Surrogate-Based Structured Uncertainty Modeling and Fixed-Structure Minimax Robust Control of a Frequency-Controlled Parallel Inverter

Frequency-controlled parallel inverters combine nonlinear switching dynamics with load-dependent periodic operation, which makes controller-oriented uncertainty modeling difficult. This paper presents a reproducible surrogate-to-robust-control workflow. A local slope calibration maps normalized switching-frequency variation to an equivalent continuous input, and four physical resistance–inductance corner linearizations are fitted by a three-state model with two real coefficient-space uncertainties. A third-order fixed-structure controller is obtained by finite-budget minimax mixed-sensitivity optimization and compared with a nominal filtered proportional–integral controller. Independent verification on a 31 × 31 uncertainty grid and a continuous worst-case search gives a peak-weighted gain of 0.028920 versus 0.089893 for the comparison controller, a 67.83% reduction in the adopted criterion; all 500 Monte Carlo closed loops are stable. Interior Jacobian errors remain below 0.010%, and a residual-augmented coefficient box preserves the robust-performance conclusion. Cycle-to-cycle nonlinear simulations cover the complete 5 × 5 physical resistance–inductance grid and both 310 A frequency branches at each of 23 feasible points. Fixed-frequency plant periodic orbits are locally contractive, while controller-in-the-loop tests settle on both branches within the tested horizon. The conclusions are local to the calibrated operating region and do not claim a global optimum or global nonlinear stability. The negative plant-orbit Floquet exponents reported here establish local contraction of the fixed-frequency physical periodic orbit; they are not interpreted as a global nonlinear closed-loop stability certificate. The normalized uncertainty square used for controller synthesis was constructed from rounded coefficient values. It includes conservative coefficient combinations that are not generated by a physical resistance–inductance pair, but the exact physical extreme of a31 at L = 0.5Lnom slightly exceeds the rounded upper limit. Accordingly, the original square is treated as a convenient design parametrization rather than as a strict physical overbound. For verification, a residual-augmented coefficient box was reconstructed from the exact analytical extrema and the measured interpolation residuals; this coverage-preserving set retains the robust-performance conclusion.