TransferFunction

Linear transfer function

    TransferFunction

Library

Modelica/Blocks/Continuous

Description

This block defines the transfer function between the input u and the output y as (nb = dimension of b, na = dimension of a):

           b[1]*s^[nb-1] + b[2]*s^[nb-2] + ... + b[nb]
   y(s) = --------------------------------------------- * u(s)
           a[1]*s^[na-1] + a[2]*s^[na-2] + ... + a[na]

State variables x are defined according to controller canonical form. Internally, vector x is scaled to improve the numerics (the states in versions before version 3.0 of the Modelica Standard Library have been not scaled). This scaling is not visible from the outside of this block because the non-scaled vector x is provided as output signal and the start value is with respect to the non-scaled vector x. Initial values of the states x can be set via parameter x_start.

Example:

     TransferFunction g(b = {2,4}, a = {1,3});

results in the following transfer function:

        2*s + 4
   y = --------- * u
         s + 3

Parameters

TransferFunction_0

NameLabelDescriptionData TypeValid Values

mo_b

b

Numerator coefficients of transfer function (e.g., 2*s+3 is specified as {2,3})

Vector

mo_a

a

Denominator coefficients of transfer function (e.g., 5*s+6 is specified as {5,6})

Vector

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 values of states

Vector

mo_y_start

y_start

Initial value of output (derivatives of y are zero up to nx-1-th derivative)

Scalar

mo_na

na

Size of Denominator of transfer function.

Scalar

mo_nb

nb

Size of Numerator of transfer function.

Scalar

mo_nx

nx

Scalar

mo_bb

bb

Vector

mo_d

d

Scalar

mo_a_end

a_end

Scalar

TransferFunction_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 vectors

true
false

mo_x/start

start

Cell of vectors

Ports

NameTypeDescriptionIO TypeNumber

u

implicit

Connector of Real input signal

input

1

y

implicit

Connector of Real output signal

output

1