Q6]A de motor is a fairly simple electric motor that uses electricity and magnetic field togenerate torque, which turns the rotor and hence give mechanical work. It can be modelledby the following differential equation:Jad w (t)dt+ (b + K₂ K) w(t) = Kt v(t)eRaWhere w (t) is the angular velocity of the motor and v(t) is the voltage applied. The constantsJ, b, and K, are associated with mechanical parts of the motor while Ke and Ra areassociated with electrical parts of the motor. All mechanical and electrical parameters areassumed to be positive.a) Define the input and output of the motor and their units.b) Is the time-model differential equation describing the motor dynamic behavior lineartime-invariant? Justify your answer.c) Let W(s) and V(s) denote the Laplace transforms of w(t) and v(t) respectively.Show that the transfer function from V(s) to W (s) is :T(s) =W(s) xV(s) s+ß=KtKtWhere x= K and B = + Koke).J RaJ Rad) Represent the system in the form of a block diagram.e) Determine the value of the steady-state gain K and the time constant T in terms ofand ß.f) Compute the pole of the motor model and conclude about its stability.g) Show that the step response of the dc motor, i.e. the angular velocity w(t) when v(t)is a unit step u(t), is given by :w (t) = (1 - e-Bt) u(t).

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Q6] A dc motor is a fairly simple electric motor that uses electricity and magnetic field t generate torque, which turns the rotor and hence give mechanical work. It can be modelle by the following differential equation: d w(t) J + (b + K₂ K¹) w(t) = K₁ v(t) . dt Ra Ra Where w(t) is the angular velocity of the motor and v(t) is the voltage applied. The constam J,b, and K, are associated with mechanical parts of the motor while Ke and Ra a associated with electrical parts of the motor. All mechanical and electrical parameters a assumed to be positive.

Q6] A dc motor is a fairly simple electric motor that uses electricity and magnetic field t generate torque, which turns the rotor and hence give mechanical work. It can be modelle by the following differential equation: d w(t) J + (b + K₂ K¹) w(t) = K₁ v(t) . dt Ra Ra Where w(t) is the angular velocity of the motor and v(t) is the voltage applied. The constam J,b, and K, are associated with mechanical parts of the motor while Ke and Ra a associated with electrical parts of the motor. All mechanical and electrical parameters a assumed to be positive.

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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