WOLFRAM SYSTEM MODELER
PIDiscrete-time PI controller |
SystemModel["Modelica.Clocked.RealSignals.Periodic.PI"]
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.
kd |
Value: Type: Real Description: Gain of discrete PI controller |
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Td |
Value: Type: Real Description: Time constant of discrete PI controller |
x |
Type: Real Description: Discrete PI state |
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u |
Type: RealInput Description: Connector of clocked, Real input signal |
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y |
Type: RealOutput Description: Connector of clocked, Real output signal |
ClockedWithDiscreteTextbookController Modelica.Clocked.Examples.SimpleControlledDrive Simple controlled drive with discrete textbook controller (period is not used in the controller) |