Derivative Gain (Kd)

Determines the contribution of restoring force proportional to the rate of change (derivative) of position error. This force acts much like viscous damping in a damped spring and mass mechanical system (for example, a shock absorber).

The PID loop computes the derivative of position error every derivative sampling period. This derivative term is multiplied by Kd every PID sample period to produce the derivative component of 16-bit DAC command output.

The formula for calculating the derivative contribution is as follows:
   
where the time between t1 and t0 is the derivative sample period.

A non-zero value for Kd is required for all systems that use torque block amplifiers (where the command output is proportional to motor torque) for the servo loop operation to be stable. Too small a Kd value will result in servo loop instability.

With velocity block amplifiers (where the command output is proportional to motor velocity), you typically set Kd to zero or to a very small value.