(Solved): Use MATLAB to plot the root locus and the transient response. (a) You are given the unity-feedback s ...

(a) You are given the unity-feedback system of the figure above, where \[ G(s)=\frac{K(s+0.02)}{s^{2}(s+4)(s+10)(s+25)} \] Use MATLAB to plot the root locus. Use a closeup of the locus (from \( -5 \) to 0 and \( -1 \) to 6 ) to find the gain, \( K \), that yields a closed-loop unit-step response, \( c(t) \), with \( 20.5 \% \) overshoot and a settling time of \( T_{s}=3 \) seconds. Mark on the time response graph all other relevant characteristics, such as the peak time, rise time, and final steady-state value.