Chemistry Reference
In-Depth Information
The resonant frequency of a piezoactuator is determined almost solely by its
maximumdisplacement (in other words, by its length). However, it can be effectively
extended by an inverse compensation method as described later. The structural
resonant frequency is enhanced by the use of a compact structure and a material that
has a large Youngs modulus to density ratio. However, a compact structure tends to
produce interferences between the three-scan axes. Aball-guide stage [2] is one choice
for avoiding such interferences. An alternative method is to use
flexures (blade
springs) that are
flexible enough to be displaced but rigid enough in the directions
perpendicular to the displacement axis [11, 12]. It should be noted that the scanner
mechanics, except for piezoacutators, has to be produced bymonolithic processing in
order to minimize the number of resonant elements.
Active damping of the x- and y-scanners is easy as their scan speed is not high
and their scan waves are known beforehand. Therefore, feedforward control for
active damping can be implemented in a digital mode. The Fourier transform of
the x-scanner displacement in an isosceles triangle, X(t), with a periodicity of T
x
is
given by
"
#
2
þ¥
k
1
2
dðÞ
2
p
1
k
2
dw
F
x
ðÞ¼
2
p
X
0
ð
k
w
Þ
ð
k
:
odd
Þ;
ð
12
:
6
Þ
0
¼¥
where X
0
is the maximum displacement and
w
¼
2
p
/T
x
. Suppose that the transfer
0
function, G
x
(i
), of the x-scanner is experimentally measured, then, the inverse
Fourier transform of F
x
(
w
) gives the driving signal, X
0
(t), to move the
x-scanner exactly in X(t). However, in practice, we need only the
rst
w
)/G
x
(i
w
15 terms
of F
x
(
w
). Thus, the driving signal is expressed as
2
X
29
X
0
2G
x
0
4X
0
p
1
k
2
1
X
0
t
ðÞ¼
ðÞ
cos k
½
w
0
t
F
ð
k
w
Þ
ð
k
:
odd
Þ;
0
j
G
x
ik
ð
w
Þj
0
k
¼
1
ð
12
:
7
Þ
where
F
(
w
) is the phase of the transfer function G
x
(i
w
). This feedforward damping
method works very well.
The above feedforward control method used to dampen the x-scanner cannot be
applied to the z-scanner since its scanwaves are unpredictable. The activeQ-control is
well known as an active damping technique and has been often used to control the
quality factor of cantilevers [13
-
16]. When this control is applied to the z-scanner, its
displacements have to be detected. However, it is dif
cult to do so. Kodera et al. [5]
developed a new method in which instead of detecting the displacements, output
signals from an electric circuit characterized with the same transfer function as the
z-scanner were used to dampen the z-scanner. With this technique, we achieved a
bandwidth of 150 kHz and a quality factor of 0.5, which resulted in a response time of
1.1
s. Thismethodworkedwell for a z-scannerwitha simple transfer functionbut not
foronewithmultiple resonantpeaks. Foractivedamping, analternativemethodcanbe
used.Thez-scanner isdriventhroughacircuitwitha transfer function1/G(s),whereG
(s) is the transfer function of the z-scanner. However, for a complicated G(s), it is very
dif
cult to design an electric circuit characterized by 1/G(s). Instead, we invented a
m
