Optimal PID controllers design for discharge pressure-temperature control of centrifugal gas compressor system using Grey Wolf optimizer

In this paper, we introduce optimal PID controllers that are designed with the help of the recently developed metaheuristic Stochastic Grey Wolf Optimizer (GWO), with the gains K_p, K_i, and K_d of the controllers chosen via the minimization of the integral quadratic tracking error function e(t). This is done so that we can achieve the best control specifications, including no overshooting, good response and settling time, and no static error. The primary goal of this design is to improve the best performance and efficiency of the BCL 505 centrifugal gas compressor system, which is installed in the Hassi R'mel Gas Field in the south of Algeria. A GE 5002C Gas Turbine entrains this system with two shafts, where the goal is for the two outputs discharge pressure and temperature P2 and T2, respectively, to coincide to its desired references, based on two PID controllers. {"references": ["B. Nail, A. Kouzou, A. Hafaifa., Digital Stabilizing and Control for Two-Wheeled Robot,\" In: Derbel, Nabil. Ghommam, Jawhar. Zhu, Quanmin (Eds.). New Developments and Advances in Robot Control. 2019. Studies in Systems, Decision and Control, vol 175. Springer.", "Katsuhiko Ogata., Discrete-time control systems, 2nd, Englewood Cli_s: Prentice-Hall, 2005.", "Benbouhenni H. Commande DTC-RNA \u00e0 36 secteurs de la MAS par r\u00e9gulateur PI-flou de la vitesse. Recueil de m\u00e9canique Vol. 2 N\u00b02 (2017) pp 181-191", "BESSOUS N., REZAOUI M.M., MERZOUK I., BORNI A., ZAROUR L. Analyse d\u00e9taill\u00e9e du contenu spectral dans le courant statorique des machines asynchrones sous un d\u00e9faut de la cassure de barres rotoriques en utilisant la technique de la MCSA-FFT. Recueil de m\u00e9canique Vol.4 N\u00b02 (2019) pp.417-429", "Ren, T.-J., Chen, T.-C., & Chen, C.-J., Motion control for a two-wheeled vehicle using a self-tuning pid controller. Control Engineering Practice, 16, 365\u2013375.", "Mirjalili S, Mirjalili SM, Lewis A., Grey Wolf Optimizer. Adv Eng Softw 69, (2014), pp. 46-61", "B. Nail, A. Kouzou, A. Hafaifa, A. Chaibet,\" Parametric identification and stabilization of turbo-compressor plant based on matrix fraction description using experimental data,\" Journal of Engineering Science and Technology, vol. 13, no. 6, (2018), pp. 1850-1868,.", "Nail, B. [et al.]. A robust fault diagnosis and forecasting approach based on Kalman filter and interval type-2 fuzzy logic for efficiency improvement of centrifugal gas compressor system. \"Diagnostyka\", (2019), vol. 20, 2, p. 57-75", "Nail, B., Hadroug, N., Hafaifa, A., Kouzou, A., Fault Detection and Localization of Centrifugal Gas Compressor System Using Fuzzy Logic and Hybrid Kernel-SVM Methods. In: Derbel, N., Ghommam, J., Zhu, Q. (eds) Diagnosis, Fault Detection & Tolerant Control. Studies in Systems, Decision and Control, vol 269. (2020)., Springer", "Bachir Nail, Belkacem Bekhiti, Vicen\u00e7 Puig, Internal stability improvement of a natural gas centrifugal compressor system based on a new optimal output feedback controller using block transformation and grey wolf optimizer, Journal of Natural Gas Science and Engineering, 85, (2021)"]}