Fractional variable order closed loop systems toolbox

The toolbox allows to simulate and tune parameters of closed-loop systems with a fractional-variable-order digital PID (FVOPID) controller.

The toolbox allows to simulate and tune parameters of closed-loop systems with a fractional-variable-order digital PID (FVOPID) controller. The toolboox is purely written in MATLAB and uses predefined Simulink models with closed loop systems, which are adjusted according to the setup selected by the user of the toolbox. Users of the toolbox are encouraged to check, validate and modify the implementation if necessary.

In the future versions of the toolbox the controller blocks implemented as C-MEX S-functions will be added to improve the performance of calculation of FVOPIDs for long simulations or high controller sampling time. Still for short simulations e.g. up to 1000-1200 samples (e.g. for 10[s]-12[s] of simulation time and sampling time equal to 0.01[s]) the time needed to execute single simulation in Simulink should be almost the same for the current implementation of FVOPID controller as for standard MATLAB discrete PID block (checked with MATLAB 2020a). This is because of the time which Simulink model needs to evaluate the closed loop system simulation by itself which for 1000 samples seems to be significantly higher than the time needed by FVOPID controller to calculate its output.

For 2500 samples the time needed for single FVOPID simulation is 2x longer than for standard PID block, while for 5000 samples the time needed for single simulation is 4x longer. This is why the toolbox (especially parameters searching) is currently intended for the simulations which do not exeed 5000 samples (which means e.g. 50[s] simulation where controller's sampling time is equal to 0.01[s], or 5[s] simulation with the sampling time set to 0.001[s]).

The toolbox is still under testing, validation and verification process. In case of any problems with the implementation, or bugs discovered (either during toolbox execution or found directly in code) please inform:

Piotr Oziabło

[e-mail]