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system are given below: i(t) (input) (output) i(t) i(t) = i1(t) + iz(t) i₂(t) = dv(t) dt reference R(S) di₁(t) v(t)= i(t)R+ L dt Assume zero initial conditions, i.e., i1(0) = 0 and v(0) = 0. Problem 2 You are supervising your young middle school cousin in their science project in which they are using the RLC circuit above to power a battery charger. The output voltage across the capacitor is used to charge the battery. Your cousin suspects the components used in the circuit to be faulty, i.e., their values might be changing over time (e.g., due to temperature at the time of experiment). When your cousin repeated the same experiment with a constant current input of i(t) = 2 u(t), they found that the output voltage v(t) could settle down to any value between 2 and 4 during different test runs, i.e., feedback controller i(t) = 2u(t) v(oo) (in steady-state) can take any value between 2 to 4 error h(t) a) Can you use Final Value Theorem to confirm that the resistor is faulty (e.g., temperature-sensitive), with its value varying between 1 and 2? G(s) C For the battery charger to work properly, the output voltage v(t) needs to be maintained within ±10% of a target value of 3 unit, i.e., (control objective) v() should stay within ±10% of the reference value of 3 unit. b) Could you help your cousin achieve this by designing a simple proportional controller? input X(s) + E(S)=R(S)-Y(s) v(t) K(s) output Y(s) Note: In the closed-loop system, X(s) = I(s) is the programmable current input, Y(s) = V(s) is the output voltage, R(s)=3/s is the reference voltage. You have already identified the plant transfer function K(s). All you need to do is design a proportional gain G, i.e., G(s) = G, such that the steady state relative tracking error is within ±10%

system are given below: i(t) (input) (output) i(t) i(t) = i1(t) + iz(t) i₂(t) = dv(t) dt reference R(S) di₁(t) v(t)= i(t)R+ L dt Assume zero initial conditions, i.e., i1(0) = 0 and v(0) = 0. Problem 2 You are supervising your young middle school cousin in their science project in which they are using the RLC circuit above to power a battery charger. The output voltage across the capacitor is used to charge the battery. Your cousin suspects the components used in the circuit to be faulty, i.e., their values might be changing over time (e.g., due to temperature at the time of experiment). When your cousin repeated the same experiment with a constant current input of i(t) = 2 u(t), they found that the output voltage v(t) could settle down to any value between 2 and 4 during different test runs, i.e., feedback controller i(t) = 2u(t) v(oo) (in steady-state) can take any value between 2 to 4 error h(t) a) Can you use Final Value Theorem to confirm that the resistor is faulty (e.g., temperature-sensitive), with its value varying between 1 and 2? G(s) C For the battery charger to work properly, the output voltage v(t) needs to be maintained within ±10% of a target value of 3 unit, i.e., (control objective) v() should stay within ±10% of the reference value of 3 unit. b) Could you help your cousin achieve this by designing a simple proportional controller? input X(s) + E(S)=R(S)-Y(s) v(t) K(s) output Y(s) Note: In the closed-loop system, X(s) = I(s) is the programmable current input, Y(s) = V(s) is the output voltage, R(s)=3/s is the reference voltage. You have already identified the plant transfer function K(s). All you need to do is design a proportional gain G, i.e., G(s) = G, such that the steady state relative tracking error is within ±10%

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Please solve part a and b, will absolutely upvote!
system are given below: i(t) (input) (output) i(t) i(t)= i(t) + iz(t) dv(t) dt di₁(t) v(t)= i(t)R+ L- dt Assume zero initial conditions, i.e., i1(0) = 0 and v(0) = 0. i2(t) = C reference R(s) Problem 2 You are supervising your young middle school cousin in their science project in which they are using the RLC circuit above to power a battery charger. The output voltage across the capacitor is used to charge the battery. Your cousin suspects the components used in the circuit to be faulty, i.e., their values might be changing over time (e.g., due to temperature at the time of experiment). When your cousin repeated the same experiment with a constant current input of i(t) = 2 u(t), they found that the output voltage v(t) could settle down to any value between 2 and 4 during different test runs, i.e., i(t) = 2 u(t) v(xo) (in steady-state) can take any value between 2 to 4 feedback controller 1₂(t) a) Can you use Final Value Theorem to confirm that the resistor is faulty (e.g., temperature-sensitive), with its value varying between 1 and 2? For the battery charger to work properly, the output voltage v(t) needs to be maintained within ±10% of a target value of 3 unit, i.e., (control objective) v(oo) should stay within ±10% of the reference value of 3 unit. C b) Could you help your cousin achieve this by designing a simple proportional controller? G(s) input X(s) v(t) error E(S)=R(S)-Y(s) K(s) output Y(s) Note: In the closed-loop system, X(s) I(s) is the programmable current input, Y(s) = V(s) is the output voltage, R(s) = 3/s is the reference voltage. You have already identified the plant transfer function K(s). All you need to do is design a proportional gain G, i.e., G(s) = G, such that the steady state relative tracking error is within ±10%. BAZAART
Transcribed Image Text:system are given below: i(t) (input) (output) i(t) i(t)= i(t) + iz(t) dv(t) dt di₁(t) v(t)= i(t)R+ L- dt Assume zero initial conditions, i.e., i1(0) = 0 and v(0) = 0. i2(t) = C reference R(s) Problem 2 You are supervising your young middle school cousin in their science project in which they are using the RLC circuit above to power a battery charger. The output voltage across the capacitor is used to charge the battery. Your cousin suspects the components used in the circuit to be faulty, i.e., their values might be changing over time (e.g., due to temperature at the time of experiment). When your cousin repeated the same experiment with a constant current input of i(t) = 2 u(t), they found that the output voltage v(t) could settle down to any value between 2 and 4 during different test runs, i.e., i(t) = 2 u(t) v(xo) (in steady-state) can take any value between 2 to 4 feedback controller 1₂(t) a) Can you use Final Value Theorem to confirm that the resistor is faulty (e.g., temperature-sensitive), with its value varying between 1 and 2? For the battery charger to work properly, the output voltage v(t) needs to be maintained within ±10% of a target value of 3 unit, i.e., (control objective) v(oo) should stay within ±10% of the reference value of 3 unit. C b) Could you help your cousin achieve this by designing a simple proportional controller? G(s) input X(s) v(t) error E(S)=R(S)-Y(s) K(s) output Y(s) Note: In the closed-loop system, X(s) I(s) is the programmable current input, Y(s) = V(s) is the output voltage, R(s) = 3/s is the reference voltage. You have already identified the plant transfer function K(s). All you need to do is design a proportional gain G, i.e., G(s) = G, such that the steady state relative tracking error is within ±10%. BAZAART
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