.IndustrialControlSystems.Applications.ControlProblems.PI_ContinuousVsDigital

Comparison between continuous time PID and its discrete time implementations

Information

Description

In this examples are compared three PID controllers:

Continuous time PID with two degrees of freedom (model PID (with Ts=0) ),
the discretised version of the continuous time PID with two degrees of freedom (model PID ),
and the digital implementation of the PID with two degrees of freedom in the incremental form (model PID_2dof ).

There controllers regulates a second order process with trasfer function

   Y(s)          (1+15s)
   ----  =  ----------------
   U(s)       (1+10s)(1+2s)

The following images show the SetPoint following and disturbance rejection without saturation

Set Point and Process Variables

Control Signals

To be noticed that the discretised version of the PID and the digital implementation of the incremental PID have the same behaviour.
The same is not valid when the saturation is introduced. If limiting the controller action between [0,2] the discrete time version and the digital one behave quite differently

Set Point and Process Variables

Control Signals

This difference is due to the nature of the digital implementation that is incremental, while the other two are positional.
This problem does not appear if the Set Point reference changes soothly, switching to a ramp Set Point signal, as shown in the following picture.

Process Variables and Control Signals with a ramp Set Point

Revisions

Industrial Control Systems (v 1.0.0) : April-May 2012