The paper presents time, frequency, and real-time properties of a fractional-order PID controller (FOPID) implemented at a STM 32 platform. The implementation uses CFE approximation and discrete version of a Grünwald–Letnikov operator (FOBD). For these implementations, experimental step responses and Bode frequency responses were measured. Real-time properties of the approximations are also examined and analyzed. Results of tests show that the use of CFE approximation allows to better keep the soft real-time requirements with an accuracy level a bit worse than when using the FOBD. The presented results can be employed in construction-embedded fractional control systems implemented at platforms with limited resources.

The inverted pendulum is an unstable system with nonlinear dynamics. The task of controlling the inverted pendulum is complex. Therefore, the inverted pendulum over the years has become one of the most important systems on which every controller is...

The paper presents the implementation of the basic fractional order element sγ on the STM32 microcontroller platform. The implementation employs the typical CFE and FOBD approximations, the accuracy of approximation as well as duration of calculations are experimentally tested. Microcontroller implementation of fractional order elements is known; however, real-time tests of such implementations have been not presented yet. Results of experiments show that both methods can be implemented at the considered platform. The FOBD approximation is more accurate, but the CFE one is faster. The presented experimental results prove that the STM32F7 family processor could be used to develop the embedded fractional-order control systems for a broad class of linear and nonlinear dynamic systems. This is crucial during the implementation of the fractional-order control in the hard real-time or embedded systems.

Two Rotor Aerodynamical System is a non-linear system in which cross-coupling occurs. In this specific case the individual rotors of the system affect both the system angles: azimuth and pitch. Therefore, both values must be used in each feedback loop. This makes it possible to use cascade control. It was decided to use FOPID as primary controllers and PID as secondary. For comparison purposes, an analogous control system with only PIDs was prepared. The coefficients were determined using the GWO algorithm. All simulations were performed in the MATLAB/Simulink environment. In addition to comparing the values of the cost function, the execution time of individual controllers was also checked.