H-Infinity-Based Flow Control Method for a Centrifugal Pumping System via Speed Regulation

Abstract:

To address the dynamic response and steady-state accuracy issues in the flow control of centrifugal pumps, this paper proposes a flow throttling control strategy based on robust H-infinity control. A comprehensive simulation model of the system is established, and combined with the design of a robust H-infinity state feedback controller, quadratic stability and disturbance suppression are achieved under uncertain conditions such as speed fluctuations. Simulation results show that the proposed method achieves faster flow tracking. In anti-disturbance tests under multiple operating conditions, the H-infinity controller demonstrates significant performance improvements compared to PI control. Specifically, at 6000 rpm, 7000 rpm, and 8000 rpm, the maximum overshoot is reduced by 82.9%, 71.4%, and nearly 0%, respectively, while the steady-state error is reduced by 20%, 50%, and 50%. In addition, the settling time is shortened by 29.0%, 62.4%, and 30.5% under these conditions. These results indicate that the proposed method not only improves the accuracy and robustness of flow control but also provides an efficient solution for industrial process control, offering significant engineering application value.

• Periodical: International Journal of Engineering Research in Africa (Volume 80)
• Pages: 81-99
• DOI: https://doi.org/10.4028/p-vQJ7L9
• Online since: July 2026
• Authors: Sen Zhou, Zhen Yan Fang, Cheng Chen, Yan Wei Wang*
• Keywords: Centrifugal Pump, Disturbance Suppression, H-Infinity, Quadratic Stability

References

[1] Mohammadi Z, Heidari F, Fasamanesh M, et al. Centrifugal pumps[M]. Transporting Operations of Food Materials Within Food Factories. Woodhead Publishing, 2023: 155-200.

DOI: 10.1016/b978-0-12-818585-8.00001-5

[2] Qazizada M E, Sviatskii V, Bozek P. Analysis performance characteristics of centrifugal pumps[J]. MM Science Journal, 2016.

DOI: 10.17973/mmsj.2016_10_201691

[3] Cooper P, Tchobanoglous G, Garbus R O, et al. Performance of centrifugal pumps[M]. Pumping Station Design. Butterworth-Heinemann, 2008: 10.1-10.44.

DOI: 10.1016/b978-185617513-5.50017-2

[4] Temel S, Yağli S, Gören S. P, pd, pi, PID controllers[J]. Middle East Technical University, Electrical and Electronics Engineering Department, 2013.

[5] Atherton D P, Majhi S. Limitations of PID controllers[C]. Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251). IEEE, 1999, 6: 3843-3847.

DOI: 10.1109/acc.1999.786236

[6] Li Z, Wu P, Wu D, et al. Experimental and numerical study of transient flow in a centrifugal pump during startup[J]. Journal of Mechanical Science and Technology, 2011, 25(3): 749-757.

DOI: 10.1007/s12206-011-0107-7

[7] Hu F F, Ma X D, Wu D Z, et al. Transient internal characteristic study of a centrifugal pump during startup process[C]. IOP Conference Series: Earth and Environmental Science. IOP Publishing, 2012, 15(4): 042016.

DOI: 10.1088/1755-1315/15/4/042016

[8] Germanov A. Design of the sensorless pressure control system for a centrifugal pump[D]. Lappeenranta University of Technology 2015.

[9] Wang Y, Zhang H, Han Z, et al. Optimization design of centrifugal pump flow control system based on adaptive control[J]. Processes, 2021, 9(9): 1538.

DOI: 10.3390/pr9091538

[10] Gevorkov L, Rassõlkin A, Kallaste A, et al. Electric drive for throttle control of centrifugal pump system[C]. 2018 IEEE 59th International Scientific Conference on Power and Electrical Engineering of Riga Technical University (RTUCON). New York: IEEE, 2018: 1-5.

DOI: 10.1109/rtucon.2018.8659887

[11] Gevorkov L, Rassolkin A, Kallaste A, et al. Simulation study of a centrifugal pumping plant's power consumption at throttling and speed control[C]. 2017 IEEE 58th International Scientific Conference on Power and Electrical Engineering of Riga Technical University (RTUCON). New York: IEEE, 2017: 1-5.

DOI: 10.1109/rtucon.2017.8124823

[12] Aboud M, Abougarair A, Emhemmed A. Robust H-infinity controller synthesis approach for uncertainties system[C]. 2023 IEEE 11th International Conference on Systems and Control (ICSC). IEEE, 2023: 506-511.

DOI: 10.1109/icsc58660.2023.10449693

[13] Bansal A, Sharma V. Design and analysis of robust H-infinity controller[J]. Control Theory and Informatics, 2013, 3(2): 7-14.

[14] Guan W, Zhang J, Wang P, et al. Head variation adaptive control of small-scale doubly-fed pumped storage units[J]. Electric Power Systems Research, 2025, 239: 111277.

DOI: 10.1016/j.epsr.2024.111277

[15] Jiakang MU, Jian SHENG. Experimental study on flow control characteristics of forward bend centrifugal pump under the PID control[J]. Experiment Science and Technology, 2025, 23(1): 103.

[16] Ji X, Wang Y, Xie H, et al. Nonlinear robust control of pump controlled single-rod actuator with observing and compensating modeling uncertainties[J]. ISA Transactions, 2025.

DOI: 10.1016/j.isatra.2025.10.053

[17] Lingfei X, Hana Z, Mab L, et al. Intelligent robust control for aviation electric fuel pump based on second order integral sliding mode with UDE[J]. J. Frankl. Inst., 361: 106811.

DOI: 10.1016/j.jfranklin.2024.106811

[18] Abut T. Modeling and optimal control of a DC motor[J]. Int. J. Eng. Trends Technol, 2016, 32(3): 146-150.

[19] Rambabu S. Modeling and control of a brushless DC motor[J]. Master of Thesis in Power Control and Drives Technology, National Institute of Technology Rourkela, 2007.

[20] Chen Y. System simulation techniques with MATLAB and simulink[M]. John Wiley & Sons, 2013.

[21] Rajaram M L, Kougianos E, Mohanty S P, et al. Wireless sensor network simulation frameworks: A tutorial review: MATLAB/Simulink bests the rest[J]. IEEE Consumer Electronics Magazine, 2016, 5(2): 63-69.

DOI: 10.1109/mce.2016.2519051

[22] Thin K C, Khaing M M, Aye K M. Design and performance analysis of centrifugal pump[J]. World Academy of Science, Engineering and Technology, 2008, 46(1): 422-429.

[23] Qazizada M E, Sviatskii V, Bozek P. Analysis performance characteristics of centrifugal pumps[J]. MM Science Journal, 2016.

DOI: 10.17973/mmsj.2016_10_201691

[24] Brestovič T, Jasminská N. Software support development for numerical solution of Ansys CFX[J]. Acta Mechanica et Automatica, 2013, 7(4).

DOI: 10.2478/ama-2013-0036

[25] Stern F, Wilson R.V., Coleman H.W., et al. Verification and validation of CFD simulations[R]. 1999.

[26] Janevska, Gordana. Mathematical modeling of pump system[C]. Electronic International Interdisciplinary Conference, Sofia: EIIC, 2013,2:455-458.

[27] Niku S B. Electromotive force: Motors, transformers, AC and DC currents[M]. Engineering Principles in Everyday Life for Non-Engineers. Cham: Springer International Publishing, 2022: 155-189.

DOI: 10.1007/978-3-031-79372-1_6

[28] Vukosavic S N. Electromotive forces[M]. Electrical Machines. New York, NY: Springer New York, 2012: 223-257.

DOI: 10.1007/978-1-4614-0400-2_10

[29] Ortega R, Espinosa G. Torque regulation of induction motors[J]. Automatica, 1993, 29(3): 621-633.

DOI: 10.1016/0005-1098(93)90059-3

[30] Verrelli C M, Savoia A, Mengoni M, et al. On-line identification of winding resistances and load torque in induction machines[J]. IEEE Transactions on Control Systems Technology, 2013, 22(4): 1629-1637.

DOI: 10.1109/tcst.2013.2285604

[31] Raibert M H. Motor control and learning by the state space model[D]. Massachusetts Institute of Technology, 1977.

[32] Ruderman M, Krettek J, Hoffmann F, et al. Optimal state space control of DC motor[J]. IFAC Proceedings Volumes, 2008, 41(2): 5796-5801.

DOI: 10.3182/20080706-5-kr-1001.00977

[33] Højberg A L, Refsgaard J C. Model uncertainty–parameter uncertainty versus conceptual models[J]. Water Science and Technology, 2005, 52(6): 177-186.

DOI: 10.2166/wst.2005.0166

[34] Spear R C, Grieb T M, Shang N. Parameter uncertainty and interaction in complex environmental models[J]. Water Resources Research, 1994, 30(11): 3159-3169.

DOI: 10.1029/94wr01732

[35] Glover K, Doyle J C. State-space formulae for all stabilizing controllers that satisfy an H∞-norm bound and relations to relations to risk sensitivity[J]. Systems & Control Letters, 1988, 11(3): 167-172.

DOI: 10.1016/0167-6911(88)90055-2

[36] Sivashankar N, Khargonekar P P. Robust stability and performance analysis of sampled-data systems[J]. IEEE Transactions on Automatic Control, 2002, 38(1): 58-69.

DOI: 10.1109/9.186312

[37] Keel L H, Bhattacharyya S P. Robust stability and performance with fixed-order controllers[J]. Automatica, 1999, 35(10): 1717-1724.

DOI: 10.1016/s0005-1098(99)00080-1

[38] Honig M L, Xiao W. Performance of reduced-rank linear interference suppression[J]. IEEE Transactions on Information Theory, 2001, 47(5): 1928-1946.

DOI: 10.1109/18.930928

[39] Subbaram H, Abend K. Interference suppression via orthogonal projections: a performance analysis[J]. IEEE Transactions on Antennas and Propagation, 2002, 41(9): 1187-1194.

DOI: 10.1109/8.247744

[40] Schmidhuber J. A 'self-referential' weight matrix[C]. International Conference on Artificial Neural Networks. London: Springer London, 1993: 446-450.

DOI: 10.1007/978-1-4471-2063-6_107

[41] Getis A, Aldstadt J. Constructing the spatial weights matrix using a local statistic[J]. Geographical Analysis, 2004, 36(2): 90-104.

DOI: 10.1111/j.1538-4632.2004.tb01127.x

[42] Alaoui M, Maker H, Mouhsen A, et al. High power PV array emulator based on state feedback controller under uniform and non-uniform insolation[J]. Transactions on Electrical and Electronic Materials, 2023, 24(1): 54-64.

DOI: 10.1007/s42341-022-00418-4

[43] Redheffer R. Inequalities for a matrix Riccati equation[J]. Journal of Mathematics and Mechanics, 1959: 349-367.

DOI: 10.1512/iumj.1959.8.58024

[44] Faibusovich L E. Matrix Riccati inequality: existence of solutions[J]. Systems & Control Letters, 1987, 9(1): 59-64.

DOI: 10.1016/0167-6911(87)90009-0

[45] Hewer G. Existence theorems for positive semidefinite and sign indefinite stabilizing solutions of h_∞ riccati equations[J]. SIAM Journal on Control and Optimization, 1993, 31(1): 16-29.

DOI: 10.1137/0331002

[46] Boukas T K, Habetler T G. High-performance induction motor speed control using exact feedback linearization with state and state derivative feedback[J]. IEEE Transactions on Power Electronics, 2004, 19(4): 1022-1028.

DOI: 10.1109/tpel.2004.830042

[47] Zhu W X, Zhang L D. A speed feedback control strategy for car-following model[J]. Physica A: Statistical Mechanics and its Applications, 2014, 413: 343-351.

DOI: 10.1016/j.physa.2014.07.030

[48] Koudar I. Variable gain differential current feedback amplifier[C]. Proceedings of the IEEE 2004 Custom Integrated Circuits Conference (IEEE Cat. No. 04CH37571).IEEE,2004:659-662.

DOI: 10.1109/cicc.2004.1358912

[49] Gift S J G, Maundy B. Improving the bandwidth gain-independence and accuracy of the current feedback amplifier[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2005, 52(3): 136-139.

DOI: 10.1109/tcsii.2004.842043

[50] Jin X.H., Zhang Y., Xu D.G. Static current error elimination algorithm for induction motor predictive current control[J]. IEEE access, 2017, 5: 15250-15259.

DOI: 10.1109/access.2017.2725269

[51] Dhiman G, Kumar V. Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems[J]. Knowledge-based Systems, 2019, 165: 169-196.

DOI: 10.1016/j.knosys.2018.11.024

[52] Clark R N. Integral of the error squared as a performance index for automatic control systems[J]. Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry, 1961, 79(6): 467-471.

DOI: 10.1109/tai.1961.6371690

[53] Hudson G, Underwood C P. A simple building modelling procedure for MATLAB/ Simulink [C]. Proceeding of Building Simulation. 1999, 99(2): 777-783.

[54] Wang L. PID control system design and automatic tuning using MATLAB/Simulink[M]. John Wiley & Sons, 2020.

DOI: 10.1002/9781119469414