Adaptive fractional order model predictive control of boost converters with grey wolf optimization tuning and...

An adaptive fractional-order model predictive control (FO-MPC) framework of DC-DC boost converters, which incorporates the Exponential Recursive Least Squares (ERLS) identification, the use of the fractional-order dynamics, and the application of the Grey Wolf Optimization (GWO) is presented in this paper. An important discovery is that the combination creates synergistic effects: ERLS convergence is improved by 47% compared to standalone implementations, since the damping of adaptation transients is of fractional-order-damping-like-density, which previous combined methods (such as Wang et al. (2020)) or (Ghamari et al. (2025)) did not provide. The ERLS algorithm allows adaptation model free and convergence in 15 samples even without the use of exact mathematical models. An optimized α = 0.85, fractional-order operator in the noise rejection case and better stability margins is observed, which is 15dB more than the traditional MPC implementations. GWO, executed offline during commissioning, achieves 25 to 30 times faster convergence than conventional metaheuristics (GA, PSO) when tuning the controller parameters. Arduino DUE (84 MHz ARM Cortex-M3) hardware validation has shown that settling time is significantly decreased to 0.42s (83% lower than the baseline), that overshoot is kept to less than 1% (95% lower than the baseline), and that steady-state error is only 20mV (87% smaller than the baseline). The controller is stable in the 30% variations in parameter and 10 times changes in load with an execution time of 85µs, which is compatible with 10 kHz control frequency. Monte Carlo simulations (n = 1000) confirm a success rate of 98.2% in combined disturbances, and statistical significance is validated using the Wilcoxon signed-rank tests (p < 0.001, Cohen's d > 2.0). The industrial use has been tested and supported with 168 h continuous operation and IEC 61000-4-3 EMI compliance test.