Problem 7. For the system given in the figure on the right-hand side, where the input is four-unit step, r(t) = 4u(t)♥ (a) Find the value of gain K that yields 30% overshoot, (b) Find the peak time and settling time for this gain, (c) Find the steady-state and peak values of the response for this gain, R(s) K s²+s+2 1. 2K C(s)

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Problem 7. For the system given in the figure on the right-hand
side, where the input is four-unit step, r(t) = 4u(t).
(a) Find the value of gain K that yields 30% overshoot,
(b) Find the peak time and settling time for this gain,
(c) Find the steady-state and peak values of the response for
this gain,
(d) Determine the value of gain K to get the fastest response
without oscillation.
R(s)
K
s² +s+2
1
2
K
C(s)
(e) Simulate this control system in Simulink and plot the responses with 30% overshoot and fastest but no
oscillation on the same plane. Measure settling times of the responses on the plot.
Transcribed Image Text:Problem 7. For the system given in the figure on the right-hand side, where the input is four-unit step, r(t) = 4u(t). (a) Find the value of gain K that yields 30% overshoot, (b) Find the peak time and settling time for this gain, (c) Find the steady-state and peak values of the response for this gain, (d) Determine the value of gain K to get the fastest response without oscillation. R(s) K s² +s+2 1 2 K C(s) (e) Simulate this control system in Simulink and plot the responses with 30% overshoot and fastest but no oscillation on the same plane. Measure settling times of the responses on the plot.
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