Improving the Control Actions of a Discrete FOPID Controller by Refining the Integral Term: Application to a 1-DOF Twin-Rotor System

This research highlights the application of unmanned aerial vehicle (UAV) control in a reduced and laboratory scale model called 1-DOF twin rotor system (1D-TRS). Although the PID controller is widely used in UAVs due to its versatility and functionality, it has precision and disturbance rejection limitations. The discrete-time fractional-order PID (FOPID) controller is a valid alternative for UAV control that requires approximating the integral and derivative terms using an infinite summation of fractional terms, from which the most representative are selected for practical implementation. For low-scale UAV models, implementation is challenging since microcontrollers must process fractional operations in discrete time into limited hardware capabilities. In this context, tuning control parameters also represents a challenge since the PID constants and the fractional order parameters must be considered. This study proposes a discrete-time FOPID controller emphasizing the integral term, utilizing the same components as a conventional FOPID but with improved tuning flexibility. Since the integral term plays a key role in reducing tracking errors, this approach enhances accuracy without significantly increasing computational complexity, ultimately resulting in an FOPI + D controller. Tuning the controller parameters is also considered an a priori idea to set $\lambda =\mu =0.5$ to leverage the capacities of the particle swarm optimization (PSO) method for adjusting the PID constants without increasing its computational cost if all the FOPID parameters were considered to perform tests and PSO calibration to obtain the desired control results. Experimental tests were conducted on the 1D-TRS using different reference signals, such as step, steps, and ramp inputs. Additionally, external disturbances were introduced during experimental scenarios. The proposed controller was compared against traditional PID and discrete FOPID controllers, with performance metrics demonstrating improved system response. The results showed that the proposed controller enhances trajectory tracking in 1D-TRS, improving both precision and robustness against disturbances. It is a valuable alternative for UAV applications where stability and tracking accuracy are critical.