INTERFEROMETRIC SENSING AND CONTROL

Transcription

1 INTERFEROMETRIC SENSING AND CONTROL IN LIGO Nergis Mavalvala October 1998 Introduction to control systems Length and alignment sensing Noise Sensitivity Length control system Noise suppression More tricks? Data? Lock Acquisition (Brent Ware)...

2 ELEMENTS OF A CONTROL SYSTEM disturbance input x d x a + x i Plant P(f) x a = PSHAx i x = x + x i d a Actuator A(f) Sensor S(f) x i = x d G( f) Filter H(f) where G( f) = PSHA Plant: system to be controlled, e.g. cavity length Sensor: sees cavity length change, e.g. photodetection/demodulation Filter: designed to suppress noise as needed Actuator: moves cavity length, e.g. suspension Upshot: when G(f) >> 1 then x i << x d plant input is much smaller than the original disturbance

3 INTERFEROMETER OPTICAL CONFIGURATION ETM 2 θ 5,φ 5 ITM 2 Michelson interferometer θ 1,φ 1 L 2 l 2 Fabry-Perot cavities θ 3,φ 3 θ 2,φ 2 θ 4,φ 4 l 1 L 1 RM BS ITM 1 ETM 1 Fabry-Perot arm cavities Dark fringe at antisymmetric port Power Recycling (G rec ~ 50) 4 longitudinal degrees of freedom 12 angular degrees of freedom

4 IFO LENGTHS: WHY CONTROL THEM? Cavity resonant linewidth: δl «m 2F Deviation from perfect destructive interference coupling of noise to GW signal e.g. laser intensity noise S( δp P = 10 7 ) δl m S( δl D ) D Deviation from perfect resonance less power build-up in ifo less GW signal P( δl C ) e.g δl C m P max arm λ Ground noise excitation ~ 10-5 m (typical µ- seismic motion of earth) Sooo, need to suppress length fluctuations due to ground noise by factor δl D 10 8 δl gnd

5 IFO ALIGNMENT: WHY CONTROL MIRROR ANGLES? Degradation of GW sensitivity ( S N) GW ( δθ i ) ( S N) GW ( δθ i = 0) δθ i 10 8 rad Misalignment input beam jitter coupling δθ rms 10 8 rad α rad/ Hz and x 10 9 m/ Hz Mirrors drift with respect to the local frame δθ i 10 7 rad

6 SOME CONTROL SYSTEMS TERMINOLOGY Transfer function (frequency response): magnitude and phase of output when input is a sinusoid of unit mag. and frequency f. Bode diagram 10 3 Magnitude Phase (deg) frequency (Hz) db = 20 log 10 G(f) Pole: magnitude falls off with f (f > f 0 ), phase lags Zero: magnitude increases with f (f < f 0 ), phase leads

7 MORE CONTROL SYSTEMS PHENOMENA Stability: control action must correspond to error signal throughout the control band x i x d but when = x 1 + G( f) i G( f) 1 Gain: gain must be high enough to adequately suppress noise input Bandwidth: frequency range over which control action is useful limited by sensor noise, actuator response Dynamic range: maximum signal cf. noise of device Multiple actuators: cross-overs use each actuator in frequency range where it is most effective BUT make sure it does not interfere with the other at frequencies where its control action is not good

8 ASIMPLE(ISH) EXAMPLE: THE PRE-STABILIZED LASER Two frequency actuators: PZT and EOM actuator 1 (PZT): large dynamic range (~400 MHz) but small bandwidth (resonances above ~200 khz) actuator 2 (EOM): small dynamic range (~200 khz), no DC response, but works out to ~100 MHz PZT Pockels Cell Laser Reference Design filters so that both actuation paths work together (no fighting) preserve dynamic range high gain where needed high bandwidth where needed stable!

9 OPEN LOOP GAINS FOR PSL FREQUENCY LOOPS Magnitude 10 5 PZT EOM total loop gain Phase (deg) frequency (Hz) G tot = G PZT + G EOM

10 LENGTH SENSING ERROR SIGNALS Heterodyne phase detection techniques Use phase modulated light at input (f ~ MHz) Cavity lengths: Pound-Drever-Hall reflection locking (carrier that is resonant in cavity beats against rf sidebands that are not) Antisymmetric port: Schnupp asymmetry / suppressed carrier scheme (dark port is not perfectly dark for rf sidebands) Signals proportional to various ifo lengths given by magnitude and phase of carrier and rf sidebands at each sensing port Antisymmetric or dark port (GW signal!) Reflection port (coupling important, i.e. sensitive to ifo loss du jour) Recycling cavity pick-off port ( picked off light is loss in rec. cav., i.e. small signal levels)

11 SIGNAL EXTRACTION ETM 2 L 2 ITM 2 ν SB l 2 L 1 ν l l 1 RM BS ITM 1 ETM 1 I Q I Q I Q L C + ε 1 l C l D + ε 3 L D L L D C ε 2 l C ( L C ) Reflected Port Anti-symmetric (Dark) Port + l D + ε 4 L D ( L C ) Recycling Pick-off Port

12 OPTICAL PLANT Antisymmetric port S anti 1 1 g cr t sb r c 'k L D sinω 1 + s m t + g cr t sb r c k l D sinω c 1 + s m t c Reflection port S refl g sb t sb r cr rˆck L D sinω m t g sb t sb r cr k l D sinω m t g rsb r cr c 'k L C cosω 1 + s m t cc s g cr rsb r c + g2 r sb rcr r M k l C cosω 1 + s m t cc Recycling cavity pick-off port S pick-off = g cr g sb t t sb rˆck L D sinω m t 5 + g cr g sb t t sb k l D sinω m t g cr gsb t r r M c ' k L cosω C s m t cc g cr g sb 1 + s p r t M r c [ g cr g sb ]k l C cosω 5 1+ s m t cc

13 FREQUENCY DEPENDENCE Magnitude L D -100 Phase db 0-20 l D degree Hz Magnitude at the anti-symmetric port Hz Phase L C -100 db 0 l C degree l D Hz in reflection of the interferometer Hz Magnitude L C -100 Phase db 40 l C degree l D Hz recycling cavity pick-off Hz

14 ALIGNMENT SENSING Angular misalignments excite higher-order transverse modes TEM 10 amplitude misalignment angle Wavefront sensor measures TEM 10 ampl. Length sensor signal: beating of carrier TEM 00 field against sideband TEM 00 field Wavefront sensor signal: Beating of carrier TEM 00 field against sideband TEM 10 field spatial map of this TEM 10 mode at modulation frequency segmented photodetector Distinguish mirrors of the interferometer by Guoy phase shift

15 ALIGNMENT OF LIGO INTERFEROMETERS mode cleaner reflected port WFS 2 WFS 3 WFS 4 transmission 2 QPD-Y Wavefront Sensor Camera Quad Detector Intensity Monitor Optical Lever ISC Table telescope & beam steering WFS 5 WFS 1 QPD-X transmission 1 pick-off dark port

16 ALIGNMENT SENSING MATRIX Signal at each sensor in Watts per normalized angle (θ D ~ 10-5 rad) Wavefront Sensor Angular degree of freedom # (port) f mod Φ RF Φ Guoy ETM ITM ETM ITM RM WFS 1 (dark) WFS 2 (refl) WFS 2b (refl) WFS 3 (refl) WFS 4 (refl WFS 5 (pick-off) f res Q f res I f res Q f NR I f NR I f res Q Frequency dependence given by transverse mode spacing rather than cavity storage time, i.e. flat response out to ~10 khz

17 Review... LAST WEEK THIS WEEK... Closed loop control system (SISO) Plant is disturbed Sensor detects disturbance Controller converts into control action actuator fights disturbance Multiple actuation paths (SIMO): PSL Control action must be coordinated LIGO interferometer (MIMO) Optical plant 4 (coupled) length degrees of freedom frequency response of 4 sensors Today Control system requirements: Noise inputs: couplings via optical plant; sensing noise; actuator response GAIN CONSTRAINTS Matrix solutions for MIMO system Differential-mode (GW) loops Non-diagonal (or crossed ) controller feedforward path Common-mode loops Nested loops closed loops within closed loops GW strain sensitivity: noise contributions

18 LENGTH SENSING MATRIX Signals in amperes of photocurrent per meter of length offset assuming current best know LIGO optical parameters using FFT model to include mirror losses Length Sensor Length Degree of Freedom Port (Sensor) Φ RF L D l D L C l C Anti (S AQ ) Q s ( 2π 90 Hz) Refl (S RQ ) Q s ( 2π 90 Hz) Pick-off (S PQ ) I s ( 2π 90 Hz) Refl (S RI ) I 0 0 Pick-off (S PI ) I s ( 2π 0.8 Hz) s ( 2π 0.8 Hz) ( 1 + s ( 2π 3.0 Hz) ) s ( 2π 0.8 Hz) ( 1 s ( 2π 0.9 Hz) ) s ( 2π 0.8 Hz)

19 CONTROL TOPOLOGY to mode cleaner S AQ S RI ETM 1 ETM 2 ETM 1 +ETM 2 S PI S PQ RM BS damping ITM 1 +ITM 2 ITM 1 ITM 2 Crossed control

20 Correlation model NOISE INPUTS: SEISMIC NOISE ground noise susp. susp. pt. pt. disp. correlation over 13 m 10 8 Displacement (m/ Hz ) Frequency (Hz) D.o.f. rms p-p ratio Ground 1.9 µm 12.4 µm 6.5 RM s.p. 2.0 µm 12.8 µm 6.4 Lm s.p. 3.0 µm 19.0 µm 6.3 Lp s.p. 3.3 µm 20.0 µm 6.0 lm s.p. 9 nm 63.0 nm 7.0 lp s.p. 20 nm 163 nm 8.1

21 SEISMIC NOISE: VERTICAL MODE f V = 13 Hz (19 Hz for beamsplitter) Q = 2000 (may be closer to 1000 sitting on stack) Coupling: s = ξ ( f ) T Q f V ; z g V zz V V z g = 10-9 m rms ; T zz = 0.5 ξ: bulk propagation (α(n 1)) + surface (β) effects Degree of freedom Displacement (m rms ) Coupling coefficient (ξ) Coupling due to Lm Earth s curvature lm mrad wedge angle (ITM) Lp Earth s curvature lp mrad wedge angle (ITM), & mrad surface angle (RM)

22 SENSING NOISE: SHOT NOISE Port power levels predicted by baseline FFT model Also used to compute DC plant matrix elements Port/Sensor Total Power (C + SB) Noise current (A/ Hz) Antisym./S AQ = 1.16 W δl m Equivalent Length Noise (DC) = m/ Hz RC pickoff/s PI = 71 mw δl p = m/ Hz RC pickoff/s PQ δl m = m/ Hz Reflected/S RI = 0.29 W δl p = m/ Hz Reflected/S RQ δl m = m/ Hz

23 GAIN CONSTRAINTS: RESIDUAL FLUCTUATIONS IFO Length/ phase Degree of freedom δlm + ( π ( 2F) )δlm δlm + ( π ( 2F) )δlm δ( k Lp) l δ( k lp) l Residual deviation Laser frequency Units Coupling mechanism m rms Amplitude noise coupling m rms Amplitude noise coupling rad rms Arm cavity power reduction rad rms Arm cavity power reduction Hz Hz mode cleaner IFO Gain (db) freq (Hz) freq (Hz)

24 GAIN CONSTRAINTS:MIRROR INTERNAL RESONANCES Require open loop gain <1 at internal mode frequency to ensure stability Force applied at magnets is transmitted to mirror surface (calculated by D. Coyne using FEA model with Q=1.3M) Mode description Resonant frequency (Hz) Transmissibility (m/n) Maximum servo gain Test Masses & RM Beamsplitter Non-axisymmetric, astigmatic mode First symmetric (drum head) mode db 9206 (calc.) 9476 (meas.) db Second symmetric mode db Non-axisymmetric, astigmatic mode db Symmetric (drum head) mode db Second symmetric mode db Solution: 80dB stopband filter centered at 9.4kHz (+ 20 db from anti-alias filter)

25 GAIN CONSTRAINTS: MISCELLANEOUS Phase Margins: designed to be at least 50 degrees for stability of response around unity gain frequency effect of delays included in predicted phase margin (though not explicitly in Matlab models) Electronics noise Three significant noise sources, sum must be 10x below SRD sensitivity: photodetector electronics noise ADC input voltage noise DAC output voltage noise Actuator dynamic ranges ranges of frequency actuators important for designing crossovers suspensions: supposed to have sufficient range by design (BS & RM ranges have recently been increased so that this is so)

26 SUMMARY OF GAIN REQUIREMENTS Degree(s) of freedom Frequency range Gain All DC db Reason achieve required residual deviation Lm, Lp, lp (lm) 9.5 khz (5.6 khz) < 135 db internal resonance of RM, TMs (BS) Lm, lm, lp 13 Hz > 20 db resonant gain vertical mode of suspensions lm > 20 Hz < 0 db sensing noise at pick-off couples to GW signal via off-diagonal plant element Lp > 40 Hz > 60 db relative to overall loop gain achieve required frequency noise suppression above 40 Hz Lp > 40 Hz > 80 db relative to overall loop gain Lp couples to GW signal via TM suspensions imbalance lp DC > 100 db residual lp couples to GW signal via demodulator phase error

27 MULTI-INPUT MULTI-OUTPUT CONTROL SYSTEM MODEL ground noise (m/rthz) thermal noise (m/rthz) shot noise (V/rtHz) stacktf + correl. model m X sp pendtf m m m L res  Pˆ V V Ĉ V S L res = Mˆ 1 ( X sp L gnd + L therm + ÂĈS shot ) Mˆ = 1ˆ ÂĈPˆ plant matrix block-diagonal treat common-mode and differential-mode d.o.f. independently

28 DIFFERENTIAL-MODE SYSTEM BLOCK DIAGRAM dm/dv C Lm S AQ C sus P Lm2AQ SN AQ pend P Lm2PQ α. P lm2aq P Lm2AQ Lm seis lm seis Lm therm lm therm Lm res lm res pend P lm2aq C sus P lm2pq SN PQ S PQ dm/dv C Lm

29 Lm SYSTEM BLOCKS 9.7e9 p = A/m plant TF V/A p = 4e6 PD pole P Lm TEST OUT 1 f e = 7.5e3 f sb = 9.5e3 filters f r = 13 Q = 100 C = 0.25 resonant gain z = 10,40,40,40 p = 0.1, overall gain TEST IN 1 C Lm TEST OUT 2 z = 40 p = 1 SUS coil driver 0.9e 6 dm/dv f p = 1 Q = 1 pendulum TF pend

30 Lm OPEN-LOOP GAIN Mag (db) Phase (deg) Frequency (Hz)

31 lm SYSTEM BLOCKS 5.3e A/m V/A p = 4e6 PD pole P lm TEST OUT 1 f b = 2e3 f sb = 5.5e3 f e = 7.5e3 filters f r = 13 Q = 100 C = 0.25 resonant gain z = 1,1,10,10 p = 0.1,0.1, overall gain TEST IN 1 C lm TEST OUT 2 z = 40 p = 1 SUS coil driver 0.9e 6 dm/dv f p = 1 Q = 1 pendulum TF lm pend z = 91 G = α.5e-7 C 12 z = 40 p = 1 SUS coil driver 0.9e 6 dm/dv f p = 1 Q = 1 pendulum TF Lm pend

32 lm OPEN-LOOP GAIN Mag (db) Phase (deg) Frequency (Hz)

33 PERFORMANCE OF DIFFERENTIAL-MODE LOOPS Performance Data Lm lm Units Gain at DC db Unity gain bandwidth Hz Phase margin degrees Gain at 9.48 khz (5.58 khz) 140 ( 141) db Residual length deviation m rms Control signal at coil driver µm rms from shot noise in the dark port from shot noise in the pick off from seismic noise read from the dark port SRD SRD/ strain/rthz Frequency (Hz)

34 NON-DIAGONAL CONTROL MATRIX AT WORK add lm control signal to Lm to cancel feedthrough of shot noise at S PI to GW signal α = 0.0 α = 0.90 α = 0.95 α = 0.97 α = 0.99 SRD SRD/ strain/rthz freq (Hz)

35 COMMON-MODE SYSTEM BLOCK DIAGRAM MCleng SOS pend SOS Hz/V C AO MCaddoff C MCL dmdv C sus C Lp S RI (V) P Φp2RI SN RI (V) Lp seis (m) pend k P Φp2PI Φp res (rad) Lp δf IOO (Hz) lp seis (m) 2π/c pend k lp φp res (rad) P φp2ri P φp2pi SN PI (V) dmdv C sus C lp S PI (V)

36 FREQUENCY CONTROL TOPOLOGY IOO LSC PSL IS MC LA IS IFO LA PSL wideband freq control MC L PSL + MC L IFO (DC 2Hz) Hz MC SERVO IFO Lp /ν laser SERVO 2 Hz 20 khz PSL freq tidal correction MC length Hz MC addoff 650 Hz 20 khz IS LA interferometric sensor length actuator length control signal frequency control signal length/frequency error signal Lp/frequency servo has three actuation paths Lp ETMs δν mode cleaner length PSL wideband actuator δν additive offset of mode cleaner servo error point

37 Lp/MCleng/MCaddoff OPEN-LOOP GAINS 250 Mag (db) IFO length MC length MC addoff total loop gain Phase (deg) Frequency (Hz)

38 PERFORMANCE SUMMARY FOR COMMON-MODE LOOPS Performance Data Lp/df lp Units Gain at DC db Unity gain bandwidth Hz Phase margin degrees Lp/MC length crossover frequency 3.7 Hz MC length/additive offset crossover freq. 650 Hz Gain at 9.48 khz db Residual phase deviations radian rms Error signals V rms Drive signals Lp: 3.1 MC leng: 1200 MC addoff: 2.3 lp: 1.1 µm rms Hz rms mhz rms

39 RESIDUAL FREQUENCY NOISE 10 3 frequency noise (Hz/rtHz) SRD/10 requirement from Lp from lp from input freq noise from shot noise at SRI from shot noise at SPI total residual freq noise freq (Hz)

40 GW STRAIN SENSITIVITY strain spectral density ( 1 Hz) seismic noise frequency noise shot noise at S AQ shot noise at S PQ (α/ε 1 = 0.00) shot noise at S PQ (α/ε 1 = 0.97) shot noise at S PQ (α/ε 1 = 0.99) h gw 0.1 h gw frequency (Hz)

41 TEST MASS DAMPING PATHS locally damped optic suspension point motion damping lm/lp servo + compensation optic motion locally free optic Loop Recycling cavity 40 Hz (m/ Hz) GW channel coupling Damping path gain 40 Hz Damping servo % 35 db DC 2nd order Hz (+ pole@20 Hz for stability) Michelson % 65 db 2nd order Hz 4th order 20 Hz, 30 db stop

42 lm AND lp LOOPS WITH TM DAMPING lm open-loop gain 10 5 beamsplitter test masses overall lm Mag (db) Phase (deg) lp open-loop gain Frequency (Hz) Mag (db) recycling mirror test masses overall lp Phase (deg) Frequency (Hz)

43 LOOKING AHEAD... Detection mode controls Noise couplings estimates? Optical plant as-built? stability? variations? Controllers nearly optimum? optimization? Actuators cross-couplings? variations? Robust control uncertainties Model errors, parameter drifts system identification (sysid) Identify control law, control variables Characterize control system elements Adaptive controls Lock Acquisition