Virtual Reference Feedback Tuning (VRFT) Adaptive Control Library written in Python. Aim of this library is to provide an implementation of the VRFT (Virtual Reference Feedback Tuning) algorithm.

You can find the package also at the following link

Author: Alessio Russo (PhD Student at KTH - alessior@kth.se)

Contributors: Alexander Berndt

Our code is released under the GPLv3 license (refer to the LICENSE file for details).

To run the library you need atleast Python 3.5.

Other dependencies:

• NumPy (1.19.5)
• SciPy (1.6.0)

• Install last stable version: execute the command pip install pythonvrft
• Install from source: git clone this repo and from the root folder execute the command pip install .

You can import the library by typing python import vrft in your code.

To learn how to use the library, check the examples located in the examples/ folder. At the moment there are examples available. Check example3 to see usage of instrumental variables.

In general the code has the following structure

from vrft import ExtendedTF    # Discrete transfer function (inherits from the scipy.signal.dlti class)
                               # Allows to sum/multiply/divide transfer functions and compute the feedback
                               # loop
from vrft import iddata        # object used to store input/output data
from vrft import compute_vrft  # VRFT algorithm

# Parameters
dt = 0.1  # sampling time

# Define a reference model
ref_model = ExtendedTF([0.6], [1, -0.4], dt=dt)   # Transfer function 0.6/(z-0.4)

# Define pre-filter
pre_filter = (1 - ref_model) * ref_model

# Define control base (PI control)
control = [ExtendedTF([1], [1, -1], dt=dt),     # Transfer function 1/(z-1)
           ExtendedTF([1, 0], [1, -1], dt=dt)]  # Transfer function z/(z-1)

# Generate input/output data from a system
u = ....  # Generate input
y = ....  # measured output

# Create an iddata object
y0 = ... # initial conditions of the system (the length depends on the order of the reference model)
data = iddata(y, u, dt, y0)

# Compute VRFT
# theta is the vector of parameters that parametrizes the control base
# C is the final controller (computed as control.dot(theta))
theta, _, _, C = compute_vrft(data, ref_model, control, pre_filter)

To execute tests run the following command from the root folder of the repo

python -m unittest

• [V. 0.0.2][26.03.2017] Implement the basic VRFT algorithm (1 DOF. offline, linear controller, controller expressed as scalar product theta*f(z))
• [V. 0.0.3][05.01.2021] Code refactoring and conversion to Python 3; Removed support for Python Control library.
• [V. 0.0.5][08.01.2021] Add Instrumental Variables (IVs) Support
• [In Progress][07.01.2021-] Add Documentation and Latex formulas
• [TODO] Add MIMO Support
• [TODO] Generalize to other kind of controllers (e.g., neural nets)
• [TODO] Add Cython support

If you find this code useful in your research, please, consider citing it:

@misc{pythonvrft, author = {Alessio Russo}, title = {Python VRFT Library}, year = 2017, doi = {}, url = { https://github.com/rssalessio/PythonVRFT } }