Environmental Engineering Reference
In-Depth Information
The corresponding plant transfer function is
= P y w
A
B 1
B 2
P yu .
A ) 1 B
P
=
C ( sI
+
D
=
C 1
D 11
D 12
(4.3)
C 2
D 21
D 22
4.3 Controller Design
4.3.1 Formulation of the H Control Problem
The H control-based design procedure for repetitive controllers proposed in (Weiss and
Hafele 1999) can be applied to design the controller. It uses additional measurement informa-
tion from the plant. The block diagram of the control system is shown in Figure 4.2, where the
controller consists of an internal model M and a stabilising compensator C . The stabilising
compensator assures the exponential stability of the entire system, which implies that the
error e converges to a small steady-state error, according to (Weiss and Hafele 1999). The
three external signals (the components of
w
) are assumed to be periodic, with a fundamental
frequency of 50 Hz.
According to Chapter 2, the internal model M is obtained from a low-pass filter W ( s )
=
ω c
10000 rad/sec, cascaded with a delay element e τ d s , where
with
ω c =
τ d is slightly
s
+ ω c
less than the fundamental period
τ =
20 ms given as
1
ω c =
τ d = τ
19
.
9ms
.
A w
0
ω c
0 . The choice of
B w
ω c
A realisation of W is W
=
=
ω c is based on a compromise:
C w
1
if
ω c is too low, only a few poles of the internal model are close to the imaginary axis, leading
to poor tracking and disturbance rejection at higher frequencies; if
ω c is too high, the system is
s
W
(
s
)
e
d
P
i d
+
e
u g
w
plant
+
in ternal m odel
u ref
M
u
i o
p
stabilising
compensator
C
Figure 4.2
Repetitive control for voltage tracking
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