ElmoMC SimplIQ Digital Servo Drives-Bell Getting Started - Manual (Page 85)

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
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 is neglected is schematically described in Figure 78.