Consider the system shown in figure 1 below. r(s) к y(s) s+2 32-3s Plant Controller Figure 1: Simple proportional contro

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Consider the system shown in figure 1 below. r(s) к y(s) s+2 32-3s Plant Controller Figure 1: Simple proportional control system Suppose the control goal is to track a step input. a. What are the poles and zeroes of the open loop system? Is the open loop system stable? Can the open loop system track a step input? b. Suppose you use proportional feedback control as shown in figure 1. Explain why the scheme above is called proportional feedback. Explain how this scheme can be used to stabilize the system (hint: try and explain the how part mathematically). c. Can you make the system stable for all values of K? Explain. d. For what values of K is the system completely oscillatory? e. For what values of K is the system stable?