PI

Proportional-Integral controller

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

Used in Examples (8)

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

ControlCircuit

Modelica.Electrical.Analog.Examples.OpAmps

Control circuit

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

Used in Components (3)

Controller

Modelica.Blocks.Examples.Noise.Utilities.Parts

Simple position controller for actuator

DQCurrentController

Modelica.Electrical.Machines.Utilities

Current controller in dq coordinate system

Controller

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Utilities

P-PI cascade controller for one axis