The equations for an armature-controlled de motor (Figure 3) are the following. The Motor's current is i and its rotational velocity is w. L where L, R, and J are the motor's inductance, resistance, and inertia; Kr and Ke are the torque constant and back emf constant; c is a viscous damping constant; and v(t) is the applied voltage. di = Use the values R = 0.8 N, L = 0.003 H, KT and J = 8 x 10-5 kg⋅m². v(t) = + -=-Ri - K₂w+v(t) dw J = K₁i - cw dt V dt a) Suppose the applied voltage is 20 V. Plot the motor's speed and current versus time. Choose the simulation time period large enough to show the motor's speed becoming constant. b) Suppose the applied voltage is trapezoidal as given below. i Plot the motor's speed versus time for 0 ≤ t ≤ 0.3 s. Also plot the applied voltage versus time. How well does the motor speed follow a trapezoidal profile? For both a) and b), the initial conditions are i(0) = 0 and w(0) = 0. You can use either MATLAB programming (read Tutorial 1 for solving ODEs) or Simulink (read Lecture 3). R 0.05 N·m/A, K₂ = 0.05 V s/rad, c = 0 400t 20 0 ≤ t < 0.05 0.05 ≤ t ≤ 0.2 -400(t - 0.2) +20 0.2 0.25 L m Kew ∙I T= Kri Figure 3. The armature-controlled de motor of Problem 3. *000

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Transcribed Image Text:The equations for an armature-controlled dc motor (Figure 3) are the following. The Motor's current is i and its rotational velocity is w. L + di where L, R, and Jare the motor's inductance, resistance, and inertia; Kō and Ke are the torque constant and back emf constant; c is a viscous damping constant; and v(t) is the applied voltage. V dt Use the values R = 0.8 , L = 0.003 H, KT = 0.05 N·m/A, K₂ = 0.05 V s/rad, c = 0 and J = 8 x 10-5 kg. m². 20-{ v(t) = = −Ri - Kew+v(t) a) Suppose the applied voltage is 20 V. Plot the motor's speed and current versus time. Choose the simulation time period large enough to show the motor's speed becoming constant. b) Suppose the applied voltage is trapezoidal as given below. R M dw dt i = Kri - cw Plot the motor's speed versus time for 0 ≤ t ≤ 0.3 s. Also plot the applied voltage versus time. How well does the motor speed follow a trapezoidal profile? For both a) and b), the initial conditions are i(0) = 0 and w(0) = 0. You can use either MATLAB programming (read Tutorial 1 for solving ODEs) or Simulink (read Lecture 3). 400t 0 ≤ t < 0.05 0.05 ≤ t ≤ 0.2 20 −400(t – 0.2) +20 0.2 <t≤ 0.25 t> 0.25 0 L mo "I K.w T= Kri Figure 3. The armature-controlled de motor of Problem 3. (0) CO

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