Fractional-variable-order digital controller design tuned with the chaotic yellow saddle goatfish algorithm for the AVR system

In this paper, an optimisation method utilising the yellow saddle goatfish algorithm (YSGA) with a new fitness function is proposed to design two types of fractional-variable-order PID (FVOPID) digital controllers for the automatic voltage regulator (AVR) system. Simulations and comparisons of the results are presented, showing that variable-order control can perform better than the existing solutions for the AVR system. Additionally, we include a stability analysis of a closed-loop system by utilisation of the Nyquist stability criterion. •Design of digital fractional-, variable-order PID controller (FVOPID).•Difference and summation orders as a function of a control error.•Use of the Chaotic Yellow Saddle Goatfish Algorithm for tuning of FVOPID controllers.•Improvement of system time characteristics by FVOPID in AVR system.•Stability analysis of closed loop for sampled systems with FVOPID digital controller.