WOLFRAM SYSTEM MODELER

PI

Discrete-time PI controller with clocked input and output signals (for periodic and aperiodic systems using the parameterization of the continuous PI controller)

Wolfram Language

In[1]:=
SystemModel["Modelica.Clocked.RealSignals.NonPeriodic.PI"]
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Discrete-time PI controller that has been derived from the continuous-time PI controller 

              1
y = k * (1 + ---) * u
             T*s
        T*s + 1
  = k * ------- * u
          T*s

by using the implicit Euler discretization formula. The block is parametrized with the gain k and the time constant T of the continuous PI block. As a result, the discrete-time form of the PI controller depends explicitly on the sample time of the controller and changing this sample time, will give still a similar performance.

Parameters (2)

k

Value:

Type: Real

Description: Gain of continuous PI controller
T

Value:

Type: Real

Description: Time constant of continuous PI controller

Outputs (1)

x

Type: Real

Description: Discrete PI state

Connectors (2)

u

Type: RealInput

Description: Connector of clocked, Real input signal
y

Type: RealOutput

Description: Connector of clocked, Real output signal

Used in Examples (6)

ClockedWithDiscreteController

Modelica.Clocked.Examples.SimpleControlledDrive

Simple controlled drive with discrete controller (period is used in the controller)

ExactlyClockedWithDiscreteController

Modelica.Clocked.Examples.SimpleControlledDrive

Simple controlled drive with discrete controller and exact periodic clocks (period is used in the controller)

ClockedWith_AD_DA_Effects

Modelica.Clocked.Examples.SimpleControlledDrive

Simple controlled drive with discrete controller and simulated AD and DA effects

SubClocked

Modelica.Clocked.Examples.CascadeControlledDrive

Drive with clocked cascade controller where clocks are defined with sub-sampling and partitions with super-sampling

SuperSampled

Modelica.Clocked.Examples.CascadeControlledDrive

Drive with clocked cascade controller where fastest partition is defined with a clock and slower partition is defined with super-sampling

AbsoluteClocks

Modelica.Clocked.Examples.CascadeControlledDrive

Drive with clocked cascade controller where all partitions are defined with exact (integer) clock that need to be compatible to each other