A feedback control system has the structure shown in the figure below. Determine the closed-loop transfer function Y(s)/R(s) R(S) K₁ s+1 K₂ -15 Y(s) (a) by block diagram manipulation (Hint: Try using 4th transformation from Table 2.5 to get started) (b) by using a signal-flow graph and Mason's signal-flow gain formula. (c) Select the gains K1 and K2 so that the closed-loop response to a step input is critically damped with two equal roots at S = -10. (Hint: For Critically Damped the Characteristic Equations will have identical roots and might look like (s+somthing)^2) Answer: K1=100 and K2=0.19 (d) Plot the critically damped response for a unit step input. What is the time required for the step response to reach 90%
A feedback control system has the structure shown in the figure below. Determine the closed-loop transfer function Y(s)/R(s) R(S) K₁ s+1 K₂ -15 Y(s) (a) by block diagram manipulation (Hint: Try using 4th transformation from Table 2.5 to get started) (b) by using a signal-flow graph and Mason's signal-flow gain formula. (c) Select the gains K1 and K2 so that the closed-loop response to a step input is critically damped with two equal roots at S = -10. (Hint: For Critically Damped the Characteristic Equations will have identical roots and might look like (s+somthing)^2) Answer: K1=100 and K2=0.19 (d) Plot the critically damped response for a unit step input. What is the time required for the step response to reach 90%
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Just wanted to check this practice problem for controls to make sure everything is correct. Have a general sense of what I am doing but want to make sure my answers are correct for an upcoming test
![A feedback control system has the structure shown in the figure below. Determine the closed-loop transfer function
Y(s)/R(s)
R(S)
K₁
s+1
K₂
-15
S
Y(s)
(a) by block diagram manipulation (Hint: Try using 4th transformation from Table 2.5 to get started)
(b) by using a signal-flow graph and Mason's signal-flow gain formula.
(c) Select the gains K1 and K2 so that the closed-loop response to a step input is critically damped with two equal roots at
S = -10.
(Hint: For Critically Damped the Characteristic Equations will have identical roots and might look like (s+somthing)^2)
Answer: K1=100 and K2=0.19
(d) Plot the critically damped response for a unit step input. What is the time required for the step response to reach 90%
of its final value (Determine Graphically)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ae913c4-0dbf-45ec-8d5e-bc4c4bbed6e6%2F6296154a-7c2e-42c6-a56d-1913aff2a01f%2Ft789q5a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A feedback control system has the structure shown in the figure below. Determine the closed-loop transfer function
Y(s)/R(s)
R(S)
K₁
s+1
K₂
-15
S
Y(s)
(a) by block diagram manipulation (Hint: Try using 4th transformation from Table 2.5 to get started)
(b) by using a signal-flow graph and Mason's signal-flow gain formula.
(c) Select the gains K1 and K2 so that the closed-loop response to a step input is critically damped with two equal roots at
S = -10.
(Hint: For Critically Damped the Characteristic Equations will have identical roots and might look like (s+somthing)^2)
Answer: K1=100 and K2=0.19
(d) Plot the critically damped response for a unit step input. What is the time required for the step response to reach 90%
of its final value (Determine Graphically)?
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