WOLFRAM SYSTEMMODELER

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: Modelica.Blocks.Types.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

Used in Examples (4)

AIMC_withLosses

Modelica.Electrical.Machines.Examples.AsynchronousInductionMachines

Test example: AsynchronousInductionMachineSquirrelCage with losses

AIMC_withLosses

Modelica.Magnetic.FundamentalWave.Examples.BasicMachines

Asynchronous 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

Used in Components (3)

Controller

Modelica.Blocks.Examples.NoiseExamples.Utilities.Parts

Simple position controller for actuator

VoltageController

Modelica.Electrical.Machines.Utilities

Voltage controller

Controller

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components

P-PI cascade controller for one axis