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WOLFRAM SYSTEM MODELER

PI

Proportional-Integral controller

Wolfram Language

In[1]:=

SystemModel["Modelica.Blocks.Continuous.PI"]

Out[1]:=

Information

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

This blocks defines the transfer function between the input u and the output y as PI system:

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

If you would like to be able to change easily between different transfer functions (FirstOrder, SecondOrder, ... ) by changing parameters, use the general model class TransferFunction instead and model a PI SISO system with parameters
b = {k*T, k}, a = {T, 0}.

Example:

   parameter: k = 0.3,  T = 0.4

   results in:
               0.4 s + 1
      y = 0.3 ----------- * u
                 0.4 s

It might be difficult to initialize the PI component in steady state due to the integrator part. This is discussed in the description of package Continuous.

Parameters (5)

k	Value: 1 Type: Real Description: Gain
T	Value: Type: Time (s) Description: Time Constant (T>0 required)
initType	Value: Init.NoInit Type: Init Description: Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output)
x_start	Value: 0 Type: Real Description: Initial or guess value of state
y_start	Value: 0 Type: Real Description: Initial value of output

Outputs (1)

x	Type: Real Description: State of block

Connectors (2)

	u	Type: RealInput Description: Connector of Real input signal
	y	Type: RealOutput Description: Connector of Real output signal

Type: RealInput

Description: Connector of Real input signal

Type: RealOutput

Description: Connector of Real output signal

Used in Examples (7)

	Continuous Modelica.Clocked.Examples.SimpleControlledDrive Simple controlled drive with continuous controller
	ClockedWithDiscretizedContinuousController Modelica.Clocked.Examples.SimpleControlledDrive Simple controlled drive with discretized continuous-time controller
	Continuous Modelica.Clocked.Examples.CascadeControlledDrive Drive with continuous-time cascade controller
	IMC_withLosses Modelica.Electrical.Machines.Examples.InductionMachines Test example: InductionMachineSquirrelCage with losses
	IMC_withLosses Modelica.Magnetic.FundamentalWave.Examples.BasicMachines.InductionMachines Induction machine with squirrel cage and losses
	IMC_withLosses Modelica.Magnetic.QuasiStatic.FundamentalWave.Examples.BasicMachines.InductionMachines Induction machine with squirrel cage and losses
	DrumBoiler Modelica.Fluid.Examples.DrumBoiler Complete drum boiler model, including evaporator and supplementary components