Motor systems models, A simple model, B.3.1 – ElmoMC SimplIQ Digital Servo Drives-Bell Getting Started User Manual
Page 85: B.3 motor systems models, B.3.1 a simple model
The SimplIQ for Steppers Getting Started & Tuning and Commissioning Guide
MAN-BELGS (Ver. 1.1)
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-45
0
-40
-30
-20
-10
0
10
20
30
d
B
deg
ω=1.5
ω=2
ω=3
ω=5
ω=10
ω=20
ω=40
ω=60
ω=80
L(j
ω)
Figure 76: An example Nichols chart
B.3 Motor Systems Models
B.3.1 A Simple Model
A motor is a device that translates electrical energy into mechanical energy.
Figure 77 is a simplified schematic representation of a fixed magnet electrical
motor.
E
L
B
,
J
,
T
,
θ
v
Constant
Field
i
R
M
Figure 77: Schematic model of a DC motor
Mathematically it can be described by the set of equations
C
T
E
E
T
B
J
i
K
T
K
K
E
dt
di
L
E
iR
v
+
+
=
=
=
=
+
+
=
θ
θ
θ
ω
&
&
&
&
(7)
where
v
is the applied voltage,
i
motor current,
R
resistance,
L
inductance,
E
back e.m.f.,
E
K
motor e.m.f. constant,
θ
=
ω &
shaft speed angle,
θ
shaft angle,
T
motor torque,
J
shaft inertia,
B
shaft viscous friction, and
C
T
shaft coulomb
friction.
For linear control systems design, Equation 7 applies for both brush and brushless
DC motors.
Equations (7) where
C
T