modelPI_ContinuousVsDigital

Comparison between continuous time PID and its discrete time implementations

▶ Simulate in your browser

Extends from Modelica.Icons.Example (Icon for runnable examples).

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

Components

Type	Name	Description
LinearSystems.Continuous.TransferFunction	P_disc
Controllers.PID	R_disc
Modelica.Blocks.Sources.Step	SetPointSTEP
Controllers.PID	R_cont
Modelica.Blocks.Math.Feedback	sum1
Modelica.Blocks.Math.Feedback	sum2
Modelica.Blocks.Sources.Step	Disturb
Modelica.Blocks.Math.Feedback	sum3
Controllers.Digital.PID_2dof	R_dig
LinearSystems.Continuous.TransferFunction	P_cont
LinearSystems.Continuous.TransferFunction	P_dig
Modelica.Blocks.Sources.Ramp	SetPointRAMP
Modelica.Blocks.Logical.Switch	switch
Modelica.Blocks.Sources.BooleanConstant	SelectSP	if true the SP is a step, otherwise is a ramp

Revisions

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