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

• Published in: Discover applied sciences Vol. 7; no. 5; pp. 402 - 36
• Main Authors: Singh, Anurag, Yadav, Shekhar, Tiwari, Nitesh, Nishad, Dinesh Kumar, Khalid, Saifullah
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 25.04.2025; Springer Nature B.V; Springer
• Subjects: Accuracy; Adaptability; Algorithms; Alternative energy sources; Applied and Technical Physics; Balanced truncation method; Boiler system; Boilers; Business metrics; Chemistry/Food Science; Comparative analysis; Complexity; Computer applications; Control systems; Controllers; Earth Sciences; Efficiency; Electric vehicles; Engineering; Environment; Heuristic methods; Krill; Materials Science; Methods; Model order reduction; Model predictive control; Model reduction; Nature-inspired computing; Optimization algorithms; Optimization techniques; Particle swarm optimization; Process controls; Proportional integral derivative; Real time; Renewable resources; Robust control; Settling; Soft computing; Statistical analysis; Statistics; Systems stability; Tuning; Balanced truncation method; Model predictive control; Control system optimization; Balanced truncation; Boiler system; Model order reduction; Soft computing; System identification; Nature-inspired computing; Computational intelligence; Industrial process control
• ISSN: 3004-9261; 2523-3963; 3004-9261; 2523-3971
• DOI: 10.1007/s42452-025-06927-0

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. Article Highlights The research introduces an innovative approach combining a balanced truncation method for model order reduction with nature-inspired optimization algorithms (PSO, KHO, HHO, MFO, SSO) for PID controller tuning in boiler systems. Integrating PID-based balanced truncation with Sparrow Search Optimization (SSO) demonstrated exceptional results in robustness and control efficiency compared to conventional tuning methods (ZN, SIMC, AMIGO, and CHR). Statistical analysis revealed that the proposed methodology achieved substantial enhancements. PSO showed the highest improvement (~ 20% in settling time), followed by HHO (~ 15% across metrics) while maintaining system stability and reducing computational complexity.