Design of a fractional order PID controller for an AVR using particle swarm optimization

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Lyapunov functions for fractional order systems (2014, methodology): “Besides, sometimes fractional order controllers are used to control integer order systems, such as Fractional Order PID controllers [5]; high gain output feedback control schemes, where the feedback gain is estimated using a fractional differential equation [6,7]; Fractional Order Model Reference Ad”
Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems (2015, background): “Fractional Order PID controllers [5]; fractional high gain output feedback controllers [6,7] and Fractional Order Model Reference Adaptive Controllers (FOMRAC) [8–14], amongst others.”
Fractional-order PD control at Hopf bifurcations in a fractional-order congestion control system (2017, methodology): “In [45], a fractional-order PID controller with the employment of particle swarm optimization was designed to improve the robustness of an automatic voltage regulator.”
Integral sliding mode control for fractional-order systems with mismatched uncertainties (2013, methodology): “Fractional-order PID controllers have been applied in many practical control systems [8, 9].”
Optimal fractional order adaptive controllers for AVR applications (2018, methodology): “These features are used in optimization problems in [37], where the parameters of the PID controller are selected by the PSO algorithm.”