Discrete to continuous time transfer function

Question

I implemented a class to identify ARX models in Python. The next step is the calculation of optimal PID parameters based on LQR. Apparently a continuous time model is required and I have the following possibilites:

• transform the discrete time model to a continuous time model,
• identify a continuous time model,
• adapt the LQR approach to determine optimal PID parameters to the discrete time domain.

In Matlab the first two approaches are easily done, but I need them in Python. Does anybody know how Matlab implemented d2c and has a reference?

Answer 1

There are a few options you can use python-control package or scipy.signal module or use harold (shameless plug: I'm the author).

Here is an example

import harold

G = harold.Transfer(1, [1, 2, 1])

H_zoh = harold.discretize(G, dt=0.1, method='zoh')

H_tus = harold.discretize(G, dt=0.1, method='tustin')

H_zoh.polynomials
Out[5]: 
(array([[0.00467884, 0.00437708]]),
 array([[ 1.        , -1.80967484,  0.81873075]]))

H_tus.polynomials
Out[6]: 
(array([[0.00226757, 0.00453515, 0.00226757]]),
 array([[ 1.        , -1.80952381,  0.8185941 ]]))

Currently zoh, foh, tustin, forward euler, backward euler is supported including undiscretizations. The documentation is found at http://harold.readthedocs.io/en/latest/index.html