Question: Problem 1. ( 30 points) Consider the control system shwon in Fig. 1, where Dc(s) is the controller, and G(s) is the double integrator, i.e.,

Problem 1. ( 30 points) Consider the control system shwon in Fig. 1, where Dc(s) is the controller, and G(s) is the double integrator, i.e., G(s)=s21. 1) (15 points) Assume that a proportional controller ( P-controller) is used to control the system, i.e., Dc(s)=K. Rewrite the closed-loop characteristic equation in the rootlocus 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., Dc(s)=KP+KDs. Suppose that KP/KD=2, then rewrite the closed-loop characteristic equation in the root-locus form 1+KDL(s)=0. Sketch the root locus for L(s). Is it possible to stabilize the system using the PD-controller? Figure 1: Control system in Problem 1

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