consider the system in figure 1 where G(s) takes the form Problem 3(9 Points) Co
ID: 2267255 • Letter: C
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consider the system in figure 1 where G(s) takes the form
Problem 3(9 Points) Consider the system in Figure 1 where G (s) takes the form 6(s) = (s+b) (s + c) (s + d) where a,b,c,d are positive constants. The closed-loop system is uncompensated when C(s) = K 2 0. We consider a compensated system with three possible types of compensators: Lag: (s) = Lead: C(s) = K +p),2p, (s+p) In what follows you are asked to choose the appropriate compensator to achieve a certain task. You are not required to design the compensator, but you are required to justify your choice. You may need to use the root locus or the Bode plots in your justification.Explanation / Answer
(A) As the lag compensator improves the steady state response of the uncompensated system, it can be used to decrease the steady state error appreciably.
(B) As the lead compensator improves transient response of the uncompensated system, it can be used to reduce the settling time appreciably and make the response become faster.
(C) As the lag compensator improves the steady state response of the uncompensated system, it can be used to increase the phase margin of the system with acceptable crossover frequency.
(D) As the lead compensator improves transient response of the uncompensated system, it can be used to increase the gain margin appreciably and make the system more stable.
(E) To obtain zero steady state error in response to a step inputs, we need a pole at the origin to increase the order of the system. Hence, PI compensator can be used to obtain no steady state error.
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