WOLFRAM SYSTEM MODELER

PI

Discrete-time PI controller

Wolfram Language

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

Information

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

This block defines a discrete-time PI controller by the formula:

// State space form:
   x(ti) = previous(x(ti)) + u(ti)/Td;
   y(ti) = kd*(x(ti) + u(ti));

// Transfer function form:
   y(z) = kd*(c*z-1)/(z-1)*u(z);
          c = 1 + 1/Td

where kd is the gain, Td is the time constant, ti is the time instant of the i-th clock tick and z is the inverse shift operator.

This discrete-time form has been derived from the continuous-time form of a PI controller by using the implicit Euler discretization formula.

Parameters (2)

kd

Value:

Type: Real

Description: Gain of discrete PI controller

Td

Value:

Type: Real

Description: Time constant of discrete 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 (1)

ClockedWithDiscreteTextbookController

Modelica.Clocked.Examples.SimpleControlledDrive

Simple controlled drive with discrete textbook controller (period is not used in the controller)