Discrete Time PID Controller (PIDz)¶

This controller is the counterpart to the ideal analog PID controller, type I. It consists of the parallel connection of a P-, a Iz and a Dz element, which can individually be switched off.

Since the same parameters exist (gain K, rate time TV and reset time TN) it allows a direct comparison between the analog and the discrete time implementation.

The output signal can be limited by two selectable anti-windup measures in the range Ymin ... Ymax.

Anti-Windup-Hold
The integration is stopped when the saturation's input signal leaves the valid range (the upper or lower limit of the saturation). As soon as the signal is reduced the integrator is released.

Anti-Windup-Reset
If the saturation's input signal exceeds the limit, the integrator's output signal is reduced so that the sum of integrator, differentiator and unit-gain equals exactly the limit (Ymax or Ymin).

Functions

Step response

Magnitude and phase response

Polar plot