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a) Given the system, specifications, and the root locus shown in Figure 2: Speci

ID: 2292910 • Letter: A

Question

a) Given the system, specifications, and the root locus shown in Figure 2:

Specifications: steady state error due to a step less than or equal to 5% Settling time due to step less than or equal to 1 second Overshoot due to step less than or equal to 12% What type of controller would you design for this system? Justify your answer. (10 points)

b) Given the system, specifications, and the root locus shown in Figure 3:

??(??) = (?? + 4)/ ??(?? + 10)(?? + 2) Specifications: Zero steady state error due to a step Overshoot due to step less than or equal to 20% What type of controller would you design for this system? Justify your answer. (10 points)

25 0.44 0:32 0.23 0.1 0.05 0.6 15 15 0 10 084 5 0 0:84 10" 10 -15 0.6 15 -20 0:32 0.23 0.1 0.05 0.44 -25 -12 -10 2 Real Axis (seconds)

Explanation / Answer

from the given root locus the system transfer function is

s + 4
-------------------
s^3 + 12 s^2 + 20 s

this is a type one system.

since there is a requirement in the improvement in transient response the type of compensator / controller must be used is a LEAD CONTROLLER.

since this is a type one system the steady state error due to step input will always be zero