modelTransferFunction

Model of a generic rational transfer function [a(m)*s^m + a(m-1)*s^(m-1) + ... + a(1)*s + a(0) ]/[b(n)*s^n + b(n-1)*s^(n-1) + ... + b(1)*s + b(0) ]

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Extends from Interfaces.DiscreteBaseBlock (Partial discrete time block interfaces).

Information

Description

Discretised version of the continuous time transfer function, defined by its numerator and denumerator.

   Y(s)     a(m)*s^m + a(m-1)*s^(m-1) + ... + a(1)*s + a(0) 
   ----  = -------------------------------------------------
   U(s)     b(n)*s^n + b(n-1)*s^(n-1) + ... + b(1)*s + b(0)

The order of the numerator cannot be higher than the denumerator one: m <= n.

Discretisation

The discretisation of the continuos time transfer function has been performed with the bilinear transformation formula

                 z - 1 
  s = ------------------------------
        z*alpha*Ts - (alpha - 1)*Ts

that is equivalent to

Forward Euler (FE) if
```
alpha = 0
```
Backward Euler (BE) if
```
alpha = 1
```
Tustin (TU) if
```
alpha = 0.5
```

Parameters

Type	Name	Default	Description
Discretisation
Real	Ts (from DiscreteBaseBlock)	0.01	Sampling time [s]
IndustrialControlSystems.LinearSystems.Discrete.Types.discrMethod	method (from DiscreteBaseBlock)	IndustrialControlSystems.LinearSystems.Discrete.Types.discrMethod.BE	Discretisation method
Block parameters
Real[:]	num	{1, 1}	Numerators coefficients (4*s + 2) is {4,2}
Real[:]	den	{2, 1, 1}	Denumerators coefficients (4*s + 2) is {4,2}
Initial conditions
Real	y_start	0	Output initial value
Boolean	initOutput	false	Initialise the output
Boolean	initSteadyState	false	Initialise at steady state
Boolean	initSteadyOutput	false	Initialise at steady output

Connectors

Type	Name	Default	Description
Modelica.Blocks.Interfaces.RealInput	u (from BaseBlock)		input
Modelica.Blocks.Interfaces.RealOutput	y (from BaseBlock)		output

Revisions

Industrial Control Systems (v 1.0.0) : April-May 2012