Back to the Future: Synergizing Fuzzy and Conventional Control

Abstract

This study revisits the fuzzy control system design problem with the motto “Fuzzy with Conventional Control,” inspired by L.A. Zadeh’s statement in the famous debate “Some Crisp Thoughts on the Fuzzy versus Conventional Control.” Focused on single-input (SI) fuzzy PIDs (FPIDs), our approach synergizes fuzzy and conventional control, presenting similar control laws to PID and fuzzy gain-scheduled (FGS) PID. Departing from traditional fuzzy control paradigms, our design methodology enhances, rather than replaces, PID controllers with fuzzy logic controllers (FLCs). We start by analyzing the internal structure of both type-1 and type-2 SI-FPIDs and commenting on their structural properties. We address the high-design complexity of FLCs by proposing an interpretable and geometrical design method that explicitly shapes fuzzy mapping (FM) according to the desired control characteristics. To provide self-tuning (ST) capability to the FPID, like the FGS-PID, we develop ST mechanisms that adapt the FM of SI-FPID according to the operating point via the derived insights. Real-world application in speed control for an industrial permanent magnet synchronous machine validates the efficacy of our designs, showcasing improved disturbance rejection and reduced control signal variation compared to FGS-PIDs and PID. This research advocates for the wider adoption of SI-FPID as a practical enhancement to PID in industrial applications, offering design simplicity and ST capabilities.