Page 293 - Modern Control Systems

Section 4.8 Design Examples 267

We conclude the analysis by considering the disturbance response. From previous
analysis we know that the transfer function from the disturbance input T d(s) to the
output Y(s) is
-G(s)
Y(s) = TM
1 + G c(s)GJs)G(s)
—r Us)-
s A + 2/75 3 + (p 2 + K D)s 2 + K Ps + K[
To investigate design specification DS4, we compute the disturbance step response
with
D 5 0
Tf\ °

This is the maximum magnitude disturbance (|r rf(f)| = DQ = 50). Since any step
disturbance of smaller magnitude (that is, (7^)1 = D 0 < 50) will result in a
smaller maximum output response, we need only to consider the maximum mag-
nitude step disturbance input when determining whether design specification DS4
is satisfied.
The unit step disturbance for each PID controller is shown in Figure 4.28. Con-
troller PID 2 meets design specification DS4 with a maximum response less than
±5% of the MAP set-point, while controllers PID 1 and 3 nearly meet the specifica-
tion. The peak output values for each controller are summarized in Table 4.2.
In summary, given the three PID controllers, we would select PID 2 as the con-
troller of choice. It meets all the design specifications while providing a reasonable
insensitivity to changes in the plant parameter. •

FIGURE 4.28
Mean arterial
pressure (MAP)
disturbance step 10
response. Time (min)