Realisation-Aware Fractional Shaping for Robust Current Control of a Frequency-Controlled Parallel-Resonant Inverter

This study evaluates whether fractional-order shaping provides a meaningful performance advantage for robust current control of a frequency-controlled parallel-resonant inverter when compared under identical conditions with strongly tuned integer-order controllers. A nested fractional extension of an integral lead–lag regulator is implemented using an explicit integrator and a finite-band Oustaloup approximation. Three controller parameterisations are optimised using matched differential-evolution searches with five independent starts and 6000 objective evaluations per start. An exact rational two-plant certificate establishes a necessary lower bound of 0.02885438 for the inherited continuous-time objective. The re-tuned integer controller achieves a worst observed gain of 0.02885823, whereas the selected fractional controller reaches 0.02890450 at λ = 1.000448. The selected order therefore lies effectively at the integer limit, and the benchmark leaves very limited numerical headroom for improvement through fractional shaping. All five evaluated controllers settle successfully across 46 branch-specific cycle-synchronous simulations using a common actual-cycle zero-order-hold implementation. With two additional command-delay cycles, two local augmented maps become unstable for both the selected fractional controller and the re-tuned integer controller. Approximation-order analysis and controller-inclusive Jacobians further distinguish measured-output settling from slowly decaying internal memory. The results therefore identify benchmark-specific limits of fractional shaping rather than a general limitation of fractional-order control.