A Review of the State-of-the-Art in Fractional-Order PID Controllers

Fractional-order (FO) PID controllers are becoming increasingly popular for various industrial applications due to the advantages they can offer. The increasing tendency toward the utilization of FOPID controllers is mainly owing to the fact that these controllers have extra tuning knobs that allow coherent adjustment of the dynamics of control systems. Nonetheless, there are several critical points that remain underexplored in the existing literature, namely: (i) What are the significant advantages of FOPID controllers in comparison with integer-order (IO) PID controllers? (ii) For the real-time implementation of FOPID controllers, approximations equivalent to high-order linear controllers are used. In this case, what are the benefits of using FOPID controllers? Lastly, (iii) What are the advantages of having a near-ideal FO behavior in the control practice? In this chapter, we attempt to address these issues through conducting a comprehensive review of relevant publications in the rapidly growing literature on FO control, outlines the milestones and disadvantages, and presents future perspectives for the industrialization of FO control. Moreover, we draw conclusions and formulate suggestions for future searches. In conclusion, this chapter helps the beginners to get started quickly and to learn how to select, tune, approximate, and implement FOPID controllers in the frequency domain.