
The SimplIQ for Steppers Getting Started & Tuning and Commissioning Guide
MAN-BELGS (Ver. 1.1)
85
-360 -315 -270 -225 -180 -135 -90 -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
M
Figure 77: Schematic model of a DC motor
Mathematically it can be described by the set of equations
CT
EE
TBJiKT
KKE
dt
di
LEiRv
++==
==
++=
θθ
θω
&&&
&
(7)
where
is the applied voltage,
i
motor current,
resistance,
inductance,
back e.m.f.,
E
K
motor e.m.f. constant,
θ=ω
shaft speed angle,
θ
shaft angle,
motor torque,
shaft inertia,
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
is neglected is schematically described in Figure 78.
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