Note: The plots using Matlab should include all important aspects related to the analysis. Specifically, the plots should show: 1. The uncompensated system. 2. The response of the uncompensated system. 3. The compensated system. 4. The response of the compensated system. These elements ensure a comprehensive representation of both the systems and their behaviors before and after compensation. Quent The forward transfer function of a unity feedback system in Figure 1 is given as: R(s) K G(s) = s(s+20)(s+40) G(s) C(s) Figure 1: A unity feedback system Use MATLAB sisotool to perform the following tasks by showing all related considerations and figures: (a) (b) Plot the Root Locus of the system Determine the uncompensated system's dominant poles, gain, and settling time, T, (at 2 % criterion) when it is operating at 20% overshoot (%OS). (c) (d) Design a lead compensator to decrease the achieve a transient response with a reduced settling time, T's(new) by a factor 2 without affecting the percent overshoot. With the obtained compensator zero (2.) and pole (P.), determine the appropriate compensated gain, Ke-