(Rigid shaft). z 1. in shaft 2:. B y. 4. 3. J m , B m. J L. 2. 1. 2. B. +. V k. K 2. Motor. . z 2. R a , L a. K i , K b. : Motor ’s current. F. r. 7. Modeling of Electromechanical Systems. Example 7.1 System with DC Motor.
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(Rigid shaft)
z1
in shaft 2:
By
4
3
Jm , Bm
JL
2
1
2
B
+
Vk
K2
Motor

z2
Ra , La
Ki , Kb
: Motor’scurrent
F
r
7. Modeling of Electromechanical Systems
Example 7.1 System with DC Motor
K2: Rotational spring constant of shaft numbered 2
Ra : Motor’s resistance
La : Motor’s inductance
Jm : Motor’s mass moment of inertia
Bm : Motor’s rotational damping coefficient
Ki : Motor’s torque constant
Kb : Motor’s back emf constant
Vk : Motor’s supply voltage
JL : Load’s mass moment of inertia
By : Rotational damping coefficient in bearings
(Rigid shaft)
z1
In shaft 2 :
By
4
3
Jm , Bm
JL
2
1
2
+
Vk
K2
DC Motor

z2
Ra , La
Ki , Kb
Lagrange Equation→
Homework 07Problem 1
Energy equations for Lagrange equation:
Input : Vk
;Generalized variables : qa, θm, θL
x(t)
k/2
Movable, m
R
b/2
Vk

+
fa(t)
C
k/2
b/2
Sabit
Example 7.2 Movable plate capacitor
Inputs: Vk(t) ve fa(t)
Generalized variables: q(t) ve x(t)
Lagrange equation→
Set of nonlinear differential equations
RungeKutta method
Linearization
Homework 07 Problem 2: Movable core inductance