Analysis of TMT Primary Mirror Control-Structure …macmardg/pubs/M1CSI_ppt.pdfControl-Structure...

Douglas MacMynowski (Caltech)Peter Thompson (Systems Tech.)Mark Sirota (TMT Observatory)

Analysis of TMT Primary Mirror Control-Structure Interaction(SPIE 7017-41)

TMT.SEN.PRE.08.046.REL01 2

Control Problems


Primary Mirror Control System (M1CS)

Sensors – measure relative displacement between segments,

estimate segment position:

Actuators: approach TBD, but candidates include – “Soft” (e.g. voice-coil), stiffened by servo loop– “Hard” (e.g. screw-type actuator), here I assume open loop

Control– Servo control loop (if soft actuators used),

~20 Hz bandwidth to obtain low frequency desired stiffness (see 7012-58)

– Global control loop: need ~1 Hz bandwidth to reject wind (see 7017-31)

Mirror cell introduces structural coupling that affects both of these


Outline

Primary Mirror Control System

Control-Structure Interaction

TMT structural dynamics

Actuator servo control loop

Global M1 control loop


Control-Structure Interaction (CSI)

Design without knowledge of structure – clear potential for problems– Control (both global & servo) can couple into structural modes

Potential for interacting control loops, e.g. each loop stable on its own, but the combination is unstable– Aubrun & Lorell study on ASCIE in early 90’s: destabilization

proportional to number of control loops– Aubrun & Lorell Keck CSI analysis: 0.5 Hz maximum bandwidth

Start with a really simple problem to build intuition (see paper), then apply to TMT M1CS– It is the ratio of total segment mass n × m to mirror cell mass M that

determines stability (not n alone)


M1 Dynamics

ui

… m

k

m m m

k kk

xi

zi

fi

Mirror cell

492

copi

es!


Computational Simplification

Use structural modes: good intuition for isolated mirror cell, but actual modes are not orthogonal when evaluated at segment loc’ns.– Use to show that coupling depends on total mass ratio μ=(n×m)/M

Analyze dynamics in Zernike basis– Coupling converges with relatively few basis vectors

More convenient to describe patterns of segment motion rather than individual segment motion

– Dynamics will be coupled; MIMO analysis is required

Z2,0 Z2,+2 Z2,-2


Telescope Structure

Finite element model of full telescope without segments- Compliance is highest at

low spatial frequency- Assume 0.5% damping

1 2 3 4 5 6 7 8 9 1010-8

10-7

10-6

Com

plia

nce

(m/N

)

Zernike basis function radial degree

Structure (LR)Segment support


Modeling Approach

Telescope FEM has no segment dynamics (intentionally)

Allows relevant segment dynamics to be added as needed for analysis using separate (detailed) FEM of segment assembly– Segment model reduced to 33 modes for CSI analysis

Telescope model and segment model connected at actuator nodes.– Projected into Zernike basis

segment (w/ rigid body modes)

cell

Connect withstiff spring


Idealized Actuator Assumptions

Soft (voice-coil) actuator:– Local position (servo) loop between force

and collocated displacement– Offload spring in parallel– Potential to add damping in parallel

Leads to a simple servo control

Hard actuator (e.g. screw + piezo):– Perfect displacement device (output =

command at all frequencies)– Pure stiffness (1e7 N/m) with zero damping

m

k=1.6e5 N/m

m

k=1e7 N/m

d

f, y


Servo open-loop TFon structure: Zernike basis

Transfer function from voice-coil force to position– In Zernike basis,

mounted on structure– Note maximum structure

resonance included is 36 Hz (static correction retained to 2000 modes, ~70 Hz)

– Note that response on different basis functions is NOT orthogonal; multivariable stabilityrobustness analysis is required! 100 101 102

10-8

10-6

10-4

Frequency (Hz)

Res

pons

e (m

/N)

Z0,0Z1,+1Z1,-1Z2,+2Z2,-2Z2,0Rigid

Coupling totelescopestructure

100

101

102

10-8

10-6

10-4

Frequency (Hz)

Res

pons

e (m

/N)

Rigid

Segmentsupportmodes

Segmentpiston/tip/tilt, onoffload spring


Servo open-loop TFon structure: Zernike basis

Transfer function from voice-coil force to position– In Zernike basis,

mounted on structure– Note maximum structure

resonance included is 36 Hz (static correction retained to 2000 modes, ~70 Hz)

– Note that response on different basis functions is NOT orthogonal; multivariable stabilityrobustness analysis is required! 100 101 102

10-8

10-6

10-4

Frequency (Hz)

Res

pons

e (m

/N)

Z0,0Z1,+1Z1,-1Z2,+2Z2,-2Z2,0Rigid

Coupling totelescopestructure

Segmentsupportmodes

Segmentpiston/tip/tilt, onoffload spring


Servo Loop Design

Two strategies:1. No change to plant: difficult to simultaneously navigate CSI with

telescope (most low frequency) and interaction with segment dynamics (high frequency)

2. Add passive damping in parallel to actuator: stabilizes 90 Hz+ segment dynamic modes

– See P. Thompson et al.for details (SPIE 7012-xx)

10-1 100 101 102106

107

108

Frequency (Hz)

Gai

n (N

/m)


Multivariable (MIMO)Robustness Evaluation

SISO analysis is not sufficient (doesn’t capture coupling)– Generalization is H∞: Want ||S||∞ < 2

(analogous to SISO GM/PM constraints)– Plot the maximum singular value

of multivariable sensitivityat each frequency

Distance tocritical point is|1+L| = |S(jω)|-1min|1+L|>1/2 ⇒GM > 6dB, PM > 30°


Servo Loop Robustness

Robustness is limited by structural modes that project almost entirely onto Zernike radial degree 2 and 3– Accurately predicted using only 10 (not 492) basis functions

0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

3

3.5

Max Zernike radial degree included

Max

Sen

sitiv

ity

||S||∞

10.5 Hz mode

0 10 20 30 40 500

0.5

1

1.5

2

2.5

3

3.5

Frequency (Hz)

σm

ax(S

)

p=0p≤ 1p≤ 2p≤ 3p≤ 4p≤ 5p≤ 6

Current design not sufficiently robust!


Global Loop

Transfer function from commanded actuator displacement to mirrormotion: Telescope structure modes are visibleGlobal control loop doesn’t depend (much) on hard vs soft actuator

100 101 10210-1

100

101

102

Frequency (Hz)

Res

pons

e (m

/m)

Soft actuatorHard actuator

100 101 102

100

101

Frequency (Hz)

Res

pons

e (m

/m) 10.5

10.313

Z2,+2Z2,-2Z2,0Rigid

Soft actuator


10-1 100 101 10210-3

10-2

10-1

100

101

Frequency (Hz)

Loop

tran

sfer

fn

Mag. 0.3, Freq. 14.8

Z2,0

Z2,-2Z2,2Rigid Base

Global Control Design

SISO analysis:– With 2-pole roll-off at 7 Hz,

maximum bandwidth ~ 2Hz (6 dB gain margin)

– Even with hard actuator, limited by telescopestructure, not 35 Hzsegment resonance


0 5 10 150

0.5

1

1.5

2

Frequency (Hz)

σm

ax(S

)

2≤ p≤ 5p=2 onlyRigid base

Global Control LoopMIMO Robustness Evaluation

1.5 Hz control bandwidth is achievable (Keck uses <0.1 Hz)– Higher bandwidth achievable at higher spatial frequency:

>2 Hz for radial degree > 4– Depends on assumed

structural dampingStability boundary predicted using 3 (not 492) basis functionsNo significant difference in global control between hard or soft actuators.

1.5 Hz controlbandwidth: ||S||∞=1.87


Conclusions

Control-structure interaction limits the achievable bandwidth of primary mirror control system– Zernike-basis analysis simplifies computation

Local control loop (soft actuator):– Challenging design, plausible with passive damping in parallel

Global control loop: – 1 Hz desired control bandwidth appears achievable– Achievable bandwidth is the same for hard or soft actuators– Depends on damping assumptions– Errors in A matrix may also limit bandwidth


Acknowledgments

The authors gratefully acknowledge the support of the TMT partner institutions. They are the Association of Canadian Universities for Research in Astronomy (ACURA), the California Institute of Technology and the University of California. This work was supported as well by the Gordon and Betty Moore Foundation, the Canada Foundation for Innovation, the Ontario Ministry of Research and Innovation, the National Research Council of Canada, the Natural Sciences and Engineering Research Council of Canada, the British Columbia Knowledge Development Fund, the Association of Universities for Research in Astronomy (AURA) and the U.S. National Science Foundation.

Analysis of TMT Primary Mirror Control-Structure …macmardg/pubs/M1CSI_ppt.pdfControl-Structure...

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