ss2tf(A, B, C, D, input=0)

A, B, C, D defines a linear state-space system with p inputs, :None:None:`q` outputs, and n state variables.

Parameters

A : array_like

State (or system) matrix of shape (n, n)

B : array_like

Input matrix of shape (n, p)

C : array_like

Output matrix of shape (q, n)

D : array_like

Feedthrough (or feedforward) matrix of shape (q, p)

input : int, optional

For multiple-input systems, the index of the input to use.

Returns

num : 2-D ndarray

Numerator(s) of the resulting transfer function(s). :None:None:`num` has one row for each of the system's outputs. Each row is a sequence representation of the numerator polynomial.

den : 1-D ndarray

Denominator of the resulting transfer function(s). :None:None:`den` is a sequence representation of the denominator polynomial.

State-space to transfer function.

Examples

Convert the state-space representation:

$$$$

\dot{\textbf{x}}(t) = \begin{bmatrix} -2 & -1 \\ 1 & 0 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \\ 0 \end{bmatrix} \textbf{u}(t) \\

\textbf{y}(t) = \begin{bmatrix} 1 & 2 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \end{bmatrix} \textbf{u}(t)

>>> A = [[-2, -1], [1, 0]]
... B = [[1], [0]]  # 2-D column vector
... C = [[1, 2]]    # 2-D row vector
... D = 1

to the transfer function:

$$H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}$$

>>> from scipy.signal import ss2tf
... ss2tf(A, B, C, D)
(array([[1., 3., 3.]]), array([ 1.,  2.,  1.]))

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal._ltisys.StateSpace scipy.signal._lti_conversion.abcd_normalize scipy.signal._ltisys.StateSpaceContinuous scipy.signal._lti_conversion.ss2tf scipy.signal._ltisys.StateSpaceDiscrete

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GitHub : /scipy/signal/_lti_conversion.py#196
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