# Derivative Sampling Period (Td)

Determines how often (in update samples) the derivative of position error is calculated.

The formula for calculating the derivative sample period from Td is as follows:

Derivative Sample Period = (Td + 1) x PID Sample Period

Because the range for Td is 0 to 63, the shortest derivative sample period is as follows:

Derivative Sample Period = 1 × 62.5 µs = 62.5 µs

The longest derivative sample period is as follows:

Derivative Sample Period = 64 × 500 µs = 32 ms

Adjusting Td provides greater flexibility in tuning the PID loop derivative term. As Td is increased, you can use a proportionally lower value of Kd for similar results. You must start the Td parameter at its default value of 2 and make small adjustments as required by the motion system configuration.

For low inertia systems, Td must be set to a small value (0 or 1) so that the derivative is calculated often enough to provide adequate damping for servo loop stability.

Systems with higher inertia can benefit from larger values of Td. Because the higher inertia means that the position error cannot change quickly, it is acceptable to calculate the derivative less often. This means you can use a lower value of Kd, have the same effective amount of damping and the system is smoother with less torque noise from the derivative term.

In higher inertia systems, using a Td of zero and therefore a larger value for Kd results in increased torque noise and motor heating without any improvement in system stability.