Fourier Neural Operator-driven transient analysis and control for supercritical CO₂ cycles

The dynamic performance and control strategies of supercritical carbon dioxide (SCO2) systems constitute a fundamental research area that demands thorough scientific exploration. This study systematically addresses several critical gaps in the transient analysis of SCO₂ systems, particularly highlighting the insufficient theoretical exploration of the system's dynamic behavior, the predominant reliance on conventional Proportional-Integral-Derivative (PID) control approaches, and the significant computational challenges in solving transient dynamics and control problems. To this end, the following research plan is proposed: first, the intrinsic principles of SCO₂ dynamic characteristics are analyzed based on the printed circuit heat exchanger (PCHE) transient model; second, system identification is performed for the SCO₂ system; and then, Model Predictive Control (MPC) and PI control-based reinforcement learning (RL-PI) suitable for the SCO₂ cycle is designed and compared with traditional PI control; and finally, a Fourier Neural Operator (FNO)-based model for the open-loop response of the SCO₂ system and its MPC controller is trained. The results shows that, at the microscopic level, the PCHE outlet temperature consists of an inertial system driven by wall heat transfer and a non-minimum phase system driven by inlet enthalpy. At the macroscopic level, efficiency exhibits non-minimum phase behavior, while net output power does not. A backpropagation (BP) neural network achieved optimal system identification, with training set fits of 97.56 % (efficiency) and 99.19 % (net output power), and validation set fits of 92.79 % and 97.75 %, respectively. MPC outperformed PI, RL-PI, and open-loop control, showing shorter response times, reduced overshoot, stronger noise immunity, and improved signal tracking. FNO successfully predicted the SCO₂ cycle's open-loop response, achieving relative errors of 10⁻⁴ for net output power and control outputs compared to MPC. The system performance was validated through numerical simulations, and results indicated that FNO has a significant advantage in computational efficiency, with memory and time reduction by 3 orders of magnitude.