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Consider the transfer function of a 2nd order system given by: G₁(s) = a/(s² + bs + k) where a, b, and k are tunable/choosable positive real constants. (a) We would like that the unit step response of this system reaches steady state in 0.5 seconds (i.e., the 2% settling time is 0.5 second) with an overshoot of 10%. Moreover, we would like that the system is at 0.75 in steady state. What are the values of a, b, and k that satisfy these characteristics? (b) If we were to double the value of k found from the previous step, how would settling time, overshoot, and final value of the system change? Please show/calculate.

Consider the transfer function of a 2nd order system given by: G₁(s) = a/(s² + bs + k) where a, b, and k are tunable/choosable positive real constants. (a) We would like that the unit step response of this system reaches steady state in 0.5 seconds (i.e., the 2% settling time is 0.5 second) with an overshoot of 10%. Moreover, we would like that the system is at 0.75 in steady state. What are the values of a, b, and k that satisfy these characteristics? (b) If we were to double the value of k found from the previous step, how would settling time, overshoot, and final value of the system change? Please show/calculate.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Consider the transfer function of a 2nd order system given by: G₁(s) = a/(s² + bs + k) where a, b, and kare tunable/choosable positive real constants. (a) We would like that the unit step response of this system reaches steady state in 0.5 seconds (i.e., the 2% settling time is 0.5 second) with an overshoot of 10%. Moreover, we would like that the system is at 0.75 in steady state. What are the values of a, b, and k that satisfy these characteristics? (b) If we were to double the value of k found from the previous step, how would settling time, overshoot, and final value of the system change? Please show/calculate.
Transcribed Image Text:Consider the transfer function of a 2nd order system given by: G₁(s) = a/(s² + bs + k) where a, b, and kare tunable/choosable positive real constants. (a) We would like that the unit step response of this system reaches steady state in 0.5 seconds (i.e., the 2% settling time is 0.5 second) with an overshoot of 10%. Moreover, we would like that the system is at 0.75 in steady state. What are the values of a, b, and k that satisfy these characteristics? (b) If we were to double the value of k found from the previous step, how would settling time, overshoot, and final value of the system change? Please show/calculate.
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