# TransferFunction

Linear transfer function

## Library

Modelica/Blocks/Continuous

## Description

This block defines the transfer function between the inputu and the output yas (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 isnot 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-scaledvector **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 |
---|---|---|---|---|

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

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

| na | Size of Denominator of transfer function. | Scalar | |

| nb | Size of Numerator of transfer function. | Scalar | |

| nx | Scalar | ||

| bb | Vector | ||

| d | Scalar | ||

| a_end | Scalar | ||

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

| No initialization (start values are used as guess values with fixed=false) | Number | 0 | |

| Steady state initialization (derivatives of states are zero) | Number | 0 | |

| Initialization with initial states | Number | 0 | |

| Initialization with initial outputs (and steady state of the states if possible) | Number | 0 | |

| x_start | Initial or guess values of states | Vector | |

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

| x | x | Structure | |

| fixed | Cell of vectors | true | |

| start | Cell of vectors |

Name | Label | Description | Data Type | Valid Values |
---|---|---|---|---|

| Number of Modifiers | Specifies the number of modifiers | Number | |

| Modifiers | Add new modifier | Structure | |

| Variable name | Cell of strings | 'x_scaled' | |

| Attribute | Cell of strings | 'start' | |

| Value |

## Ports

Name | Type | Description | IO Type | Number |
---|---|---|---|---|

| implicit | Connector of Real input signal | input | 1 |

| implicit | Connector of Real output signal | output | 1 |