Model order reduction of boiler system using nature-inspired metaheuristic optimization of PID controller

Abstract Boiler system control presents significant challenges due to its complex, high-order dynamics, which make real-time control computationally demanding. Traditional model order reduction (MOR) techniques often compromise system accuracy, while conventional Proportional-Integral-Derivative (PID) tuning methods struggle with nonlinearities and dynamic uncertainties. This study proposes a dual-stage optimization framework that integrates balanced truncation-based model order reduction with nature-inspired metaheuristic algorithms for PID controller tuning to address these issues. The PID controllers are optimized using both classical methods such as Ziegler-Nichols (ZN), Simple Internal Model Control (SIMC), Approximate M-Constrained Integral Gain Optimization (AMIGO), and Chien-Hrones-Reswick (CHR), as well as advanced optimization techniques like Particle Swarm Optimization (PSO), Krill Herd Optimization (KHO), Harris Hawks Optimization (HHO), Moth-Flame Optimization (MFO), and Sparrow Search Optimization (SSO). Experimental results demonstrate that the PSO-optimized PID controller achieves a 20% reduction in settling time and a 14.68% improvement in Integral Square Error (ISE) compared to conventional tuning methods. The HHO-based approach improves overall performance by 15%, while SSO significantly reduces computational complexity by 65% while maintaining 98% system accuracy. Statistical analysis (p < 0.05) confirms the robustness of the proposed methodology, showing a 45% reduction in standard deviation compared to traditional approaches. The proposed framework offers a scalable, computationally efficient, and high-performance solution for industrial boiler control systems, ensuring improved stability, faster response times, and real-time adaptability over existing strategies.