ElmoMC SimplIQ Digital Servo Drives-Bell Command Reference - Manual (Page 291)

8.1.1 Automatic Gain Scheduling
The most common reason to change the control filter on the fly is a speed change.
When the motor moves very slowly, the encoder count frequency is slow. Because
speed estimates are based on encoder differences, it follows that the speed readouts
suffer great delays.
An example:
Suppose a control loop with a bandwidth of 300 Hz, and with the motor traveling at
500 count/sec. The average speed delay is
500
1
1msec
2
=
×
. At 300 Hz, this costs the
phase margin of 360 0 0 30 1 0 .0
Ч Ч =108 deg. As phase margins rarely exceed 50 deg, it
is not possible for the controller to remain stable.
The Digital Feedback Technologies tools consider these low-speed delays when
producing controller design.
The design result is a battery of 16 controllers; each fits a different time delay, thus
fitting another speed. The figure below depicts this.
Refernce
speed
LPF,
Antisymmetric,
1
st
order
•
Absolute
Value
1
2 speed
×
Delay
estimate
Controller #1
Controller #2
Controller#3
...
Controller #15
Controller #16
Selector
GS[4],GS[5]
Figure 17: Gain scheduling
The absolute reference speed is filtered. The gain scheduling function uses this filtered
speed to select the control filter to use from the bank of 16 controllers.
The low-pass filter is not symmetric: GS[4] sets the time constant when the speed
demand increases, GS[5] sets the time constant for speed demand decrease.
The separation is since when speed demand increases, we want the controller to
swiftly adapt and apply full bandwidth. On the other hand, when speed decreases we
allow some time for the actual speed to really be there, and only than reduce gains.
The gain scheduling is derived from the speed reference, not from the speed
feedback. This ensures that the gain scheduled control scheme will remain stable.
SimplIQ for Steppers Application Note The Position and Speed Controller
MAN-STECR (Ver. 1.1)
92