Introduction to single-input, single-output fractional control

This is a tutorial study to introduce fractional control to a reader with a background in control theory. Fractional controllers are those making use of fractional-order derivatives and integrals, and have been receiving increased attention over the last few years because of the robust performance (in the face of plant gain variations and even plant uncertainties in general) they can achieve. The study covers the fundamentals of the theory of derivatives and integrals with arbitrary real or complex orders, fractional transfer functions and their approximations, identification of fractional transfer function models from experimental data, first- and second-generation Crone controller, fractional proportional-integral-derivative (PID) control and third-generation Crone control.