Question 3 a) An automotive engineer is modelling the electrical circuit of an automotive proximity sensor. The engineer has come up with the following equation for the model of the circuit: f(t) = 2y + y(t) dt in which y(t) is the output and f(t) is the input. The engineer wants to find the transfer function of this model. Can you please help the engineer work out the transfer function along with the time constant and system's gain? Assume all initial conditions are zero. In your answer please include all calculations required. b) A fellow automotive engineer from the same automotive firm is developing a new control strategy for a passenger vehicle cabin's heating system. The system is modelled with the following 1st order differential equation, dy 2. dt + y = 0.8u in which y(t) is the output and u(t) is the input. Assuming all initial conditions are zero, help the engineer determine the response, y, if u = 5. Please show all calculations and workings in your answer. Hint: Given the initial conditions and the value of u, solve the differential equation using Laplace Transform and then convert the s- domain expression into time domain expression.
Question 3 a) An automotive engineer is modelling the electrical circuit of an automotive proximity sensor. The engineer has come up with the following equation for the model of the circuit: f(t) = 2y + y(t) dt in which y(t) is the output and f(t) is the input. The engineer wants to find the transfer function of this model. Can you please help the engineer work out the transfer function along with the time constant and system's gain? Assume all initial conditions are zero. In your answer please include all calculations required. b) A fellow automotive engineer from the same automotive firm is developing a new control strategy for a passenger vehicle cabin's heating system. The system is modelled with the following 1st order differential equation, dy 2. dt + y = 0.8u in which y(t) is the output and u(t) is the input. Assuming all initial conditions are zero, help the engineer determine the response, y, if u = 5. Please show all calculations and workings in your answer. Hint: Given the initial conditions and the value of u, solve the differential equation using Laplace Transform and then convert the s- domain expression into time domain expression.
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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Transcribed Image Text:Question 3
a) An automotive engineer is modelling the electrical circuit of an automotive proximity sensor. The engineer has
come up with the following equation for the model of the circuit:
f(t) = 2 + y(t)
dy
dt
in which y(t) is the output and f(t) is the input. The engineer wants to find the transfer function of this model. Can
you please help the engineer work out the transfer function along with the time constant and system's gain?
Assume all initial conditions are zero. In your answer please include all calculations required.
b) A fellow automotive engineer from the same automotive firm is developing a new control strategy for a
passenger vehicle cabin's heating system. The system is modelled with the following 1st order differential
equation,
2
dy
dt
+ y = 0.8u
in which y(t) is the output and u(t) is the input. Assuming all initial conditions are zero, help the engineer
determine the response, y, if u = 5. Please show all calculations and workings in your answer. Hint: Given the initial
conditions and the value of u, solve the differential equation using Laplace Transform and then convert the s-
domain expression into time domain expression.
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