You are here: Glossary > Lead-Lag PID Compensator

Lead-Lag PID Compensator

The typical configuration of the servo loop is a lead-lag implementation of a Proportional-Integral-Derivative (PID) compensator. It uses the transfer function that follows.

Where:

C is the full Proportional-Integral-Derivative compensator.

S is the variable for the Laplace transform.

K is the value of the ServoLoopGainK Parameter, which directly scales the feedback control effort.

Kip is the value of the ServoLoopGainKip Parameter and Kiv is the value of the ServoLoopGainKiv Parameter. They correspond to the two real-axis zeros of the transfer function in units of hertz (Hz).

In the lead-lag implementation of a Proportional-Integral-Derivative (PID) compensator, there are no servo gains that directly correspond to each of the P-I-D contributions. You can calculate the P-I-D contributions from the standard servo gains. Refer to the equations that follow:

Where:

P is the Proportional contribution of PID.

K is the value of the ServoLoopGainK Parameter.

Kip is the value of the ServoLoopGainKip Parameter.

Kiv is the value of the ServoLoopGainKiv Parameter.

I is the Integral contribution of PID.

D is the Derivative contribution of PID.