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Licensed Unlicensed Requires Authentication Published by De Gruyter September 15, 2022

Optimization of PID controller for water level control of the nuclear steam generator using PSO and GA

Omid Safarzadeh ORCID logo EMAIL logo and Amir Tizdast
From the journal Kerntechnik


The water level control system implicated in the nuclear steam generator has played an essential role in unexpected shutdowns of the power plant. According to reports, about 25% of the emergency power blackouts are caused by improper level control systems. The effectiveness of optimization methods in designing a controller is currently proved in different disciplines. The novelty of this paper is the proportional integral derivative (PID) controller tuning of nuclear steam generator by particle swarm optimization (PSO) and genetic algorithm (GA) for the lowest steady-state error, overshoot, undershoot, and settling time. Different types of the cost function are employed to obtain the controller gains. The integral of the absolute error (IAE), square error (ISE), time-weighted average error (ITAE), time-weighted square error (ITSE), and a weighted function based on overshoot, undershoot, and settling time are used. The gain scheduling of optimized PIDs is used to have an entire operating range control system. The desired load-following and stability of the optimized PID controller are investigated under both time and frequency domains using trajectory tracking, disturbance rejection, and Nichols chart criterion.

Corresponding author: Omid Safarzadeh, Faculty of Engineering, Shahed University, Tehran, Iran, E-mail:

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.


Han, Z., Qi, H., Wang, L., Menhas, M.I., and Fei, M. (2018). Water level control of nuclear power plant steam generator based on intelligent virtual reference feedback tuning. In: Advances in green energy systems and smart grid. Springer, Singapore, pp. 14–23.10.1007/978-981-13-2381-2_2Search in Google Scholar

Irving, E., Miossec, C., and Tassart, J. (1979). Towards efficient full automatic operation of the PWR steam generator with water level adaptive control. In: Proc. 2nd int. conf. boiler dynamics and control in nuclear power stations. British Nuclear Energy Society, Bournemouth, U.K., pp. 309–329.Search in Google Scholar

Kennedy, J. and Eberhart, R.C. (1995). Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks. Piscataway, NJ, pp. 1942–1948.10.1109/ICNN.1995.488968Search in Google Scholar

Kong, X., Zhang, J., Xiao, Y., Qian, L., Su, L., Chen, B., and Xu, M. (2018). Performance optimization for steam generator level control based on a revised simultaneous perturbation stochastic approximation algorithm. In: 3rd International conference on intelligent green building and smart grid (IGBSG). Yi-Lan, Taiwan, pp. 1–4.10.1109/IGBSG.2018.8393526Search in Google Scholar

Menon, S.K. and Parlos, A.G. (1992). Gain-scheduled nonlinear control of U-tube steam generator water level. Nucl. Sci. Eng. 111: 294–308, in Google Scholar

Mousakazemi, S.M.H. and Ayoobian, N. (2019). Robust tuned PID controller with PSO based on two-point kinetic model and adaptive disturbance rejection for a PWR-type reactor. Prog. Nucl. Energy 111: 183–194, in Google Scholar

Mousakazemi, S.M.H., Ayoobian, N., and Ansarifar, G.R. (2018a). Control of the pressurized water nuclear reactors power using optimized proportional–integral–derivative controller with particle swarm optimization algorithm. Nucl. Eng. Technol. 50: 877–885, in Google Scholar

Mousakazemi, S.M.H., Ayoobian, N., and Ansarifar, G.R. (2018b). Control of the reactor core power in PWR using optimized PID controller with the real-coded GA. Ann. Nucl. Energy 118: 107–121, in Google Scholar

Rahmati, M. (2014). Multivariate control of the steam generator water levels and reactor power using quantitative feedback theory (in Persian), M.Sc. Thesis. Faculty of Engineering, Shahid Beheshti University.Search in Google Scholar

Razali, N.M. and Geraghty, J. (2011). Genetic algorithm performance with different selection strategies in solving TSP. In: Proceedings of the world congress on engineering (WCE). International Association of Engineers, London, U.K., pp. 1–6.Search in Google Scholar

Salehi, A., Safarzadeh, O., and Kazemi, M.H. (2019). Fractional order PID control of steam generator water level for nuclear steam supply systems. Nucl. Eng. Des. 342: 45–59, in Google Scholar

Wang, P., Yan, X., and Zhao, F. (2019). Multi-objective optimization of control parameters for a pressurized water reactor pressurizer using a genetic algorithm. Ann. Nucl. Energy 124: 9–20, in Google Scholar

Zarei, M. (2019). An optimization based output power regulation in small modular reactors. Nucl. Eng. Des. 344: 144–152, in Google Scholar

Zeng, W., Zhu, W., Hui, T., Chen, L., Xie, J., and Yu, T. (2020). An IMC-PID controller with particle swarm optimization algorithm for MSBR core power control. Nucl. Eng. Des. 360: 110513, in Google Scholar

Received: 2021-10-13
Published Online: 2022-09-15
Published in Print: 2022-10-26

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