E5.12 The Ferris wheel is often featured at state fairs and carnivals. George Ferris was born in Galesburg, Illinois, in 1859; he later moved to Nevada and then graduated from Rensselaer Polytechnic Institute in 1881. By 1891, Ferris had considerable experience with iron, steel, and bridge construction. He conceived and constructed his famous wheel for the 1893 Columbian Exposition in Chicago [8]. Consider the requirement that the steady-state speed must be controlled to within 5% of the desired speed for the Ferris wheel speed control system shown in Figure E5.12. (a) Determine the required gain K to achieve the steady-state requirement. (b) For the gain of part (a), determine and plot the tracking error for a unit step disturbance. Does the speed change more than 5%? (Set R(s) = 0 and recall that the tracking error E(s)-R(s)-T(s).) E(s) = R(s) - Y(s) Figure E5.12 Speed control of a Ferris wheel. R(s) Desired speed Controller K 8+9 Disturbance T(s) Wheel and motor dynamics s+6 (5+2)(x+4) Y(s) Speed of rotation
E5.12 The Ferris wheel is often featured at state fairs and carnivals. George Ferris was born in Galesburg, Illinois, in 1859; he later moved to Nevada and then graduated from Rensselaer Polytechnic Institute in 1881. By 1891, Ferris had considerable experience with iron, steel, and bridge construction. He conceived and constructed his famous wheel for the 1893 Columbian Exposition in Chicago [8]. Consider the requirement that the steady-state speed must be controlled to within 5% of the desired speed for the Ferris wheel speed control system shown in Figure E5.12. (a) Determine the required gain K to achieve the steady-state requirement. (b) For the gain of part (a), determine and plot the tracking error for a unit step disturbance. Does the speed change more than 5%? (Set R(s) = 0 and recall that the tracking error E(s)-R(s)-T(s).) E(s) = R(s) - Y(s) Figure E5.12 Speed control of a Ferris wheel. R(s) Desired speed Controller K 8+9 Disturbance T(s) Wheel and motor dynamics s+6 (5+2)(x+4) Y(s) Speed of rotation
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![E5.12 The Ferris wheel is often featured at state fairs and carnivals.
George Ferris was born in Galesburg, Illinois, in 1859; he later moved to
Nevada and then graduated from Rensselaer Polytechnic Institute in
1881. By 1891, Ferris had considerable experience with iron, steel, and
bridge construction. He conceived and constructed his famous wheel for
the 1893 Columbian Exposition in Chicago [8]. Consider the requirement
that the steady-state speed must be controlled to within 5% of the
desired speed for the Ferris wheel speed control system shown in Figure
E5.12.
(a) Determine the required gain K to achieve the steady-state
requirement.
(b) For the gain of part (a), determine and plot the tracking error for a
unit step disturbance. Does the speed change more than 5%? (Set
R(s) = 0 and recall that the tracking error E(s)-R(s)-T(s).)
E(s) = R(s) - Y(s)
Figure E5.12
Speed control of a Ferris wheel.
R(s)
Desired
speed
Controller
K
8+9
Disturbance
T(s)
Wheel and
motor dynamics
s+6
(5+2)(x+4)
Y(s)
Speed of
rotation](https://content.bartleby.com/qna-images/question/3f6c81c7-9a41-4014-8916-60df888d5014/d39cb1ce-907c-4a0b-88c3-eb1853a103bb/yr4uxph_processed.jpeg)
Transcribed Image Text:E5.12 The Ferris wheel is often featured at state fairs and carnivals.
George Ferris was born in Galesburg, Illinois, in 1859; he later moved to
Nevada and then graduated from Rensselaer Polytechnic Institute in
1881. By 1891, Ferris had considerable experience with iron, steel, and
bridge construction. He conceived and constructed his famous wheel for
the 1893 Columbian Exposition in Chicago [8]. Consider the requirement
that the steady-state speed must be controlled to within 5% of the
desired speed for the Ferris wheel speed control system shown in Figure
E5.12.
(a) Determine the required gain K to achieve the steady-state
requirement.
(b) For the gain of part (a), determine and plot the tracking error for a
unit step disturbance. Does the speed change more than 5%? (Set
R(s) = 0 and recall that the tracking error E(s)-R(s)-T(s).)
E(s) = R(s) - Y(s)
Figure E5.12
Speed control of a Ferris wheel.
R(s)
Desired
speed
Controller
K
8+9
Disturbance
T(s)
Wheel and
motor dynamics
s+6
(5+2)(x+4)
Y(s)
Speed of
rotation
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