+
q
r
w
1
z
U
+
3
U
v
2
e
U
U
Q
Figure 7.5 redrawn.
Figure
7.6
+
q
r
w
1
z
U
+
3
e
v
Q
U
2
U
Figure 7.6 redrawn.
Figure
7.7
7.3.1
Modified Controller Paradigm for a Stable Plant
As an example of the modi ed controller paradigm, we consider the special case of
a stable plant (see section 7.2.4). Since the plant is stable, the nominal controller
nom = 0 stabilizes the plant.
K
How do we modify the zero controller to produce and accept ? One obvious
e
v
method is to add into , and let be the di erence between and yu , which
v
u
e
y
P
u
ensures that the closed-loop transfer matrix from to is zero, as required by the
v
e
modi ed controller paradigm. This is shown in gure 7.8.
From gure 7.8 we see that
1 = zw
U
P
2 = zu
U
P
3 = yw
U
P
:
To apply the second step of the modi ed controller paradigm, we connect a stable
7.3 MODIFIED CONTROLLER PARADIGM
161
w
z
P
y
u
+
r
nom = 0
q
K
+
q
yu
+
r
P
;
v
e
One method of extracting and injecting when the plant is
Figure
7.8
e
v
stable.
w
z
P
y
u
+
r
nom = 0
q
K
+
q
yu
+
r
P
;
Q
v
e
K
The modied controller paradigm, for a stable plant, using the
Figure
7.9
augmented controller shown in gure 7.8.
162