
-
Previous Article
Optimal stop-loss reinsurance with joint utility constraints
- JIMO Home
- This Issue
-
Next Article
An alternating linearization bundle method for a class of nonconvex optimization problem with inexact information
An adaptive dynamic programming method for torque ripple minimization of PMSM
1. | School of Automation and engineering, University of Electronic Science and Technology of China, China |
2. | The Shenzhen Energy Storage Power Generation Co., Ltd. of China Southern Power Grid, China |
The imperfect sinusoidal flux distribution, cogging torque, and current measurement errors can cause periodic torque ripple in the permanent magnet synchronous motor (PMSM). These ripples are reflected in the periodic oscillation of the motor speed and torque, causing vibration at low speeds and noise at high speeds. As a high-precision tracking application, ripple degrades the application performance of PMSM. In this paper, an adaptive dynamic programming (ADP) scheme is proposed to reduce the periodic torque ripples. An optimal controller is designed by iterative control algorithm using robust adaptive dynamic programming theory and strategic iterative technique. ADP is combined with the existing Proportional-Integral (PI) current controller and generates compensated reference current iteratively from cycle to cycle so as to minimize the mean square torque error. As a result, an optimization problem is constructed and an optimal controller is obtained. The simulation results show that the robust adaptive dynamic programming achieves lower torque ripple and shorter dynamic adjustment time during steady-state operation, thus meeting the requirements of steady speed state and the dynamic performance of the regulation system.
References:
[1] |
T. Banks,
Matrix Theory, Nuclear Phys. B Proc. Suppl., 67 (1997), 180-224.
doi: 10.1016/S0920-5632(98)00130-3. |
[2] |
H. J. Brascamp and E. H. Lieb,
Best constants in Young's inequality, its converse, and its generalization to more than three functions, Advances in Math., 20 (1976), 151-173.
doi: 10.1016/0001-8708(76)90184-5. |
[3] |
Y. Cho, et al., Torque-ripple minimization and fast dynamic scheme for torque predictive control of permanent-magnet synchronous motors, IEEE Transactions on Power Electronics, 30 (2015), 2182–2190.
doi: 10.1109/TPEL.2014.2326192. |
[4] |
J. Chu,
Suppressing speed ripples of permanent magnetic synchronous motor based on a method, Trans. of China Electrotechnical Society, 24 (2009), 43-49.
|
[5] |
S. U. Chung, et al., Fractional slot concentrated winding PMSM with consequent pole rotor
for a low-speed direct drive: Reduction of rare earth permanent magnet, IEEE Trans. on
Energy Conversion, 30 (2015), 103–109.
doi: 10.1109/TEC.2014.2352365. |
[6] |
J. Fiala and F. H. Guenther,
Handbook of intelligent control: Neural, fuzzy, and adaptive approaches, Neural Networks, 7 (1994), 851-852.
|
[7] |
D. C. Hanselman,
Minimum torque ripple, maximum efficiency excitation of brushless permanent magnet motors, IEEE Transactions on Industr. Electronics, 41 (1994), 292-300.
doi: 10.1109/41.293899. |
[8] |
B. H. Lam, et al., Torque ripple minimization in PM synchronous motors an iterative learning control approach, IEEE Internat. Conference on Power Electronics and Drive Systems, 1999.
doi: 10.1109/PEDS.1999.794551. |
[9] |
F. L. Lewis and D. Liu, Reinforcement learning and approximate dynamic programming for feedback control, John Wiley & Sons, 2013.
doi: 10.1002/9781118453988. |
[10] |
D. Ma and H. Lin, Accelerated iterative learning control of speed ripple suppression for a seeker servo motor, Algorithms, 11 (2018).
doi: 10.3390/a11100152. |
[11] |
G. Madescu, et al., Effects of stator slot magnetic wedges on the induction motor performances, Optimization of Electrical and Electronic Equipment (OPTIM), 13th International Conference on IEEE, 2012.
doi: 10.1109/optim.2012.6231861. |
[12] |
S. G. Min and B. Sarlioglu,
Advantages and characteristic analysis of slotless rotary PM machines in comparison with conventional laminated design using statistical technique, IEEE Trans. on Transpor. Electrification, 4 (2018), 517-524.
doi: 10.1109/TTE.2018.2810230. |
[13] |
A. R. I. Mohamed and E. F. El-Saadany,
A current control scheme with an adaptive internal model for torque ripple minimization and robust current regulation in PMSM drive systems, IEEE Trans. on Energy Conversion, 23 (2008), 92-100.
doi: 10.1109/TEC.2007.914352. |
[14] |
N. Nakao,
Suppressing pulsating torques: Torque ripple control for synchronous motors, IEEE Industry Appl. Magazine, 21 (2015), 33-44.
doi: 10.1109/MIAS.2013.2288383. |
[15] |
P. M. Pardalos, Approximate dynamic programming: solving the curses of dimensionality, Optimization Methods and Software, 24 (2009), 155.
doi: 10.1080/10556780802583108. |
[16] |
M. Pinsky, Introduction to Fourier Analysis and Wavelets, 102, American Mathematical Society, Providence, RI, 2009.
doi: 10.1090/gsm/102. |
[17] |
W. Qian, S. K. Panda and J. X. Xu,
Torque ripple minimization in PM synchronous motors using iterative learning control, IEEE Transactions on Power Electronics, 19 (2004), 272-279.
doi: 10.1109/TPEL.2003.820537. |
[18] |
J. Si, et al., Handbook of Learning and Approximate Dynamic Programming, John Wiley & Sons, 2004.
doi: 10.1002/9780470544785. |
[19] |
R. Song, W. Xiao and Q. Wei, Neuro-control to energy minimization for a class of chaotic systems based on ADP algorithm, in International Conference on Intelligent Science and Big Data Engineering, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 2013.
doi: 10.1007/978-3-642-42057-3_78. |
[20] |
P. J. Werbos, Using ADP to understand and replicate brain intelligence: The next level design?, in Neurodynamics of Cognition and Consciousness, Understanding Complex Systems, Springer, Berlin, Heidelberg, 2007,109–123.
doi: 10.1007/978-3-540-73267-9_6. |
[21] |
J. Wu, et al., Adaptive dual heuristic programming based on delta-bar-delta learning rule, in International Symposium on Neural Networks, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 2011, 11–20.
doi: 10.1007/978-3-642-21111-9_2. |
[22] |
C. Xia, et al., A novel direct torque control of matrix converter-fed PMSM drives using duty
cycle control for torque ripple reduction, IEEE Trans. on Industr. Electronics, 61 (2013),
2700–2713.
doi: 10.1109/TIE.2013.2276039. |
[23] |
Y. Yan, et al., Torque ripple minimization of PMSM using PI type iterative learning control, 40th Annual Conference of the IEEE Industrial Electronics Society, 2014.
doi: 10.1109/IECON.2014.7048612. |
[24] |
R. Yuan and Z. Q. Zhu,
Reduction of both harmonic current and torque ripple for dual three-phase permanent-magnet synchronous machine using modified switching-table-based direct torque control, IEEE Trans. on Industr. Electronics, 62 (2015), 6671-6683.
doi: 10.1109/TIE.2015.2448511. |
[25] |
J. P. Yun, et al., Torque ripples minimization in PMSM using variable step-size normalized iterative learning control, IEEE Conference on Robotics, Automation and Mechatronics, 2006.
doi: 10.1109/RAMECH.2006.252747. |
[26] |
Z. Zhu, Q. S. Ruangsinchaiwanich and D. Howe,
Synthesis of cogging-torque waveform from analysis of a single stator slot, IEEE Trans. on Indust. Appl., 42 (2006), 650-657.
doi: 10.1109/TIA.2006.872930. |
show all references
References:
[1] |
T. Banks,
Matrix Theory, Nuclear Phys. B Proc. Suppl., 67 (1997), 180-224.
doi: 10.1016/S0920-5632(98)00130-3. |
[2] |
H. J. Brascamp and E. H. Lieb,
Best constants in Young's inequality, its converse, and its generalization to more than three functions, Advances in Math., 20 (1976), 151-173.
doi: 10.1016/0001-8708(76)90184-5. |
[3] |
Y. Cho, et al., Torque-ripple minimization and fast dynamic scheme for torque predictive control of permanent-magnet synchronous motors, IEEE Transactions on Power Electronics, 30 (2015), 2182–2190.
doi: 10.1109/TPEL.2014.2326192. |
[4] |
J. Chu,
Suppressing speed ripples of permanent magnetic synchronous motor based on a method, Trans. of China Electrotechnical Society, 24 (2009), 43-49.
|
[5] |
S. U. Chung, et al., Fractional slot concentrated winding PMSM with consequent pole rotor
for a low-speed direct drive: Reduction of rare earth permanent magnet, IEEE Trans. on
Energy Conversion, 30 (2015), 103–109.
doi: 10.1109/TEC.2014.2352365. |
[6] |
J. Fiala and F. H. Guenther,
Handbook of intelligent control: Neural, fuzzy, and adaptive approaches, Neural Networks, 7 (1994), 851-852.
|
[7] |
D. C. Hanselman,
Minimum torque ripple, maximum efficiency excitation of brushless permanent magnet motors, IEEE Transactions on Industr. Electronics, 41 (1994), 292-300.
doi: 10.1109/41.293899. |
[8] |
B. H. Lam, et al., Torque ripple minimization in PM synchronous motors an iterative learning control approach, IEEE Internat. Conference on Power Electronics and Drive Systems, 1999.
doi: 10.1109/PEDS.1999.794551. |
[9] |
F. L. Lewis and D. Liu, Reinforcement learning and approximate dynamic programming for feedback control, John Wiley & Sons, 2013.
doi: 10.1002/9781118453988. |
[10] |
D. Ma and H. Lin, Accelerated iterative learning control of speed ripple suppression for a seeker servo motor, Algorithms, 11 (2018).
doi: 10.3390/a11100152. |
[11] |
G. Madescu, et al., Effects of stator slot magnetic wedges on the induction motor performances, Optimization of Electrical and Electronic Equipment (OPTIM), 13th International Conference on IEEE, 2012.
doi: 10.1109/optim.2012.6231861. |
[12] |
S. G. Min and B. Sarlioglu,
Advantages and characteristic analysis of slotless rotary PM machines in comparison with conventional laminated design using statistical technique, IEEE Trans. on Transpor. Electrification, 4 (2018), 517-524.
doi: 10.1109/TTE.2018.2810230. |
[13] |
A. R. I. Mohamed and E. F. El-Saadany,
A current control scheme with an adaptive internal model for torque ripple minimization and robust current regulation in PMSM drive systems, IEEE Trans. on Energy Conversion, 23 (2008), 92-100.
doi: 10.1109/TEC.2007.914352. |
[14] |
N. Nakao,
Suppressing pulsating torques: Torque ripple control for synchronous motors, IEEE Industry Appl. Magazine, 21 (2015), 33-44.
doi: 10.1109/MIAS.2013.2288383. |
[15] |
P. M. Pardalos, Approximate dynamic programming: solving the curses of dimensionality, Optimization Methods and Software, 24 (2009), 155.
doi: 10.1080/10556780802583108. |
[16] |
M. Pinsky, Introduction to Fourier Analysis and Wavelets, 102, American Mathematical Society, Providence, RI, 2009.
doi: 10.1090/gsm/102. |
[17] |
W. Qian, S. K. Panda and J. X. Xu,
Torque ripple minimization in PM synchronous motors using iterative learning control, IEEE Transactions on Power Electronics, 19 (2004), 272-279.
doi: 10.1109/TPEL.2003.820537. |
[18] |
J. Si, et al., Handbook of Learning and Approximate Dynamic Programming, John Wiley & Sons, 2004.
doi: 10.1002/9780470544785. |
[19] |
R. Song, W. Xiao and Q. Wei, Neuro-control to energy minimization for a class of chaotic systems based on ADP algorithm, in International Conference on Intelligent Science and Big Data Engineering, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 2013.
doi: 10.1007/978-3-642-42057-3_78. |
[20] |
P. J. Werbos, Using ADP to understand and replicate brain intelligence: The next level design?, in Neurodynamics of Cognition and Consciousness, Understanding Complex Systems, Springer, Berlin, Heidelberg, 2007,109–123.
doi: 10.1007/978-3-540-73267-9_6. |
[21] |
J. Wu, et al., Adaptive dual heuristic programming based on delta-bar-delta learning rule, in International Symposium on Neural Networks, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 2011, 11–20.
doi: 10.1007/978-3-642-21111-9_2. |
[22] |
C. Xia, et al., A novel direct torque control of matrix converter-fed PMSM drives using duty
cycle control for torque ripple reduction, IEEE Trans. on Industr. Electronics, 61 (2013),
2700–2713.
doi: 10.1109/TIE.2013.2276039. |
[23] |
Y. Yan, et al., Torque ripple minimization of PMSM using PI type iterative learning control, 40th Annual Conference of the IEEE Industrial Electronics Society, 2014.
doi: 10.1109/IECON.2014.7048612. |
[24] |
R. Yuan and Z. Q. Zhu,
Reduction of both harmonic current and torque ripple for dual three-phase permanent-magnet synchronous machine using modified switching-table-based direct torque control, IEEE Trans. on Industr. Electronics, 62 (2015), 6671-6683.
doi: 10.1109/TIE.2015.2448511. |
[25] |
J. P. Yun, et al., Torque ripples minimization in PMSM using variable step-size normalized iterative learning control, IEEE Conference on Robotics, Automation and Mechatronics, 2006.
doi: 10.1109/RAMECH.2006.252747. |
[26] |
Z. Zhu, Q. S. Ruangsinchaiwanich and D. Howe,
Synthesis of cogging-torque waveform from analysis of a single stator slot, IEEE Trans. on Indust. Appl., 42 (2006), 650-657.
doi: 10.1109/TIA.2006.872930. |









Characteristic | Symbol | Value |
Stator phase resistance | R | 2.875Ω |
d and q-axes | ${L_d} = {L_q}$ | 8.5mH |
Number of pole pairs | ${p_n}$ | 4 |
viscous damping | B | 0.008 N. m. s |
Torque constant | ${K_t}$ | 1.05 N. m |
Rotational inertia | J | 0.003kg.m2 |
Characteristic | Symbol | Value |
Stator phase resistance | R | 2.875Ω |
d and q-axes | ${L_d} = {L_q}$ | 8.5mH |
Number of pole pairs | ${p_n}$ | 4 |
viscous damping | B | 0.008 N. m. s |
Torque constant | ${K_t}$ | 1.05 N. m |
Rotational inertia | J | 0.003kg.m2 |
Speed at 500r/min | Speed range(r/min) | Fluctuation error |
ADP controller | 499.8802-500.1253 | 0.2451 |
PI controller | 495.6341-502.8779 | 7.2438 |
Speed at 50r/min | Speed range(r/min) | Fluctuation error |
ADP controller | 49.7712-50.2942 | 0.5230 |
PI controller | 46.3281-53.5526 | 7.2279 |
Speed at 500r/min | Speed range(r/min) | Fluctuation error |
ADP controller | 499.8802-500.1253 | 0.2451 |
PI controller | 495.6341-502.8779 | 7.2438 |
Speed at 50r/min | Speed range(r/min) | Fluctuation error |
ADP controller | 49.7712-50.2942 | 0.5230 |
PI controller | 46.3281-53.5526 | 7.2279 |
Load torque at 1.6Nm | Torque range(Nm) | Fluctuation error |
ADP controller | 1.5603-1.6428 | 0.0825 |
PI controller | 0.3482-3.0570 | 2.7088 |
Load torque at 9.0Nm | Torque range(Nm) | Fluctuation error |
ADP controller | 8.9603-9.1562 | 0.1959 |
PI controller | 6.9523-12.1328 | 5.1805 |
Load torque at 1.6Nm | Torque range(Nm) | Fluctuation error |
ADP controller | 1.5603-1.6428 | 0.0825 |
PI controller | 0.3482-3.0570 | 2.7088 |
Load torque at 9.0Nm | Torque range(Nm) | Fluctuation error |
ADP controller | 8.9603-9.1562 | 0.1959 |
PI controller | 6.9523-12.1328 | 5.1805 |
[1] |
Vladimir Djordjevic, Vladimir Stojanovic, Hongfeng Tao, Xiaona Song, Shuping He, Weinan Gao. Data-driven control of hydraulic servo actuator based on adaptive dynamic programming. Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1633-1650. doi: 10.3934/dcdss.2021145 |
[2] |
Jean Blaise Teguia, Alain Soup Tewa Kammogne, Stella Germaine Tsakoue Ganmene, Martin Siewe Siewe, Godpromesse Kenne. Fuzzy-enhanced robust fault-tolerant control of IFOC motor with matched and mismatched disturbances. Mathematical Foundations of Computing, 2022 doi: 10.3934/mfc.2022006 |
[3] |
Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure and Applied Analysis, 2012, 11 (6) : 2473-2485. doi: 10.3934/cpaa.2012.11.2473 |
[4] |
Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial and Management Optimization, 2008, 4 (1) : 1-15. doi: 10.3934/jimo.2008.4.1 |
[5] |
Matthew H. Henry, Yacov Y. Haimes. Robust multiobjective dynamic programming: Minimax envelopes for efficient decisionmaking under scenario uncertainty. Journal of Industrial and Management Optimization, 2009, 5 (4) : 791-824. doi: 10.3934/jimo.2009.5.791 |
[6] |
Yaobang Ye, Zongyu Zuo, Michael Basin. Robust adaptive sliding mode tracking control for a rigid body based on Lie subgroups of SO(3). Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1823-1837. doi: 10.3934/dcdss.2022010 |
[7] |
Xiangying Meng, Quanbao Ji, John Rinzel. Firing control of ink gland motor cells in Aplysia californica. Discrete and Continuous Dynamical Systems - B, 2011, 16 (2) : 529-545. doi: 10.3934/dcdsb.2011.16.529 |
[8] |
Zhongliang Deng, Enwen Hu. Error minimization with global optimization for difference of convex functions. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1027-1033. doi: 10.3934/dcdss.2019070 |
[9] |
Ramasamy Kavikumar, Boomipalagan Kaviarasan, Yong-Gwon Lee, Oh-Min Kwon, Rathinasamy Sakthivel, Seong-Gon Choi. Robust dynamic sliding mode control design for interval type-2 fuzzy systems. Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1839-1858. doi: 10.3934/dcdss.2022014 |
[10] |
Xue Lu, Niall Adams, Nikolas Kantas. On adaptive estimation for dynamic Bernoulli bandits. Foundations of Data Science, 2019, 1 (2) : 197-225. doi: 10.3934/fods.2019009 |
[11] |
Tamar Friedlander, Naama Brenner. Adaptive response and enlargement of dynamic range. Mathematical Biosciences & Engineering, 2011, 8 (2) : 515-528. doi: 10.3934/mbe.2011.8.515 |
[12] |
Silvia Faggian. Boundary control problems with convex cost and dynamic programming in infinite dimension part II: Existence for HJB. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 323-346. doi: 10.3934/dcds.2005.12.323 |
[13] |
Guy Barles, Ariela Briani, Emmanuel Trélat. Value function for regional control problems via dynamic programming and Pontryagin maximum principle. Mathematical Control and Related Fields, 2018, 8 (3&4) : 509-533. doi: 10.3934/mcrf.2018021 |
[14] |
Ruotian Gao, Wenxun Xing. Robust sensitivity analysis for linear programming with ellipsoidal perturbation. Journal of Industrial and Management Optimization, 2020, 16 (4) : 2029-2044. doi: 10.3934/jimo.2019041 |
[15] |
Jérôme Renault. General limit value in dynamic programming. Journal of Dynamics and Games, 2014, 1 (3) : 471-484. doi: 10.3934/jdg.2014.1.471 |
[16] |
Alain Bossavit. Magnetic forces in and on a magnet. Discrete and Continuous Dynamical Systems - S, 2019, 12 (6) : 1589-1600. doi: 10.3934/dcdss.2019108 |
[17] |
Araz Hashemi, George Yin, Le Yi Wang. Sign-error adaptive filtering algorithms involving Markovian parameters. Mathematical Control and Related Fields, 2015, 5 (4) : 781-806. doi: 10.3934/mcrf.2015.5.781 |
[18] |
Alexey G. Mazko. Positivity, robust stability and comparison of dynamic systems. Conference Publications, 2011, 2011 (Special) : 1042-1051. doi: 10.3934/proc.2011.2011.1042 |
[19] |
Li-Bin Liu, Ying Liang, Jian Zhang, Xiaobing Bao. A robust adaptive grid method for singularly perturbed Burger-Huxley equations. Electronic Research Archive, 2020, 28 (4) : 1439-1457. doi: 10.3934/era.2020076 |
[20] |
Yves Dumont, Frederic Chiroleu. Vector control for the Chikungunya disease. Mathematical Biosciences & Engineering, 2010, 7 (2) : 313-345. doi: 10.3934/mbe.2010.7.313 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]