2010 American Control Conference
Marriott Waterfront, Baltimore, MD, USA
June 30-July 02, 2010
FrC08.5
Apply Tapping Mode Atomic Force Microscope
with CD/DVD Pickup Head in Fluid
Shih-Hsun Yen, Jim-Wei Wu, and Li-Chen Fu
Abstract—This paper proposes a tapping mode scanning
sample type Atomic Force Microscope (AFM) equipped with
a CD/DVD pick-up-head (PUH) used to measure the
deflection of the cantilever beam of the probe in the liquid.
To start with, we build an adaptive Quality-Factor-controller
(Q-controller) to modulate the interaction force between the
tip and the sample. To implement the above systems, we have
designed a novel AFM mechanism and proposed an adaptive
sliding-mode controller for it. For testing the system
capability and analyzing the biomorphic change of the
sample in liquid, we have conducted a series of experiments,
and the results can help us to understand more about the
mechanism of the sample in liquid.
I. INTRODUCTION
Biological samples can be imaged with AFM in either
of the two imaging modes: contact mode or tapping mode
[1][2]. For AFM studies, biological materials are often
both delicate and tenuously immobilized on a surface,
even more so in fluid than in air. As a result, the vertical
and shear forces exerted on the sample via the tip in
contact mode can damage the sample by compressing,
tearing, or removing it from the surface[3].
Applications of fluid tapping mode AFM [4] [5] in
biology are constantly growing and the data obtained with
this technique are improving, especially in terms of
resolution. Even dynamic processes can be observed
almost as they would occur in vivo [6]. So far, in the
literature there exists an AFM which is developed using
CD/DVD PUH [7] [8] [9]. A PUH is light enough to be
carried for rapid scan so that the sample can remain fully
stationary. Besides, a cost-effective, and lightweight
system with good scanning performance will be needed
for scientific development and is valuable in industrial
applications. The goal of this research is to design an AFM
with the aforementioned features. Utilizing an optical
pickup device as the measuring system and developing an
advanced feedback controller are the appropriate methods
to realize such a system [10][11]. For the former, there
still exists difficulty in employing CD/DVD PUH in liquid,
namely, the measuring system will encounter refraction
problem when the light has to go through different media,
and hence a novel mechanical design has been hereby
designed to solve this tough situation. As for the latter, this
research build an adaptive Q control, for adjusting the Q
S. H. Yen and J. W. Wu are with the Department of Electrical
Engineering, National Taiwan University, Taipei, Taiwan, ROC.
(e-mail:[email protected])
L. C. Fu is with the Department of Electrical Engineering and
Department of Computer Science and Information Engineering,
National
Taiwan
University,
Taipei,
Taiwan,
ROC.
(e-mail:[email protected])
This work was supported by National Science of Council under the
grant NSC 98-2218-E-002-014.
978-1-4244-7425-7/10/$26.00 ©2010 AACC
factor of a piezo-actuated bimorph probe dynamically
during scanning when necessary [12][13][14]. Specifically,
in our approach the Q factor of the probe is modified
adaptively depending on the profile of the surface being
scanned.
There are four sections in this paper. Section II
describes the system design from the viewpoint of
hardware/software. Then, in section III adaptive Q control
and adaptive sliding- mode control are proposed and
analyzed to assure satisfactory operating performance of
the designed AFM. Numerical simulation and extensive
experiments are also provided in this chapter to validate
our design. In the final section, we will make a conclusion
summarizing the hereby obtained achievements.
II. SYSTEM DESIGN
A schematic diagram of the experimental setup of an
AFM driven in the amplitude modulation mode (tapping
mode) is shown in Fig. 1. The cantilever is driven at a
fixed frequency by a constant sinusoidal signal originating
from the lock-in amplifier, and the resulting oscillating
amplitude is also detected by the lock-in amplifier. The
PC-based controller we have designed will use that signal
to adjust the z-scanner. The piezoelectric tube scanner is
driven by a homemade high voltage amplifier, whose
operation range is -200 V to +200 V. The scanning range
is 35 µm × 35 µm × 9 µm in x-direction, y-direction, and
z-direction, respectively.
Figure 1. Schematic drawing of the experimental setup of the AFM
system using the constant excitation mode. A PC-based controller is used
to compensate the xy-trajectory and to reduce the tracking error in z-axis.
Unlike other commercial AFM, we use CD/DVD PUH
to detect the cantilever’s oscillation amplitude in this work.
It is worthy to note that positions of all elements of the
entire AFM setup may change due to heat or other factors,
and therefore we should properly adjust our system to
make sure the laser beam focuses on the tip. When we
6549
operate the AFM in liquid, the laser beam can be refracted
or scattered and it’s hard to focus it at a focal point. As a
result, we construct a mechanism to ensure the laser beam
does focus on the tip without suffering from refraction or
scattering. Besides, this mechanism can prevent
movement of the laser spot when the scanner is moved
upward and downward.
The kernel element of the designed AFM system is the
pickup head (as shown in Fig. 4), which is used to
measure the cantilever deflection. As mentioned earlier,
the relative positions of different components may change
due to temperature variation or other factors, but the laser
beam always needs to focus on the tip exactly. Besides,
the probe may be worn away by scanning [15], thereby a
precision tuning mechanism (see Fig. 2) needs to be
incorporated to solve this problem. The mechanism
includes a precision miniature linear stage, a piezoelectric
element (bimorph), a magnet, and a magnetic mount. The
piezoelectric element [16][17][18] is to oscillate the
cantilever in tapping mode operation; the magnetic mount
is to fix the probe; the rest are to enable precise
repositioning of the probe which is just newly installed,
replacing the previous obsolete one. In normal situation,
the cantilever should reveal high Q-factor property in the
frequency response so that a slight shift in the driving
frequency may induce significant decrease in oscillation
amplitude. To prevent this from happening, a function
generator based on direct digital synthesized (DDS)
technology is incorporated in the system. During the
calibration process, the focusing error (FE) signal is
monitored to confirm at the middle the linear region of
operation.
The precision miniature linear stage is to establish the
ability to reposition the probe whenever the probe is
shifted, and resolution and weight of the stage are 0.01
mm and 0.1 kg, respectively. The above arrangement
implies that the repositioning accuracy is improved
significantly and the total weight of the AFM platform is
still kept light. Overall speaking, the precision miniature
linear stage can offer more robust and steadier
performance while reducing operational inconvenience.
(see Fig. 3(b)).
By resorting to water capillary
phenomenon, a good environment for liquid scanning has
been created. Such a novel design can fit the liquid
environment well since we can prevent the probe while
scanning the sample from back-and-forth motion between
liquid and air media causing excessive disturbance to the
path of the laser beam shed on the back of the tip. Another
advantageous feature of this design is that we can alleviate
the problem with variation of the focal point of the laser
beam due to refraction caused by immersing of the probe
in liquid medium. The last but not the least, such design
also makes the process of calibrating the probe’s light path
quite easily in liquid experiment.
(a)
(b)
Figure 3. (a) The view of reduced refraction design, (b) the views of
the enlarged kernel parts of the AFM system.
Figure 4. The view of the DVD PUH.
III. TAPPING MODE TYPE AFM
Figure 2. The view of the precision tuning mechanism.
In order to scan the sample immersed in the water, one
special novel mechanism has been designed (see Fig. 3(a)),
so that a cover slip can be inserted between the probe and
the CD/DVD PUH lens through the guiding chamfers
located at the two inner edges of the above mechanism
A. Operation Scheme
Tapping mode is a very useful technique. The cantilever
of the probe is oscillated vertically by a small
piezoelectric element near it is resonance frequency. The
amplitude and phase of the cantilever during the scanning
process is usually measured by a lock-in amplifier, and the
topography image is obtained by monitoring these
changes. Because of the short intermittent contact, tapping
mode AFM greatly reduces irreversible destructions on
sample surfaces, so that it has been widely used for
non-destructive imaging of soft and fragile materials such
6550
as polymers and biological samples. The lateral force is
also greatly reduced in contrast with the case of contact
mode, but the resolution of the imaging is still limited by
the tip radius.
With the help of the adaptive Q-Control module [19], it
is possible to reduce the damping of the dynamic system,
i.e. to increase the effective quality factor of the oscillating
cantilever and thereby to enlarge the regime of
net-attractive interaction forces. Therefore, delicate and
highly sensitive surface structures that originally can not
be scanned with a standard scanning force microscope can
now be characterized with high resolution after applying
adaptive Q-Control. As a result, the effective quality (Q)
factor of the probe increases momentarily which in turn
increases the oscillation amplitude of the probe. This
causes a sudden increase in the magnitude of the error
signal and the control signal sent to the vertical direction
actuator adjusting the position of the sample with respect
to the probe tip. The scanning system responds faster to
the downward steps, leading to scan speeds faster than the
conventional PI controller with or without standard Q
control.
B. Adaptive Sliding-Mode Controller
In order to design a controller which can properly
handle piezoelectric nonlinearity and system uncertainty,
and meanwhile can gain high robustness and self-tuning
property, we propose an adaptive sliding-mode controller
for the tapping mode type AFM operation[20] [21]. To
start with, a linear second order model can be used to
represent the actuator’s nominal dynamics:
ɺɺ
z + a1 zɺ + a0 z = bu ,
(3)
Nevertheless, we have made some assumptions to simplify
the model of the plant. Those assumptions may result in
some inaccuracies of the plant model. Thus, two
additional disturbance terms need to be added into eq. (3)
yielding a model more closer to the real plant, which can
be expressed as:
ɺɺ
e = ɺɺ
zd + a1 zɺ + a0 z − bu + wc + wv
satisfies || wc
(4)
+ wv ||≦wmax, where wmax is a constant.
Then, a sliding surface variable, s, is chosen as:
s = eɺ + λ e
(5)
where λ is positive parameter to be designed.
The sliding surface variable is designed such that the
system is exponentially stable when the system state
constantly lie on the sliding surface. Therefore, the
problem is reduced to guaranteeing that the state of the
system can reach the sliding surface, or in the case of
bounded tracking some region around the surface. The
purpose is to force the tracking error to zero or to some
very small residual set. Then, taking the time derivative of
eq. (5), we have, i.e.,
sɺ = eɺɺ + λ eɺ
= ( ɺɺ
zd + a1 zɺ + a0 z − bu + wc + wv ) + λ eɺ
(6)
Based on eq. (6), the control law is designed as:
u AS = bˆ−1 (aˆ1 zɺ + aˆ0 z + ɺɺ
zd + wˆ c + λ eɺ + κ s + η sat ( s))
(7)
where κ > 0 and η > |wmax|. Moreover, b̂ and ŵc are the
estimated values of b and wc, respectively, and sat(.) is the
saturation function with boundary layer width ε defined
as:
1

s
sat ( s ) ≡ 
ε
 −1
(1)
where z stands for the displacement of the vertical actuator
moving the sample, b is the forcing coefficient of the
control input u, a1 and a0 represent the damping and the
stiffness of the system, respectively. The parameters a1, a0
and b can be well estimated via an off-line identification
test.
We assume that zd is a desired constant height between
tip and sample, and the control goal is to change z to
maintain the tip-sample distance at a desired value zd. The
tracking error can then be defined as:
e ≡ zd − z
(2)
Substituting eq. (1) into eq. (2), we have :
eɺɺ = ɺɺ
zd − ( − a1 zɺ − a0 z + bu )
= ɺɺ
zd + a1 zɺ + a0 z − bu
where wc represents a constant system uncertainty, and wv
represents a varying system uncertainty. Note that we here
assume that the varying uncertainty term is bounded and
s >ε
if
−ε ≤ s ≤ ε ,
(8)
s < −ε
Substituting eq. (7) into eq. (4), we can obtain
ɺɺ
e = aɶ1 zɺ + aɶ 0 z + wɶ c + w v − bɶ u A S − λ eɺ
− κ s − η sa t ( s )
(9)
where the estimation errors are defined as:
aɶ1 = a1 − aˆ1 , aɶ0 = a0 − aˆ0
bɶ = b − bˆ , wɶ c = wc − wˆ c
(10)
By applying appropriate gains κ, η, and λ, we can
accelerate the convergence and force the error to a small
residual error set in a shorter period of time.
In the following stability analysis, the adaptation law
has to be proposed in order to eliminate the estimation
errors as much as possible. Based on adaptive control
theory, we define a Lyapunov function candidate V, which
is a positive definite function:
1
1
1
1
1
(11)
V = s2 + aɶ12τ1−1 + aɶ02τ0−1 + bɶ2τ2−1 + wɶc2τ3−1
2
2
2
2
2
where τ0, τ1, τ2, and τ3, are positive constants. In the
6551
next step, differentiating the Lyapunov function candidate,
we obtain:
ɶ ɶɺτ −1 + wɶ wɶɺ τ −1
Vɺ = ssɺ + aɶ1aɶɺ1τ 1−1 + aɶ0 aɶɺτ 0 −1 + bb
2
c c 3
(12)
Substituting eqs. (6) and (9) into eq. (12), we can derive
the following:
−1
Vɺ = −s [ηsat (s) − wv ] − κ s2 + aɶ1 (aɺɶ1τ1 + szɺ)
ɺ −1
−1
−1
+ aɶ0 (aɶɺ0τ 0 + sz) + bɶ(bɶτ 2 − suAS ) + wɶ c (wɶɺ cτ 3 + s)
By the latent purpose to make
adaptation law as
(13)
Vɺ ≤ 0 , we design the
aɺˆ1 = − aɺɶ1 = τ 1szɺ − τ 1σ 1aˆ1

aˆɺ0 = − aɺɶ0 = τ 0 sz − τ 0σ 0 aˆ0
ɺ
ɺ
bˆ = −bɶ = −τ 2 su AS − τ 2σ 2bˆ
ɺ
 wˆ c = − wɺɶ c = τ 3 s − τ 3σ 3 wˆ c
ɶ ˆσ
Vɺ = − s [η sat ( s ) − wv ] − κ s 2 + aɶ1a?1σ 1 + aɶ 0 a0σ 0 + bb
2
+ wɶ c wˆ cσ 3
C. Numerical simulation
Referring to sweep-sine identification experiment, the
parameters of the plant are listed below: a0 = 1.02 × 108 ,
2
≤ −σ 1 aɶ1 + σ 1 aɶ1 a1
2
2
[ aɶ1 − a1 ]
Substituting inequalities (16) into (14), we can derive:
σ
σ
2
2
2
2
Vɺ ≤ − s [η sat ( s ) − wv ] − 1 [ aɶ1 − a1 ] − 0 [ aɶ 0 − a0 ]
2
2
−
σ2 ɶ 2
σ
2
2
2
[ b − b ] − 3 [ wɶ c − wc ]
2
2
(17)
If 0 < α < min {2κ , σ 0 , σ 1 , σ 2 , σ 3 } is chosen, then we
focus on the following two cases:
Case 1.
From the above discussions in Case 1 and Case 2, we can
conclude that for:
1
w2 ε
V ≥ V0 = σ 1a12 + σ 0 a02 + σ 2b 2 + σ 3 wc2  + max ,Vɺ ≤ 0
2
4η
ɺ
which implies that V and V ∈ L∞ . Finally, we can
(16)
2
2
(19)
further show that the tracking error will converge to a
residual set. The plant with uncertainties and the bounded
disturbance can be controlled by this adaptive
sliding-mode controller stably. According to the control
theory, the tracking error will converge to a residual set in
order of σ i , i = 0.3 and ε .
σ 1aɶ1aˆ1 = σ 1aɶ1 (a1 − aɶ1 ) = −σ 1 aɶ1 + σ 1aɶ1a1
σ1
1
w2 ε
≤ −αV + σ1a12 +σ0a02 +σ2b2 +σ3wc2  + max
2
4η
(15)
From eq. (19), the range of each term is derived from:
1
1 2 1 2
= −σ 1[ ( aɶ1 − a1 )2 + aɶ1 − a1 ]
2
2
2
s ≤ ε,
1
Vɺ ≤ −s[ηsat(s) − wv ] −αV + σ1a12 +σ0a02 +σ2b2 +σ3wc2 
2
s
1


= − s η − wv  −αV + σ1a12 +σ0a02 +σ2b2 +σ3wc2 
2
 ε

1
2η
= − s − swv −αV + σ1a12 +σ0a02 +σ2b2 +σ3wc2 
ε
2
1
2η
≤ − s + s wmax −αV + σ1a12 +σ0a02 +σ2b2 +σ3wc2 
ε
2
2
2
wmax
ε wmax
ε
1
2η
+
−αV + σ1a12 +σ0a02 +σ2b2 +σ3wc2 
= − s + wmax s −
ε
4η
4η
2
(14)
Substituting eq. (14) and the inequality η > |wmax| into eq.
(13), we can then derive:
≤−
Case 2.
s >ε ,
1
Vɺ ≤ − s [η sat ( s ) − wv ] − αV + σ 1a12 + σ 0 a02 + σ 2b 2 + σ 3 wc2 
2
 s

1
= − s η − wv  − αV + σ 1a12 + σ 0 a02 + σ 2b 2 + σ 3 wc2 
2
 s

1
= − η s + swv − αV + σ 1a12 + σ 0 a02 + σ 2b 2 + σ 3 wc2 
2
1
≤ −η s + s wmax − αV + σ 1a12 + σ 0 a02 + σ 2b 2 + σ 3 wc2 
2
1
= − s (η − wmsx ) − αV + σ 1a12 + σ 0 a02 + σ 2b 2 + σ 3 wc2 
2
1
2
2
≤ −αV + σ 1a1 + σ 0 a0 + σ 2b 2 + σ 3 wc2 
(18)
2
a1 = 5.25 × 102 , and b = 2.38 . The parameters of the
adaptive sliding-mode controller are listed as follows:
λ = 50, κ = 10, η = 1, τ 0 = 10, τ1 = 5, τ 2 = 1, τ 3 = 50
The sliding-mode controller can reduce the tracking
error quickly. On the other hand, the adaptive law enables
the controller to be equipped with self-correcting
capability that may improve performance significantly. As
seen in Fig. 5, the controlled z position approaches the
desired value, and after 1.4 seconds the error is suppressed
within 2 nm.
The frequency response can give an overview of the
oscillation properties of the system. The resonance curve
of the cantilever of the AFM probe will be changed in
shape while changing the Q factor. As shown in Fig. 6,
o
with the phase shift set to 90 , Gset = 50, G0 = 10, and the
effective Q factor, Qeff, increased to 300, the resonance
peak of the amplitude curve is significantly enhanced.
6552
the liquid and be exempt from a significant force due to the
surface tension. This cover slip is 0.12 mm thick, which is
thin enough that the laser beam will not be refracted too
much. The fine layer of water between the cover slip and
the cantilever beam tends to make the laser beam focus on
different positions. But the novel design which can clip
cover slip can completely solve this problem.
Figure 7. The enlarged picture of the core parts of the AFM system.
Figure 5. Numerical simulation of z-scanner tracking a standard
grating. The reference (blue line) step height is 200 nm. (a) is the
simulation result and (b) is the enlargement.
Figure 8. Standard grating and depth: 107.5 nm, pitch: 3 µm.
B. Scanning results in liquid
Figure 6.
and G
set
Amplitude vs. frequency curve with adaptive Q control
= 50,G 0 = 10
IV. Experiments
A. Hardware Setup
The core parts of the experimental setup is illustrated in
Fig. 7. As shown in Fig. 7, the CD/DVD PUH is fixed on
the frame and relatively above the probe mount, and
furthermore the cover slip which are attached to the
precision tuning mechanism and cover slip holder.
The sample used in the following experiment is a test
grating (Calibration grating set TGS1 is intended for z-axis
calibration of the scanning probe microscope and
nonlinearity measurements, and is formed on the layer of
SiO2. The vertical depth is 107.5 nm, and the horizontal
pitch is 3 µm, NT-MDT Inc.) with three-dimensional array
of small squares on the sample surface as shown in Fig. 8.
This calibration grating is a silicon step height standard
mounted on 15 mm puck.
To ensure the cantilever beam is totally immersed in the
liquid, a cover slip is placed over the probe. The liquid will
be absorbed between this cover slip and the sample, and
hence we can avoid operating the probe at the surface of
There are some resonant peaks appearing at different
frequencies while the tip is oscillating in liquid. Through
the amplitude-distance curve experiment, we can figure out
which one is the real resonant frequency. After these
pre-works, the scan experiment in liquid can be started.
Although the fine layer of water between the cover slip and
the cantilever beam will change the focal spot of the laser
beam. But the cover slip will be clipped by our novel
design during the sample approaching process, and then the
thickness of the water layer will not be altered so that the
light path calibration can be done before scanning. In other
words, the cantilever beam does oscillate at the focal point
exactly. Therefore, the signal read from the opto-electric
integrated circuit (OEIC) can represent the real bending
information of the cantilever, and the corresponding height
information can characterize the real topography.
The scanning results and the reconstructed 3D
topography images in liquid are shown in Figs. 9 and 10.
The morphology is clear and identifiable. The scanning
ranges are 12 µm × 12 µm and 4.5 µm × 4.5 µm,
respectively. The scan speed is 8 seconds per line. The
expected result is seen in this figure. Through the above
experiments, this proposed system performs satisfactory
efficiency while scanning in liquid. Moreover, the
implemented mechanism and controllers realize most of the
design concept and solve previously encountered problems.
In the liquid experiment results, Fig. 10 shows that the
original standard rectangular forms become curving. All of
the observed discrepancies can be explained as that the
6553
laser beam of the CD/DVD pickup head is refracting the
light more or less due to its motion between liquid and air
media. But high scanning quality cannot be denied by these
discrepancies. In addition, the holistic topography is clear
and stable which means this type AFM utilizing DVD
pickup head can be employed in the life science field and
may lead to significant contribution.
[4]
[5]
[6]
[7]
[8]
[9]
[10]
Fig. 9. Scanning topography and the virtual 3D topography image in
liquid. The total scanning range is 12 µm×12 µm.
[11]
[12]
[13]
[14]
Fig. 10. Scanning topography and the virtual 3D topography image in
liquid. The total scanning range is 4.5 µm×4.5µm.
[15]
V. Conclusion
[16]
A novel tapping mode atomic force microscopy
(AFM) applying a CD/DVD pickup head (PUH) operating
in liquid has been proposed in this paper. In addition, the
characteristics of the fluid and the influence of Q-factor on
the drag force also have been analyzed to overcome the
problem with significant drag force affecting the
performance of the cantilever beam applied to the fluid.
A model-based adaptive sliding-mode controller has
been designed for vertical z-scanner to reduce the tracking
error. In numerical simulation, the maximum transient
tracking error is less than 3 nm, and the steady state error
is less than 2 nm. These novel mechanism and controller
design are capable of investigating changes in local
surface properties with nano-scale spatial resolution.
Moreover, the clear topography and satisfactory scanning
performance of the calibration grating can be obtained
from our extensive experiments in liquid.
[17]
[18]
[19]
[20]
[21]
REFERENCES
[1]
[2]
[3]
J. Tamayo and R. Garcia. “Deformation, contact time, and phase
contrast in tapping mode scanning force microscopy.” Langmuir,
12:4430-4435, 1996.
R. W. Stark, T. Drobek, and W. M. Heckle, “Tapping-mode atomic
force microscopy and phase-imaging in higher eigenmodes,”
Applied Physics Letters, vol. 74, no. 22, pp. 3296-3298, 1999.
R. W. Stark, G. Schitter, and A. Stemmer. “Tuning the interaction
forces in tapping mode atomic force microscopy,” Physical Review
B, 68(8):85401, 2003.
6554
P. K. Hansma, J. P. Cleveland, M. Radmacher, D. A. Walters, P. E.
Hillner, M. Bezanilla, M. Fritz, D. Vie, H. G. Hansma, and C. B.
Prater. “Tapping mode atomic force microscopy in liquids.”
Applied Physics Letters, 64:1738, 1994. 10
C. A. J. Putman, K. O. Van der Werf, B. G. De Grooth, N. F. Van
Hulst, and J. Greve. “Tapping mode atomic force microscopy in
liquid.” Applied Physics Letters, 64:2454, 1994.
Y. Martin, D. W. Abraham, and H. K. Wickramasinghe.
“High-resolution capacitance measurement and potentiometry by
force microscopy.,” Applied Physics Letters, 52:1103, 1988.
D. W. Pohl, W. Denk, and M. Lanz. “Optical stethoscopy: Image
recording with resolution ¸λ/20,” Applied Physics Letters, 44:651,
1984.
F. Quercioli, B. Tiribilli, and A. Bartoli, “Interferometry with
optical pickups,” Optics Letters, vol. 24, pp. 670-672, 1999.
T. R. Armstrong and M. P. Fitzgerald. “An autocollimator based on
the laser head of a compact disc player. Measurement Science and
Technology,” 3:1072-1076, 1992.
K. Y. Huang, E. T. Hwu, H. Y. Chow, and S. K. Hung.
“Development of an optical pickup system for measuring the
displacement of the micro cantilever in scanning probe
microscope,” IEEE International Conference on Mechatronics,
pages 695-698, 2005.
E. T. Hwu, K. Y. Huang S. K. Hung, and I. S. Hwang.
“Measurement of cantilever displacement using a compact
disk/digital versatile disk pickup head.” International Conference
on Scanning Tunneling Microscopy/Spectroscopy and Related
Techniques, pages 2368-2371, 2005.
J. Tamayo and L. Lechuga. “Increasing the q factor in the constant
excitation mode of frequency-modulation atomic force microscopy
in liquid,” Applied Physics Letters, 82:2919, 2003.
H. Holscher, D. Ebeling, and U. D. Schwarz. “Theory of
q-controlled dynamic force microscopy in air,” Journal of Applied
Physics, 99:084311, 2006.
T. R. Rodriguez and R. Garcia. “Theory of q control in atomic
force microscopy.,” Applied Physics Letters, 82:4821, 2003.
C. C. Williams and H. K. Wickramasinghe, “Scanning thermal
profiler,” Applied Physics Letters, vol. 49, no. 23, pp. 1587-1589,
1986.
B. M. Chen, T. H. Lee, C. C. Hang, Y. Guo, and S. Weerasooriya.
“An H1 almost disturbance decoupling robust controller design for
a piezoelectric bimorph actuator with hysteresis.” IEEE
Transactions on Control Systems Technology, 7(2):160-174, 1999.
K. K. Leang and S. Devasia. “Iterative feedforward compensation
of hysteresis in piezo positioners.” Proceedings of the 42nd IEEE
Conference on Decision and Control, 3:2626-2631, 2003.
K. Furutani, M. Urushibata, and N. Mohri. “Improvement of
control method for piezoelectric actuator by combining induced
charge feedback with inverse transfer function compensation.”
Proceedings of the 1998 IEEE international Conference on
Robotics & Automation Leuven, Belgium., 2:1504-1509, 1998.
I. Gunev, A. Varol, S. Karaman, and C. Basdogan. “Adaptive Q
control for tapping-mode nanoscanning using a piezoactuated
bimorph probe.” Review of Scientific Instruments 78, 043707,
2007.
K. Takahashi, K. Tateishi, Y. Tomita, and S. Ohsawa. “Application
of the sliding-mode controller to optical disk drives.” Japanese
Journal of Applied Physics, 43(no. 7 b):4801-4805, 2004.
C. L. Hwang, Y. M. Chen, and C. Jan. “Trajectory tracking of
large-displacement piezoelectric actuators using a nonlinear
observer-based variable structure con- trol.” IEEE Transactions on
Control Systems Technology, 13(1):56-66, 2005.