In this study, a demand-contributed load frequency control (LFC) strategy is proposed for frequency stabilization in a solar-wind-based autonomous microgrid system (AMGS). The proposed control framework employs a structurally enhanced version of the classical proportional-integral (PI) controller, augmented with a one plus derivative filter (PI-(1 + DF)) scheme. To optimize the controller parameters, a physics-inspired metaheuristic technique known as the Fick's Law Optimization (FLO) is implemented. This controller is designed to address the complex dynamics and uncertainties of the AMGS, which comprises renewable sources (solar and wind), conventional diesel engine generator (DEG), and flexible demand-side contributors such as electric vehicles (EVs), heat pumps (HPs), and freezers. Furthermore, realistic nonlinearities like governor dead band (GDB) and generation rate constraints (GRC) are incorporated into the model to ensure practical relevance. Comparative analysis reveals that the FLO-optimized PI-(1 + DF) controller significantly outperforms recent state-of-the-art algorithms such as the Mine Blast Algorithm (MBA) and the Sine Cosine Algorithm (SCA) in terms of settling time, peak overshoot, and various objective functions. Simulation results conducted in MATLAB/Simulink confirm the efficacy and robustness of the proposed approach, successfully maintaining frequency deviation within acceptable limits even under severe disturbances. Furthermore, robustness tests with ± 50% parametric variations demonstrate the controller's resilience and adaptability in highly uncertain environments. The peak overshoots (Hz) for a ± 50% variation in MG parameters are 0.02, 0.05, and 0.06, while the corresponding undershoots (Hz) are - 0.957, -0.72, and - 0.48. Similarly, for variations in the droop constant (R) the overshoots (Hz) are 0.074, 0.065, and 0.064, and the undershoots (Hz) are - 0.724, -0.725, and - 0.729, respectively.
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