TF2SS

Purpose:

Converts a system in transfer function form to state-space form.

Syntax:

(A, B, C, D) = TF2SS(num, den)

num

-

A matrix, the numerator coefficients in descending powers of s with as many rows as there are outputs.

den

-

A series, the denominator coefficients in descending powers of s.

Returns:

Matrices A, B, C, D of the state space transformation in controller canonical form.

Example:

For the system:

 

image\tf2ss02.gif

 

num = {{0, 1, 3},

       {1, 1, 10}}; 

 

den = {1, 0.1, 1};

 

(A, B, C, D) = tf2ss(num, den);

 

A == {{-0.1, -1.0},

      { 1.0, 0.0}} 

 

B == {1.0, 0.0}

 

C == {{1.0, 3.0},

      {0.9, 9.0}} 

 

D == {0.0, 1.0}

Remarks:

TF2SS converts a system specified in transfer function form to an equivalent state-space matrix representation such that a single input, multiple output transfer function:

 

image\tf2ss01.gif

 

is converted to state-space form:

 

image\bilinear05.gif

 

where A, B, C, D are the matrices of the state space transformation in controller canonical form:

 

The conversion also works for discrete systems. For discrete systems, the input coefficients represent the system:

 

image\zplane03.gif

 

When specifying a discrete systems, pad the numerator and/or denominator with zeros to make them the same length.

See Also:

BILINEAR

FILTEQ

TF2CAS

TF2SOS

TF2ZP

TF2ZPK