Robust fractional-order [proportional integral derivative] controller design with specification constraints: more flat phase idea

Abstract

This paper presents a new design methodology for robust fractional-order controllers with more than three parameters for first-order plus dead time systems using the synthesis scheme of the ‘more flat phase’ idea for a fractional-order controller with [proportional integral derivative] (FO[PID]) structure. The stability region of the FO[PID] controller and the synthesis scheme with the ‘more flat phase’ idea are illustrated through a simulation example. The corresponding pseudo-codes of the synthesis scheme are also summarised. The implementation and approximation error of the FO[PID] controller are also discussed. Likewise, the superiority of the FO[PID] controller designed with the ‘more flat phase’ idea is verified by additional simulations and experimental results where the closed-loop system with FO[PID] controller is not sensitive to the variations of the loop gain, ensuring satisfactory control performance. Obtained results show high potential in practical industrial applications.

KEYWORDS:

• Fractional-order [proportional integral derivative] controller
• specification constraints
• first order plus dead time system
• more flat phase
• achievable region

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author would like to give thanks to the Science & Technology Research Project in Henan Province of China [grant number 212102311052].