The transfer function between the control voltage v(s) (the input) and the speed w(s), and the shaft angle 0(s) of the motion of a DC motor is given in the following figure; e,(s) K, v(s) w(s) G(s) G,(s) → „(s) 0.2 G(s) %D s + 0.104 1 G2 (s) : = - Find the steady state speed of the motor when an input voltage of v(t) = 10 volts is applied and the feedback loop is broken (i.e., motor is working open loop). b. Now assume feedback loop is active and find the closed loop transfer function а. m between 0 ,(s) and e„(s). m c. Calculate maximum value of K1 that can be used if an oversh desired. (You may use the figure in page 8 of this test.) of Mp<16% is

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The transfer function between the control voltage v(s) (the input) and the speed w(s),
and the shaft angle 0(s) of the motion of a DC motor is given in the following figure;
0,(s)
K,
v(s)
w(s)
G(s)
G,(s)
→ (s)
0.2
G(s)
s + 0.104
G2(s)
S
a. Find the steady state speed of the motor when an input voltage of v(t)
is applied and the feedback loop is broken (i.e., motor is working open loop).
b. Now assume feedback loop is active and find the closed loop transfer function
between e
volts
m
0,(s)
and
0„(s).
c. Calculate maximum value of K1 that can be used if an overshoot of Mp<16% is
desired. (You may use the figure in page 8 of this test.)
d. Calculate range of values of K1 that will provide a rise time of less than 4.5
seconds. (Ignore the Mp constraint of part c)
Transcribed Image Text:The transfer function between the control voltage v(s) (the input) and the speed w(s), and the shaft angle 0(s) of the motion of a DC motor is given in the following figure; 0,(s) K, v(s) w(s) G(s) G,(s) → (s) 0.2 G(s) s + 0.104 G2(s) S a. Find the steady state speed of the motor when an input voltage of v(t) is applied and the feedback loop is broken (i.e., motor is working open loop). b. Now assume feedback loop is active and find the closed loop transfer function between e volts m 0,(s) and 0„(s). c. Calculate maximum value of K1 that can be used if an overshoot of Mp<16% is desired. (You may use the figure in page 8 of this test.) d. Calculate range of values of K1 that will provide a rise time of less than 4.5 seconds. (Ignore the Mp constraint of part c)
100
90
80
70
60
50
30
16%
20
5%
10
0.
0.0
0.2
0.4
0.6
0.8
1.0
40
(%) "w
Transcribed Image Text:100 90 80 70 60 50 30 16% 20 5% 10 0. 0.0 0.2 0.4 0.6 0.8 1.0 40 (%) "w
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