TF2SS
Converts a continuous-time or discrete-time polynomial transfer function into an equivalent state-space representation.
A state-space model provides a time-domain representation of the system dynamics using a set of first-order differential (or difference) equations, defined by the matrices \mathbf{A}, \mathbf{B}, \mathbf{C}, and \mathbf{D}.
Because state-space realizations are not unique (the same transfer function can be represented by infinitely many state-space models depending on the choice of state variables), this function returns a generic realization created by the slycot or scipy backend methods.
Excel Usage
=TF2SS(num, den)num(list[list], required): Polynomial coefficients of the numerator, in descending powers of s.den(list[list], required): Polynomial coefficients of the denominator, in descending powers of s.
Returns (str): String representation of the resulting state-space model.
Example 1: 1/(s+1) -> State-Space
Inputs:
| num | den | |
|---|---|---|
| 1 | 1 | 1 |
Excel formula:
=TF2SS({1}, {1,1})Expected output:
"<StateSpace>: sys[2]\nInputs (1): ['u[0]']\nOutputs (1): ['y[0]']\nStates (1): ['x[0]']\n\nA = [[-1.]]\n\nB = [[1.]]\n\nC = [[1.]]\n\nD = [[0.]]"
Example 2: (s+2)/(s^2+3s+2) -> State-Space
Inputs:
| num | den | |||
|---|---|---|---|---|
| 1 | 2 | 1 | 3 | 2 |
Excel formula:
=TF2SS({1,2}, {1,3,2})Expected output:
"<StateSpace>: sys[6]\nInputs (1): ['u[0]']\nOutputs (1): ['y[0]']\nStates (2): ['x[0]', 'x[1]']\n\nA = [[-3. -2.]\n [ 1. 0.]]\n\nB = [[1.]\n [0.]]\n\nC = [[1. 2.]]\n\nD = [[0.]]"
Example 3: 1/s -> State space
Inputs:
| num | den | |
|---|---|---|
| 1 | 1 | 0 |
Excel formula:
=TF2SS({1}, {1,0})Expected output:
"<StateSpace>: sys[10]\nInputs (1): ['u[0]']\nOutputs (1): ['y[0]']\nStates (1): ['x[0]']\n\nA = [[-0.]]\n\nB = [[1.]]\n\nC = [[1.]]\n\nD = [[0.]]"
Example 4: Third order system
Inputs:
| num | den | ||||
|---|---|---|---|---|---|
| 2 | 1 | 1 | 4 | 5 | 2 |
Excel formula:
=TF2SS({2,1}, {1,4,5,2})Expected output:
"<StateSpace>: sys[14]\nInputs (1): ['u[0]']\nOutputs (1): ['y[0]']\nStates (3): ['x[0]', 'x[1]', 'x[2]']\n\nA = [[-4. -5. -2.]\n [ 1. 0. 0.]\n [ 0. 1. 0.]]\n\nB = [[1.]\n [0.]\n [0.]]\n\nC = [[0. 2. 1.]]\n\nD = [[0.]]"
Python Code
Show Code
import control as ct
import numpy as np
def tf2ss(num, den):
"""
Convert a transfer function object back into a state-space system object.
See: https://python-control.readthedocs.io/en/latest/generated/control.tf2ss.html
This example function is provided as-is without any representation of accuracy.
Args:
num (list[list]): Polynomial coefficients of the numerator, in descending powers of s.
den (list[list]): Polynomial coefficients of the denominator, in descending powers of s.
Returns:
str: String representation of the resulting state-space model.
"""
try:
def flatten_to_1d(x):
if not isinstance(x, list):
return [float(x)] if str(x) != "" else []
flat = []
for row in x:
if isinstance(row, list):
for val in row:
if str(val) != "":
flat.append(float(val))
elif str(row) != "":
flat.append(float(row))
return flat
num_arr = flatten_to_1d(num)
den_arr = flatten_to_1d(den)
if not num_arr or not den_arr:
return "Error: Numerator and denominator coefficients must be provided"
if all(d == 0 for d in den_arr):
return "Error: Denominator cannot be zero"
try:
sys_ss = ct.tf2ss(num_arr, den_arr, method='scipy')
except TypeError:
sys_ss = ct.tf2ss(num_arr, den_arr)
# For Excel output, we must return a rectangular array. Let's return the string representations.
return str(sys_ss)
except Exception as e:
return f"Error: {str(e)}"