(Solved): 4. The following Root Locus plot is obtained using Matlab for the following feedback system. (1) D ...

4. The following Root Locus plot is obtained using Matlab for the following feedback system. (1) Determine the departing angle \( \phi_{1, d e p} \) from a pole at \( -1+j 3 \). (2) The closed loop system becomes unstable when the root locus crosses an imaginary axis. In the above plot, the point A shows when the root locus crosses the imaginary axis. Using the following RL rule of \( K=\frac{\left|s_{1}-p_{1}\right|\left|s_{1}-p_{2}\right| \cdots\left|s_{1}-p_{n}\right|}{\left|s_{1}-z_{1}\right|\left|s_{1}-z_{2}\right| \cdots\left|s_{1}-z_{m}\right|} \) validate the value of the gain \( K=44.6 \) in the plot at A. Note that \( K \) of \( 44.6 \) is an approximate value for \( \mathrm{CL} \) pole of \( 0+j 3.67 \).