Swedish Embedded Control Systems Toolbox

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This is a control systems design library written in pure C that provides you with advanced algorithms for control, state estimation and model identification specifically designed for use on embedded systems. It has been adopted for use with embedded systems and Swedish Embedded Platform SDK

Community: https://swedishembedded.com/community
Consulting: https://swedishembedded.com/consulting
Training: https://swedishembedded.com/tag/training

It library is fully compatible with Zephyr RTOS so you can simply add it as a module to your west.yml file and start using it.

It is focused on practical numerical methods that work best in realtime embedded environment without any complex dependencies.

It uses no dynamic memory allocation. All operations are done on C arrays. The functions provided by this library are generic implementations that can be used to implement controllers that use specific array sizes.

Original library is based on excellent work by Daniel Mårtensson who has developed the original algorithms in C and GNU Octave.

This library provides following functionality:

Artificial Intelligence
- Astar algorithm for quick path finding
- Point-in-polygon algorithm for checking if a point is inside the area
Control Engineering
- Kalman filter update
- Linear Quadratic Integral regulator
- Model predictive Control
- Model Reference Adaptive Control
- Transfer function to state space
- Stability check
- Continuous to discrete
Filtering
- Monte Carlo Simulation
- Comming soon: Particle filter
- Filtfilt
- Square Root Unscented Kalman Filter
Linear Algebra
- Balance matrix
- Cholesky decomposition
- Cholesky update
- QR decomposition
- LUP decomposition
- Determinant
- Discrete Lyapunov solver
- Eigenvalues symmetric + Eigenvectors
- Random real eigenvalues and random imaginary eigenvalues
- Hankel matrix
- Inverse
- Pseudo inverse
- Linear solver
- Nonlinear solver
- Multiplication
- Singular Value Decomposition Golup Reinsch
- Singular Value Decomposition Jacobi One Sided
- Transpose
- Matrix sum
- Norm
- Matrix exponential
Miscellaneous
- Concatenate
- Cut matrix
- Insert sub matrix into matrix
- Print matrix or vector
- Saturation
- Sign
- Randn
- Mean
- Standard deviation
- Value min
- Value max
Optimization
- Linear programming maximization
- Linear programming minimization
System Identification
- Observer Kalman Filter identification
- Eigensystem Realization Algorithm
- Recursive Least Square with forgetting factor and kalman filter identification
- Square Root Unscented Kalman Filter for parameter estimation

Building locally

The library core library should build just fine using the standard cmake approach:

mkdir build
cmake ..
make && make test

Building and running examples

The tests inside this repository are created to be buildable on top of Swedish Embedded Platform SDK. If you are using 'swedishembedded/build:latest' docker image then you should be able to simply run:

west init -l .
west update
./scripts/test

If you want to build locally, you should be able to do so by installing west, running west init and then installing the SDK dependencies locally:

pip3 install -g west
mkdir workspace && cd workspace
# it is important that you clone into a workspace!
git clone git@github.com:swedishembedded/control.git
west init -l .
west update
../sdk/scripts/install-sdk

This will install several different cross compilation toolchains and all the other tools you need in order to build firmware for a wide variety of architectures.

To build and run individual tests on specific boards you can do like this:

west boards # list boards
west build -p -b <board> tests/ai -t run # build and run
west build -t run # do a subsequent run after building for the first time

Building documentation

  apt update &&  
    apt install -qy 
    libglib2.0-dev
    libglib2.0-dev-bin
    libgtest-dev
    ruby2.7-dev
    libcairo2-dev
    libpango1.0-dev
    libgdk-pixbuf2.0-dev
    libxml2-dev
  pip install asciidoxy
  gem install asciidoctor-mathematical
  mkdir build &&
    cd build &&
    cmake .. &&
    make docs

How to help to build on this control toolbox

If you are interested in contributing to this library, feel free to raise a pull request.

GNU Octave Functions

Installing GNU Octave's Control-Toolbox or MATLAB's Control-Toolbox/System Identification Toolbox WILL cause problems with this toolbox because they are using the same function names. This toolbox implements better versions of the original functions so you should either use this toolbox inside you .m file or opt for using the default gnuoctave implementations - but not both.

System Identification Toolbox

OKID for multivariable hydraulic systems or temperature systems
ERA-DC for mechanical damped systems in the time plane
SINDY for multivariable abritary nonlinear systems
RLS for all kind of arbitary single input and single output systems (Use this first!)
OCID for linear feedback systems (I haven't found any real world practice for this method yet)
FILTFILT2 for low pass filtering without phase delay
SPA for spectral analysis
IDBODE for mechanical damped systems in the frequency plane
RPCA for filtering data and images
ICA for separating signals so they are independent from each other
SR-UKF-Parameter-Estimation for finding parameters from an very complex system of equation if data is available
SR-UKF-State-Estimation for filtering noise and estimate the state of a system
SVM for classification of data
N4SID for MIMO, SIMO, MISO or SISO state space systems
MOESP for MIMO, SIMO, MISO or SISO state space systems
PIMOESP for MIMO, SIMO, MISO, or SISO state space systems

State space model identification methods

|Function|Description|Status|Model |--------|-----------|------|----- |eradc|Eigensystem Realization Algorithm Data Correlation|Done|MIMO |okid|Observer Kalman Filter Identification|Done|MIMO |ocid|Observer Controller Identification|Done|MIMO |rls|Recursive Least Square|Done|SISO

Nonlinear system identification methods

|Function|Description|Status|Model |--------|-----------|------|----- |sindy|Sparse Identification of Nonlinear Dynamics|Done|MIMO |sr_ukf_parameter_estimation|Estimate parameters for a nonlinear system. Notice that this is parameter estimation. Not system identification.|Done|MIMO |sr_ukf_state_estimation|Estimate states for a nonlinear system. This is system identification|Done|MIMO

Subspace identification algorithms

|Function|Description|Status|Model |--------|-----------|------|----- |moesp|Multivariable Output-Error State Space|Done|MIMO |pimoesp|Past-Input Multivariable Output-Error State Space|Done|MIMO |n4sid|Numerical algorithms for Subspace State Space System IDentification|Done|MIMO

Analysis and filtering

|Function|Description|Status |--------|-----------|------ |spa|Plot bode spectral analysis plot using Fast Fourier Transform|Done |filtfilt2|Zero phase filtering with low pass filter|Done |idbode|Plot bode diagram from frequency data|Done |rpca|Filter data using Robust Principal Component Analysis|Done |ica|Separate signals from each other so they are independent|Done

Classification

|Function|Description|Status |--------|-----------|------ |Svm|Support Vector Machine with C code generation|Done |--------|-----------|------

Control systems design toolbox

These functions are used for control system design.

Model creation

|Function name|Description|Status|MIMO|TF/SS|Discrete |-------------|-----------|------|----|-----|-------- |tf|Crate transfer function model|Done|No|N/N|Y |zpk|Create zero-pole-gain model|Done|No|N/N|Y |ss|Create state space model|Done|Yes|N/N|Y

Model transformation

|Function name|Description|Status|MIMO|TF/SS|Discrete |-------------|-----------|------|----|-----|-------- |minreal|Minimal realization|Done|Yes|Y/Y|Y |balreal|Balanced realization|Done|Yes|N/Y|Y |modred|Model reduction|Done|Yes|N/Y|Y |append|Append systems|Done|Yes|Y/Y|Y |feedback|Feedback model|Done|Yes|Y/Y|Y |series|Serial model|Done|Yes|Y/Y|Y |parallel|Parallel model|Done|Yes|Y/Y|Y |pade|Internal time delay to model|Done|Yes|Y/N|Y |referencegain|Create gain for better tracking|Done|Yes|N/Y|Y

Model data access

|Function name|Description|Status|MIMO|TF/SS|Discrete |-------------|-----------|------|----|-----|-------- |dcgain|Get the low frequency gain|Done|Yes|Y/Y|Y |pzmap|Plot poles and zeros|Done|Yes|Y/Y|Y |damp|Get the damping|Done|Yes|Y/Y|Y |pole|Get poles|Done|Yes|Y/Y|Y |zero|zeros for SISO |Done|No|Y/Y|Y |tzero|zeros for MIMO |Done|Yes|N/Y|Y

Model conversions

|Function name|Description|Status|MIMO|TF/SS|Discrete |-------------|-----------|------|----|-----|-------- |c2d|Convert continuous to discrete|Done|Yes|Y/Y|N |c2dt|Convert continuous to discrete with delay|Done|Yes|Y/Y|N |d2c|Convert discrete to continuous|Done|Yes|Y/Y|Y |d2d|Rediscrete the model|Done|Yes|Y/Y|Y |tf2ss|Transfer function to state space|Done|No|Y/N|Y |ss2tf|State space to transfer function|Done|Yes|N/Y|Y

Frequency domain analysis

|Function name|Description|Status|MIMO|TF/SS|Discrete |-------------|-----------|------|----|-----|-------- |evalfr|Get one frequency|Done|Yes|Y/Y|Y |freqresp|Get multiple frequencies|Done|Yes|Y/Y|Y |bode|Bode diagram|Done|Yes|Y/Y|Y |bodemag|Bode diagram without phase|Done|Yes|Y/Y|Y |nyquist|Nyquist diagram|Done|Yes|Y/Y|Y |sigma|Singular value diagram|Done|Yes|Y/Y|Y |margin|Stability margins|Done|Yes|Y/Y|Y |allmargin|Show all margin|Done|Yes|Y/Y|Y |sensitivity|Show sensitivity margins|Done|Yes|Y/Y|Y |db2mag|Convert dB to magnintude|Done|Yes|Y/Y|Y |mag2db|Conver magnintude to dB|Done|Yes|Y/Y|Y |rlocus|Root locus plot|Done|Yes|Y/Y|Y |rlocfind|Find the

Control

Install / Use

README