Hardware Reference
In-Depth Information
Figure 3.37: Feedback control system.
such that
G
c
G
p
1+G
c
G
p
I
s
r
,
= G
clp
I
s
r
y =
,
(3.60)
has a desirable step response. Here G
clp
is the closed-loop transfer function.
The advantages of this two degree-of-freedom structure are,
1. I
s
can be selected such that slow dynamics in the transfer function from
r
to y is removed,
2. feedback controller G
c
can be designed to produce relatively fast closed-
loop poles. However, feedback control does not shape the zeros of the
closed loop transfer function. The input shaper I
s
can be designed to
relocate the zeros and, in addition, possibly the poles, and
3. I
s
can be designed to filter out the high frequency components in the
command signal r
.
Example 1: When the closed-loop transfer function represented by
G
clp
(z)=
z
−d
N
clp
(z
−1
)N
−
clp
(z
−1
)
D
clp
(z
−1
)
(3.61)
clp
(z
−1
) represents all the zeros outside the unit circle and N
clp
(z
−1
)
those inside the unit circle, I
s
can use the form of ZPET controller [124]:
−
where N
I
s
=
z
d
D
clp
(z
−1
)N
−
clp
(z)
clp
(1)]
2
N
clp
(z
−1
)
.
(3.62)
−
[N
This results in
−
−
clp
(z)
clp
(z
−1
)N
y =
N
r
.
(3.63)
−
clp
(1)]
2
[N
In this case, the performance is limited by the non-minimum phase zeros of
the closed-loop system if the control signal is not saturated.
