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4. The motion of the pitch angle of the helicopter in Figure 3 can be described using the following transfer function, where is the angular displacement, and T is the input torque: a) G(s) = ©(s) = 5 T(s) 7s2 +21s+7 Figure 3 Find the value of the damping ratio and report type of response (i.e., underdamped, overdamped, or critically damped). Designing a Proportional-plus-Derivative (PD) controller to control the angular displacement with negative unity feedback. b) c) d) Draw a block diagram of the closed-loop system with the PD controller. Find the PD controller gains such that the peak time of the closed-loop response is л/4 seconds and the 2% settling time is 4/3 seconds. For the closed-loop system, find the value of the damping ratio and report type of response. Find the steady-state error of the closed-loop system to a unit step input. Comment on the effect of the PD controller on the steady-state error. In order to eliminate the steady-state error, which control action is needed?

4. The motion of the pitch angle of the helicopter in Figure 3 can be described using the following transfer function, where is the angular displacement, and T is the input torque: a) G(s) = ©(s) = 5 T(s) 7s2 +21s+7 Figure 3 Find the value of the damping ratio and report type of response (i.e., underdamped, overdamped, or critically damped). Designing a Proportional-plus-Derivative (PD) controller to control the angular displacement with negative unity feedback. b) c) d) Draw a block diagram of the closed-loop system with the PD controller. Find the PD controller gains such that the peak time of the closed-loop response is л/4 seconds and the 2% settling time is 4/3 seconds. For the closed-loop system, find the value of the damping ratio and report type of response. Find the steady-state error of the closed-loop system to a unit step input. Comment on the effect of the PD controller on the steady-state error. In order to eliminate the steady-state error, which control action is needed?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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4. The motion of the pitch angle of the helicopter in Figure 3 can be described using the following transfer function, where is the angular displacement, and T is the input torque: a) G(s) = ©(s) = 5 T(s) 7s2 +21s+7 Figure 3 Find the value of the damping ratio and report type of response (i.e., underdamped, overdamped, or critically damped). Designing a Proportional-plus-Derivative (PD) controller to control the angular displacement with negative unity feedback. b) c) d) Draw a block diagram of the closed-loop system with the PD controller. Find the PD controller gains such that the peak time of the closed-loop response is л/4 seconds and the 2% settling time is 4/3 seconds. For the closed-loop system, find the value of the damping ratio and report type of response. Find the steady-state error of the closed-loop system to a unit step input. Comment on the effect of the PD controller on the steady-state error. In order to eliminate the steady-state error, which control action is needed?
Transcribed Image Text:4. The motion of the pitch angle of the helicopter in Figure 3 can be described using the following transfer function, where is the angular displacement, and T is the input torque: a) G(s) = ©(s) = 5 T(s) 7s2 +21s+7 Figure 3 Find the value of the damping ratio and report type of response (i.e., underdamped, overdamped, or critically damped). Designing a Proportional-plus-Derivative (PD) controller to control the angular displacement with negative unity feedback. b) c) d) Draw a block diagram of the closed-loop system with the PD controller. Find the PD controller gains such that the peak time of the closed-loop response is л/4 seconds and the 2% settling time is 4/3 seconds. For the closed-loop system, find the value of the damping ratio and report type of response. Find the steady-state error of the closed-loop system to a unit step input. Comment on the effect of the PD controller on the steady-state error. In order to eliminate the steady-state error, which control action is needed?
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