Page 67 - Modern Control Systems

Problems 41
system is, in fact, a multivariate system, and the P1.12 An automatic turning gear for windmills was in-
variables x, v, w, v, Z, and u are vector variables. In vented by Meikle in about 1750 [1, 11]. The fantail
other words, the variable x represents many heart gear shown in Figure PI. 12 automatically turns the
variables .rj, x 2,. • •, x„. Examine the model of the windmill into the wind. The fantail windmill at right
heart-rate control system and add or delete blocks, if angle to the mainsail is used to turn the turret. The
necessary. Determine a control system model of one gear ratio is of the order of 3000 to 1. Discuss the
of the following physiological control systems: operation of the windmill, and establish the feed-
back operation that maintains the main sails into
1. Respiratory control system
2. Adrenaline control system the wind.
3. Human arm control system
4. Eye control system
5. Pancreas and the blood-sugar-level control
system
6. Circulatory system
P1.10 The role of air traffic control systems is increasing
as airplane traffic increases at busy airports. Engineers
are developing air traffic control systems and collision
avoidance systems using the Global Positioning Sys-
tem (GPS) navigation satellites [34, 55]. GPS allows
each aircraft to know its position in the airspace land-
ing corridor very precisely. Sketch a block diagram de-
picting how an air traffic controller might use GPS for
aircraft collision avoidance.
Pl.ll Automatic control of water level using a float level
was used in the Middle East for a water clock [1,11].
The water clock (Figure PI.11) was used from some- FIGUREP1.12 Automatic turning gear for windmills.
(From Newton, Gould, and Kaiser, Analytical Design of
time before Christ until the 17th century. Discuss the Linear Feedback Controls. Wiley, New York, 1957, with
operation of the water clock, and establish how the permission.)
float provides a feedback control that maintains the ac-
curacy of the clock. Sketch a block diagram of the feed-
back system. P1.13 A common example of a two-input control system
is a home shower with separate valves for hot and cold
water. The objective is to obtain (1) a desired temper-
ature of the shower water and (2) a desired flow of
water. Sketch a block diagram of the closed-loop control
system.
P1.14 Adam Smith (1723-1790) discussed the issue of
free competition between the participants of an econ-
omy in his book Wealth of Nations. It may be said that
Smith employed social feedback mechanisms to ex-
plain his theories [41]. Smith suggests that (1) the
available workers as a whole compare the various
possible employments and enter that one offering the
greatest rewards, and (2) in any employment the re-
wards diminish as the number of competing workers
rises. Let r = total of rewards averaged over all
trades, c = total of rewards in a particular trade, and
q = influx of workers into the specific trade. Sketch a
feedback system to represent this system.
P1.15 Small computers are used in automobiles to con-
trol emissions and obtain improved gas mileage. A
FIGURE P1.11 Water clock. (From Newton, Gould, and computer-controlled fuel injection system that auto-
Kaiser, Analytical Design of Linear Feedback Controls. Wiley, matically adjusts the fuel-air mixture ratio could im-
New York, 1957, with permission.) prove gas mileage and reduce unwanted polluting