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Fig. 1. Control diagram of micro-stage system
Through the interface circuit, D/A converter the digital signal from computer is
amplified by driving power to produce a control DC voltage to control piezoelectric
actuator and the micro stage produces the output of micro displacement driven by
piezoelectric actuator. The micro displacement from micro stage is detected by a
displacement sensor and it is returned to the computer through A/D data acquisition
circuit. Then the closed-loop control for micro stage can be fulfilled by computer
according to the deviation.
2.2 Transfer Function of Micro-Stage System
Piezoelectric actuator is equivalent to a capacitive component [5], which is a
first-order inertial link. So its transfer function is given as follows:
k
.
(1)
G
(
s
)
= Ts
m
1
+
1
where k is the coefficient of voltage to displacement, T is the time constant.
Micro-stage system can be simplified as mass-spring-damping second-order
systems and its transfer function can be expressed by the following equation:
2
k
ω
.
G
(
s
)
=
n
(2)
2
2
s
2
+
2
ξω
+
ω
n
n
DC driving power supply amplifies the analog voltage signal from D/A converter,
which can control piezoelectric actuator, and its transfer function can be given as:
Gs k
3 ()
=
.
(3)
v
It can be seen from Fig. 1 that each part connects in series and an output of the
former link is an input of the next link input. So according to the transfer functions
established in every part, the open-loop transfer function of micro-stage system can be
calculated as:
2
k
ω
.
Gs
()
=
nn
(4)
(
+
)(
2
+
2
+
2
)
Ts
s
ξω
ω
n
n
kkk
=
where
.
n
m
v
 
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