Hardware Reference
In-Depth Information
design target. One can use any design method, such as lag-lead compensation,
to deal with this SISO problem.
This approach is illustrated using the same design problem stated for the
parallel structure. Since the VCM actuator has a phase lag of approximately
180
◦
at frequencies below 1 kHz, we can choose a lag compensator with pole at
p
1
= −2/2πf
h
as C
2
(s) to produce a phase delay of approximately 60
◦
at f
h
so that the phase difference between the outputs of PZT and VCM actuators
is less than 120
◦
at the hand-off frequency f
h
.Accordinglywechoose:
C
1
(s)=1,
(3.164)
¯
¯
k
s
2
/
g
m
p
1
s +1
1
p
1
s +1
.
C
2
(s)=
(3.165)
s=j2πf
h
s.t. P
SISO
has no non minimum phase zeros.
The new SISO plant model P
SISO
(s) that includes C
1
and C
2
has a -40 dB/dec
slope at frequencies below f
h
and about a -20 dB/dec slope for frequencies
above f
h
. One need to verify whether the zeros in P
SISO
arestableornot.
To design the controller for the SISO plant P
SISO
, we can elevate the low
frequency gain and adjust the overall loop gain such that the compensated loop
has a 0 dB crossover at f
m
. A lag compensator with a pole at p
c
= −8/2πf
h
and a zero at z
c
= −1.25/2πf
h
canbeusedforthispurpose.Thecompensator
is selected as:
C
SISO
(s)=k
c
z
c
s +1
p
c
s +1
,
(3.166)
with
¯
¯
(p
c
s +1)
(z
c
s +1)P
SISO
k
c
=
.
s=j2πf
m
Results obtained for the design of servo controller for a dual-stage actuator
using the PQ method are shown in Figures 3.83 to 3.89. For this design
example, we chose f
h
= 400 Hz, f
m
= 2000 Hz, and achieve a open loop
bandwidth of 2000 Hz. The phase margin and gain margin are overly optimistic
because the actuator resonances are neglected in this example.
The PQ method provides a simple but effective way to allocate the con-
trol effort between two actuators of a dual-stage actuation system. One can
use various optimal control methods instead of the simple lag compensator as
shown above to design the controller for the compensated model P
SISO
.
3.7.4 Decoupled Master-Slave Structure with Actuator
Saturation
The decoupled master slave (DMS) configuration is shown in Figure 3.90. For
this configuration, the open loop transfer function L
dms
(s), the closed-loop
