Page 285 - Modern Control Systems

Section 4.8 Design Examples 259

Magnitude of sensitivity vs. frequency
1.10 i
1 ' ' ! . II . i
1.05 •N. • 1 !
I " V j ^ ^-1 ^
1.00 . . ; _ . ! ' -+- i i J i ' Mi
ivity 0.95 i - j
sensit 0.90 ! ! : ; ! -
i
de of 0.85 "T t u - r -
gnitu 0.80 i.i .1 ; 1 " T'j i j ...: 1
2 0.75 .._. 1 . - 1 - • "If 1
i .1
0.70
FIGURE 4.22 i : \ '. • : i
The magnitude of 0.65 |i :-4 ft
the sensitivity of the \ : f 1 i
closed-loop system 0.60 1 ! 1
for the Mars rover 1 10° 10 10-
vehicle. Frequency (rad/s)

As shown in Section 4.4, the output of the closed-loop system with a unit step
disturbance, T d{s) = 1/s, is
.
y(O0) . lim J _ — I 1 1 . i (4 68)
/ v } 2 v J
s^o \(s + 4s+ 3 +K)j s 3 + K
When K = 2, y(oo) = 1/5. Because we seek to minimize the effect of the distur-
bance, it is clear that a larger value of K would be desirable. An increased value of
K, such as K = 50, will further reduce the effect of the disturbance as well as reduce
the magnitude of the sensitivity (Equation 4.66). However, as we increase K beyond
K = 50, the transient performance of the system for the ramp input, r(t), begins to
deteriorate. •

EXAMPLE 4.4 Blood pressure control during anesthesia

The objectives of anethesia are to eliminate pain, awareness, and natural reflexes so
that surgery can be conducted safely. Before about 150 years ago, alcohol, opium
and cannabis were used to achieve these goals, but they proved inadequate [23].
Pain relief was insufficient both in magnitude and duration; too little pain medica-
tion and the patient felt great pain, too much medication and the patient died or be-
came comatose. In the 1850s ether was used successfully in the United States in
tooth extractions, and shortly thereafter other means of achieving unconsciousness
safely were developed, including the use of chloroform and nitrous oxide.
In a modern operating room, the depth of anesthesia is the responsibility of
the anesthetist. Many vital parameters, such as blood pressure, heart rate, tem-
perature, blood oxygenation, and exhaled carbon dioxide, are controlled within
acceptable bounds by the anesthetist. Of course, to ensure patient safety, ade-
quate anesthesia must be maintained during the entire surgical procedure. Any