PI

Proportional-Integral controller

    PI

Library

Modelica/Blocks/Continuous

Description

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

PI_0

NameLabelDescriptionData TypeValid Values

mo_k

k

Gain

Scalar

mo_T

T

Time Constant (T>0 required)

Scalar

mo_initType

initType

Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output)

Structure

mo_initType/choice1

No initialization (start values are used as guess values with fixed=false)

Number

0
1

mo_initType/choice2

Steady state initialization (derivatives of states are zero)

Number

0
1

mo_initType/choice3

Initialization with initial states

Number

0
1

mo_initType/choice4

Initialization with initial outputs (and steady state of the states if possible)

Number

0
1

mo_x_start

x_start

Initial or guess value of state

Scalar

mo_y_start

y_start

Initial value of output

Scalar

PI_1

NameLabelDescriptionData TypeValid Values

mo_u

u

u

Structure

mo_u/fixed

fixed

Cell of scalars

true
false

mo_u/start

start

Cell of scalars

mo_y

y

y

Structure

mo_y/fixed

fixed

Cell of scalars

true
false

mo_y/start

start

Cell of scalars

mo_x

x

x

Structure

mo_x/fixed

fixed

Cell of scalars

true
false

mo_x/start

start

Cell of scalars

Ports

NameTypeDescriptionIO TypeNumber

u

implicit

Connector of Real input signal

input

1

y

implicit

Connector of Real output signal

output

1