https://github.com/SciFracX/FractionalSystems.jl

Fractional order systems toolbox in Julia.
https://github.com/SciFracX/FractionalSystems.jl

control-systems dynamical-systems fractional-calculus fractional-differential-equations fractional-pid fractional-systems julia modeling numerical-analysis pid-controller

Last synced: 3 months ago
JSON representation

Fractional order systems toolbox in Julia.

• Host: GitHub
• URL: https://github.com/SciFracX/FractionalSystems.jl
• Owner: SciFracX
• License: mit
• Created: 2021-12-19T14:57:12.000Z (almost 3 years ago)
• Default Branch: master
• Last Pushed: 2023-12-23T11:38:42.000Z (11 months ago)
• Last Synced: 2024-07-12T17:17:41.058Z (4 months ago)
• Topics: control-systems, dynamical-systems, fractional-calculus, fractional-differential-equations, fractional-pid, fractional-systems, julia, modeling, numerical-analysis, pid-controller
• Language: Julia
• Homepage: https://scifracx.github.io/FractionalSystems.jl/dev/
• Size: 427 KB
• Stars: 8
• Watchers: 2
• Forks: 3
• Open Issues: 2
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

Awesome Lists containing this project

• awesome-sciml - SciFracX/FractionalSystems.jl: Fractional order modeling and analysis in Julia.

README

        
# FractionalSystems.jl









  

    

  

  

    

  

  

    

  

  

    

  





  

    

  

  

    

  

  

    

  



FractionalSystems.jl is a Julia toolbox can be used to model and analyse the fractional order systems.

## Get Started

To add the FractionalSystems.jl, using the Julia package manager:

```julia

pkg> add FractionalSystems

```

### Basic FOTF and FOSS

Fractional order transfer functions and fractional order state space are the basic elements in fractional control system, it is esay to create them in FractionalSystems.jl:

```julia

julia> tf = fotf([1, 2], [0.3, 0.4], [1, 2], [0.5, 0.6], 2)

FOTF

s^{0.3} + 2s^{0.4}

------------------ exp(-2*s)     

s^{0.5} + 2s^{0.6}

```

```julia

julia> sys = foss([-5 0; 0 -5],[2; 2],[3 3],[0], 0.5, 1, 1, 1)

FOSS

A =

 -5   0

  0  -5

B =

 2

 2

C =

 3  3

D =

 0

Descriptor matrix:

E =

1

Time delay is 1

α = 0.5

Initial state vector x₀ = 1

```

## Analyzing methods

To see the root locus of a fractional order system:

```julia

julia> G = fotf([1], [0], [1, 10, 35, 50, 24], [3.5, 2.8, 2.1, 1.4, 0.7])

julia> rlocus(G)

```

![rlocus](examples/rlocusexample.png)

## Notice

The FractionalSystems.jl can be seen as the combination of [FOTF](https://www.mathworks.com/matlabcentral/fileexchange/60874-fotf-toolbox), [FOMCON](https://fomcon.net/) and [ControlSystems.jl](https://github.com/JuliaControl/ControlSystems.jl)

We are working hard on FractionalSystems.jl to provide performant features as much as possible, if you are interested, don't hesitate to get in touch:)