Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale1 LTP dynamics and control D. Bortoluzzi, M. Da Lio, S. Vitale University of Trento

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale2 The LTP basic mode of operation

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale3 DOF Dc-force compensation TM- stabilisation Drag-free in measurement bandwidth Drag-free at low frequency Test-mass 1 x  y  z        Test-mass 2 x  y  z       

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale4 LTP is an autonomous dynamical system

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale5 Requirements given for S/C control DOFReadout noiseThrust noiseTotal relative displ. x S/C y 2S/C y 1S/C z 1S/C z 2S/C  1S/C TM-S/C relative displacement Readout noise External forces on S/C suppressed by drag-free control loop

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale6 LTP Multibody model Inertial reference frame Spacecraft body fixed reference frame S/C-LTP mechanical interface reference frame Optical bench body fixed reference frame Electrode housings reference frames Test masses body fixed reference frames Defined frames Spacecraft (Inertial Frame) Test mass 1 (S/C frame) Test mass 1 (EH frame) … Coordinates

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale7 Distortions Displacements of H1, H2 (readout references) frames due to distortions occurring: A) within the spacecraft (S/C-mechanical interface frame) (in S/C frame) B) within the LTP (mechanical interface frame- optical bench frame-electrode housings frames)

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale8 Forces and torques Picture of forces F sc, T sc : total force and torque (in SC frame) applied by LTP onto the S/C f e, t e : total force and torque of environmental origin on TMs f LTP, t LTP: total force and torque on TMs originated within the LTP or the S/C f 12, t 12 : force and torque between TM1 and TM2 f h, t h : total force and torque on TMs caused by the interaction between TMs and their housings (it includes actuation force and torque)

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale9 Dynamics 1: test-masses Dynamics 2: reaction on spacecraft Readouts TM-S/C coupling TM-S/C relative displacementTM-EH couplingTM-EH relative displacement Inverse of mass matrix TM-EH space-independent coupling TM-EH relative displacementCapacitive readout cross-talk Capacitive readout noise Stray forces capacitive actuationMass matrix OB-S/C relative position S/C motion TM-S/C space-independent coupling Optical readout cross-talk TM-EH relative displacement Optical readout noise

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale10 Symbolic form (for instance: inertia) Numeric form (for instance: stiffness & cross-talk) Matrices provided

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale11 Noise

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale12 Example: x(t) signal obtained from given x readout noise spectral density Example: force noise spectral density obtained from sampled signal

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale13

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale14 Simulation results

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale15 Simulation results

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale16 Compensating negative stiffness k p = N/m and dc forces N/10 -7 N/m  1 mm Low frequency suspension

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale17 Single input single output control laws Actuation cross-talkLow frequency suspension laws matrixCapacitive readout

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale18 Dc force compensation only

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale19 + TM stabilisation

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale20 Optimised control Robust against knowledge of parameters

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale21 x(s) h(s) y(s) Numerical implementation of control laws

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale22 ARMA basic step

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale23 TM motion after a force step N Low frequency suspension control Numerical implementation of control is good Very long damping time Stiffer TM actuation needed for emergency

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale24 Limits of the low-frequency actuation: Low damping Low maximum force Limit to stiffness Limit to maximum force Different operational mode (accelerometer mode) is defined in which larger maximum force can be exerted with larger stiffness (up to hardware limit)

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale25 x1,…,x6 Transfer functions parameters upload Threshold detector DC force offsets Fd1,…, Fd6 DC comp. a DC comp. b TM stabiliz a TM stabiliz b SCIENCE MODE Suspension c Suspension d ACCELEROMETER MODE LARGE AMPLITUDE MODE TBC Transfer functions selection External command Low frequency sine wave Charge measurement dither Poles, zeroes, gain Suspension switch Caging command Charge measurement command Channels combinator Ch1, ch2,… Calibration parameters upload Capacitive actuation functional block diagram

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale26 x1,…,x6 Transfer functions parameters upload Threshold detector DC force offsets Fd1,…, Fd6 Capacitive actuation functional block diagram DC comp. a DC comp. b TM stabiliz a TM stabiliz b SCIENCE MODE Suspension c Suspension d ACCELEROMETER MODE LARGE AMPLITUDE MODE TBC Transfer functions selection External command Low frequency sine wave Charge measurement dither Poles, zeroes, gain Suspension switch Caging command Charge measurement command Channels combinator Ch1, ch2,… Calibration parameters upload Capacitive actuation functional block diagram

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale27 x1,…,x6 Transfer functions parameters upload Threshold detector DC force offsets Fd1,…, Fd6 Capacitive actuation functional block diagram DC comp. a DC comp. b TM stabiliz a TM stabiliz b SCIENCE MODE Suspension c Suspension d ACCELEROMETER MODE LARGE AMPLITUDE MODE TBC Transfer functions selection External command Low frequency sine wave Charge measurement dither Poles, zeroes, gain Suspension switch Caging command Charge measurement command Channels combinator Ch1, ch2,… Calibration parameters upload Capacitive actuation functional block diagram

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale28 Accelerometer mode: high damping, large force TM motion after a force step N Accelerometer mode control damping time shorter

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale29 Transition to-from accelerometer mode requested to damp long term transitory Needs adjustment of long term behaviour TM subjected to force step Accelerometer mode threshold TM motion arrested TM moved towards EH center Passage to low frequency suspension law

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale30 Dc-force dominate Low frequency suspension and accelerometer mode asyntotic behaviour must be the same to avoid overshoot at handover Adjust low frequency gain

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale31 Capacitive actuation 1 Carrier waveform synthesis 3 IS FEE DAC 4 TM Fd1,…, Fd6 V1,…, V12 V1(t)..V12(t) Capacitive model equation parameters upload Carrier waveform parameters upload x1,…,x6 F to V conversion 2 F to V conversion 2 Switch Optical metrology Capacitive sensing Switch forces ADC Command

Penn State, 20 th -24 th July TH INTERNATIONAL LISA S YMPOSIUM D. Bortoluzzi, M. Da Lio, S. Vitale32 Summary: LTP dynamics mathematical model Capacitive actuation control laws: low frequency suspension and accelerometer mode Noise models Simulations results of a drag-free and attitude control system matching the requirements given