Question: Consider the control system shwon in Fig. 1, where De(s) is the controller, and G(s) is the double integrator, i.e., G(s) 1 - 1)

Consider the control system shwon in Fig. 1, where De(s) is the

Consider the control system shwon in Fig. 1, where De(s) is the controller, and G(s) is the double integrator, i.e., G(s) 1 - 1) (15 points) Assume that a proportional controller (P-controller) is used to control the system, i.e., De(s) H K. Rewrite the closed-loop characteristic equation in the root- locus form 1 + KL(s) = 0. Sketch the root locus for L(s). Is it possible to stabilize the system using the P-controller? 2) (15 points) Assume that a proportional-derivative controller (PD-controller) is used to control the system, i.e., De(s) = Kp + Kps. Suppose that Kp/Kp = 2, then rewrite the closed-loop characteristic equation in the root-locus form 1 + KpL(s) = 0. Sketch the root locus for L(s). Is it possible to stabilize the system using the PD-controller? DAS) Gls) -OY Figure 1: Control system in Problem 1.

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