Mutual influence of PID and FOPID controllers on different axes of the 3D crane

The article presents 3D crane control with PID and FOPID (which is an extension of the classic PID with fractional parts) controllers in various configurations. 5 controllers are needed to control the crane - 3 for controlling the XYZ axes and 2 for influencing the angular position $\alpha$ and $\beta$. 3 sets of simulations were prepared. The first version includes 5 FOPID regulators that serve as a benchmark for comparisons. In two subsequent sets, the FOPID controllers on one axis and the corresponding angle for this axis were replaced with PID controllers (X axis $+\alpha$ angle and Y axis $+\beta$ angle). Matlab/Simulink environment was used to prepare the simulation. Later in the article all the results were compared with each other. GWO optimization was used to prepare the best coefficients for individual controllers.