ElmoMC SimplIQ Digital Servo Drives-Bell Getting Started - Manual (Page 86)

The SimplIQ for Steppers Getting Started & Tuning and Commissioning Guide
MAN-BELGS (Ver. 1.1)
86
R
1
T
K
i
Ls
−
J
1
s
1
B
−
E
K
+ θ
⋅
_
v T
Figure 78: Block diagram of the simplified DC motor model
The transfer function from voltage input, v , to motor shaft angle,
θ
, is
( )
R
L
,
K K
JR
;
s s s
K /
v
e
E T
m
m e m
E = τ = τ
τ τ + τ +
=
θ
2 1
1
& (8)
Usually,
e
τ
is much smaller then
m
τ
. The electrical time constant
e
τ
is normally
in the order of magnitude of 1 msec, whereas in low friction systems
m
τ
may be
in the order of 1 sec. If
m e
τ τ <<
, we can replace
m
s
τ
in the denominator of (8)
by
( )
e m
s
τ + τ
to get the approximation
( )( )
s s s
K
v
e m
E
τ τ
θ
+ +
=
1 1
/ 1
& (9)
Equation (9) is a common expression found in the literature and suits feedback
design where resonance effects can be neglected. We will now describe and
analyze motors with resonance.
B.3.2 Model with Flexible Transmission (resonance)
Figure 79 is a schematic representation of a ‘constant field’ motor with the load
connected to the motor shaft by a flexible axis.
L
B
Motor Load
1
M
2
M
ML
d
ML
c
M
θ
M
B
L
θ
Figure 79: Schematic connection of load via flexible coupling