(Solved): \#4: DC Motor Position Control using Proportional \& Integral Controller Consider the following fe ...

\#4: DC Motor Position Control using Proportional \& Integral Controller Consider the following feedback control system Assume \( G_{p}(s)=\frac{Y(s)}{U(s)}=\frac{10}{s(s+1)} \) and \( K(s)=K \), which is a proportional controller. (2a) Find the transfer functions of the closed-loop system, \( \frac{Y(s)}{R(s)} \) and \( \frac{E(s)}{R(s)} \). (2b) How to choose the value of \( K \) to achieve a desired damping ratio? (2c) What is the characteristic equation of the closed-loop system? What are the poles of the closed-loop system? (2e) Describe what determines the maximum overshoot and the time it occurs.