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5. Consider the feedback control system shown in Fig. 5. Let $K_p = 0$, i.e., the controller is an integral controller $K(s) = K_i/s$. (5a) Determine the value of $K_i$ so that the closed-loop system has damping ratio $\zeta = 0.707$. (5b) Then find the natural frequency $\omega_n$ and the transfer functions $Y(s) / R(s)$ and $U(s) / R(s)$ of the closed-loop system. (5c) Plot the output response $y(t)$ and control input $u(t)$ due to the reference input $r(t) = 20u_\text{}(t)$ on separate graphs using these two transfer functions and the MATLAB \"step\" command. Page 1 of 2 Fig.5 $G(s) = \frac{145.5}{s + 43.14}$ $K(s) = K_p + \frac{K_i}{s}$

          5. Consider the feedback control system shown in Fig. 5. Let $K_p = 0$, i.e., the controller is an integral controller $K(s) = K_i/s$.
(5a) Determine the value of $K_i$ so that the closed-loop system has damping ratio $\zeta = 0.707$.
(5b) Then find the natural frequency $\omega_n$ and the transfer functions $Y(s) / R(s)$ and $U(s) / R(s)$ of the closed-loop system.
(5c) Plot the output response $y(t)$ and control input $u(t)$ due to the reference input $r(t) = 20u_\text{}(t)$ on separate graphs using these two transfer functions and the MATLAB \"step\" command.
Page 1 of 2
Fig.5
$G(s) = \frac{145.5}{s + 43.14}$
$K(s) = K_p + \frac{K_i}{s}$

5. Consider the feedback control system shown in Fig. 5. Let Kp = 0, i.e., the controller is an integral controller K(s) = Ki/s.
(5a) Determine the value of Ki so that the closed-loop system has damping ratio ζ = 0.707.
(5b) Then find the natural frequency and the transfer functions Y(s) / R(s) and U(s) / R(s) of the closed-loop system.
(5c) Plot the output response y(t) and control input u(t) due to the reference input r(t) = 20u(t) on separate graphs using these two transfer functions and the MATLAB s̈tepc̈ommand.
Page 1 of 2
Fig.5
G(s) = (145.5)/(s + 43.14)
K(s) = Kp + (Ki)/(s)

Added by Parker R.

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