TransferFunctionLinear transfer function 
This information is part of the Modelica Standard Library maintained by the Modelica Association.
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^[nb1] + b[2]*s^[nb2] + ... + b[nb] y(s) =  * u(s) a[1]*s^[na1] + a[2]*s^[na2] + ... + 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 nonscaled vector x is provided as output signal and the start value is with respect to the nonscaled 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
b 
Value: {1} Type: Real[:] Description: Numerator coefficients of transfer function (e.g., 2*s+3 is specified as {2,3}) 

a 
Value: {1} Type: Real[:] Description: Denominator coefficients of transfer function (e.g., 5*s+6 is specified as {5,6}) 
initType 
Value: Modelica.Blocks.Types.Init.NoInit Type: Init Description: Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output) 
x_start 
Value: zeros(nx) Type: Real[size(a, 1)  1] Description: Initial or guess values of states 
y_start 
Value: 0 Type: Real Description: Initial value of output (derivatives of y are zero up to nx1th derivative) 
x 
Type: Real[size(a, 1)  1] Description: State of transfer function from controller canonical form 

u 
Type: RealInput Description: Connector of Real input signal 


y 
Type: RealOutput Description: Connector of Real output signal 
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