How Bandwidth (and Load Inertia) Determine Tuning Gains
Referenced Parameters
| Parameter | Description | Drive Keyword |
|---|---|---|
|
IL.KP |
Current Loop Proportional Gain |
|
|
VL.KI |
Velocity Loop Integral Gain |
|
|
VL.KP |
Velocity Loop Proportional Gain |
VL.KP
VL.KP = 2π * BW * (JM + JL) * 0.0001 / Kt
Notes:
• Where JM and JL are in units of kg-cm²
• BW is in units of Hz
• Kt is in units of N-m / Arms
VL.KP will bring the gain of the system up to a specific performance rating (bandwidth)
Therefore it is based on how strong the motor is (Kt – motor torque constant) and how much mass is attached to the motor (JM – motor shaft mass and JL – load mass).
VL.KI / VL.KP
VL.KI = BW * tan(2.5 deg)
Notes:
•
BW is in units of Hz
•
VL.KI is in units of Hz
There is no standard to how much velocity integral gain is needed on a system. The slider tuner makes a conservative assumption and sets the Velocity Loop Integral gain to contribute only 2.5 degrees of phase loss at the bandwidth requested.
PL.KP = BW * tan(2.5 deg)* 2π
Notes:
•
BW is in units of Hz
•
PL.KP is in units of (rev/s)/rev - can be converted to Hz by dividing by 2π
The needed position proportional gain will also vary from system to system. The slider tuner sets the Position Proportional Gain to contribute only 2.5 degrees of phase loss at the bandwidth requested.
Note:
All systems are different. Integral gains can be sensitive to mechanical oscillations and friction, the slider tuner may not be appropriate for some applications.
IL.KP = IL BW * 2π * Motor Inductance
Notes:
•
BW is in units of Hz
First a current loop bandwidth must be calculated
IL BW = 75Hz/tan(5) = 857Hz
Next, IL BW is clamped between 1000Hz and 2000Hz to maintain numerical accuracy and stability
IL BW = 1000
Note:
Default tuning will leave the current loop with ~1000Hz bandwidth. If manual tuning is used to achieve more than a few hundred Hz, IL.KP will need to be manually increased appropriately
