Find the equations for a DC motor with the equivalent electric circuit shown, Assume the rotor has inertia Jm andviscous friction coefficient b.Figure 2.34DC motor: (a) electriccircuit of the armature;(b) free-body diagramof the rotorRa1. the output m2. the output w == 0m-(a)Laīe=Kom0mbom(b)-m², b =In Example 2.15 of Chapter 2, assume that Jm = 0.02 kg ·0.005Nm sec, K₁ = K₂ = 0.5, Rå = 2.5 ₪, and La = 0.1H. Findthe transfer function between the input va and

Given Data: An Armature controlled DC motor with, Armature resistance Ra=2.5 𝞨 Armature…

Answered: nd the equations for a DC motor with…

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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Question

Find the equations for a DC motor with the equivalent electric circuit shown, Assume the rotor has inertia Jm and
viscous friction coefficient b.
Figure 2.34
DC motor: (a) electric
circuit of the armature;
(b) free-body diagram
of the rotor
Ra
1. the output m
2. the output w =
= 0m-
(a)
La
ī
e=Kom
0m
bom
(b)
-
m², b =
In Example 2.15 of Chapter 2, assume that Jm = 0.02 kg ·
0.005Nm sec, K₁ = K₂ = 0.5, Rå = 2.5 ₪, and La = 0.1H. Find
the transfer function between the input va and

Expert Solution

Step 1

Given Data:

An Armature controlled DC motor with,
- Armature resistance $R_{a} = 2.5 𝞨$
- Armature Inductance $L_{a} = 0.1 H$
- Armature voltage = $V_{a} V$
- Armature Current = $i_{a} A$
- Back EMF = $e V$
- Inertia $J_{m} = 0.02 {kg m}^{2}$
- Viscous friction Coefficient $b = 0.005 N-m . s$
- EMF Constant $K_{e} = 0.5$
- Torque Constant $K_{t} = 0.5$
- Angular Speed = $ω rad/s$
- Angular velocity $= θ_{m} degree$
Free body diagram and circuit diagram of DC motor

To Find:

Transfer function $\frac{θ_{m} (s)}{V_{a} (s)}$
Transfer function $\frac{V_{a} (s)}{ω (s)}$

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