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

 

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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. 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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