Designing a fuzzy-based PID controller for separation control in the backward-facing step flow

Flow separation and high drag can lead to increased energy consumption and potential device failure in some applications. We present a novel concept that mitigates these effects on the Backward Facing Step by controlling a single sinusoidal synthetic jet actuator located on the step wall. We conducted numerical simulations at Reynolds numbers of 200, 300, and 400 using a finite-volume flow solver. The numerical results were validated against existing literature data. Transfer functions for the system were derived from these numerical results. The actuator is regulated using a Proportional-Integral-Derivative (PID) controller. We also compared the performance effects of three PID parameter tuning methods: the classical Ziegler–Nichols (referred to as PID), fuzzy PID (FPID), and optimized fuzzy PID (OptFPID). The results indicated that FPID is more efficient than the conventional PID controller, showing a 17.39% reduction in recirculation length compared to scenarios without a synthetic jet. Physical interpretations revealed that the corner vortex is wider and taller when a jet is present, suggesting the expansion of the recirculation region toward the step wall, which leads to a decrease in recirculation length.