FractionalSystems.jl

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

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

pkg> add FractionalSystems

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> 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> 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

To see the root locus of a fractional order system:

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

The FractionalSystems.jl can be seen as the combination of FOTF, FOMCON and 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:)