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# How a PI Controller in a VFD Speed Control Works

Mike Keefe | November 21st, 2019

Across KEB’s line of inverters, a PI controller is used whenever closed-loop control is utilized.  This blog post and the accompanying YouTube video describe how this PI controller is used in a VFD to provide precise speed and torque control of the motor.

## What is the PI Algorithm?

The PI (Proportional and Integral) controller is a commonly used method in control systems to correct for error between the commanded setpoint and the actual value based on some type of feedback. KEB drives implement the PI controller in the speed control portion of the closed-loop control block diagram.

In the case of KEB drives, the PI controller is implemented in the speed control portion of the closed-loop control block diagram.  The command speed could be from a PLC, while the provided feedback can be from an encoder or calculated based on our Sensorless Closed Loop (SCL) control.

The first step of the PI controller is simply to calculate the margin of error between the commanded and actual speed at that specific point of time.  This error is then fed into the PI control algorithm, which can be broken into its respective Proportional and Integral parts.

### Proportional Control

The first step of the PI controller in a VFD is the proportional control, which is the simpler of the two.  The proportional control is used to immediately respond to any error between the command and actual speeds.  The larger the error, the more effect the proportional controller will have on the output in order to eliminate the error as quickly as possible.

The first term in this section is the Bias.  This is a constant value and is typically set equal to the initial commanded output.  Thus with no initial error, there would be a smooth transition from open to closed loop.

Added to this bias are the product of the error at that point in time and the proportional controller gain.  This gain is a programmable value in the KEB drive.  The higher the value, the quicker the control will adapt to error.  However, if the gain is too high, it will overshoot the command because it is over-controlling. Graphs showing VFD command speed (Black) vs. actual speed (Pink).

### Integral Control

The second step of the PI controller is the integral control, which adds a little bit more complexity to the control.  The integral control is used to eliminate long-term error and offset in the system.

Integral control still uses the proportional controller gain but adds the integral controller time constant, which is also programmable in the drive.  These two parameters influence each other, so it may take some trial and error in tuning the control to get them at their ideal values when first starting up a system.

Importantly, the integral control considers the complete integral sum of the error rather than the current size of the error.   Thus, the integral control will still be affecting the output if there is a built-up long-term error, even if there is no error at that specific point in time.  The other thing to note about the integral term is that it is dividing by the integral time constant.  Because of this, a smaller value will have more effect on the control. Graph showing the command speed (depicted with right angles) and the actual speed (curved line) as they eventually synchronize over time.