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A permanent magnet brushed DC motor (the type of motor that spins when connected to a constant voltage) can be described by the simplified model re + d- Kv, where o is the angle of the motor shaft, v is the voltage applied to the motor, r isa positive constant known as the motor time constant, and K de is a positive constant known as the motor speed constant. Dots indicate time derivatives, so d a) Find the transfer function for the motor (assuming initial conditions are zero), assuming v is the input and e is the output. (Use P(1) = C{ve) and O- CO) b) Consider the applied voltage is v) - M)-t - 2). Find the Laplace transform P(a) of the applied voltage. c) Uve the transfer function to find O), the Laplace domain position of the motor, when voltage P(4) from part b is applied to the motor. Use K-5, rl d) Use the inverse Laplace transform to compute ) for t>0. e) Sketch or plot the input voltage v) (defined in part b) and output position ) (computed in part d). Do these make sense based on how you expect a permanent magnet DC motor to behave?

A permanent magnet brushed DC motor (the type of motor that spins when connected to a constant voltage) can be described by the simplified model re + d- Kv, where o is the angle of the motor shaft, v is the voltage applied to the motor, r isa positive constant known as the motor time constant, and K de is a positive constant known as the motor speed constant. Dots indicate time derivatives, so d a) Find the transfer function for the motor (assuming initial conditions are zero), assuming v is the input and e is the output. (Use P(1) = C{ve) and O- CO) b) Consider the applied voltage is v) - M)-t - 2). Find the Laplace transform P(a) of the applied voltage. c) Uve the transfer function to find O), the Laplace domain position of the motor, when voltage P(4) from part b is applied to the motor. Use K-5, rl d) Use the inverse Laplace transform to compute ) for t>0. e) Sketch or plot the input voltage v) (defined in part b) and output position ) (computed in part d). Do these make sense based on how you expect a permanent magnet DC motor to behave?

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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Part d and e.

A permanent magnet brushed DC motor (the type of motor that spins when connected to a constant voltage) can be described by the simplified model re +ở - Kv, where e is the angle of the motor shaft, v is the voltage applied to the motor, r isa positive constant known as the motor time constant, and K de is a positive constant known as the motor speed constant. Dots indicate time derivatives, so ở d'e a) Find the transfer function for the motor (assuming initial conditions are zero), assuming v is the input and e is the output. (Use P(s) - C(vt)) and O- ClO) b) Consider the applied voltage is v) - t)- (t - 2). Find the Laplace transform P(s) of the applied voltage. c) Use the transfer function to find O(s), the Laplace domain position of the motor, when voltage P(3) from part b is applied to the motor. Use K-5, rm1 d) Use the inverse Laplace transform to compute ) for :>0. e) Sketch or plot the input voltage vr) (defined in part b) and output position e) (computed in part d). Do these make sense based on how you expect a permanent magnet DC motor to behave?
Transcribed Image Text:A permanent magnet brushed DC motor (the type of motor that spins when connected to a constant voltage) can be described by the simplified model re +ở - Kv, where e is the angle of the motor shaft, v is the voltage applied to the motor, r isa positive constant known as the motor time constant, and K de is a positive constant known as the motor speed constant. Dots indicate time derivatives, so ở d'e a) Find the transfer function for the motor (assuming initial conditions are zero), assuming v is the input and e is the output. (Use P(s) - C(vt)) and O- ClO) b) Consider the applied voltage is v) - t)- (t - 2). Find the Laplace transform P(s) of the applied voltage. c) Use the transfer function to find O(s), the Laplace domain position of the motor, when voltage P(3) from part b is applied to the motor. Use K-5, rm1 d) Use the inverse Laplace transform to compute ) for :>0. e) Sketch or plot the input voltage vr) (defined in part b) and output position e) (computed in part d). Do these make sense based on how you expect a permanent magnet DC motor to behave?
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