UBIQUITOUS FRACTIONAL ORDER CONTROLS

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Stability of Fractional-Order Systems with Rational Orders (2008, unknown): “The fractional order calculus plays an important role in physics [45,60,67], thermodynamics [31,57], electrical circuits theory and fractances [7,12,14,21,40,71], mechatronics systems [55], signal processing [56, 68], chemical mixing [41], chaos theory [62, 64], and biological system as well [23].”
Smith Predictor Based Fractional‐Order‐Filter PID Controllers Design for Long Time Delay Systems (2017, background): “It is intuitively true, as also argued in [6,7], that the fractional order models require much more than classical proportional–integral–derivative (PID) controllers to achieve good closed loop performance.”
Tuning and implementation methods for fractional-order controllers (2012, background): “As already noted in [8, 9], fractional-order control, namely fractional PID controllers, could be ubiquitous in industry.”
Fractional control of heat diffusion systems (2008, background): “The PID controller is more flexible and gives the possibility of adjusting more carefully the closed-loop system characteristics [17].”
Fractional order control - A tutorial (2009, background): “Furthermore, we also believe that based on some real world examples, fractional order control is ubiquitous when the dynamic system is of distributed parameter nature [ 13 ].”