-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Modeling VRALA, the Next-GenerationActuator for High-Density,
Tick Secondary
Mirrors for AstronomyComsol for Adaptive Optics
C. Del Vecchio1 G. Agapito1 G. Tomassi2
E. de Santis2
1INAF-OAA Florence, Italy2University of Cassino – DAEMI Cassino,
Italy
2010 Comsol Conference Paris, Nov 19 2010
Presented at the COMSOL Conference 2010 Paris
http://www.comsol.com/conf_cd_2011_eu
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Outline
1 BackgroundThe AO PrincipleThe Design Drivers
2 StaticsThe ApproachThe Model
3 DynamicsThe Governing EquationsThe Open-Loop ResponseThe
Closed-Loop Response
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Outline
1 BackgroundThe AO PrincipleThe Design Drivers
2 StaticsThe ApproachThe Model
3 DynamicsThe Governing EquationsThe Open-Loop ResponseThe
Closed-Loop Response
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Compensating the Atmospheric TurbulenceThe Control System
Concept
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Adaptive Optics on board the TelescopeSystem Overview
[Riccardi et al., 2004]
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Actuating the DM & Sensing the DisplacementsThe LBT
Voice-Coil Actuator
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Outline
1 BackgroundThe AO PrincipleThe Design Drivers
2 StaticsThe ApproachThe Model
3 DynamicsThe Governing EquationsThe Open-Loop ResponseThe
Closed-Loop Response
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Basic Requirements of High Order DM’sThe Specs are very
Severe
rms force (turbulence correction) .363 Nmax force (static) .36
Nmax force (dynamic) 1.27 Nstroke (usable) ±100 µmstroke
(mechanical) ±150 µmbandwidth 1 kHztypical inter-actuator spacing
25 mmtypical actuator length ≤ 60 mmtypical mover mass ≤ 10× 10−3
kgDC resistance 2 to 2.5 Ω
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
DM Stiffness vs. DM Thickness & Act SpacingThe Plate
Stiffness is Strongly Non-Linear
The plate stiffnessKflex ∝ t3 × (1/d)4
t = thickness d = dimension
What ifthe inter-actuator spacing is slightly reducedthe
thickness is slightly increased
HIGHER ORDER DM d = 30→ 25 mm (16%)ELT PANELS t = 1.6→ 2 mm
(20%)
} 2×Kflex
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Design Criterion: Avoid Thermal PollutionThe (usual) Basic
Question and the (enhanced) Answer
reduce the local seeing⇓
reduce any local heating⇓
given the force, reduce the power⇓
maximize the efficiency(the force-to-power ratio)
WHILE
♣ respecting the geometry♣ minimizing the emi
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Design Criterion: Avoid Thermal PollutionThe (usual) Basic
Question and the (enhanced) Answer
reduce the local seeing⇓
reduce any local heating⇓
given the force, reduce the power⇓
maximize the efficiency(the force-to-power ratio)
WHILE
♣ respecting the geometry♣ minimizing the emi
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Design Criterion: Avoid Thermal PollutionThe (usual) Basic
Question and the (enhanced) Answer
reduce the local seeing⇓
reduce any local heating⇓
given the force, reduce the power⇓
maximize the efficiency(the force-to-power ratio)
WHILE
♣ respecting the geometry♣ minimizing the emi
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Design Criterion: Avoid Thermal PollutionThe (usual) Basic
Question and the (enhanced) Answer
reduce the local seeing⇓
reduce any local heating⇓
given the force, reduce the power⇓
maximize the efficiency(the force-to-power ratio)
WHILE
♣ respecting the geometry♣ minimizing the emi
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Design Criterion: Avoid Thermal PollutionThe (usual) Basic
Question and the (enhanced) Answer
reduce the local seeing⇓
reduce any local heating⇓
given the force, reduce the power⇓
maximize the efficiency(the force-to-power ratio)
WHILE
♣ respecting the geometry♣ minimizing the emi
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Design Criterion: Avoid Thermal PollutionThe (usual) Basic
Question and the (enhanced) Answer
reduce the local seeing⇓
reduce any local heating⇓
given the force, reduce the power⇓
maximize the efficiency(the force-to-power ratio)
WHILE
♣ respecting the geometry♣ minimizing the emi
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Design Criterion: Avoid Thermal PollutionThe (usual) Basic
Question and the (enhanced) Answer
reduce the local seeing⇓
reduce any local heating⇓
given the force, reduce the power⇓
maximize the efficiency(the force-to-power ratio)
WHILE
♣ respecting the geometry♣ minimizing the emi
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Design Criterion: Avoid Thermal PollutionThe (usual) Basic
Question and the (enhanced) Answer
reduce the local seeing⇓
reduce any local heating⇓
given the force, reduce the power⇓
maximize the efficiency(the force-to-power ratio)
WHILE
♣ respecting the geometry♣ minimizing the emi
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Outline
1 BackgroundThe AO PrincipleThe Design Drivers
2 StaticsThe ApproachThe Model
3 DynamicsThe Governing EquationsThe Open-Loop ResponseThe
Closed-Loop Response
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Electromagnetic CoreVariable Reluctance LM: F =
ZS−1
2(H · B) n + (n · H) BT dS
[Del Vecchio et al., 2010]
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Electromagnetic CoreVariable Reluctance LM: F =
ZS−1
2(H · B) n + (n · H) BT dS
[Del Vecchio et al., 2010]
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Electromagnetic CoreVariable Reluctance LM: F =
ZS−1
2(H · B) n + (n · H) BT dS
[Del Vecchio et al., 2010]
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Outline
1 BackgroundThe AO PrincipleThe Design Drivers
2 StaticsThe ApproachThe Model
3 DynamicsThe Governing EquationsThe Open-Loop ResponseThe
Closed-Loop Response
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Full Coil ApproximationThe Filling Factor ϕ Dramatically
Reduces the DOF’s
StaticRf =
ϕN2 R
J2f = ϕJ2 = ϕ
(I
Aw
)2Ff = 1ϕF
V f =√ϕ
N VTransientJf = N IAw
V indf = NV ind
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Numerical Optimization IA Single Matlab Script to Fully
Calculate the Magnetic Response
geometry define the (very simple!) basic components inthe r -z
plane
meshing get the elements (typically 10000) and embedthem in the
azimuthal currents applicationmode
physics definethe physical properties of the chosenmaterials
(via tables or plots provided bythe manufacturers), including the
airthe input external current density (with theproper correction
factor)
solution solve the non linear system (of typically
20000equations) for Aϕ
post-proc. compute the magnetic force via the Maxwellstress
tensor (multiplying by ϕ)
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Numerical Optimization IIMaterials & Geometry: �max ≈ 7
N×W−1
mat 64% of 17× 17 combinations � ≥ 6 N×W−1geom � = �
(hmov , rstato ,W ,H,R
)7→ � = �
(W ,H,R
)⇓
�� ��Iron losses≤ 1.6% of the DC power, via frequency
analysis
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Numerical Optimization IIIPrototypes: the Magnetostatics
results are experimentally confirmed
value Pure Fe FerriteR1 [mm] 1.5 1.5R2 [mm] 6 4.5R3 [mm] 11 9R4
[mm] 12.5 10.75h [mm] 12 5turns 400 85
force [N] 1.95 0.71voltage [V] 1 0.75current [A] 0.2 0.8power
[W] 0.2 0.6� [N ×W−1] 9.75 1.18
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Analytical OptimizationThe Comsol Results Match the
Analytical Ones
rstati ↪→ R1R −W/2 ↪→ R2R + W/2 ↪→ R3
rstato ↪→ R4H ↪→ h
� = K(R24 − R23 + R22 − R21)(R3 − R2)
R3 + R2
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Outline
1 BackgroundThe AO PrincipleThe Design Drivers
2 StaticsThe ApproachThe Model
3 DynamicsThe Governing EquationsThe Open-Loop ResponseThe
Closed-Loop Response
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Setting Up the ModelThe Full Coil is Implemented
Multi-Physically
Aφ︸︷︷︸m/s
⊗ r , z︸︷︷︸ALE
⊗F = (M + m0)z̈︸ ︷︷ ︸ODE
⊗ (Vext − Vind )/R︸ ︷︷ ︸coupling eq
where Vext = IextR Iext =√ϕ AAw
V f =∫
A
(−ef + Jfρ)2πrA
dA
where∫
A
ef 2πrA
dA is V indf
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Outline
1 BackgroundThe AO PrincipleThe Design Drivers
2 StaticsThe ApproachThe Model
3 DynamicsThe Governing EquationsThe Open-Loop ResponseThe
Closed-Loop Response
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Electromagnetic InertiaEnergy Balance
P(t) = Vi(t) = PFe + PCu︸ ︷︷ ︸Pheat
+Pmagn + Pkinet
Pheat � P ⇒ P≈{
Pmagn for t ≤ .8Pmagn + Pkinet for t > .8�� ��The e/m inertia
is a big issue for the control system
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Electromagnetic InertiaEnergy Balance
P(t) = Vi(t) = PFe + PCu︸ ︷︷ ︸Pheat
+Pmagn + Pkinet
Pheat � P ⇒ P≈{
Pmagn for t ≤ .8Pmagn + Pkinet for t > .8�� ��The e/m inertia
is a big issue for the control system
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Electromagnetic InertiaEnergy Balance
P(t) = Vi(t) = PFe + PCu︸ ︷︷ ︸Pheat
+Pmagn + Pkinet
The stored magnetic energy
Pmagn =∫
V
(∫ B0
H dB
)dV
defined via Comsol functionsafter Matlab numerical
integration
Pheat � P ⇒ P≈{
Pmagn for t ≤ .8Pmagn + Pkinet for t > .8�� ��The e/m inertia
is a big issue for the control system
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Outline
1 BackgroundThe AO PrincipleThe Design Drivers
2 StaticsThe ApproachThe Model
3 DynamicsThe Governing EquationsThe Open-Loop ResponseThe
Closed-Loop Response
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Real-Time-Updating LQR IThe Block Diagram
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Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Real-Time-Updating LQR IIDesign Principles
the state x is defined as x(k) = [ I(k) z̈(k) ż(k) z(k)
]′(sampling @ 50 kHz at each pk )
I = current signalz = position feedback (z ⇒ ż ⇒ z̈)
at each k step, the system matrices update determinesA(p) and
B(p) in x(k + 1) = A(p)x(k) + B(p)u(k)
A(p) 7→B(p) 7→ LQR(p,λ) 7→ F (k) (control matrix)
2 limits: |Ii | ≤ Imax &∣∣∣∣dIidt
∣∣∣∣ ≤ dImaxIi 7→ coil current splitter 7→
{I ti if Ii > 0Ibi if Ii < 0�� ��λ is the forgetting
factor, according to RLS theory
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Real-Time-Updating LQR IIIThe 2 Transfer Functions
The plant is the combination of 2 TF’s
1 F = f (z, I), non linear, but linearized @ p = (z̄, Ī) byf
(z, I) ≈ k(p) + kz(p)δz + kI(p)δI
k(p) = f (p)kz(p) =
∂f (z,I)∂z
∣∣∣(p)
kI(p) =∂f (z,I)
∂I
∣∣∣(p)
2 I(s)Ii (s)
= 1ωs+1 , a first order low-pass filter
ω is the time constantI(s) is the Laplace transform of the coil
currentIi (s) is the Laplace transform of the input current
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Closed-Loop ResultsThe Step Response
z0 = 0; δ = 1 to 5 µm
�� ��ts for δ = 4 and 5 µm exceed by 10% the goal
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Closed-Loop ResultsThe Step Response
z0 = −100 to 100 µm; δ = 1 µm
�� ��ts ≤ 1 ms
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Closed-Loop ResultsThe Step Response
z0 = −100 to 100 µm; δ = 2 µm
�� ��ts ≤ 1 ms
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
The Closed-Loop ResultsThe Step Response
The maximum average powercomputed over the entire time
domain
ranges from 1.3 to 10.7 mW
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Lessons Learned & Future Work
A challenging projectThe high-order, long-stroke, very large
deformable mirrorsof the next generation telescopes require very
large forces
and unprecedented actuator densities. The simple and
veryeffective magnetic circuit of VRALA is well-suited to
accomplishing this goal.
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Lessons Learned & Future Work
The actuator can accomplish the demandingspecifications with
� = 7 N×W−1 → low power dissipationts = .71 ms for δ = 1 µm→
high speed
Φ ≥ 25 mm→ small separationsThe Comsol results are (statically)
verified by
two very simple, preliminary prototypesan analytical
optimization
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Lessons Learned & Future Work
Further pushing the technology boundariesVRALA, the last chapter
of the short but rich history of theAO technology has established
many achievements. The
encouraging results indicate the near future developments.
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Lessons Learned & Future Work
Complete prototype (provided with a feedback capacitive
sensor)possible construction issuesclosed loop responsepower
dissipation
Further computationspossible alternative control system
designsclosed loop frequency responserefined multiphysics
(HT+NS+SM)
cooling system designmagneto-mechanics as a function of T
3D modelingwhole system simulation (mutual effects)effects of
tolerances/errors
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Some Final Explanations
�� ��Variable Reluctance Adaptive mirror Linear Actuator
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Some Final Explanations
Vråla To roar(Swedish) (English)
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
BackgroundThe AO Principle
The Design Drivers
StaticsThe Approach
The Model
DynamicsThe GoverningEquations
The Open-LoopResponse
The Closed-LoopResponse
Summary
Some Final Explanations
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
Appendix
For Further Reading I
Del Vecchio, C., Marignetti, F., Agapito, G., Tomassi, G.,and
Riccardi, A. (2010).Vrala: Designing and prototyping a
novel,high-efficiency actuator for large adaptive mirrors.In
Ellerbroek, B. L., Hart, M., Hubin, N., and Wizinowich,P. L.,
editors, Adaptive Optics Systems, volume 7036 ofProc. SPIE.
SPIE.
-
Vrala
Del Vecchio,Agapito,Tomassi,de Santis
Appendix
For Further Reading II
Riccardi, A., Brusa, G., Xompero, M., Zanotti, D., DelVecchio,
C., Salinari, P., Ranfagni, P., Gallieni, D., Biasi,R.,
Andrighettoni, M., Miller, S., and Mantegazza, P.(2004).The
adaptive secondary mirrors for the Large BinocularTelescope: a
progress report.In Bonaccini Calia, D., Ellerbroek, B. L., and
Ragazzoni,R., editors, Advancements in Adaptive Optics, volume5490
of Proc. SPIE, pages 1564–1571. SPIE.
BackgroundThe AO PrincipleThe Design Drivers
StaticsThe ApproachThe Model
DynamicsThe Governing EquationsThe Open-Loop ResponseThe
Closed-Loop Response
SummaryAppendix
