Proximate Time-Optimal Control of Flying-Capacitor Multi-Level Converters Using a Fixed Frequency PID Framework

The paper proposes a near time-optimal control method for flying-capacitor multi-level (FCML) converters to improve the transient performance under large-signal output voltage reference or step-load transients. The proposed control scheme is based on a simple voltage-mode proportional-integral-derivative (PID) framework, in which the proportional gain is tuned using a state-plane diagram to achieve proximate time-optimal transient recovery. A direct output voltage derivative replaces the capacitor current, while a small integral gain is enabled only during the steady-state operation. Importantly, the proposed control scheme uses a single unified controller structure and a fixed-frequency modulator at all times, which ensures seamless transitions between transients and steady-state operation. The approach is verified on an eight-level digitally controlled GaN-based FCML prototype. Experimental results obtained using the proposed approach demonstrate a five-fold reduction in the rise time and a two-fold reduction in the fall time compared to a conventional small-signal based tuning methods, for a step-reference transient from 25 V to 180 V and back respectively, at $v_{in}=200 {\mathrm V}$ and load resistance $R=100 \Omega$.