k2 Problem 1. (30 points) Consider the plant with transfer function G(s) standard feedback configuration with the controller De(s) = k + some parameters. s+1' = 1 = - connected in S where k and k are 1) Rewrite the closed-loop characteristic equation in the form 1+ KL(s) = 0, suitable for k2. the root locus method. You can assume for simplicity that k 2) Sketch the root locus for L(s). Explain what rules you used to plot it. Describe the behavior of the root locus branches as K varies from 0 to +. + Ro De(s) G(s) Y Figure 1: Control system in Problem 1.