Post on 12-Jul-2020
Atomic Force MicroscopyHigh-Performance Demodulation and Model-Based Nanomechani-cal Identification
Michael R. P. Ragazzon
Department of Engineering Cybernetics,Norwegian University of Science and Technology (NTNU)
November 18, 2019,KTH Royal Institute of Technology, Stockholm
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Outline
Introduction
High-performance DemodulationProblem FormulationLyapunov DemodulatorComparison of Demodulation TechniquesGeneralized Lyapunov demodulator
Model-based Nanomechanical IdentificationIntroductionSystem modelingParameter identificationOperation ModesExperimentsConclusion
Research Directions
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 1
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Outline
Introduction
High-performance DemodulationProblem FormulationLyapunov DemodulatorComparison of Demodulation TechniquesGeneralized Lyapunov demodulator
Model-based Nanomechanical IdentificationIntroductionSystem modelingParameter identificationOperation ModesExperimentsConclusion
Research Directions
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 2
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
About me
About me
— From Oslo, Norway.
— Graduated with Master’s (2013) and PhD (2018) at NTNU in Trondheim.
— Currently Postdoc. at NTNU.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 3
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Introduction
Atomic force microscopy (AFM)
Mirror
Functiongenerator
Demodulator
ControllerUz
A
xyz Piezoactuator
Aref
Piezo modulator
DetectorLaser
Sample
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 4
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Outline
Introduction
High-performance DemodulationProblem FormulationLyapunov DemodulatorComparison of Demodulation TechniquesGeneralized Lyapunov demodulator
Model-based Nanomechanical IdentificationIntroductionSystem modelingParameter identificationOperation ModesExperimentsConclusion
Research Directions
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 5
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Problem Formulation
Problem Formulation
Estimate amplitude a(t) and phase ϕ(t) in
z(t) = a(t) sin(ω0t + ϕ(t)). (1)
Evaluate in terms of the following metrics:
— Tracking bandwidth
— Noise evaluation (total integrated noise, TIN)
— Rejection of frequency components away from ω0 (off-mode rejection)
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 6
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Problem Formulation
Problem Formulation
Estimate amplitude a(t) and phase ϕ(t) in
z(t) = a(t) sin(ω0t + ϕ(t)). (1)
Evaluate in terms of the following metrics:
— Tracking bandwidth
— Noise evaluation (total integrated noise, TIN)
— Rejection of frequency components away from ω0 (off-mode rejection)
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 6
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Problem Formulation
AFM Demodulation Techniques
Demodulators
Rectification(non-synchronous)
Mixing(synchronous)
Open loop Closed loop
- Mean abs. deviation- Peak detection- RMS-to-DC- Peak hold
- Lock-in amplifier- HB lock-in amplifier- Coherent
- Kalman filter- Lyapunov demodulator
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 7
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Problem Formulation
AFM Demodulation Techniques
Demodulators
Rectification(non-synchronous)
Mixing(synchronous)
Open loop Closed loop
- Mean abs. deviation- Peak detection- RMS-to-DC- Peak hold
- Lock-in amplifier- HB lock-in amplifier- Coherent
- Kalman filter- Lyapunov demodulator
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 7
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Lyapunov Demodulator
Lyapunov DemodulatorUpdate law given by1
˙x = γc(z − z
), (2)
z = cT x (3)
where γ determines the estimation bandwidth.
[sin(ω0t)cos(ω0t)
]
z a‖·‖2
eγ 1
s−x
c
φatan2(·)
1Michael R P Ragazzon, Michael G Ruppert, David M Harcombe, Andrew J Fleming, andJan Tommy Gravdahl (2018). “Lyapunov Estimator for High-Speed Demodulation in Dynamic Mode AtomicForce Microscopy”. IEEE Transactions on Control Systems Technology 26.2, pp. 765–772.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 8
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Lyapunov Demodulator
Experimental Results
−80
−60
−40
−20
0
Magnitude(dB)
LIA slow
LIA fast
Lyapunov slow
Lyapunov fast
0.1 1 10 100−360
−270
−180
−90
0
Frequency (kHz)
Phase
[deg]
Frequency response
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 9
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Lyapunov Demodulator
Experimental Results
0 0.1 0.2 0.3 0.40
0.5
1
1.5
2
Time (ms)
Amplitude(V
) Input
LIA fast
Lyapunov fast
Time domain
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 9
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Lyapunov Demodulator
Lock-in amplifier vs Lyapunov
0.5 1 10 50
1
10
100
Bandwidth (kHz)
TIN
(mV)
LIA
Lyapunov
Total integrated noise (TIN) vs bandwidth
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 10
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Comparison of Demodulation Techniques
Sensitivity to other frequency components
Off-mode rejection2
2Michael G Ruppert, David M Harcombe, Michael R P Ragazzon, S O Reza Moheimani, andAndrew J Fleming (2017). “A Review of Demodulation Techniques for Amplitude-Modulation Atomic ForceMicroscopy”. Beilstein Journal of Nanotechnology 8.1, pp. 1407–1426.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 11
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Comparison of Demodulation Techniques
High-speed AFM Experiments
High-speed AFM experiment, 31 lines per second (∼8 s per image).Top: LIA at low bandwidth. Bottom: Lyapunov at high bandwidth.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 12
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Comparison of Demodulation Techniques
Multifrequency Lyapunov AFM Experiment
Phase demodulation at the first five harmonics of the cantilever.3
3David M Harcombe, Michael G Ruppert, Michael R P Ragazzon, and Andrew J Fleming (2018).“Lyapunov Estimation for High-Speed Demodulation in Multifrequency Atomic Force Microscopy”. BeilsteinJournal of Nanotechnology 9.1, pp. 490–498.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 13
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Generalized Lyapunov demodulator
Generalized Lyapunov demodulator4
— Lyapunov demodulator achieves high demodulation bandwidth.
— However, only first-order filtering.• Can we increase the filter order?
4Michael R P Ragazzon, Saverio Messineo, Jan Tommy Gravdahl, David M Harcombe, andMichael G Ruppert (2019). “Generalized Lyapunov Demodulator for Amplitude and Phase Estimation by theInternal Model Principle”. In Proc. IFAC Mechatronics. Vienna, Austria, p. 6.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 14
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Generalized Lyapunov demodulator
Indirect filter design
K Gu
y
v2
Amplitude andphase retrieval
a
ωc
r
Modulated signal(measurement)
Internal model of sinusoidInternal filter
Demodulator loop, T Composer
ϕ
a
ϕε
v1
— Design K (s) such that the demodulator loop T (s) becomes a desiredbandpass shape.
— Perfect tracking is guaranteed for any stable K (s).
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 15
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Generalized Lyapunov demodulator
Direct filter design
−ωc
s
Tr
v2
Amplitude andphase retrieval
a
Demodulator filterComposer ϕ
v1
— Design T (s) directly as a bandpass filter.
— Perfect tracking is guaranteed by the condition T (jωc) = 1.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 16
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Generalized Lyapunov demodulator
Direct filter design
−ωc
s
Tr
v2
Amplitude andphase retrieval
a
Demodulator filterComposer ϕ
v1
— Design T (s) directly as a bandpass filter.
— Perfect tracking is guaranteed by the condition T (jωc) = 1.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 16
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Generalized Lyapunov demodulator
Bode plot T (s)
30 35 40 45 50 55 60 65 70 75 80−40
−20
0
Magnitude(d
B)
30 35 40 45 50 55 60 65 70 75 80
−200
0
200
Frequency (kHz)
Phase
(deg
)
3 kHz bandwidth
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 17
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Generalized Lyapunov demodulator
Tracking frequency response
0.1 1 10 100
−40
−20
0
Frequency (kHz)
Magnitude(d
B)
1 10 100 1000
Frequency (kHz)
3 kHz bandwidth 30 kHz bandwidth
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 18
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Outline
Introduction
High-performance DemodulationProblem FormulationLyapunov DemodulatorComparison of Demodulation TechniquesGeneralized Lyapunov demodulator
Model-based Nanomechanical IdentificationIntroductionSystem modelingParameter identificationOperation ModesExperimentsConclusion
Research Directions
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 19
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Introduction
Introduction
— Single- and multifrequency AFM allow mechanical properties to be gathered.
— However, interaction forces are inherently nonlinear and often requires:• linearization• multifrequency demodulation• consideration of harmonics
to relate the observables to mechanical properties.
— Here, we relate the sample properties directly from the observables usingtime-domain dynamic models.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 20
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Introduction
Introduction
— Single- and multifrequency AFM allow mechanical properties to be gathered.
— However, interaction forces are inherently nonlinear and often requires:• linearization• multifrequency demodulation• consideration of harmonics
to relate the observables to mechanical properties.
— Here, we relate the sample properties directly from the observables usingtime-domain dynamic models.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 20
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Introduction
Introduction
— Single- and multifrequency AFM allow mechanical properties to be gathered.
— However, interaction forces are inherently nonlinear and often requires:• linearization• multifrequency demodulation• consideration of harmonics
to relate the observables to mechanical properties.
— Here, we relate the sample properties directly from the observables usingtime-domain dynamic models.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 20
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
System modeling
Cantilever dynamics
Approximation by first resonance mode.
MD + KD + CD = Fmod + Fts. (4)
x
z
Z
Z0
D
R
Rest position
Tip
Sample
Cantileverdeflection
X
h
δ
K,C
k, c
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 21
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
System modeling
Contact model
Modified Hertz contact model.
Fts = E ′δ32 + cδ (5)
E = 34 R−
12 (1− ν2)E ′ (6)
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 22
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Parameter identification
Parametric model
Combining the previous cantilever and sample models gives the system
Ms2D + CsD + KD − Fmod = csδ + E ′δ1.5. (7)
Rewrite (7) as
w ′ =[
cE ′
]T [ sδδ1.5
](8)
= θTφ′ (9)
Persistently exciting φ→ exponential convergence of parameters.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 23
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Parameter identification
Parametric model
Combining the previous cantilever and sample models gives the system
Ms2D + CsD + KD − Fmod = csδ + E ′δ1.5. (7)
Rewrite (7) as
w ′ =[
cE ′
]T [ sδδ1.5
](8)
= θTφ′ (9)
Persistently exciting φ→ exponential convergence of parameters.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 23
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Parameter identification
Parametric model
Combining the previous cantilever and sample models gives the system
Ms2D + CsD + KD − Fmod = csδ + E ′δ1.5. (7)
Rewrite (7) as
w ′ =[
cE ′
]T [ sδδ1.5
](8)
= θTφ′ (9)
Persistently exciting φ→ exponential convergence of parameters.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 23
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Parameter identification
Parameter estimator
Least squares method with forgetting factor.5
w = θTφ (10)
ε = (w − w)/m2 (11)
m2 = 1 + αφTφ (12)˙θ = Pεφ (13)
P = βP− PφφT
m2P (14)
P(0) = P0 (15)
5P A Ioannou and J Sun (1996). “Robust Adaptive Control”. Upper Saddle River, NJ: Prentice Hall.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 24
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Operation Modes
Procedure
x
y
Cantilever tip
t
Z0
Fmod
X
DSample
Intermittent contact
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 25
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Operation Modes
Procedure
x
y
Cantilever tip
t
Z0
Fmod
X
DSample
In-contact dynamic mode.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 26
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Experiments
Experimental setup
Park Systems XE-70 AFM and setup.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 27
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Experiments
Experiment: Two-component Polymer Sample
0 0.5 1 1.50
0.5
1
1.5
X (µm)
Y(µm
)
0
20
40
60
nm
(a) Topography
0 0.5 1 1.50
0.5
1
1.5
X (µm)
Y(µm
)
1.2
1.4
1.6
1.8
nm
(b) Amplitude
0 0.5 1 1.50
0.5
1
1.5
X (µm)
Y(µm
)
107
108
109
Pa
(c) Elastic modulus
0 0.5 1 1.50
0.5
1
1.5
X (µm)
Y(µm
)
0
50
100
µNs/m
(d) Damping coefficient
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 28
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Experiments
Experiment: Two-component Polymer Sample
0 1 2 3 4 5 60
100
200
Time (s)
Z(nm)
Z mean
Z envelope
(a) Vertical tip position
0 1 2 3 4 5 60
2
4
6
8·10−5
Time (s)
c(N
s/m)
0
5
10
15
20
25
k(N
/m)
(b) Parameter estimates
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 29
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Conclusion
Advantages
— Handles nonlinear force interactions naturally.
— Time-domain approach, circumvents the need• for linearization,• to consider harmonics,• demodulation, either single- or multifrequency.
— Can modify the cantilever and sample dynamics separately.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 30
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Conclusion
Challenges
— Signal-to-noise ratio of the cantilever is frequency dependent.
— Some nonlinear parametric models are challenging.• Eg. adhesion and plasticity.
— Can we trust the deflection signal under in-contact dynamic mode?
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 31
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Outline
Introduction
High-performance DemodulationProblem FormulationLyapunov DemodulatorComparison of Demodulation TechniquesGeneralized Lyapunov demodulator
Model-based Nanomechanical IdentificationIntroductionSystem modelingParameter identificationOperation ModesExperimentsConclusion
Research Directions
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 32
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Research Directions
Issues with in-contact dynamic mode
Laser
Sample
xy Piezoactuator
Shaker
z Piezo
Z
Photodetector
In-contact dynamic mode
Can the deflection measurement be trusted?
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 33
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Research Directions
Tip-actuated cantilever
Sample
xy Piezoactuator
Shaker
z Piezo
Z
Magneticfield
Magneticparticle
Fm
Tip-actuated cantilever
Can the deflection measurement be trusted?
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 34
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Research Directions
Model improvements
k0
k1 k2
d1 d2 dj
kj
Generalized Maxwell model
— Extension to more general, frequency dependent viscoelastic models.
— Deeper insight into the forces involved.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 35
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Research Directions
Model improvements
Sample
xy Piezoactuator
Shaker
z PiezoZ0
D
Fd (D)
Fk (D)Fts(δ; S)
External and internal cantilever forces
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 36
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Thank You
Thank you for your attention!
Questions?
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 37
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Bonus slides
Noise vs Bandwidth
Total integrated noise
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 38
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Bonus slides
Experimental setup
Ux, Uy , Uz
State machine(control logic)
D
D,Fmod
DA
DDemodulator
XYZControllerdX, dY, dZ
X, Y
Z δ
h
Parameter estimator
Leastsquares
estimator
k, cw
φSignal
filtering
Z0
A′ sin(ω0t)FmodEnable estimator
Block diagram of the control logic and parameter estimator.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 39
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Bonus slides
Experimental setup
— Implemented on a commercial AFM, Park Systems XE-70.
— All aspects controlled by our own algorithms.
— Real-time implementation at 200 kHz on a dSpace computer.
— Spherical carbon tip cantilever, radius 40 nm (B40_CONTR).
— Cantiler parameters M,K ,C determined a priori.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 40
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Bonus slides
Plant dynamics
Cantileverdynamics
XYActuator
hFts
Fmod
Uz
Ux, Uy X,Y X, Y
D
D
Z0Z0 Z δ Sample
k, cZ
Actuator
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 41
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Bonus slides
Experimental results: Time-varying parameters
0 50 100−2
−1
0
1
2·10−5
Time (s)
c(N
s/m
)
−0.5
0
0.5
k(N
/m)
Time-varying sample parameter estimates during indentation.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 42
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Bibliography
Bibliography I
Harcombe, David M, Michael G Ruppert, Michael R P Ragazzon, and Andrew J Fleming(2018). “Lyapunov Estimation for High-Speed Demodulation in Multifrequency AtomicForce Microscopy”. Beilstein Journal of Nanotechnology 9.1, pp. 490–498.
Ioannou, P A and J Sun (1996). “Robust Adaptive Control”. Upper Saddle River, NJ: PrenticeHall.
Ragazzon, Michael R. P. (2018). “Parameter Estimation in Atomic Force Microscopy:Nanomechanical Properties and High-Speed Demodulation”. PhD Thesis. Trondheim,Norway: NTNU, Norwegian University of Science and Technology.
Ragazzon, Michael R P, Saverio Messineo, Jan Tommy Gravdahl, David M Harcombe, andMichael G Ruppert (2019). “Generalized Lyapunov Demodulator for Amplitude and PhaseEstimation by the Internal Model Principle”. In Proc. IFAC Mechatronics. Vienna, Austria.
Ragazzon, Michael R P, Michael G Ruppert, David M Harcombe, Andrew J Fleming, andJan Tommy Gravdahl (2018). “Lyapunov Estimator for High-Speed Demodulation inDynamic Mode Atomic Force Microscopy”. IEEE Transactions on Control SystemsTechnology 26.2, pp. 765–772.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 43
Introduction High-performance Demodulation Model-based Nanomechanical Identification Research Directions
Bibliography
Bibliography II
Ragazzon, M.R.P., J.T. Gravdahl, and K.Y. Pettersen (2018). “Model-Based Identification ofNanomechanical Properties in Atomic Force Microscopy: Theory and Experiments”. IEEETransactions on Control Systems Technology.
Ruppert, Michael G, David M Harcombe, Michael R P Ragazzon, S O Reza Moheimani, andAndrew J Fleming (2017). “A Review of Demodulation Techniques forAmplitude-Modulation Atomic Force Microscopy”. Beilstein Journal of Nanotechnology 8.1,pp. 1407–1426.
Michael R. P. Ragazzon Atomic Force Microscopy: Demodulation and Model-Based Identification 44