Chapter 4 ControllerSynthesis
MATRIXx Xmath Robust Control Module 4-4 ni.com
The transfer matrix G can be viewed as a model of the underlying system
dynamics with v and u as generalized forces that produce effects in the
performance signals z and measured signals y.
The weight Win is used to model the exogenous input v by v=Winw.
Similarly, the critical performance variables in the vector z are weighted to
form the normal critical variables e=Woutz.
In general, the input weight Win can be viewed as a dynamic model of the
exogenous inputs and the output weight Wout as the inverse of the desired
performance. As an illustration, consider the plant configuration in
Figure 4-3.
Figure 4-3. Typical Plant Configuration
The exogenous input vectors d and n represent disturbances and sensor
noise, respectively. These are generated by passing normalized
unpredictable signals, ωdist and ωnoise, through stable transfer matrices,
Wdist and Wnoise, respectively. The critical performance variables are some
regulated variables yreg, as well as the actuator commands u. These are
weighed by the transfer matrices Wreg and Wact to form the normalized error
variables ereg and eact. The sensed variables ysens are contaminated by
additive noise n to form the measured signal y. The transfer matrix Gdyn
represents the underlying system dynamics. Observe that the transfer
matrix G, as defined in [BBK88], consists of Gdyn with some special
output/input connections among the variables n and u as depicted in
Figure 4-3. This is in the form of the familiar LQG setup, except that
wd
n
y
reg
y
sens
u
e
u
y
P
W
dist
w
dist
W
in
W
reg
W
out
w
e
W
noise
w
noise
e
reg
e
act
W
act
G
dyn
G