modelTestPD_bias

Test of the Proportional + Derivative controller with bias

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

Information

Description

In this example have been tested the proportional + Derivative controller.
The process to be controlled has the following transfer function

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

There are three processes:

without controller,
with a PD controller,
and a PD controller with bias signal

The output signal of the process without control diverges (due to the presence of an integrator) and is not reported.
In the closed loop system, the proportional + derivative controller cannot reach the SP reference, but it remains in a neighborhood of it. In this case theparameter Kp can reduce the amplitude of such a neighborhood. The disturb (red signal) can be rejected using the bias signal of the controller (pink line), otherwise the action does not reach a satisfactory performance (the Process Variable move away from the Set Point reference).

Discrete time

If the model parameter Ts is >=0 the continuous time controllers are replaced by their discrete time versions.
The effect of various discretisation method can be studied.

Parameters

Type	Name	Default	Description
Sampling time
Real	Ts	0	if Ts>=0 then discrete time controller, otherwise continuous time

Components

Type	Name	Default	Description
Modelica.Blocks.Sources.Step	SPstep
PD	R
Modelica.Blocks.Math.Feedback	sub2
PD	R_Bias
Modelica.Blocks.Math.Feedback	sub3
Modelica.Blocks.Sources.TimeTable	Disturbance
LinearSystems.Continuous.TransferFunction	ProcessCtrl
LinearSystems.Continuous.TransferFunction	processNoCtrl
LinearSystems.Continuous.TransferFunction	ProcessBias
Modelica.Blocks.Math.Feedback	sub1

Revisions

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