Comparison of speed control techniques in field oriented control of permanent magnet synchronous motor: Lyapunov approach

Yıl 2023, Cilt: 41 Sayı: 6, 1177 - 1196, 29.12.2023

Ahmet İlkkan Açıkgöz , İbrahim Alışkan

Öz

The main focus of this study is the minimization of Permanent Magnet Synchronous Motors (PMSM) steady-state speed error. In order to do this, a Lyapunov candidate function that contained the speed error is defined and a Based Lyapunov Theory (BLT) speed controller is designed. The novelty of this paper is the smoother pre-filter applied to the reference speed guarantees the stable operation of the nonlinear controller at step change in reference signal. The pre-filter design is carried out in a way that does not have a negative effect on the settling time, which is one of the step response characteristics. A proportional-integral (PI) speed controller is designed for comparison. FOC technique is used for inverter control. As the speed controller of the system, PI and BLT controllers are designed separately. Simulation studies are run in MATLAB/Simulink. PI speed controller coefficients are determined using the pole assignment method. For this purpose, PI coefficients for operating the controller at the selected frequency and the desired damping ratio are calculated. Stability analyses are carried out for PI and BLT speed controllers. A low pass filter that allows the system to apply a smoothed reference speed is designed in order to eliminate the range in which the derivative of the reference speed used in the BLT speed controller is undefined. Three different simulations are modeled. In the first one, the reference speed is changed in both directions by step function, under constant load torque. The speed and torque performances of both speed controllers are compared with the performance criteria including settling time, overshoot, peak value, peak time, root mean squared error (RMSE), and integral of time weighed absolute error (ITAE), and the results of the comparison are shown in figures and tables. In addition, a second simulation including reference load changes is made to model load torque disturbance as a robustness test, and a third simulation containing resistance changes is made to model parameter uncertainty are carried out. Both transient response and steady state response of controllers against parameter changes are examined in simulation 2 and 3. With the proposed BLT controller, the transient and steady-state response of the speed is improved both at the time of torque change and at the time of winding resistance change. The results are given in figures and tables.

Anahtar Kelimeler

PMSM, Speed Control, Signal Smoothing, Nonlinear Control, FOC, Vector Control, SVPWM, Lyapunov Function, PI, Barbalat’s Lemma, Stability Analysis, RMSE, ITAE

Kaynakça

• REFERENCES
• [1] Nirowski G, Plackner K, Piepenbreier B, Tolle H. New permanent field synchronous motor with integrated inverters. In: Proceeding of ICEM’90; 1990. p. 124–131.
• [2] Rashid M. Power electronics handbook. 3rd ed. USA: Elsevier Inc.; 2011.
• [3] Xiao X, Chen C, Zhang M. Dynamic permanent magnet flux estimation of permanent magnet synchronous machines. IEEE Trans on Applied Superconductivity 2010;20:1085–1088. [CrossRef]
• [4] Proca AB, Keyhani A, El-Antably A, Lu W, Dai M. Analytical model for permanent magnet motors with surface mounted magnets. IEEE Trans Energy Convers 2003;18:386–391. [CrossRef]
• [5] Mohamed YAI. A Hybrid-type variable-structure instantaneous torque control with a robust adaptive torque observer for a high-performance direct-drive PMSM. IEEE Trans Ind Electron 2007;54:2491–2499. [CrossRef]
• [6] Krishnan R. Selection criteria for servo motor drives. IEEE Trans on Ind Appl 1987;23:270–275. [CrossRef]
• [7] Choi HH, Kim EK, Yu DY, Jung JW, Kim TH. Precise PI speed control of permanent magnet synchronous motor with a simple learning feedforward compensation. Electr Eng 2017;99:133–139. [CrossRef]
• [8] Balda JC, Pillay P. Speed controller design for a vector-controlled permanent magnet synchronous motor drive with parameter variations. In: Conference record of the 1990 IEEE industry applications society annual meeting USA; 1990. p. 163–168.
• [9] Adam AA, Elnady A. Adaptive steering-based HDTC algorithm for PMSM. Asian J Control 2019:1–19. [CrossRef]
• [10] Singh KV, Bansal HO, Singh D. A comprehensive review on hybrid electric vehicles: architectures and components. J Mod Transport 2019;27:77–107. [CrossRef]
• [11] Xiao X, Chen C. Reduction of torque ripple due to demagnetization in PMSM using current compensation. IEEE Trans Appl Superconductivity 2010;20:1068–1071. [CrossRef]
• [12] Binns KJ, Jabbar MA. High-field self-starting permanent-magnet synchronous motor. IEE Proceedings B, Electric Power Appl 1981;128:157–160. [CrossRef]
• [13] Sünter S, Altun H. Control of a permanent magnet synchronous motor fed by a direct AC-AC converter. Electr Eng 2005;87:83–92. [CrossRef]
• [14] Guven S, Usta MA, Okumus HI. An improved sensorless DTC-SVM for three-level inverter-fed permanent magnet synchronous motor drive. Electr Eng 2018;100:2553–2567. [CrossRef]
• [15] Hernandez OS, Magdaleno JR, Caporal RM, Huerta EB. HIL simulation of the DTC for a three-level inverter fed a PMSM with neutral-point balancing control based on FPGA. Electr Eng 2018;100:1441–1454. [CrossRef]
• [16] Campos PJ, Coria LN, Trujillo L. Nonlinear speed sensorless control of a surface-mounted PMSM based on a Thau observer. Electr Eng 2018;100:177–193. [CrossRef]
• [17] Choi Y, Choi HH, Jung J. Feedback linearization direct torque control with reduced torque and flux ripple for IPMSM drives. IEEE Trans Power Electron 2016;31:3728–3737. [CrossRef]
• [18] Jezernik K, Korelic J, Horvat R. PMSM sliding mode FPGA-based control for torque ripple reduction. IEEE Trans Power Electron 2013;28:3549–3556. [CrossRef]
• [19] Aliskan I, Gulez K, Tuna G, Mumcu TV, Altun Y. Nonlinear speed controller supported by direct torque control algorithm and space vector modulation for induction motors in electrical vehicles. Elektronika Ir Elektrotechnika 2013;19:41–46. [CrossRef]
• [20] Mumcu TV, Aliskan I, Gulez K, Tuna G. Reducing moment and current fluctuations of induction motor system of electrical vehicles by using adaptive field oriented control. Elektronika Ir Elektrotechnika 2013;19:21–24. [CrossRef]
• [21] Hasse K. Zum dynamischen verhalten der asynchronmachine bei betrieb mit variable standerfrequenz und standerspannung. ETZ-A. 1968;89:77–81.
• [22] Blaschke F. Das prizip der feldorientierung, die grundlage fur die TRNSVEKTOR-regelung von asynchnmachinen. Siemens Zeitschrift 1971;45:757–768.
• [23] Utkin V, Guldner J, Shi J. Sliding mode control in electro-mechanical systems. 2nd ed. New York: CRC Press; 2009.
• [24] Bida VM, Samokhvalov DV, Al-Mahturi FS. PMSM vector control techniques – a survey. In: 2018 IEEE Conference of Russian young researchers in electrical and electronic engineering (ElConRus); 2018. p. 577–581. [CrossRef]
• [25] Acikgoz AI, Aliskan I. Comparison of inverter control techniques in field oriented control of permanent magnet synchronous motor. In: Turkish national committee of automatic control Turkey; 2016. p. 322–327.
• [26] Li Q, Huang S. A novel method to suppress mid – frequency vibrations with a high speed-loop gain for PMSM control. J Power Electron 2016;16:1076–1086. [CrossRef]
• [27] Aström KJ, Hagglund T. Advanced PID Controlor. ISA instrumentation, systems and automation Society; 2006.
• [28] Lina W, Kun X, Lillo L, Empringham L, Wheeler P. PI controller relay auto – tunning using delay and phase marjin in PMSM drives. Chin J Aeronautics 2014;27:1527–1537. [CrossRef]
• [29] Rao VMV. Performance analysis of speed control of dc motor using P, PI, PD and PID controllers. Int J Eng Res Technol 2013;2:60–66.
• [30] Ogata K. Modern Control Engineering. 5th ed. Prentice Hall Inc.; 2010.
• [31] Ziegler JG, Nichols NB. Optimum setting for automatic controllers. Trans Am Soc Mech Eng 1942;64:759–768. [CrossRef]
• [32] Shahat A, Shewy H. Permanent magnet synchronous drive system for mechatronics applications. Int J Res Rev Appl Sci 2010;4:323–328.
• [33] Zheng W, Luo Y, Pi Y, Chen Y. Improved frequency domain design method for the fractional order proportional-integral-derivative controller optimal design: a case study of permanent magnet synchronous motor speed control. IET Control Theory Appl 2018;12:2478–2487. [CrossRef]
• [34] Zheng W, Luo Y, Chen Y, Pi Y, Yu W. An improved frequency-domain method for the fractional order PIλDµ controller optimal design. In: 3rd IFAC conference on advances in proportional- integral-derivative control Belgium; 2018. p. 681–686. [CrossRef]
• [35] Zhang G, Furusho J. Speed control of two-inertia system by PI/PID control. IEEE Trans Ind Electron 2000;47:603–609. [CrossRef]
• [36] Cao X, Fan L. Real-time PI controller based on pole assignment theory for permanent magnet synchronous motor. In: Proceedings of the IEEE international conference on automation and logistics China; 2008. p. 221–215.
• [37] Suh G, Hyun DS, Park JI, Lee KD, Lee SG. Design of a pole placement controller for reducing oscillation and settling time in a two-inertia motor system. In: IECON’01 The 27th annual conference of the IEEE industrial electronics society; 2001. p. 615–620.
• [38] Chakraborty AK, Sharma N. Control of permanent magnet synchronous motor (PMSM) using vector control approach. In: 2016 IEEE/PES Transmission and distribution conference and exposition (T&D); 2016. p. 1–5. [CrossRef]
• [39] Wang L, Chai S, Yoo D, Gan L, Ng K. PID and Predictive Control of Electrical Drives and Power Converters Using Matlab/Simulink. New York: IEEE Press Wiley; 2015. [CrossRef]
• [40] Pilla R, Santukumari K. Design and simulation of the control system for inverte-fed permanent magnet synchronous motor drive. Indonesian J Electr Eng Comput Sci 2018;12:958–967. [CrossRef]
• [41] Lyapunov MA. Problème général de la stabilitédu mouvement. Ann Fac Sci Toulouse 1907;9:203–474 (Translation of the original paper published in 1892 in Comm Soc Math Kharkow and reprinted as vol. 17 in Ann. Math Studies, Princeton University Press, Princeton, N.J., 1949). [CrossRef]
• [42] Quassaid M, Cherkaoui M, Nejmi A, Maaroufi M . Nonlinear torque control for PMSM: A lyapunov technique approach. World Acad Sci Eng Technol Int J Electr Comput Eng 2007;1:918921.
• [43] Shahgholian G, Hamidpour HR. Analysis and design of a nonlinear torque controller for PMSM drive system – A lyapunov technique approach. IJTPE J 2014;6:7076.
• [44] Quassaid M, Cherkaoui M, Zidani Y. A nonlinear speed control for a PM synchronous motor using an adaptive backstepping control approach. In: IEEE ICIT 2004;12871292.
• [45] Zaltni D, Sbita L, Abdelkrim MN. Nonlinear speed control using adaptive sliding mode and lyapunov approaches for PMSM fed by a 3-levels NPC inverter. J Electr Syst 2010;6:350360.
• [46] Prior G, Krstic M. Quantized-input control lyapunov approach for permanent magnet synchronous motor drives. IEEE Trans Control Syst Technol. 2013;21:17841794. [CrossRef]
• [47] Khalil HK. Nonlinear Systems. 2nd ed. Prentice Hall Inc.; 1996.
• [48] Yıldız F, Aliskan I, Engin SN. Control of O2 consumption in jet loop bioreactors by means of lyapunov based nonlinear controller. In: ELECO’08 Electrical-Electronics-Computer Symposium. Turkey; 2016.
• [49] Implementing Space Vector Modulation with the ADMCF32X. Analog Devices Inc.; 2010;1—22.
• [50] Ramana P, Kumar BS, Mary KA, Kalavathi MS. Comparison of various PWM techniques for field oriented control VSI FED PMSM drive. IJAREEIE 2013;2: 29282936.
• [51] Space Vector Generator With Quadrature Control. Texas Instruments; 2012;112.
• [52] Kumar KV, Michael PA, John JP, Kumar SS. Simulation and comparison of SPWM and SVPWM control for three Phase Inverter. ARPN J Eng Appl Sci 2010;5:6174.
• [53] Field Orientated Control of 3-Phase AC-Motors. Texas Instruments Europe; 1998;124.
• [54] Digital Motor Control Application Note SPRU485A. Texas Instruments; 2003.
• [55] Ogata K. System Dynamics. 4th ed. USA: Pearson Education Inc.; 2004.
• [56] Parks PC. A. M. lyapunov’s stability theory – 100 years on. IMA J Math Control Inf 1992;9:275303. [CrossRef]
• [57] Slotine J, Li W. Applied Nonlinear Control. 4th ed. USA: Prentice Hall Inc.; 1991.
• [58] Fontes FACC, Magni L. A generalization of barbalat’s lemma with applications to robust model predictive control. In: MTNS' 04 Proceedings of 16th International Symposium on Mathematical Theory of Networks and Systems. Belgium; 2004:15.
• [59] Lin CK, Liu TH, Fu LC. Adaptive backstepping PI sliding-mode control for interior permanent magnet synchronous motor drive systems. In: American Control Conference. 2011:40754080.
• [60] Wu Z, Xia Y, Xie X. Stochastic barbalat’s lemma and its applications. IEEE Trans Automat Contr 2012;57:15371543. [CrossRef]
• [61] Khadija K, Benyounes M, Khalil BI, Rachid BM. A simple and robust speed tracking control of PMSM. Przeglad Elektrotechniczny (Electr Rev) 2011;87:202207.
• [62] Karabacak M, Eskikurt HI. Speed and current regulation of a permanent magnet synchronous motor via nonlinear and adaptive backstepping control. Math Comput Model 2011;53: 20152030. [CrossRef]
• [63] Kim W, Shin D, Chung CC. The lyapunov-based controller with a passive nonlinear observer to improve position tracking performance of microstepping in permanent magnet stepper motors. Automatica 2012;48:30643074. [CrossRef]
• [64] Jon R, Wang Z, Luo C, Jong M. Adaptive robust speed control based on recurrent elman neural network for sensorless PMSM servo drives. Neurocomputing 2017;227:131141. [CrossRef]
• [65] Yang Q, Zhu M, Jiang T, Fu K. Speed tracking control of permanent magnet synchronous motor based on high gain controller. In: ICMCA 2017 2nd International Conference on Mechanical Control and Automation 2017:4651. [CrossRef]
• [66] Labiod S, Zibra A, Boubakir A. Backstepping speed control for permanent magnet synchronous motors with unknown load torque. In: ICEEA’ 10th International Conference on Electrical Engineering, Electronics and Automatic 2010:15.