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The transfer function of a plant is given as: 25 T(s)= s²+3.5s+25 a) Find the poles of the system b) Use MATLAB to plot the time response of the system to unit step input. c) What is the overshoot percentage, the peak time, rise time, and 5% settling time? d) What can be done to reduce overshoot? Proportional Controller e) Draw a block diagram for the system and include a proportional controller with Proportional gain, Kp and a negative unity feedback loop. f) What value of Kp is required to achieve damping of 5=0.707 with Kp >0. Proportional-plus-derivative (PD) Controller g) Replace the proportional controller with a PD controller. Design the controller such that the damped frequency, @d, remains the same as the one in the original second order system T(s) and the damping ratio becomes <= 0.707? h) Find the steady-state response and steady-state error of the system to a unit step input. i) How would you reduce the steady-state error of the system? Proportional-plus-integral-plus-derivative (PID) Controller j) Add a PID controller with the controller gains of Kp and Ka found in part g). Find the integral controller gain K; such that one of the poles is -5. k) For part j), obtain the other poles. Is the system stable based on the poles?

The transfer function of a plant is given as: 25 T(s)= s²+3.5s+25 a) Find the poles of the system b) Use MATLAB to plot the time response of the system to unit step input. c) What is the overshoot percentage, the peak time, rise time, and 5% settling time? d) What can be done to reduce overshoot? Proportional Controller e) Draw a block diagram for the system and include a proportional controller with Proportional gain, Kp and a negative unity feedback loop. f) What value of Kp is required to achieve damping of 5=0.707 with Kp >0. Proportional-plus-derivative (PD) Controller g) Replace the proportional controller with a PD controller. Design the controller such that the damped frequency, @d, remains the same as the one in the original second order system T(s) and the damping ratio becomes <= 0.707? h) Find the steady-state response and steady-state error of the system to a unit step input. i) How would you reduce the steady-state error of the system? Proportional-plus-integral-plus-derivative (PID) Controller j) Add a PID controller with the controller gains of Kp and Ka found in part g). Find the integral controller gain K; such that one of the poles is -5. k) For part j), obtain the other poles. Is the system stable based on the poles?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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The transfer function of a plant is given as: 25 T(s)= s²+3.5s+25 a) Find the poles of the system b) Use MATLAB to plot the time response of the system to unit step input. c) What is the overshoot percentage, the peak time, rise time, and 5% settling time? d) What can be done to reduce overshoot? Proportional Controller e) Draw a block diagram for the system and include a proportional controller with Proportional gain, Kp and a negative unity feedback loop. f) What value of Kp is required to achieve damping of 5=0.707 with Kp >0. Proportional-plus-derivative (PD) Controller g) Replace the proportional controller with a PD controller. Design the controller such that the damped frequency, @d, remains the same as the one in the original second order system T(s) and the damping ratio becomes <= 0.707? h) Find the steady-state response and steady-state error of the system to a unit step input. i) How would you reduce the steady-state error of the system? Proportional-plus-integral-plus-derivative (PID) Controller j) Add a PID controller with the controller gains of Kp and Ka found in part g). Find the integral controller gain K; such that one of the poles is -5. k) For part j), obtain the other poles. Is the system stable based on the poles?
Transcribed Image Text:The transfer function of a plant is given as: 25 T(s)= s²+3.5s+25 a) Find the poles of the system b) Use MATLAB to plot the time response of the system to unit step input. c) What is the overshoot percentage, the peak time, rise time, and 5% settling time? d) What can be done to reduce overshoot? Proportional Controller e) Draw a block diagram for the system and include a proportional controller with Proportional gain, Kp and a negative unity feedback loop. f) What value of Kp is required to achieve damping of 5=0.707 with Kp >0. Proportional-plus-derivative (PD) Controller g) Replace the proportional controller with a PD controller. Design the controller such that the damped frequency, @d, remains the same as the one in the original second order system T(s) and the damping ratio becomes <= 0.707? h) Find the steady-state response and steady-state error of the system to a unit step input. i) How would you reduce the steady-state error of the system? Proportional-plus-integral-plus-derivative (PID) Controller j) Add a PID controller with the controller gains of Kp and Ka found in part g). Find the integral controller gain K; such that one of the poles is -5. k) For part j), obtain the other poles. Is the system stable based on the poles?
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