.IndustrialControlSystems.LinearSystems.Discrete.TransferFunction

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
```

Revisions

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