مروری بر کنترل پدیده سرج و مدل‌سازی در کمپرسورهای گریز از مرکز

الموضوعات :

عادل خسروی ¹ ( دانشکده مهندسی برق- واحد نجف آباد، دانشگاه آزاد اسلامی، نجف آباد، ایران )
عباس چترایی ² ( دانشکده مهندسی برق- واحد نجف آباد، دانشگاه آزاد اسلامی، نجف آباد، ایران )
غضنفر شاهقلیان ³ ( مرکز تحقیقات ریز شبکه های هوشمند- واحد نجف آباد، دانشگاه آزاد اسلامی، نجف آباد، ایران )
سید محمد کارگر ⁴ ( دانشکده مهندسی برق- واحد نجف آباد، دانشگاه آزاد اسلامی، نجف آباد، ایران )

تاريخ الإرسال : 11 الأحد , جمادى الثانية, 1442 تاريخ التأكيد : 16 الأربعاء , رمضان, 1442 تاريخ الإصدار : 10 السبت , شوال, 1442

الکلمات المفتاحية: مدل‌سازی, کمپرسور, فازی, پدیده سرج, کنترل سرج, فیدبک,

ملخص المقالة :

کمپرسورها به دلیل کاربرد گسترده‌ای که در صنایع مختلف برای فشرده‌سازی و انتقال گازها دارند از اهمیت ویژه‌ای برخوردار هستند. با توجه به افزایش روزافزون کاربرد کمپرسورها در صنعت، تعیین یک مدل ریاضی برای کمپرسور جهت طراحی سیستم کنترلی، تجزیه ‌و تحلیل و شبیه سازی کامپیوتری آن بسیار مهم است. همچنین در سال‌های اخیر مدل سازی های هوشمند نظیر شبکه عصبی و فازی به علت عملکرد واقع‌بینانه‌تر این مدل ها مورد توجه محققین قرارگرفته است و از انواع آن برای مدل سازی استفاده ‌شده است. روش های هوشمند دارای قابلیت بالایی برای برقراری ارتباط بین داده های ورودی و خروجی است. پدیده سرج در کمپرسورها یک مورد چالش برانگیز بوده چرا که خیلی سریع اتفاق افتاده و باعث آسیب به کمپرسور و مراحل تولید خواهد شد. این پدیده به صورت یک ناپایداری در جریان کاری کمپرسور تعریف می شود. کنترل پدیده سرج باعث گسترش محدوده عملیاتی کارکرد کمپرسور می گردد و از رخداد این پدیده جلوگیری می کند. در این مقاله مروری بر مدل سازی، پدیده سرج و انواع کنترل فعال و غیرفعال سرج بررسی می گردد. برای مدل سازی مدل مورگریتز و مدل های هوشمند مورد بررسی قرار گرفته اند که با توجه به نتایج به دست آمده می توان بیان کرد که مدل مورگریتز با گذشت زمان خطای بیشتری نسبت به مدل های هوشمند دارد و مدل مناسبی برای کمپرسور نیست. در ادامه کنترل پدیده سرج در کمپرسور به روش های فعال و غیرفعال بررسی می شود که کنترل کمپرسور در روش فعال نیازی به منحنی عملکرد کمپرسور نیست ولی در روش غیرفعال با استفاده از منحنی عملکرد و ایجاد حاشیه امنیت از خط سرج کمپرسور را کنترل نموده تا وارد پدیده سرج نشود. همین امر باعث می شود که عملکرد کنترل فعال نسبت به کنترل غیرفعال بهینه تر و مناسب تر باشد.

المصادر:

[1] L. Esteki, A.A. Zamani, S.M. Kargar, S.A. Mousavi, “Automatic generation control of multi-area power system using a fuzzy wavelet neural network load frequency controller combined with shuffled frog leaping algorithm”, Majlesi Journal of Electrical Engineering, vol. 7, no. 4, pp. 55-63, Dec. 2013.

[2] S.H. Mozafarpoor-Khoshrodi, G. Shahgholian, " Improvement of perturb and observe method for maximum power point tracking in wind energy conversion system using fuzzy controller", Energy Equipment and Systems, vol. 4, no. 2, pp. 111-122, Autumn 2016 (doi: 10.22059/EES.2016.23031).

[3] G. Shahgholian, “An overview of hydroelectric power plant: Operation, modeling, and control”, Journal of Renewable Energy and Environment, vol. 7, no. 3, pp. 14-28, Summer 2020 (doi: 10.30501/JREE.20­20.2­2­15­67.1087).

[4] E. Hosseini, G. Shahgholian, "Partial- or full-power production in WECS: A survey of control and structural strategies", European Power Electronics and Drives, vol. 27, no. 3, pp. 125-142, Dec. 2017 (doi: 10.1080/0­93­9­8368.2017.1413161).

[5] H. U. Frutschi, "Closed-cycle gas turbines: Operating experience and future potential", ASME Press, pp. 9–77, 2005 (doi: 10.1115/1.802264).

[6] Z. Tian, B. Jiang, A. Malik, Q. Zheng, "Axial helium compressor for high-temperature gas-cooled reactor: A review", Annals of Nuclear Energy, vol. 130, pp. 54-68, Aug. 2019 (doi: 10.1016/j.anucene.2019.02.032).

[7] M.H. Ahmadi, M.A. Nazari, R. Ghasempour, F. Pourfayaz, M. Rahimzadeh, T.A. Ming, "A review onsolar-assisted gas turbines", Energy Science And Engineering, vol. 6, no. 6, pp. 658-674, Dec. 2018 (doi: 1­0­.100­2/e­se3.238).

[8] S.M. Kargar, A.A. Zamani, M. Mohamadi, “The fuzzy controller design with imperialist competitive algorithm for the compressor system with gas turbine”, Majlesi Journal of Mechatronic Systems, vol. 1, no. 2, pp. 25-29, June 2012. 

[9] A.A. Bazmi, G. Zahedi, "Sustainable energy systems: Role of optimization modeling techniques in power generation and supply- A review", Renewable and Sustainable Energy Reviews, vol. 15, no. 8, pp. 3460-3500, Oct. 2011 (doi: 10.1016/j.rser.2011.05.003).

[10] S. Nazari, J. Siegel, A. Stefanopoulou, "Optimal energy management for a mild hybrid vehicle with electric and hybrid engine boosting systems", IEEE Trans. on Vehicular Technology, vol. 68, no. 4, pp. 3386-3399, April 2019 (doi: 10.1109/TVT.2019.2898868).

[11] J.H. Marais, "An integrated approach to optimise energy consumption of mine compressed air systems", Ph.D Thesis, School of Electrical, Electronic and Computer Engineering, North-West University, Potchefstroom, South Africa, 2012.

[12] J. Vermeulen, C. Cilliers, J.H. Marais, "Cost-effective compressor control to reduce oversupply of compr­essed air", Proceeding of the IEEE/ICUE, Cape Town, South Africa, pp. 1-7, Aug. 2017 (doi: 10.23919/I­CU­­E.­2­017.8068013)

[13] Z. He, X.Yang, D. Li, W.Wu, "Dynamic characteristics of a swing compressor for an air conditioning system at different discharge pressures", International Journal of Refrigeration, vol. 112, pp. 125-135, April 2020 (doi: 10.1016/j.ijrefrig.2019.12.021).

[14] S. Woo, M. Pecht, D. L. O'Neal, "Reliability design and case study of the domestic compressor subjected to repetitive internal stresses", Reliability Engineering and System Safety, vol. 193, Article Number. 106604, Jan. 2020 (doi: 10.1016/j.ress.2019.106604).

[15] M. M.Tanveer, C. R.Bradshaw, " Quantitative and qualitative evaluation of various positive-displacement compressor modeling platforms", International Journal of Refrigeration, Vol:119, pp. 48-63, 2020 (doi: 10.1­0­16/j.ijrefrig.2020.07.009)

[16] I.H. Bell, D. Ziviani, V. Lemort, C.R. Bradshaw, M. Mathison, W.T. Horton, J.E. Braun, E.A. Groll, "PDSim: A general quasi-steady modeling approach for positive displacement compressors and expanders", International Journal of Refrigeration, vol. 110, pp. 310-322, 2020 (doi: 10.1016/j.ijrefrig.2019.09.002)

[17] I.H. Bell, E.A. Groll, J.E. Braun, W. TravisHorton, "A computationally efficient hybrid leakage model for po­si­tive displacement compressors and expanders", International Journal of Refrigeration, vol. 36, no. 7, pp. 1965-1973, Nov. 2013 (doi: 10.1016/j.ijrefrig.2013.01.005).

[18] Z. Deng, H. Shen, K. Wang, H. Jin, "Vibration improvement and dynamic balance automatic optimization of rotor compressor", Proceeding of the IEEE/WCMEIM, pp. 224-228, Shanghai, China, Nov. 2019 (doi: 10.11­09/WCMEIM48965.2019.00049)

[19] H. Sheng, W. Huang, T. Zhang, “Output feedback control of surge and rotating stall in axial compressors”, Asian Journal of Control, vol. 19, no. 2, pp. 599-605, March 2017 (doi: 10.1002/asjc.1384).

[20] N. Fujisawa, T. Inui, Y. Ota, "Evolution process of diffuser stall in a centrifugal compressor with vaned diffu­ser", Journal of Turbomachinery, Vol. 141, No. 4, pp. 1-10, April 2019 (doi: 10.111­5/1.4042249).

[21] T. Nehler, "Linking energy efficiency measures in industrial compressed air systems with non-energy benefits– A review", Renewable and Sustainable Energy Reviews, vol. 89, pp. 72-87, June 2018 (doi: 10.1016/j.rser.2018.02.018)

[22] K. Srinivasan, "Identification of optimum inter-stage pressure for two-stage transcritical carbon dioxide refrigeration cycles", The Journal of Supercritical Fluids, vol. 58, no. 1, pp. 26-30, Aug. 2011 (doi: 10.1016/j.supflu.2011.04.015)

[23] G. Wang, X. Zhang, "Thermoeconomic optimization and comparison of the simple single-stage transcritical carbon dioxide vapor compression cycle with different subcooling methods for district heating and cooling", Energy Conversion and Management, vol. 185,  pp. 740-757, April 2019 (doi: 10.1016/j.enconman.201­9.0­2­.­024).

[24] F. Willems, B. Jager, "Modeling and control of compressor flow instabilities", IEEE Control Systems Magazine, vol. 19, no. 5, pp. 8-18, Oct. 1999 (doi: 10.1109/37.793434).

[25] A. Khosravi, A. Chatraei, G. Shahgholian, S.M. Kargar, “Modeling of K-250 compressor using NARX and hierarchical fuzzy model”, Iranian Journal of Electrical and Computer Engineering, vol. 18, no. 3, pp. 191-198, Autumn 2020 (in Persian).

[26] M. Righi, V. Pachidis, L. Könözsy, L. Pawsey, "Three-dimensional through-flow modeling of axial flow compressor rotating stall and surge", Aerospace Science and Technology, vol. 78, pp. 271–279, July 2018 (doi: 10.1016/j.ast.2018.04.021).

[27] Y.J. Jung, H. Jeon, Y. Jung, K.J. Lee, M. Choi, "Effects of recessed blade tips on stall margin in a transonic axial compressor", Aerospace Science and Technology, vol. 54, pp. 41–48, July 2016 (doi: 10.1016/j­.ast.2­01­­6.­04.009).

[28] G. Shahgholian, "Review of power system stabilizer: Application, modeling, analysis and control strategy", Int­ern­ational Journal on Technical and Physical Problems of Engineering, vol. 5, No. 3, pp. 41-52, Sept. 2013.

[29] G. Shahgholian, “Modeling and simulation of a two-mass resonant system with speed controller”, International Journal of Information and Electronics Engineering, vol. 3, no. 5, pp. 448-452, Sept. 2013 (doi: 10.7763/IJIEE.2013.V3.355).

[30] G. Shahgholian, P. Shafaghi, "State space modeling and eigenvalue analysis of the permanent magnet DC motor drive system", Proceeding of the IEEE/ICECT, pp. 63-67, Kuala Lumpur, Malaysia, May 2010 (doi: 10.11­09/IC­ECTECH.2010.54799 87).

[31] G. Shahgholian, J. Faiz, P. Shafaghi, "Analysis and simulation of speed control for two-mass resonant syst­e­m", Proceeding of the IEEE/ICCEE, pp. 666-670, Dubai, United Arab Emirates, Dec. 2009 (doi: 10.110­9/I­CCE­E.2009.41).

[32] T.K. Ibrahim, M.M. Rahman, A.N.A. Alla, "Study on the effective parameter of gas turbine model with intercooled compression process", International Journal of Scientific Research and Essays, vol. 23, pp. 3760-3770, 2010 (doi: 10.2298/tsci111016143i).

[33] I. Komargodski, M. Naor, E. Yogev, " White-box vs. black-box complexity of search problems: Ramsey and graph property testing", Journal of the ACM, vol. 66, July 2019 ( doi: 10.1145/3341106).

[34] A. Fonti, G. Comodi, S. Pizzuti, A. Arteconi, L. Helsen, " Low order grey-box model for short-term thermal behavior prediction in buildings", Energy Procedia, vol. 105, pp. 2107-2112, May 2017 (doi: 10.10­16/j.e­gyp­ro. 2017.03.592).

[35] K. Ažman, J. Kocijan, "Application of gaussian processes for black-box modelling of biosystemes", ISA Transactions, vol. 46, pp. 443-457, Oct. 2007 (doi: 10.1016/j.isatra.2007.04.001).

[36] M. Rampazzo, D. Tognin, M. Pagan, L. Carniello, A. Beghi, "Modelling simulation and real-time control of a laboratory tid generation system", Control Engineering, vol. 83, pp. 165-175, Feb. 2019 (doi: 10.101­6/J.­CO­­NENGPRAC.2018.10.016).

[37] O.O. Badmus, S. Chowdhury, K.M. Eveker, C.N. Net, "Control-oriented high-frequency turbomachinery mo­de­ling: Single-stage compres-sion system one-dimensional model", Journal of Turbomachinery, vol. 117, no. 1, pp. 47–61, Jan. 1995 (doi: 10.1115/1.2835643).

[38] E. Aghadavoodi, G. Shahgholian, "A new practical feed-forward cascade analyze for close loop ident­ific­ation of combustion control loop system through RANFIS and NARX", Applied Thermal Engine­ering, vol. 133, pp. 381-395, March 2018 (doi: 10.1016/j.applthermaleng.2018.01.075).

[39] T Iura, W.D. Rannie, "Observations of propagating stall in axial-flow compressor", Trans. ASME, vol. 76, pp. 463–471, 1954 (doi: 10.1007/BF01600530).

[40]  F.E. Marble, "Propagation of stall in a compressor blade row", Journal of the Aeronautical Sciences, vol. 22, no. 8, pp. 541-554, 1953 (doi: 10.2514/8.3395).

[41] E.M. Greitzer, "Surge and rotating stall in axial flow compressors, Part I: Theoretical Compression System Model", Journal of  Engineering for Gas Turbinr and Power, vol. 98, no. 2, pp. 190-198, April 1976 (doi: 10.1115/1.3446138).

[42] F.K. Moore, E.M. Greitzer, "A theory of post-stall transients in axial compression systems: Part II-appli­ca­ti­o­n", Journal of Engineering for Gas Turbines and Power, vol. 108, pp. 231-239, 1986 (doi: 10.11­15/1.­3239893).

[43] D. Hanbay, A. Baylar, M. Batan, "Prediction of aeration efficiency on stepped cascades by using least square support vector machines", Expert Systems with Applications, vol. 36, pp. 4248-4252 2009 (doi: 10.1­01­6/j.eswa.2008.03.003).

[44] J. Kohonen, S. Reinikainen, K. Aaljoki, "Non-linear PLS approach in score surface", Chemometrics and Intelligent Laboratory Systems, vol. 97, pp. 159-163, 2009 (doi: 10.1016/j.chemolab.2009.03.010).

[45] H. Saxen, F. Pettersson, "Nonlinear prediction of the hot metal silicon content in the blast furnace", ISIJ International, vol. 47, no. 12, pp. 1732-1737, 2007 (doi: 10.2355/isijinternational.47.1732).

[46] J. Chen, "A predictive system for blast furnaces by integrating a neural network with qualitative analysis", Engineering Applications of Artificial Intelligence, vol. 14, pp. 77-85, 2001 (doi: 10.1016/S0952-197­6(0­0)0­0062-2).

[47] H. Sun, H. Haitao, W. Jingwei, D. Guoliang, L. Geping, W. Xuyang, L. Zhongyuan, "A theory-based explicit calculation model for variable speed scroll compressors with vapor injection", International Journal of Refrigeration, vol. 88, pp. 402-412, April 2018 (doi: 10.1016/j.ijrefrig.2018.01.016).

[48] K. Liang, "Analysis of oil-free linear compressor operated at high pressure ra- tios for household refrigeration", Energy, vol. 151, pp. 324–331, May 2018 (doi:10.1016/j.energy.2018.03.068).

[49] J. Helvoirt, B. Jager, M. Steinbuch, J. Smeulers, "Modeling and identification of centrifugal compressor dynamics with approximate realizations", Proceedings of the IEEE/CCA, Toronto, Canada, Aug. 2017 (doi: 10.11­09/CCA. 2017.1507335).

[50] J. Li, J. Du, C. Nie, H. Zhang, "Review of tip air injection to improve stall margin in axial compressors", Progress in Aerospace Sciences, vol. 106, pp. 15-31, April 2019 (doi: 10.1016/j.paerosci.2019.01.005).

[51] X. Zheng, Z. Li, "Blade-end treatment to improve the performance of axial compressors: An overview", Progress in Aerospace Sciences, vol. 88, pp. 1-14, Jan. 2017 (doi: 10.1016/j.paerosci.2016.09.001).

[52] M.A. Azizi, J. Brouwer, "Progress in solid oxide fuel cell-gas turbine hybrid power systems: System design and analysis, transient operation, controls and optimization", Applied Energy, vol. 215, pp. 237-289, April 2018 (doi: 10.1016/j.apenergy.2018.01.098).

[53] K.  Liang, "A review of linear compressors for refrigeration", International Journal of Refrigeration, vol. 84, pp. 253-273, Dec. 2017 (doi: 10.1016/j.ijrefrig.2017.08.015).

[54] G. Gu, A. Sparks, S. S. Banda, "An overview of rotating stall and surge control for axial flow compressors", IEEE Trans. on Control Systems Technology, vol. 7, no. 6, pp. 639-647, Nov. 1999 (doi: 10.1109/87.799­664).

[55]  C. He, H. Li, Z. Li, X. Zhao, "An improved bistable stochastic resonance and its application on weak fault characteristic identification of centrifugal compressor blades", Journal of Sound and Vibration, vol. 442, pp. 677-697, March 2019 (doi: 10.1016/j.jsv.2018.11.016).

[56] L. Der-Cherng, S. Chau-Chung, H. Jeng-Tze, "Robust stabilization of a centrifugal compressor with spool dynamics", IEEE Trans. on Control Systems Technology, vol. 12, pp. 966-972, 2004 (doi: 10.1109/TCST.­2­00­4.833611)

[57] P. Aaslid, "Modelling of variable speed centrifugal compressors for anti-surge control", Master Thesis, Norwegian University of Science and Technology, June 2009.

[58] D. Zhao, B. Blunier, F. Gao, M. Dou, A. Miraoui, "Control of an ultrahigh-speed centrifugal compressor for the air management of fuel cell systems", IEEE Trans. on Industry Applications, vol. 50, no. 3, pp. 2225-2234, May/June 2014 (doi: 10.1109/TIA.2013.2282838).

[59] X. Ma, S. Zheng, K. Wang, "Active surge control for magnetically suspended centrifugal compressors using a variable equilibrium point approach", IEEE Trans. on Industrial Electronics, vol. 66, no. 12, pp. 9383 – 9393, Dec. 2019 (doi: 10.1109/TIE.2019.2891412).

[60] C. Yue-yan, L. Shao-zhong, S. Xing-ke, "The research of antisurge control on air separation compressor", Proceeding of the IEEE/ICISE), pp. 1613-1616, Hangzhou, China, Dec. 2010 (doi: 10.1109/ICISE.2010­.5­6­9­1­419).

[61] H. Imani, M. R. Jahed-Motlagh, K. Salahshoor, A. Ramezani,  A. Moarefianpur, "A novel tube model pred­ic­tive control for surge instability in compressor system including piping acoustic", Journal Cogent Engineering, vol. 4, no. 1, pp. 1-16, Dec. 2017 (doi: doi.org/10.1080/23311916.2017.1409373).

[62] A. Cortinovisa, H.J. Ferreaua, D. Lewandowskib, M. Mercangöz, "Experimental evaluation of MPC-based anti-surge and process control for electric driven centrifugal gas compressors", Journal of Process Control, vol. 34, pp. 13-25, Oct. 2015 (doi: 10.1016/j.jprocont.2015.07.001).

[63] M. Ghanavati, A. Chakravarthy, "Demand-side energy management by use of a design-then-approximate controller for aggregated thermostatic loads", IEEE Trans. on Control Systems Technology, vol. 26, no. 4, pp.1439-1448, July 2018 (doi: 10.1109/TCST.2017.2705157).

[64] C. Wang, C. Shao, Y. Han, "Centrifugal compressor surge control using nonlinear model predictive control based on LS-SVM", Proceeding of the IEEE/ISSCAA, pp. 466-471, China, Harbin, June  2010 (doi: 10.110­9/IS­SCAA.2010.5633206)

[65] H. Sheng, Q. Chen, J. LiZefan, L. Wang, T. Zhang, "Robust adaptive backstepping active control of compressor surge based on wavelet neural network", Aerospace Science and Technology, vol.106,  Article Number: 106139, Nov. 2020 (doi: 10.1016/j.ast.2020.106139).

[66] R.S. Shehata, H.A. Abdullah, F.F.G. Areed, "Fuzzy logic surge control in constant speed centrifugal com­pr­e­ssors", Proceeding of the IEEE/CCECE, pp. 653-658, Niagara Falls, ON, Canada, May 2008 (doi: 1­0­.11­0­9/C­CECE.2008.4564616).

[67] S. Lin, C. Yang, P. Wu and Z. Song, "Fuzzy logic surge control in variable speed axial compressors", Proce­eding of the IEEE/ICCA, pp. 1178-1183, China, Hangzhou, June 2013 (doi: 10.1109/ICCA.20­13.65­6­51­18).

[68] G. Shahgholian, "Modelling and simulation of low-head hydro turbine for small signal stability analysis in power system", Journal of Renewable Energy and Environment, vol. 3, no. 3, pp. 11-20, Summer 2016 (doi: 10.30501/JREE.2016.70088).

[69] I. Calero, C.A. Cañizares, K. Bhattacharya, "Implementation of transient stability model of compressed air energy storage systems", IEEE Trans. on Power Systems, vol. 35, no. 6, pp. 4734-4744, Nov. 2020 (doi: 10.1109/TPWRS.2020.2995787).

[70] A Kiani, B. Fani, G Shahgholian, “A multi-agent solution to multi-thread protection of DG-dominated dis­tr­ib­ution networks”, International Journal of Electrical Power and Energy Systems, vol. 130, Article Num­ber: 106921, Sept. 2021 (doi: 10.1016/j.ijepes.2021.106921).

[71] R. Mehrad, S.M. Kargar, “Integrated model predictive fault-tolerant control, and fault detection based on the parity space approach for a reverse osmosis desalination unit”, Transactions of the Institute of Measurement and Control, vol. 42, no. 10, pp. 1882-1894, June 2020 (doi: 10.1177/0142331219898942).

[72] A. Guyen, J. Lauber, M. Dambrine, "Robust H∞ control forthe turbocharged air system using the multiple model approach", Proceeding of the IEEE/IECON, pp. 2464-2469, Montreal, QC, Canada, Oct. 2012 (doi: 10.1109/IECON.2012.6388860)

[73] K.E. Hansen, P.Jorgensen, P.S. Larsen, "Experimental and theoretical study of surge in a small centrifugal compressor", Journal of Fluids Engineering, vol. 10, no. 3, Sept. 1981 (doi: 10.1115/1.3240796).

[74] C. Meuleman, "Measurement and unsteady flow modelling of centrifugal compressor surge", Ph.D. Thesis, Technische Universiteit Eindhoven: Eindhoven, The Netherlands, 2002 (doi: 10.6100/IR557873).

[75]  D. Fink, N. Cumpsty, E.M. Greitzer, "Surge dynamics in a free-spool centrifugal compressor system", Journal of Turbomachinery, vol. 114, no. 2, pp. 321-332, April 1992 (doi: 10.1115/1.2929146).

[76] S.Y. Yoon, Z. Lin, C. Goyne, P.E. Allaire, "An enhanced Greitzer compressor model with pipeline dyna­mic­sincluded", Proceedings of the IEEE/ACC, pp. 4731-4736, San Francisco, CA, USA, June/July 2011 (doi: 10.1109/ACC.2011.5991119).

[77]  F. Willems, A.G. Jager, de, "Modeling and control of compressor flow instabilities”, IEEE Control Systems Magazine, vol. 19, no. 5, pp. 8-18, Oct. 1999 (doi: 10.1109/37.793434).

[78] A. Jaeschke, K. Kabalyk, F. Grapow, G. Liskiewicz, "Analysis of unstable plenum in system volome: Mathematical modelling and experimental results", Proceedings of the ASME Turbo Expo, Oslo, vol. 2, 2018 (doi: 10.1115/GT2018-76727).

[79] L. Horodko, "Time-frequency analysis of the surge onset in the centrifugal blower", Symkom, pp. 299-306, 2015 (doi: 10.1515/eng-2015-0040).

[80] G.L. Arnulfi, P. Giannattasio, C. Giusto, A.F. Massardo, D. Micheli, P. Pinamonti "Multistage centrifugal compressor surge analysis: Part II—Numerical simulation and dynamic control parameters evaluation". Journal of Turbomachinery, vol. 121, no. 2, pp. 312-320, April 1992.

[81] F. Willems, W. P. M. H. Heemels, B. de Jager, A. A. Stoorvogel, "Positive feedback stabilization of centrifugal compressor surge", Automatica, vol. 38, no. 2, pp. 311–318, Feb. 2002 (doi: 10.1016/S0005-10­98­(01)00202-3).

[82] J.T. Gravdahl, F. Willems, B. de Jager, O. Egeland, "Modeling ofsurge in free-spool centrifugal compr­ess­or­s: Experimental validation", Journal of Propulsion and Power, vol. 20, no. 5, pp.849–857, Sept./Oct. 2004 (doi: 10.2514/1.10052).

[83] J.T. Gravdahl, O. Egeland, "A Moore-Greitzer model with spool dynamics", Proceeding of the IEEE/CDC, pp. 0191-2216, San Diego, CA, USA, Dec. 1997 (doi: 10.1109/CDC.1997.64975).

[84] J.M. Haynes, G.J. Hendricks, A.H. Epstein, "Active stabilization of rotating stall in a three-stage axial compressor", ASME Journal of Turbomachinery, vol. 116, no. 2, pp. 226-239, April 1994 (doi: 10.111­5/1.2­928­357).

[85] J.D. Paduano, "Modeling for control of rotating stall", Automatica, vol. 30, no. 9, pp. 1357-1373, Sept. 1994 (doi: 10.1016/0005-1098(94)90001-9).

[86]  G.J. Hendricks, J.S. Sabnis, M.R. Feulner, "Analysis of instability inception in high-speed multistage axial-flow compressors", ASME Journal of Turbomachinery, vol. 119, no. 4, pp. 714-722, Oct. 1997 (doi: 10.1­11­5/1­.2841181).

[87] E. M. Gruber, C. Bordons, and A. Oliva, "The stability of pumping systems- The 1980 freeman scholar lecture", Journal of Fluids Engineering, vol. 103, no. 2, pp. 193-242, Jun. 1981 (doi: 10.1115/1.3241725).

[88]  J.T. Gravdahl, O. Egeland, S.O. Vatland, "Drive torque actuation in active surge control of centrifugal co­m­p­ressors", Automatica, vol. 38, no. 11, pp. 1881-1893, Nov. 2002 (doi: 10.1016/S0005-1098(02)00113-9).

[89] ]J.T. Gravdahl, O. Egeland, "Centrifugal compressor surge and speed control", IEEE Trans. on Control Systems. Technology, vol. 7, no. 5, pp. 567-579, Sept. 1999 (doi: 10.1109/87.784420).

[90] J.T Gravdahl, F. Willems, B. Jager, O. Egeland, "Modeling of surge in free-spool centrifugal compressors: Experimental validation", Journal of Propulsion and Power, vol. 20, no. 5, pp. 849-857, May 2012 (doi: 10.25­14/1.10052).

[91] K. Song, C. Jeong, C. Han, "Hybrid compressor model for optimal operation of CDA system", Computer Aided Chemical Engineering, vol. 28, pp. 889-894, 2010 (doi: 10.1016/S1570-7946(10)28149-X).

[92] T. Turunen-Saaresti, P. Röyttä, J. Honkatukia, J. Backman, "Predicting off-design range and performance of refrigeration cycle with two-stage centrifugal compressor and flash intercooler", International Journal of Refrigeration, vol. 33, no. 6, pp. 1152-1160, Sept. 2010 (doi: 10.1016/j.ijrefrig.2010.04.008)

[93] T. Turunen-Saaresti, P. Röyttä, J. Honkatukia, "Optimising the refrigeration cycle with a two-stage cen­tri­fu­gal compressor and a flash intercooler", International Journal of Refrigeration, vol. 32, no. 6, pp. 1366-1375, Sept. 2009 (doi: 10.1016/j.ijrefrig.2009.01.006).

[94] D. Popova, "Neuro-fuzzy modeling of compressor unit performance", Proceeding opf the IEEE/RPC, pp. 1-3, Vladivostok, Russian, Aug. 2018 (doi: 10.1109/RPC.2018.8482214).

[95] J.T. Gravdahl, F. Willems, B. Jager, O. Egeland, "Modeling forsurge control of centrifugal compressors: C­o­m­pa­rison with experiment", Proceeding ov the IEEE/CDC, vol. 2, pp. 1341–1346, Sydney, NSW, Australia, Dec. 2002 (doi: 10.1109/CDC.2000.912043).

[96] F. Chu, F. Wang, X. Wang, S. Zhang, "A model for parameter esti-mation of multistage centrifugal compressor and compressor performanceanalysis using genetic algorithm", Science China Technological Sciences, vol. 55, no. 11, pp. 3163–3175, 2012 (doi: 10.1007/s11431-012-5029-9).

[97] M. Cicciotti, D.P. Xenos, A.E. Bouaswaig, N.F. Thornhill, R.F. Martinez-Botas, "Physical modelling of industrial multistage cen-trifugal compressors for monitoring and simulation", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 229, pp. 3433–3448, Mar. 2015 (doi: 10.1177/0954406215572433).

[98] S. Sanaye, M. Dehghandokht, H. Mohammadbeigi, S. Bahrami, "Modeling of rotary vane compressor applying artificial neural network", International Journal of Refrigeration, vol. 34, no. 3, pp. 764–772, May 2011 (doi: 10.1016/j.ijrefrig.2010.12.007).

[99] K. Ghorbanian, M. Gholamrezaei, "An artificial neural networkapproach to compressor performance prediction", Applied Energy, vol. 86, no. 7–8, pp. 1210–1221, July/Aug. 2009 (doi: 10.1016/j.ape­nergy.20­08.0­6.006).

[100] X. Wu, Y. Li, "Self-learning based centrifugal compressor surge map-ping with computationally efficient adaptive asymmetric support vectormachine", Journal of Dynamic Systems, Measurement, and Control, vol. 134, no. 5, Article Number: 051008, Sept. 2012 (doi: 10.1115/1.4006219).

[101] J. Fei, N. Zhao, Y. Shi, Y. Feng, Z. Wang, "Compressor performanceprediction using a novel feed-forward neural network based on Gaussiankernel function", Advances in Mechanical Engineering, vol. 8, no. 1, pp. 1–14, Jan. 2016 (10.1177/1687814016628396).

[102] S. Chen, S A.  Billings, P M.  Grant, "Recursive hybrid algorithm for nonlinear identification using radial basis function networks", lnternational Journal of Control, vol. 55, no. 5, pp. 1051-1070, Oct. 2007 (doi: 10­.1­0­80/­00207­179208934272).

[103] Z. Tian, B. Gu, L. Yang, Y. Lu, "Hybrid ANN—PLS approach to scrollcompressor thermodynamic performance prediction", Applied Thermal Engineering, vol. 77, pp. 113–120, Feb. 2015 (doi: 10.1016/j.applt­herma­leng.2014.12.023).

[104] J.D. Lewins, "Optimizing an intercooled compressor for an ideal gas model", International Journal of Mechanical Engineering Education, vol. 31, no. 1, pp. 190-200, July 2003 (doi: 10.7227/IJMEE.31.3.1).

[105] R. Dehner, A. Selamet, P. Keller, M. Becker, "Simulation of deep surge in a turbocharger compression system", Journal Turbomach, vol. 138, no. 11, Article Number: 111002, 2016 (doi .org /10 .1115 /1.403­3260).

[106] H. Sun, H. Haitao, W. Jingwei, D. Guoliang, L. Geping, W. Xuyang, L. Zhongyuan, "A theory-based explicit calculation model for variable speed scroll compressors with vapor injection", International Journal of Refrigeration, vol. 88, pp. 402-412, April 2018 (doi: 10.1016/j.ijrefrig.2018.01.016).

[107] N. Daroogheh, "Centrifugal compressor identification using lolimot", Proceeding of the IEEE/CCDC, pp. 771-774, Guilin, China, June 2009 (doi:10.1109/CCDC.2009.5191867).

[108] R. Dehner, A. Selamet, P. Keller, M. Becker, "Simulation of mild surge in a tur-bocharger compression system", SAE International Journal Engines, vol. 3, no. 2, pp. 197-212, Jan. 2010 (doi: 10.4271/2010-01-2142).

[109] S. Teramoto, "Analysis of the entire surge cycle of a multi-stage high-speed com-pressor", Annual Research Briefs, Center for Turbulence Research, Stanford University, pp.205–218, 2008.

[110] C. Robinson, M. Casey, "An optimization technique for radial compressor im-pellers",ASME Turbo Expo: Power for Land, Sea and Air, pp. 2401-2411, Aug. 2009 (doi: 10.1115/GT2008-50561)

[111] K. Do Won, K. Tong Seop "Model-based performance diagnostics of heavy-duty gas turbines using compressor map adaptation". Applied Energy, vol. 212, pp. 1345-1359, Feb. 2018 (doi: 10.1016/j.ap­ene­rg­y.2­017.12.126).

[112] J.W. Yoon, S.Wilailak, J. Bae, C. Lee, I. Kim, "Surge analysis in a centrifugal compressor using a dimensionless surge number", Chemical Engineering Research and Design, vol. 164, pp. 240-247, Dec. 2020 (doi: 10.1016/j.cherd.2020.10.004).

[113] Q. Huang, M. Zhang, X. Zheng, "Compressor surge based on a 1D-3D coupled method – Part 2: Surge investigation", Aerospace Science and Technology, vol. 90, pp. 289-298, July 2019 (doi: 10.1016/j.ast­.2019­.0­4.042)

[114] K. M. Arthur, H. Basu, S. Y. Yoon, "Stabilization of compressor surge in systems with uncertain equi­libr­iu­m flow", ISA Transactions, vol. 93, pp. 115–124, Oct. 2019 (doi: 10.1016/j.isatra.2019.03.004).

[115] Y. Xu, H. Guo, X. Zhang, X. Lin, L. Wang, Y. Zhang, H. Chen, "Comprehensiveexergy analysis of the dynamic process of compressed air energy storage systemwith low-temperature thermal energy storage", Applied Thermal Engineering, vol. 147, pp. 684-693, Jan. 2019 (doi: 10.1016/j.applth­ermal­en­g.20­18­.10.11­5).

[116] J. Sun, Z. Zuo, Q. Liang, X. Zhou, W. Guo, H. Chen, "Theoretical and experimental study on effects of humidity on centrifugalcompressor performance", Applied Thermal Engineering, vol. 147, Artiacla Number: 115300, June 2020 (doi: 10.1016/j.applthermaleng.2020.115300).

[117] M. Mojaddam, K.R. Pullen,"Optimization of a centrifugal compressor usingthe design of experiment technique", Applied Sciences, vol. 9, no. 2, Article Number: 291, Jan. 2019. (doi: 10.3390/app9020291)

[118] J. Sun, J. Zhao, K. Wang, "Online surge detection method based on axial displacement sensor of MSCC", IEEE Sensors Journal, vol. 19, no. 15, pp. 6029-6036, Aug. 2019 (doi: 10.1109/JSE­N.20­19.29­093­1­1).

[119] H. Jiang, Z. Li, K. Liang, "A novel sensorless stroke detection technique using low-cost inductive coil for resonant free-piston machines", IEEE Trans. on Industrial Electronics, vol. 68, no. 2, pp. 1087-1094, Feb. 2021 (doi: 10.1109/TIE.2020.2965468).

[120] J.H. Horlock, "Compressor performance with water injection", Proceeding of the ASME Turbo Expo,  New Orleans, Louisiana, June 2001 (doi: 10.1115/2001-GT-0343).

[121] A. Cortinovis, D. Pareschi, M. Mercangoez, T. Besselmann, "Model predictive anti-surge control of centrifugal compressors with variable-speed drives", IFAC Proceedings Volumes, vol. 45, pp. 251-256, 2012 (doi: 10.3182/20120531-2-NO-4020.00052).

[122] A.J. White, A.J. Meacock, "An evaluation of the effects ofwater injection on compressorperformance",  Journal of Engineering for Gas Turbines and Power, pp. 748-754, Oct. 2004 (doi: 10.1115/1.1765125).

[123] Y. Zhang, S. Zheng, Q. Chen, J. Fang, "Surge detection approach for magnetically suspended cent­rifu­g­a­l compressors using adaptive frequency estimator", IEEE Trans. on Industrial Electronics, vol. 65, no. 7, pp. 5733-5742, July 2018 (doi: 10.1109/TIE.2017.2774728)

[124] G. Torrisi, S. Grammatico, M. Morari, R. S. Smith, "Model predictive control approaches for centri­fu­g­a­l compression systems”, Proceeding of the IEEE/CDC, pp. 4320-4325, Japan, Osaka, 2015 (doi: 10­.1­109/C­DC.2015.7402893)

[125] J.T. Gravdahl, O. Egeland, "Compressor surge and Rotating stall modeling and control", Springer, 1999 (ISBN: 978-1-4471-0827-6).

[126] S. Tavakoli, l. Griffin, P. Fleming, "An overview of compressor instabilities: Basic concepts and control", IFAC Proceedings Volumes, vol. 37, pp. 523-528, June 2004 (doi: 10.1016/S1474-6670(17)32228-0).

[127] R. Dehner, A. Selamet, P. Keller, M. Becker, "Simulation of mild surge in a turbocharger compression system", SAE International Journal of Engines, vol. 3, no. 2, pp.197-212, 2010 (doi: 10.4271/2010-01-2142).

[128] M.G. Rose, K. Irmler, M. Schleer, D. Stahlecker, R.S. Abhari, "Classic surge in a centrifugal compr­es­s­or", Journal ASME, pp. 729-740, Feb. 2009 (doi: 10.1115/GT2003-38476).

[129] Z. Wang, J. Li, K. Fan, W. Ma, H. Lei, "Prediction method for low speed characteristicsof compressor based on modified similaritytheory with genetic algorithm", IEEE ACCESS, vol. 6, pp. 36834-36839, June 2018 (doi: 10.1109/ACCESS.2018.2846049).

[130] I. Shahin, M. Gadala, M. Alqaradawi, O. Badr, "Large eddy simulationfor a deep surge cyclein a high-speed centrifugalcompressor with vaneddiffuser", Journal of Turbomachinery, vol. 137, no. 10, Article Number: 101007, Oct. 2015 (doi: /10.1115/1.4030790).

[131] K.K. Botros, J.F. Henderson, "Developments in centrifugalcompressor surge control- A technology assessment", Journal of Turbomachinery, vol. 116, pp. 240-349, April 1994 (doi: 10.1115/1.2928358).

[132] J.O. Lamell, T. Trumbo, T.F. Nestli, "Offshore platform poweredwith new electrical motor drive system", Proceeding of the IEEE/PCICON, pp. 259-266, Denver, Co, USA, Sept. 2005 (doi: 10.1109/PCIC­O­N.20­05.1524562)

[133] G. Torrisi, S. Mariéthoz, R.S. Smith, M. Morari, "Comparison ofthe efficiency of different magnetiz­at­i­on strategies for a variable speedinduction machine drive", Proceeding of the  EPE, pp. 1-15, Switzerland, Geneva, Sept. 2015 (doi: 10.1109/EPE.2015.7309387).

[134] H.P. Bloch, "A practical guide to compressor technology", JohnWiley and Sons, 2006 (ISSBN: 9780471727934 ).

[135] F. Blanchini, P. Giannatasio, P. Pinamonti, D. Micheli, "Experimental evaluation of a high-gain control for compres-sor surge suppression", ASME Journal of Turbomachinery, vol. 124, no. 1, pp. 27-35, Jan. 2002 (doi: 10.1115/1.1413475).

[136] A.H. Epstein, E.F. Williams, E.M. Greitzer, "Active suppression ofaerodynamic instabilities in turbom­achi­nery", Journal of Propulsion and Power, vol. 5, no. 2, pp. 204-211, 1989 (doi: 10.2514/3.23137)..

[137] C. Rodgers, "Centrifugal compressor inlet guide vanes for increased surge margin", Journal of Turbomachinery, pp. 696-702, Oct. 1991 (doi: 10.1115/1.2929136).

[138] A.J.M. Van Tonder, "Automation of compressor networks through a dynamic control system", Ph.D Thesis, School of Electrical, Electronic and Computer Engineering, North-West University, Potchefstroom, South Africa, 2014.

[139] K. O. Boinov, E. A. Lomonova, A. J. A. Vandenput, A. Tyagunov, "Surge control of the electrically driven centrifugal compressor", IEEE Trans. on Industry Applications, vol. 42, no. 6, pp. 1523-1531, Nov./Dec. 2006 (doi: 10.1109/TIA.2006.882683).

[140] B. Nail, B. Bekhiti, V. 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, vol. 85, Article Number: 103697, Jan. 2021 (doi: 10.1016/j.jngse.2020.103697).

[141] S.D.P. Ramdoss, J. Wu J. Feng, V. Patel, "Application of dynamic simulation in the design, operation, and troubleshooting of compressor systems", Proceeding of the TS, pp. 95–106, USA, Texas 2007 (doi: 10.21423/R1TM0X).

[142] C. J. R. Kriel, J. H. Marais, and M. Kleingeld, "Modernising underground compressed air DSM projects to reduce operating costs", Proceeding of the IEEE/ICUE, pp. 1-6, Cape Town, South Africa, Aug, 2014 (doi: 10.1109/ICUE.2014.6904169).

[143] J. Cheng, R. Li, F.F. Choobineh, Q. Hu, S. Mei, "Dispatchable generation of a novel compressed-air assisted wind turbine and its operation mechanism", IEEE Trans. on Sustainable Energy, vol. 10, no. 4, pp. 2201-2210, Oct. 2019 (doi: 10.1109/TSTE.2018.2883068).

[144] A. Hafaifa,B. Rachid, G. Mouloud, "Modelling of surge phenomena in a centrifugal compressor: experimental analysis for control", Systems Science and Control Engineering, vol. 2, pp. 632–641, 2014 (doi: 10.1080/21642583.2014.956269).

[145] B. bohagen, J.T. Gravdahl, "Active surge control of compressor system using drive torque", Journal of Engineering, vol. 44, no. 4, pp. 1135-1140, April 2008 (doi: 10.1016/j.automatica.2007.11.002).

[146] J. Galindo, J. Serrano, C. Guardiola, C. Cervello, "Surge limit definition in a specific test bench for thecharacterization of automotive turbochargers", Experimental Thermal and Fluid Science, vol. 30, no. 5, pp. 449-462, May 2006 (doi: 10.1016/j.expthermflusci.2005.06.002).

[147] J. T. Gravdahl, O. Egeland, "Compressor surge and rotat-ing stall: Modeling and control", London: Springer Verlag, 1999.

[148] G. Torrisi, S. Grammatico, A. Cortinovis, M. Mercangöz, M. Morari, R.S. Smith, "Model predictive approa­ches for  active surge control in centrifugal compressors", IEEE Trans. on Control Systems Techn­olo­g­y, vol. 25, no. 6, pp. 1947-1960, Nov. 2017 (doi: 10.1109/TCST.2016.2636027).

[149] A. Stoicescu, O. Dumitrescu, G. Fetea, "Automated multi-eeference control for centrifugal compressor", Proceeding of the IEEE/CIEM, pp. 167-171, Timisoara, Romania, Oct. 2019 (doi: 10.1109­/CIE­M46­456.2019.8937654).

[150] S. Gao, X. Qian, Y. Wang, X. He, J. Yin, " LS-SVM based anti-surge predictive control of centrifugal compressor", Proceeding of the IEEE/CCDC, pp. 618-621, Yinchuan, China, May 2016 (doi: 10.110­9/CCD­C.2016.7531059).

[151] T. Hirano, T. Uchida, H. Tsujita,"Control of surge in centrifugal compressor byusing a nozzle injection system: Universality in optimal position of injection nozzle", International Journal of Rotating Machinery, Article ID: 259293,  Nov. 2012 (doi: 10.1155/2012/259293).

[152] API Standard 617, “Axial and centrifugal compressors and expander-compressors forpetroleum, chemicals and gas industry services”, American Petroleuvm Institute,Washington, DC, 7^th Edition, July 2002.

[153] N. Branley Shaun, K. Narayanan, "A total integrated approach", Conoco Phillips, Australia PTY LTD, Tech. Rep., West Perth, WA,Australia, 2012.

[154] F. Laaouad, M. Bouguerra, A. Hafaifa, A. Iratni, "Nonlinear Sensitive Control of Centrifugal Compressor", World Academy of Science, Engineering and Technology, vol. 2, pp. 167-172, 2007.

[155] N. Dukle, K. Narayanan, "Validating anti-surge control systems", Petroleum technology quarterly, vol. 8, pp. 87–96, Summer 2003.

[156] J. S. Simon and L. Valavani, "A Lyapunov based nonlinear controlscheme for stabilizing a basic compression system using a close-coupledcontrol valve",  Proceeding of the IEEE/ACC, pp. 2398-2406,  Boston, MA, USA, June 1991 (doi: 10.23919/ACC.1991.4791832).

[157] M.D. Hathaway, G. Herrick, "Unsteady simulation of the stall inception process in the compression system of a US army helicopter gas turbine engine- final year progress", Proceeding of the IEEE/DOD-UFC, pp. 160-173, Nashville, TN, USA, June 2005 (doi: 10.1109/DODUGC.2005.72).

[158] H. Tamaki, "Experimental study on surge inception ina centrifugal compressor", International Journal of Fluid Machinery and Systems, vol. 2, no. 4, pp. 409-417, 2009 (doi: 10.5293/IJFMS.2009.2.4.409).

[159] B. Chetate, R. Zamoum, A. Fegriche, M. Boumdin, "PID and novel approach of PI fuzzy logic con­tro­lle­rs for active surge in centrifugal compressor", Arabian Journal for Science and Engine­ering, vol. 38,  pp 1405–1414, 2013 (doi: 10.1007/s13369-013-0601-6).

[160] A. khsheem,"Active control of surge compressor system", Journal of Electrical and Electronic Systems, pp. 1-5, 2018 (doi: 10.4172/2332-0796.1000267).

[161] M. Asadzadeh, F. Shabani "Centrifugal compressor active surge controller design based on fuzzy type II", Proceeding of the IEEE/TPEC, College Station, TX, USA, Feb. 2018 (doi: 10.1109/TPEC.201­8.831­207­9).

[162] D. Zhao; B. Blunier; F. Gao, M. Dou, A. Miraoui, "Control of an ultrahigh-speed centrifugal compr­ess­o­r for the air management of fuel cell systems", IEEE Trans. on Industry Applications, vol. 50, no. 3, pp. 2225-2234, May/June 2014 (doi: 10.1109/TIA.2013.2282838).

[163] G. Quartarone, N. Anglani, "Simulation and performance comparison of a real-time controller for a fixed-speed multipressure compressor", IEEE Trans. on Industry Applications, vol. 51, no. 1, pp.744-752, Jan./Feb. 2015 (doi: 10.1109/TIA.2014.2332641).

[164] H. J. Ahn, M. S. Park, D. Sanadgol, I. H. Park, D. C. Han, E.H. Maslen, "A pressure output feedback control of turbo compressor surge with a thrust magnetic bearing actuator", Journal of Mechanical Science and Technology, vol. 23, pp 1406–141, 2009 .

[165] G. Bartolini, A. Muntoni, A. Pisano, E. Usai, "Compressor surge suppression by second-order sliding mode control technique", IFAC Proceedings Volumes, vol. 41, no. 2, pp. 6238-6244, July 2008 (doi: 10.3182/2­00­8­0706-5-KR-1001.2469).

[166] M. Ghanavati, K. Salahshoor, M. R. J. Motlagh, A. Ramazani, A. Moarefianpour,"A novel combined approach for gas compressors surge suppression based on robust adaptive control and backstepping", Journal of Mechanical Science and Technology, vol. 32, pp. 823-833, 2018.

[167] M.T. Ziabari, M.R. Jahed-Motlagh, K. Salahshoor, A. Ramezani, A. Moarefianpur, "Robust adaptive control ofsurge instability in constant speed centrifugal compressorsusing", Cogent Engineering, vol. 4, no. 1, Article Number: 1339335, July 2017 (doi: 10.1080/23311916.2017.1339335)

[168] N. Zhang, M. Malekgoudarzi,"Compressor surge control using a new robustadaptive method in the presence of uncertaintyand unmatched disturbance", Systems Science and Control Engineering, vol. 8, no. 1, pp. 405-412, July ­­­­­­­2020 (doi: 10.1080/21642583.2020.1785970).

[169] A. Neverlien, S. Moe, J. T. Gravdahl, "Compressor surge control using lyapunov neural networks", Modeling, Identification and Contro, vol. 41, no. 2, pp. 41-48, 2020 (doi: 10.4173/mic.2020.2.1).

[170] H. Imani, M.R. Jahed-Motlagh, K. Salahshoor, A. Ramezani, A. Moarefianpur, D. Pham, "Robust decentralizedmodel predictive control approach for a multi-compressorsystem surge instability including piping acoustic".CogentEngineering, vol. 5, no. 1, Article Number: 1483811, Aug. 2018 (doi: 10.1080/233­1­1­916­.2018.1483811).

[171] C. J. Backi, D. Krishnamoorthy, A. Verheyleweghen, S. Skogestad, "Combined nonlinear moving hor­iz­­on estimation and model predictive control applied to a compressor for active surge control", Proceeding of the IEEE/CCTA, pp. 1552-1557, Copenhagen, Denmark, Aug. 2018 (doi: 10.1109/CCTA.20­18.851­159­6).

[172] S. Lin, Ch. Yangn, P. Wun, Z. Song, "Active surge control for variable speed axial compressor", ISA Transactions,vol. 53, pp. 1389-1395, 2014 (doi: 10.1016/j.isatra.2013.12.031).

[173] H. Sheng, W. Huang, T. Zhang, X. Huang, "Active/passive hybrid control system for compressor surge based on fuzzy logic", Journal of Engineering for Gas Turbines and Power, vol. 136, no. 9, Article Number: 092601, Sept. 2014 (doi:10.1115/1.4026953).

[174] Y. Ren, L. Zhang, Y. Ye, W. Liang, H. Yang, "Reliability assessment of anti-surge control system in centrifugal compressor", Proceeding of the IEEE/ICCIS, pp. 1240-1243, Chongqing, China, Aug. 2012 (doi: 10.1109/ICCIS.2012.218).

[175] J.J. Moghaddam, M.H. Farahani, N. Amanifard, "A neural network-based sliding-mode control for rotating stall and surge in axial compressors", Applied Soft Computing, vol. 11, no. 1, pp. 1036-1043, Jan. 2011 (doi: 10.1016/j.asoc.2010.02.002).

[176] H.M. Harrison, N.L. Key, "A new approach to modeling slip and work input for centrifugal compressors", Journal of Engineering for Gas Turbines and Power, vol. 143, no. 2, Article Number: 021013, 2021 (doi: 10.1115/1.4049412).

[177] B. Bohagen, J.T. Gravdahl, "On active surge control of compressors using a mass flow observer", Proceedings of the IEEE/CDC, vol. 4, pp. 3684-3689, Las Vegas, NV, USA, Dec. 2002 (doi: 10.1109/CD­C­.20­02.1184936).

[178] G. Torrisi, V. Jaramillo, J.R. Ottewill, S. Mariéthoz, M. Morari, R.S. Smith, "Active surge control of electrically driven centrifugal compressors", Proceeding of the IEEE/ECC, pp. 1614-1619, Linz, Austria, July 2015 (doi: 10.1109/ECC.2015.7330768).

[179] H. Sheng, W. Huang, T. Zhang, "Output feedback control of surge and rotating stall in axial compressors", Asian Journal of Control, vol. 19, no. 2, pp. 599-605, March 2017 (doi: 10.1002/asjc.1384).

[180] H. Sheng, W. Huang, T. Zhang, X. Huang, "Robust adaptive fuzzy control of compressor surge using backstep-ping", Arabian Journal for Science and Engineering, vol. 39, pp. 9301-9308, 2014 (doi: 10.10­07/s1­­3369-014-1448-1)

[181] M. Shafieian, M. Zavar, M. Rahmanian, "Simulation and control of surge phenomenon in centrifugal compressors", Traitement du Signal , vol. 36, no. 3, pp. 259-264, Sept. 2019 (doi: 10.18280/ts.360309).