Reliability-Based Multi-Objective Design of an FOPID Controller for Solar Furnaces Under Stochastic Parameter Uncertainties

Reliable solar energy harvesting demands advanced control strategies capable of maintaining thermal precision despite inherent environmental unpredictability. This research addresses the critical challenge of temperature regulation in the solar furnace system, which is hindered by severe non-linearities and stochastic environmental uncertainties. The study aims to transition Fractional-Order PID (FOPID) control from theoretical design to reliable industrial application by accounting for the Uncertain Design Vector (UDV) during the tuning phase. A Reliability-Based Design Optimization (RBDO) framework is proposed, utilizing a hybrid Multi-Objective Imperialist Competitive Algorithm (MOICA) integrated with Monte Carlo Analysis (MCAR). This approach simultaneously optimizes the Maximum Sensitivity (Ms), the integral of Time-weighted Absolute Error (ITAE) and their sensitivities, while ensuring physical realizability through the FOPID structure. Crucially, the simulation results demonstrate that the RBDO-tuned FOPID design achieves optimal performance levels comparable to deterministic methods while significantly reducing the overall system sensitivity by 35% to 55% compared to both deterministic and literature-based methods (GA-FOPID and PSO-FOPID). The study concludes that integrating probabilistic reliability into multi-objective metaheuristics provides a robust control strategy for high-temperature solar facilities, effectively mitigating the performance degradation caused by real-world parameter fluctuations and ensuring consistent operational stability.