Initial Work on Suspension Diagonalisation

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Initial Work on Suspension Diagonalisation
August 2004

• Bryan W Barr

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Basic Concept
UR
UL
LR
LL
Force is applied to the mass by applying a signal
to the 4 coils (UL, UR, LL and LR).
If the force is not the same from all 4 coils
then the mass will not be pushed cleanly in
position, but will have some element of pitch and
yaw motion. The aim of diagonalisation is to
adjust the amplitude of the signals going to each
coil such that the total force applied has
minimal pitch and yaw coupling.
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Step by Step

• Take transfer function of pos-gtpitch and pos-gtyaw
  as a reference
• Diagonalise at low frequency DC (note coil
  gains)
• Diagonalise at high frequency 25 Hz (note coil
  gains)
• Work out the HF/DC ratio for all four coils
• Generate a filter to convert HF (gain1) to DC
  (gainratio) and apply them to the Pos Output
  Filter
• Take transfer function of pos-gtpitch and pos-gtyaw
  and compare with reference it should be better

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Diagonalise at DC

• Essentially, I went the simple route (possibly
  not the best though) of applying a DC offset of a
  few thousand counts to the LSC path of an optic
• Concentrating on the BS optic since thats the
  one that seemed to have the highest priority
• Before applying the offset note the values of
  the OSEM PITCH and YAW (oplevs change more but
  arent available on all optics)
• Apply offset and change the coil gains stepwise
  (and symmetrically) until the PITCH and YAW
  values are back to the start position
• Check by changing the offset if the values
  change then its not diagonalised

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Diagonalise at HF

• This time, a sine wave is applied to the LSC_EXC
  point of the optic (at 25Hz) I found 10000
  counts to be OK-ish
• Take a power spectrum of the signal around the
  sine wave frequency at least 10 averages and
  using a BW of 0.1Hz can probably play around
  with this though
• Note the values of the peaks produced and adjust
  the coil gains to reduce the height of the PITCH
  and YAW peaks

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HF diagonalised

• No before picture here. Only after.
• Here Pos156, Pit3.5, Yaw1.1 are the
  optimised diagonalisation peaks at 25 Hz

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Matrices

• DC matrix 1.004 1.019
• 0.792 1.005
• HF matrix 1.014 1.014
• 0.986 0.986
• Relative gains 1.010 0.995
• 1.014 0.981

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Filter Shape

• ULPOS DC-gtHF filter
• Note the gain
• difference between
• low and high freq.

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Transfer functions

• Reference plot After filters

Note the poor YAW performance. Thought alignment
may have drifted so reset DC alignment and tried
again.
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After DC Matrix Reset

• Reference plot After filters

YAW is much better but PITCH is worse than for
previous matrix and both are worse at
high frequency. Hmmn have I done something daft?
The answer to that is a resounding yes!
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Ooops! Had the Silly Thing in Reverse!

• Rather embarrassingly, it appears I cant count
  properly in order to convert to DC from HF one
  requires gains of DC/HF instead of HF/DC
• I quickly threw together some filters and did a
  transfer function

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New Improved Formulae

• Reference plot With Proper Filters

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Status

• Not the best we can get? Probably not the
  question is how do we get better
• Possibly change the filter resonant frequency to
  adjust the coupling at the pendulum peak may
  not be correct
• Is there a better way of diagonalising?
• Currently, only the BS is done
• Could quickly diagonalise at DC for the other
  suspensions in the interim but the HF part takes
  longer

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The End

• Needs more work
• Comments, suggestions and insults all welcome.
• Back in 6 weeks

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Details

• The files included here can be found in
  caltech/dvsave/bryan/
• Also, the small bit of scripting which I used to
  diagonalise at DC is in the scripts/test/
  directory