Q6 The block diagram shown in Figure Q6 is used Proportional controller to control a motor speed in a belt conveyor system. The plant transfer function is given by: 1 Gp(s) : %3D (s² + 9s + 20) R(s) + C(s) Kp Gp(S)

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Q6 The block diagram shown in Figure Q6 is used Proportional controller to control
a motor speed in a belt conveyor system. The plant transfer function is given by:
1
Gp(s) =
(s² + 9s + 20)
R(s) +
C(s)
Кр
Gp(s)
Figure Q6
(i). Develop the transfer function.
(ii). Evaluate whether the closed loop system is stable for control gain Kp= 3.
(iii). Compute the controller gain Kp so that step response shows 30%
overshoot.
(iv). Estimate the settling time for a step response input if the controller gain
Kp = 0.6.
Transcribed Image Text:Q6 The block diagram shown in Figure Q6 is used Proportional controller to control a motor speed in a belt conveyor system. The plant transfer function is given by: 1 Gp(s) = (s² + 9s + 20) R(s) + C(s) Кр Gp(s) Figure Q6 (i). Develop the transfer function. (ii). Evaluate whether the closed loop system is stable for control gain Kp= 3. (iii). Compute the controller gain Kp so that step response shows 30% overshoot. (iv). Estimate the settling time for a step response input if the controller gain Kp = 0.6.
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