left: simulation and measurement on top of the IP »Right: the residual predicted RMS on the test mass, using as input the measured motion on top of the IP

23. Thursday, 18 March 2004 Andrea Viceré, Urbino University 23/34 Next step: steer the mirror Force response from the reference mass is simple »Just the response of a pendulum MUCH more complex is the response from the marionette »This stage is necessary for yaw and pitch, and desirable for coarse longitudinal action Problem: not easy to tune the simulation parameters »Poor inputs »No permanent sensors to monitor the motion of the elements.

24. Thursday, 18 March 2004 Andrea Viceré, Urbino University 24/34 A system identification problem… Isolate the less known element: the steering filter Suspend and add a mock payload Actuate using the standard coils Read the motion in 3D using small LVDTs mounted on its surface Register inputs and outpus, compare with the model and tune its parameter With A.Di Virgilio et al.

25. Thursday, 18 March 2004 Andrea Viceré, Urbino University 25/34 …with some difficulties »Left: a fitted linear model between inputs and outputs successfully fits the output spectrum  good data quality »Right: a model based on physics gives a less successful fit  extra DOF are excited, which the model ignores.

26. Thursday, 18 March 2004 Andrea Viceré, Urbino University 26/34 Why a good model is needed? To be able to reach high gains, transfer functions like this are needed with good accuracy The pole/zero structure depends on the gain of the inertial damping! A (well tuned) model is indispensable to build an adaptive control loop TF marionette -> mirror, along the beam direction

27. Thursday, 18 March 2004 Andrea Viceré, Urbino University 27/34 TF measurement: the “lavatrice” »A fiber Mach-Zender interferometer »Angular motion by beam translation, using a PSD, in open loop. »Longitudinal motions picked up by fringe interference, in closed loop, using a PZT to lock the interferometer »A single stage suspension is sufficient to reduce the seismic noise at a level which allows TF measurements. L.Di Fiore, E.Calloni et al. Suspended platforms Fiber

28. Thursday, 18 March 2004 Andrea Viceré, Urbino University 28/34 Angular (yaw) TF on West Input »The color of the data points is related to different runs, with different levels of input force. »The line is NOT the simulation, but a zero/pole fit to the data!! »The measurement is taken with inertial damping on, to have some control on the mirror position Exp. Data: L.Di Fiore

29. Thursday, 18 March 2004 Andrea Viceré, Urbino University 29/34 Still the yaw, against simulation Main features ok Low frequency resonances shifted: wrong momenta of inertia for the filters. After tuning, one expects good agreement … Exp. Data: L. Di Fiore

30. Thursday, 18 March 2004 Andrea Viceré, Urbino University 30/34 Pitch motion Similar scenario: reasonable agreement, some tuning to be done. Note the zero/pole at 30 mHz in the experimental data: it is a mixing with longitudinal motion. Exp. Data: L. Di Fiore

31. Thursday, 18 March 2004 Andrea Viceré, Urbino University 31/34 Longitudinal TF from steering filter Quite a large disagreement … still some tuning work is required! This TF was less critical for the CITF: the noise level allowed to lock from the reference mass Exp. Data: L. Di Fiore

32. Thursday, 18 March 2004 Andrea Viceré, Urbino University 32/34 Higher order modes They are required in the TD simulation if they creep into the control band »A TD simulation can include a finite number of modes, correspondingly enlarging the # of DOF Two possible approaches »Split the elastic elements into smaller parts, each treated in the potential approximation »Resort to the FE method The FE method is widely believed to be more flexible »However, care must be exerted into choosing the splitting, especially with elements (like the suspension wires) which do not bend uniformly during their motion. The problem is that one can completely ruin the low frequency behaviour, obtaining a worse model!

33. Thursday, 18 March 2004 Andrea Viceré, Urbino University 33/34 Example: wires and suspension blades Left: a suspension wire. Right: a vertical blade »The stress in the blades is uniformly distributed  equi-spaced FE are fine

34. Thursday, 18 March 2004 Andrea Viceré, Urbino University 34/34 Some problems and issues Simulation tuning. Hard to get all the parameters right »The blueprints are only a partial help »Measurements are generally noisy and possible only for a few TFs »It would be useful a systematic procedure for translating the MIMO models obtained by system identification into constraints on the phyiscal parameters Dissipation »How one can efficiently model in TD the internal dissipation? »Currently, we just tune the value of Q at resonances, but we use a viscous dissipation model, that is we modify the stress-strain relation as Thermal noise »Is it possible/needed to model thermal noise in the TD ? »Is it practical/useful to exploit the mechanical model used for control purposes also to predict/model the thermal noise? Or is it better to work directly in ANSYS and forget about simplified models?