focont 0.1.1

Fixed order controller design tool

Focont

Static output feedback and fixed order controller design package for Python

Static output feedback (SOF)

The SOF is the simplest feedback controller structure. It basically feedbacks the system output to the system input after multiplying a constant gain matrix.

This package can calculate a stabilizing SOF gain which also optimizes the norm of the closed loop system.

However, this algorithm works under sufficient conditions. If the problem parameters (listed below) is not appropriate, the algorithm fails and prints an error message.

(See the article, https://journals.sagepub.com/doi/abs/10.1177/0142331220943071 , and the PhD thesis, http://hdl.handle.net/11693/54900 , for detailed information and analysis)

The algorithm is purposedly developed for discrete time systems, but it also works for continuous time systems when the SOF is calculated for the zero-order hold discretized version with a sufficiently large sampling frequency.

System definition can be provided by a JSON or MATLAB mat file. The required entries in the file are:

• A: (2d array) System matrix
• B: (2d array) Input matrix
• C: (2d array) Output matrix,

where (A, B) is stabilizable and (C, A) is observable (it is recommended to solve for the observable part of the system if (C, A) is detectable).

If you want to adjust const function weights, these should also be provided:

• Q: (2d array) Cost function weight for the state variables (similar to LQR problem)
• R: (2d array) Cost function weight for the system input.

If (A, B, C) defines a continuous time system, these should also be provided:

• type: (string) 'C' (which means continuous, 'D' means discrete)
• Ts: (number) Sampling period

Fixed order controller

Furthermore, the algorithm can be used to calculate fixed-order controllers. This need additional entries in the described JSON or mat file;

• structure: (string) 'FO' (meaning fixed-order or 'SOF' for SOF controller)
• controller_order: (integer) The order of controller (by default it is chosen as the number of inputs)

Installation

Create and activate a virtual environment (this step is not required but recommended). Then,

pip install -r requirements.txt

or

pip install numpy scipy

Finally,

pip install .

Also,

It can be installed with pip from pypi.

pip install focont

Example

from focont import foc, system

pdata = system.load(json_or_mat_filename)
foc.solve(pdata)
foc.print_results(pdata)

You can find json and mat file examples in the /tests directory.