scaling

By popular demand, the topic scaling will be discusses in closer detail.

ecmc has to scaling factors for each joint, firstly the drive scaling, secondly the encoder scaling.

drive scaling

Drive scaling deals with the relation of the drive output (typically a 16- or 32-bit register) to axis velocity. Scaling is similar, but slightly different for stepper drives and servo drives

stepper motor drives

The scaling for the Ex70xx slaves will be explained based on two very common examples.

simple linear axis

Assumptions:

• 200 full-steps/rev motor
• lead screw pitch: 5 mm/rev
• Register 0x8012:05 is set to 1 –> 2000 full-steps max step rate (default for ECMC, check for other slaves!)
• velocitySetpoint is in 16-bits.

drive:
  numerator: 50        # Fastest speed in engineering units (2000 full steps / s --> 10 rev/s * 5 mm/rev --> 50 mm/s)
  denominator:  32768  # I/O range 2^15, because 16-bit register, half is forward, the other half is backward

explanation

The denominator is 32768 because the velocitySetpoint is a 16-register for the Beckhoff stepper drives. Thus, half of the full range is reserved for positive (forward) motion, the remaining half for negative (backward) motion. This means that at full output the motor would receive 2000 full-steps per second. It is irrelevant whether the motor can actually spin this fast as this a purely theoretical value! Since we have established that the motor spins at 10 rev/s at full output, the conversion to engineering units is trivial and yields 50 mm/s, based on the lead screw pitch.

rotational axis

Assumptions:

• 400 full-steps/rev motor
• drive train ratio: 36 deg/rev
• Register 0x8012:05 is set to 1 –> 2000 full-steps max step rate (default for ECMC, check for other slaves!)
• velocitySetpoint is in 16-bits.

drive:
  numerator: 180       # Fastest speed in engineering units (2000 full steps / s --> 5 rev/s * 36 deg/rev --> 180 deg/s)
  denominator:  32768  # I/O range 2^15, because 16-bit register, half is forward, the other half is backward

explanation

At full output, the motor receives 2000 full-steps/s, which results in 5 rev/s due to the higher full-step count of the motor. The drive train ratio is specified as 10 motor revolutions per 360 degree on the output or 36 deg/rev. Therefore, the resulting velocity of the motor in EGUs is 180 deg/s. Please note that this is not the actual maximum velocity, but rather a theoretical scaling factor for the PID-loop.

servo motor drives

This section is based on the Beckhoff servo motor drives (Ex72xx), AX-drives or drives from other vendors might differ. The Ex72xx servo motor drives from Beckhoff use a 32-bit register for the velocity setpoint. Therefore, the denominator takes on a value of 2^31 = 2147483648.

As for the numerator, the situation is a bit more complicated. The AM81xx synchronous motors come with different pole counts, most have 3 pole pairs, but some have 4. Naturally, this results in a different scaling for either type. At full output a 3 pole pair motor would spin at 8000 revolutions per second! Respectively, the 4 pole pair motor will assume 6000 rev/s. Since no servo motor will ever reach such speeds and the value is only used for the PID-loop scaling, no difference is noticeable in real life applications. Except when a motor is replaced by a different model with deviating pole pair count.

The following example shows a 3 pole pair motor scaled for operation in degrees. Therefore, the numerator equals 8000 rev/s * 360 deg/rev = 2880000 deg/s.

drive:
  numerator: 2880000         # Fastest speed in engineering units (8000 rev/s * 360 deg/rev)
  denominator:  2147483648   # I/O range 2^31, because 32-bit register, half is forward, the other half is backward

encoder scaling

This scaling ratio describes the relation of encoder counts and engineering units of the axis.

Unlike the drive scaling, the encoder scaling is much simpler. It represents merely the relation between the observed counts on the encoder and the displacement of the load.

closed-loop

Scaling absolute encoders is simple. This example shows a 32-bit encoder with 4096 ticks/mm, for an axis operated in mm.

encoder:
  numerator: 1
  denominator: 4096
  type: 1         # Type: 0=Incremental, 1=Absolute
  bits: 32        # Total bit count of encoder raw data

explanation

none, this should be simple enough!

open-loop

Obviously, for open-loop operation there is no encoder. In this case the internal step counter of the stepper motor drive is used as “encoder”. In the example below such a case is presented, with an explanation.

encoder:
  numerator: 0.125    # 0.125 mm/rev lead screw
  denominator: 12800  # 200 full-steps/rev with 64 micro-steps/full-step
  type: 0         # Type: 0=Incremental, 1=Absolute
  bits: 16        # Total bit count of encoder raw data

explanation

The internal step counter operates in micro-steps. For most drives this value assumes 64, if uncertain consult the respective manual of the drive. In case of a 200 full-steps/rev motor, the denominator therefore will be set to 200*64=12800. As for the numerator, this is simply the displacement observed for one full motor revolution. As the step counter is incremental, the type: 0 has to be set. The step counter is of type uint16, thus the bits: 16 setting, which is important to handle the over-/underflow.