Consider a plant G(s)- 3+3 (3 1)(s + 8 +17) controlled by a proportional controller gain...

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Consider a plant G(s)- 3+3 (3− 1)(s² + 8 +17) controlled by a proportional controller gain K in a negative unitary feedback loop. 3.1) Sketch or use MATLAB to draw the root-locus for the system and determine an appropriate range of the controller gain for stability. As you increase the value of K, do you expect to see an increase or a decrease in the settling time of the unit-step response to the closed-loop system? Please justify your answers. 3.2) Assume a closed-loop system is already designed to be stable, but the resulting gain and phase margins are quite small. What type of compensator (lead or lag) would you add to the system so as to improve these margins? Please justify your answer in detail. 3.3) Pick a proportional control gain from your range in 3.1) and determine the corresponding gain margin for that design. Is it possible to design a controller you've specified in 3.2) to double the original gain margin. If so, please provide such a design and it's bode plots to show the gain margin. If not possible, please justify your answer. Consider a plant G(s)- 3+3 (3− 1)(s² + 8 +17) controlled by a proportional controller gain K in a negative unitary feedback loop. 3.1) Sketch or use MATLAB to draw the root-locus for the system and determine an appropriate range of the controller gain for stability. As you increase the value of K, do you expect to see an increase or a decrease in the settling time of the unit-step response to the closed-loop system? Please justify your answers. 3.2) Assume a closed-loop system is already designed to be stable, but the resulting gain and phase margins are quite small. What type of compensator (lead or lag) would you add to the system so as to improve these margins? Please justify your answer in detail. 3.3) Pick a proportional control gain from your range in 3.1) and determine the corresponding gain margin for that design. Is it possible to design a controller you've specified in 3.2) to double the original gain margin. If so, please provide such a design and it's bode plots to show the gain margin. If not possible, please justify your answer.