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QUESTION 1 A motor is an electromechanical component that yields an angular displacement output for a voltage input, that is, a mechanical output generated by an electrical input. Figure (a), (b) and (c) below shows the motor's schematic, the block diagram and a typical equivalent mechanical loading on a motor, (0) Ra ww0000 - Part 2.. + Armature (0)| circuit (a) Tm(1) (1) fro Fixed field eeee Rotor T(0) (0) E() Dm G(s) (b) 0(x) where Ra and La are the resistance and inductance of the armature circuit, vb(t) is the voltage generated in the armature circuit. Tm(t) is the torque developed by the motor, Jm the equivalent inertia, Dm the equivalent viscous damping, ea(t) the input voltage, and m(t) the angular displacement output. Part 1. If given the torque T (t) = Ke (t)-K₂ de (t), where K, and K2 are two parameters of a motor, find dt differential equations to describe the relationship between input ea(t) and output 8(t) in time domain. Then derive a transfer function Om(s)/Ea(s) in the s-domain which models the motor. For the transfer function obtained in part 1, if a unit feedback is applied, find out the closed-loop system transfer function, and calculate the closed-loop system response to a step input ea(t)=1.3, given 0(s) if part 1 were 1 K₁ K2 Dm Jm 1. (Assume open-loop transfer function G(s) = - = E (s) s(s+2) unsuccessful)

QUESTION 1 A motor is an electromechanical component that yields an angular displacement output for a voltage input, that is, a mechanical output generated by an electrical input. Figure (a), (b) and (c) below shows the motor's schematic, the block diagram and a typical equivalent mechanical loading on a motor, (0) Ra ww0000 - Part 2.. + Armature (0)| circuit (a) Tm(1) (1) fro Fixed field eeee Rotor T(0) (0) E() Dm G(s) (b) 0(x) where Ra and La are the resistance and inductance of the armature circuit, vb(t) is the voltage generated in the armature circuit. Tm(t) is the torque developed by the motor, Jm the equivalent inertia, Dm the equivalent viscous damping, ea(t) the input voltage, and m(t) the angular displacement output. Part 1. If given the torque T (t) = Ke (t)-K₂ de (t), where K, and K2 are two parameters of a motor, find dt differential equations to describe the relationship between input ea(t) and output 8(t) in time domain. Then derive a transfer function Om(s)/Ea(s) in the s-domain which models the motor. For the transfer function obtained in part 1, if a unit feedback is applied, find out the closed-loop system transfer function, and calculate the closed-loop system response to a step input ea(t)=1.3, given 0(s) if part 1 were 1 K₁ K2 Dm Jm 1. (Assume open-loop transfer function G(s) = - = E (s) s(s+2) unsuccessful)

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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QUESTION 1 A motor is an electromechanical component that yields an angular displacement output for a voltage input, that is, a mechanical output generated by an electrical input. Figure (a), (b) and (c) below shows the motor's schematic, the block diagram and a typical equivalent mechanical loading on a motor, (0) R₂ 0000 Armature (1) circuit (a) Tm(1) (1) fro Fixed field elle Rotor Tm(1) ein E (s) Dm G(s) (b) 0,(x) (C) where Ra and La are the resistance and inductance of the armature circuit, vo(t) is the voltage generated in the armature circuit. Tm(t) is the torque developed by the motor, Jm the equivalent inertia, Dm the equivalent viscous damping, ea(t) the input voltage, and Om(t) the angular displacement output. Part 1. If given the torque T (t) = Ke (t)-K₂ differential equations to describe the relationship between input ea(t) and output Om(t) in time domain. Then derive a transfer function Om(s)/Ea(s) in the s-domain which models the motor. Part 2.. For the transfer function obtained in part 1, if a unit feedback is applied, find out the closed-loop system transfer function, and calculate the closed-loop system response to a step input ea(t)=1.3, given 0(s) K₁ K2=Dm Jm=1. (Assume open-loop transfer function G(s)=- if part 1 were E (s) unsuccessful) de(t), where K, and K2 are two parameters of a motor, find dt = 1 s(s+2)
Transcribed Image Text:QUESTION 1 A motor is an electromechanical component that yields an angular displacement output for a voltage input, that is, a mechanical output generated by an electrical input. Figure (a), (b) and (c) below shows the motor's schematic, the block diagram and a typical equivalent mechanical loading on a motor, (0) R₂ 0000 Armature (1) circuit (a) Tm(1) (1) fro Fixed field elle Rotor Tm(1) ein E (s) Dm G(s) (b) 0,(x) (C) where Ra and La are the resistance and inductance of the armature circuit, vo(t) is the voltage generated in the armature circuit. Tm(t) is the torque developed by the motor, Jm the equivalent inertia, Dm the equivalent viscous damping, ea(t) the input voltage, and Om(t) the angular displacement output. Part 1. If given the torque T (t) = Ke (t)-K₂ differential equations to describe the relationship between input ea(t) and output Om(t) in time domain. Then derive a transfer function Om(s)/Ea(s) in the s-domain which models the motor. Part 2.. For the transfer function obtained in part 1, if a unit feedback is applied, find out the closed-loop system transfer function, and calculate the closed-loop system response to a step input ea(t)=1.3, given 0(s) K₁ K2=Dm Jm=1. (Assume open-loop transfer function G(s)=- if part 1 were E (s) unsuccessful) de(t), where K, and K2 are two parameters of a motor, find dt = 1 s(s+2)
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