Integral Gain

Type:	Axis Parameter Register
Address:	RMC75: Gain Set #0: %MDn.62 Gain Set #1: %MDn.129 where n = 12 + the axis number RMC150: Gain Set #0: %MDn.62 Gain Set #1: %MDn.129 where n = 24 + the axis number RMC200: Gain Set #0: %MDn.201 Gain Set #1: %MDn.231 where n = 384 + the axis number
System Tag:	Gain Set #0: _Axis[n ].IntGain Gain Set #1: _Axis[n].IntGain_2 where n is the axis number
How to Find:	Axes Parameters Pane, All tab: Position/Velocity Control
Data Type:	REAL
Units:	Position Control: %/(pu∙sec) Velocity control: %/((pu/sec)∙sec) % = percent of maximum Control Output (default is 10V)
Range:	≥ 0
Default Value:	0

Description

General

This gain helps compensate for changing system dynamics, such as varying loads, and often aids the axis in rapidly reaching the Command Position or Command Velocity. A low gain slows the response of the axis to changes and may keep the axis from reaching the Command Position or Command Velocity. A gain that is too high may make the axis oscillate.

The Integral Gain controls how much of the Control Output is generated due to the accumulated Position Error or Velocity Error while in position control or velocity control, respectively. Position control is defined as when the Current Control Mode is Position PID. Velocity control is defined as when the Current Control Mode is Velocity PID.

Each gain of the axis contributes to the Control Output. The contribution from the Integral Gain is called the Integral Output Term. For both PID and I-PD, each control loop, the Integral Gain is multiplied by the control loop time and Position Error or Velocity Error and added to the Integral Output Term. The Integral Output term is added to the PFID Output.

See the Tuning topic for details on how to properly adjust the Integral Gain.

The Integral Gain may be disabled or only be allowed to decrease the Integral output Term under certain conditions. See below for more details.

Advanced: I-PD

This gain is the most important gain for I-PD control. It must be non-zero in I-PD mode. If it is zero, it will cause a run-time error. A higher value will increase the response. A value that is too high will cause oscillation and instability.

Special Conditions

Integrator Hold

The Integral Gain can be disabled by the user by setting the Integrator Mode to Always Held. The Integrator Output Term will be held at the value at the time it was set.

The Integrator Hold does not apply to Position I-PD or Velocity I-PD, since the integrator is an important part of the I-PD control.

Integrator Adjust

The Integral Output Term can be manually adjusted with the Integrator Adjust (70) command. This is useful for clearing it if it has "wound up" for some reason. See the Integrator Adjust (70) topic for more details.

Integral Gain is Zero

If the Integral Gain is zero, the Integral Output Term will be set to zero.

Output Limiting

When the sum of the Proportional Term and the Integral Term reaches 100%, the Integral Output Term may be reduced to limit the PFID Output. This helps to avoid overshoot. This applies to all control modes.

Example:

If the Proportional Output Term is 60%, and the Integral Output Term is 50%, then the total is 110%. This will be limited to 100%, so the Integral Output Term will be set to 40%.

Wind-Down Only

In the Position PID control mode, the Integral Output Term will only be allowed to decrease in the following conditions:.

Within Deadband Window
When the target is stopped, and the Position Error is less than the Deadband Tolerance, the Integral Output Term will only be allowed to wind down. In systems with a deadband, this avoids ratcheting the axis back and forth around the deadband. See the Output Deadband topic for more details.
Within one-half count of Command Position
When the axis is within one-half count of the Command Position, the Integral Gain is only allowed to decrease the Integral Output Term. This is similar to the deadband case. Except in the rare case when the axis is scaled such that the transducer feedback counts match up exactly with the position units, there will always be a small difference between the Command Position and the nearest feedback count. Normally, this would cause the axis to "hunt" for the command position. Constraining the Integral Output Term to only decrease prevents the axis from "hunting".

Mathematical Definition

PID and I-PD

The Integral Output Term is calculated from the Integral Gain as follows:

In = (en x Ki x T) + In-1

where

In = Integral Term [% of maximum Control Output]

en = Position Error at sample n [cu]

Ki = Integral Gain [% / (cu x sec)]

T = Time period of control loop [sec]

cu = control unit (position-unit or velocity-unit)

The Integral Gain units are: percent of the maximum Control Output per unit of control (position, velocity, pressure, force etc) of Position Error times time. The maximum Control Output is 10V, but can be changed using the Output Scale parameter.