scipy.signal.ss2tf¶
- scipy.signal.ss2tf(A, B, C, D, input=0)[source]¶
State-space to transfer function.
A, B, C, D defines a linear state-space system with p inputs, q outputs, and n state variables.
- Parameters
- Aarray_like
State (or system) matrix of shape
(n, n)- Barray_like
Input matrix of shape
(n, p)- Carray_like
Output matrix of shape
(q, n)- Darray_like
Feedthrough (or feedforward) matrix of shape
(q, p)- inputint, optional
For multiple-input systems, the index of the input to use.
- Returns
- num2-D ndarray
Numerator(s) of the resulting transfer function(s). num has one row for each of the system’s outputs. Each row is a sequence representation of the numerator polynomial.
- den1-D ndarray
Denominator of the resulting transfer function(s). den is a sequence representation of the denominator polynomial.
Examples
Convert the state-space representation:
\[ \begin{align}\begin{aligned}\begin{split}\dot{\textbf{x}}(t) = \begin{bmatrix} -2 & -1 \\ 1 & 0 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \\ 0 \end{bmatrix} \textbf{u}(t) \\\end{split}\\\textbf{y}(t) = \begin{bmatrix} 1 & 2 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \end{bmatrix} \textbf{u}(t)\end{aligned}\end{align} \]>>> 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.]))