Using MatLab, sovle following systems:

1. Consider the control system shown in the figure. Plot the root loci using MATLAB. K + 0.4 s(s 3.6) 2. Consider a unity-feedback system with the following feedforward transfer function G(s): K (s 2)2 G(s) = (n4)(s + 5) Plot root loci for the system with MATLAB. 3. Consider a unity-feedback control system with the following feedforward transfer function: K(s 25) 404s,+ 1600 G(s) = Plot root loci for the system with MATLAB. Show that the system is stable for all values of K > 0. 4. Consider an open loop system with a transfer function Y(s) U(s) 3 +7 H(s) =-= +5s15Xs +20) Design a feedback controller for the system by using the root locus method. Use the following design criteria: Overshoot = 596, Rise time = 1 second