Control of the Keck and CELTTelescopesDouglas G. MacMartinControl & Dynamical SystemsCalifornia Institute of TechnologyTelescope Control Problems• Primary mirror active control system (ACS)– Correct mirror figure due to gravity, wind,…• Adaptive optics (AO)– Compensate for atmospheric turbulenceLight from starPrimary mirrorInstrumentWavefront sensorDeformablemirrorAdaptive opticsKeck Primary Mirror:-36 segments- 108 actuators0.9 mCELT30m (20xx)Hale (Palomar)5m (1948)Keck 10m (1992)System Block Diagram• Notes:1Distortion relevant at multiple layers2Gravity impacts segments directly, and through distortion of journals etc.?3Wind impacts segments directly, and through base motion of telescope on (non-rigid) ground4Other sources include machinery vibration; pumps, bearings, drives,…5Wavefront sensor probably not required6May need to control secondary mirror; rigid body motion (hexapod or at supports) or flexibility (tertiary?)7Potential multiple AO mirrors, multiple wavefront sensors (Secondary as DM for AO?)8Tip/tilt control may require feedback from instruments (“final” wavefront)AtmosphereScience objectwavefront Distortion1(turbulence)PrimaryMirrorSecondaryMirrorAO Def. Mirror(s)ScientificInstrumentsGravity2Wind3ThermalWindSeismicGravityOther4FSMNatural, Laserguide starsEdgeSensorsKPM5SegmentActuatorsWavefrontSensorsKAO7DM ActuatorsKSM6KTT8Primary Mirror Control Problem• Out-of-plane motion of segments is tightly controlled• Performance goal (CELT):– Primary mirror residual wavefront error < 45 nm rms*from ALL sources– Segment out-of-plane alignment (controlled) wavefront error < 18 nm rms•Sensor noise• Actuator “noise” (precision)• Uncompensated disturbances• Disturbances:– Gravity: slow, mostly predictable, 1.2 mm max (70 nm/s)– Wind: approximate disturbance spectrum guessed at.• 3 dof actuation on each segment• Relative displacement sensors between each inter-segment edge*Specification with Adaptive Optics; only errors uncorrectable by AO (primarily segment edge discontinuities) contributeActuator locations(three per segment)Sensor locations(two per inter-segment edge)6204168Sensors3240108Actuators108036SegmentsCELTKeckControl HardwareCELTKeckKeck Actuator• Roller screw, 24:1 hydraulic reduction• Roller screw is reliable, but Keck has ~1 actuator failure per year due to hydraulic• Some backlash• Local feedback loop used to obtain desired outputCELT Actuator• Voice-coil with trim motor offload• Local feedback loop used to obtain desired output and stiffnessPrecision Sensor Design• CELT design:– Differential capacitance measurement– Components mounted directly on segment edges– Gain is sensitive to gap• Keck design:– Measure differential capacitance– Sensor noise ~ 1 nm / √Hz– (Expensive) precision interlocking componentsbDynamics y = C x + δ+ ηSensorSystem influencematrix (from geometry)Sensor noiseDesired sensorreadings (fromalignment camera)xk+1 = Axk+ Buky = Cxk+ Dukxk+1= xk+ gk+ wk+ ukState vector:Displacementat actuator locationsControl input: treat as displacement actuator (assuming local loop)Disturbance:Predictable component, Random componentNO dynamics! ( A = I )Ignored for Keck,Need to include for CELTControl ProblemControl: (i) estimate x from y, (ii) integral control(iii) feedforward of predicted disturbance componentGemini• Mirror is 20 cm thick, deforms under gravity• 120 actuators used to maintain optical qualityAdaptive Optics:Correct for Atmospheric Distortion• Source is turbulence at multiple levels in atmosphere (Kolmogorov model)• Detect wavefront (Hartmann-Shack sensor), m×m array of subapertures• Deformable mirror used to invert– May need multiple mirrors, each to invert one layer of atmosphere, to increase isoplanatic angle• Can use science object, natural guide star, or laser guide star– May need multiple LGS to increase isoplanatic angleKeck Adaptive Optics on/offInsert picture of deformable mirror here.Keck AO: Deformable MirrorShack-Hartmann Wavefront SensingCurrent Palomar AO Geometry• 241 actuators (‘o’)• 256 element Shack-Hartmann wavefront sensor (‘+’)– (384 sensor measurements not obscured by secondary)• Structural dynamics are outside of control bandwidthDynamics y = C x + ηSensorSystem influencematrix (from geometry)Sensor noisexk+1 = Axk+ Buky = Cxk+ Dukxk+1= xk+ wk+ ukState vector:Displacementat actuator locationsControl input: treat as displacement actuatorDisturbance:Random componentNO dynamics! ( A = I )Control ProblemControl: (i) estimate x from y, (ii) Proportional-integral (PI) controlPalomar AO FSM Transfer Function100101102-20-15-10-50Magnitude (dB)100101102-270-180-900Frequency (Hz)Phase (deg)Plant:• Nonlinear gain, differs for different channels• Roughly constant• Phase lag due to time delay• High frequency modesLoop Transfer Function: PI controller100101102-30-20-100102030Magnitude (dB)Loop transfer function, KI = 0.66 KP = 0.15fsm A (max)fsm A (min)fsm B (min)100101102-270-180-900Phase (deg)Frequency (Hz)Controller:u = (KI/s + KP)x• Integral to boost low frequency gain• Proportional term to improve phase at crossover.• Bandwidth ~ 10 Hz•Gain margin ~ 10 dB, phase margin ~ 60°10-110010110-210-1100101Frequency (Hz)SensitivityComputed sensitivityS=1/(1+L)matches prediction!10-210-110010110-410-310-210-1100Frequency (Hz)Magnitude (dB)Open-loop Closed-loopPerformanceCELT AO Requirements(“diffraction-limited” (180 nm rms) at 1 µm)• Deformable Mirrors– 3-4 mirrors, conjugate to different layers in the atmosphere– Each mirror with ~7000 actuators• Wavefront sensors– Roughly double the number of actuator degrees of freedom • Laser guide stars– To provide information anywhere in the sky, create your own stars…• Excite sodium layer at 90km– Need 7-11 lasers for reasonable field of view• Control loop– 20,000 actuators and 40,000 sensors– Need to close loop at ~ 1kHz– Wait 25 years for Moore’s law to catch up, or– Be more intelligent about local control…7368 ActuatorsCELT views of EuropaVisible Galileo image convolved to 0.5 arcsec resolution (AO off) (seeing-limited)Visible Galileo image convolved to 0.007 arcsec resolution (AO on)(diffraction-limited at 1µm)CELT: Galaxy EvolutionCourtesy of M. BolteChajnantorMauna
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