Consider the following 2nd order open loop system j(t)+a?(t) + Ky(t) = R(s) Let Transfer Function of this system be G(s). If this system is used in a unity feedback control system (block diagram shown below), find the transfer function of the closed-loop system, C(s)/R(s), and then find the values of K and a such that the response of the closed-loop system to a unit step input has a peak time tp = ? sec and rise time tr= 5/6 sec. What is the maximum overshoot? Ku(t) G(s) C(s)

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Consider the following 2 nd order open loop system

\overset{y}{¨} (t) + a \overset{y}{?} (t) + Ky (t) = K u (t)

Let Transfer Function of this system be

G (s)

. If this system is used in a unity feedback control system (block diagram shown below), find the transfer function of the closed-loop system,

C (s) / R (s)

, and then find the values of

K

and

a

such that the response of the closed-loop system to a unit step input has a peak time

t_{p} = ? sec

and rise time

t_{r} = 5 ? /6 sec

. What is the maximum overshoot?

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