TransferFunction
Linear transfer function
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
| Name | Label | Description | Data Type | Valid 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 | |
mo_initType/choice2 | Steady state initialization (derivatives of states are zero) | Number | 0 | |
mo_initType/choice3 | Initialization with initial states | Number | 0 | |
mo_initType/choice4 | Initialization with initial outputs (and steady state of the states if possible) | Number | 0 | |
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 |
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_u | u | u | Structure | |
mo_u/fixed | fixed | Cell of scalars | true | |
mo_u/start | start | Cell of scalars | ||
mo_y | y | y | Structure | |
mo_y/fixed | fixed | Cell of scalars | true | |
mo_y/start | start | Cell of scalars | ||
mo_x | x | x | Structure | |
mo_x/fixed | fixed | Cell of vectors | true | |
mo_x/start | start | Cell of vectors |
Ports
| Name | Type | Description | IO Type | Number |
|---|---|---|---|---|
u | implicit | Connector of Real input signal | input | 1 |
y | implicit | Connector of Real output signal | output | 1 |