基于二次型价值函数的双电机转矩同步系统有限集模型预测控制
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摘要
在多电机系统有限集模型预测控制(finite control set model predictive control,FCS-MPC)中,随着电机数量的增加,加权求和型价值函数中权重系数的数量也随之增加,整定变得困难。对此,在对双电机转矩同步系统进行统一建模的基础上,通过构造二次型价值函数,将3个权重系数的整定问题转化为1个权重系数矩阵的求解问题。在二次型价值函数中应用由离线求解算法得到的权重系数矩阵能够保证系统的李雅普诺夫稳定性,从而可在连续控制周期内保证各误差收敛。在齿轮传动双电机转矩同步控制系统实验平台上对该算法进行实验验证,结果表明:将离线自整定后的权重系数矩阵用于二次型价值函数中,能使FCS-MPC控制下电机的跟踪误差和同步误差具有良好的收敛性。从理论和实验上证明了基于二次型价值函数的FCS-MPC算法能保证各电机较好的跟踪性能和转矩同步性能,同时该控制策略为拓展到多电机系统提供了可能。
In the multi-motor system finite control set model predictive control(FCS-MPC), the tuning of weight coefficients in the weighted sum cost function(WSCF) is becoming complex when the number of motors increases.Based on the unified model of a dual-motor torque synchronization system, this paper replaced the WSCF with a quadratic form cost function(QFCF), thereby, the tuning of the three weight coefficients was converted into the solving of a weight coefficient matrix. The Lyapunov stability of system can be guaranteed by applying the weight coefficient matrix obtained by the offline solution algorithm to the QFCF, so the errors can be guaranteed to converge in the continuous control periods. Experiments were performed on a gear drive two-motor torque synchronization control system. The results show that, in the dual-motor FCS-MPC, the applying of the QFCF, whose weight coefficient matrix is auto-tuned offline, can make the tracking errors and synchronization error converge. This paper proves theoretically and experimentally that the FCS-MPC algorithm based on QFCF can ensure tracking performance and torque synchronization performance of the motors, meanwhile, the control strategy provides the possibility to expand to multi-motor system.
In the multi-motor system finite control set model predictive control(FCS-MPC), the tuning of weight coefficients in the weighted sum cost function(WSCF) is becoming complex when the number of motors increases.Based on the unified model of a dual-motor torque synchronization system, this paper replaced the WSCF with a quadratic form cost function(QFCF), thereby, the tuning of the three weight coefficients was converted into the solving of a weight coefficient matrix. The Lyapunov stability of system can be guaranteed by applying the weight coefficient matrix obtained by the offline solution algorithm to the QFCF, so the errors can be guaranteed to converge in the continuous control periods. Experiments were performed on a gear drive two-motor torque synchronization control system. The results show that, in the dual-motor FCS-MPC, the applying of the QFCF, whose weight coefficient matrix is auto-tuned offline, can make the tracking errors and synchronization error converge. This paper proves theoretically and experimentally that the FCS-MPC algorithm based on QFCF can ensure tracking performance and torque synchronization performance of the motors, meanwhile, the control strategy provides the possibility to expand to multi-motor system.
引文
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[19]Ahmed A A,Koh B K,Park H S,et al.Finite-control set model predictive control method for torque control of induction motors using a state tracking cost index[J].IEEE Transactions on Industrial Electronics,2017,64(3):1916-1928.
[20]Aristidou P,Fabozzi D,Van Cutsem T.Dynamic simulation of large-scale power systems using a parallel Schur-complement-based decomposition method[J].IEEETransactions on Parallel and Distributed Systems,2014,25(10):2561-2570.
[2]Tseng S K,Liu T H,Hsu J W,et al.Implementation of online maximum efficiency tracking control for a dual-motor drive system[J].IET Electric Power Applications,2015,9(7):449-458.
[3]陈炜,刘旭,史婷娜,等.双轴联动系统广义预测交叉耦合位置控制[J].控制理论与应用,2018,35(3):399-406.Chen Wei,Liu Xu,Shi Tingna,et al.Generalized predictive cross-coupling position control of biaxial motion system[J].Control Theory&Applications,2018,35(3):399-406(in Chinese).
[4]Li Z,Tang J.A novel approach of fixed joint multi-motor power balance control[C]//IEEE International Conference on Electrical Machines and Systems.Wuhan,China:IEEE,2008:1567-1570.
[5]Bogiatzidis I X,Safacas A N,Mitronikas E D,et al.Anovel control strategy applicable for a dual AC drive with common mechanical load[J].IEEE Transactions on Industry Applications,2012,48(6):2022-2036.
[6]孙伟,于泳,王高林,等.基于矢量控制的异步电机预测电流控制算法[J].中国电机工程学报,2014,34(21):3448-3455.Sun Wei,Yu Yong,Wang Gaolin,et al.A predictive current control scheme for induction motor with vector control[J].Proceedings of the CSEE,2014,34(21):3448-3455(in Chinese).
[7]杨建飞,胡育文.永磁同步电机最优直接转矩控制[J].中国电机工程学报,2011,31(27):109-115.Yang Jianfei,Hu Yuwen,et al.Optimal direct torque control of permanent magnet synchronous motor[J].Proceedings of the CSEE,2011,31(27):109-115(in Chinese).
[8]Villarroel F,Espinoza J R,Rojas C A,et al.Multi-objective switching state selector for finite-states model predictive control based on fuzzy decision making in a matrix converter[J].IEEE Transactions on Industrial Electronics,2013,60(2):589-599.
[9]Lv S S,Lin H.Model predictive direct torque control for PMSM with duty cycle optimization[C]//IEEEInternational Conference on Instrumentation and Measurement,Computer,Communication and Control.Qinhuangdao,China:IEEE,2015:866-871.
[10]郑泽东,王奎,李永东,等.采用模型预测控制的交流电机电流控制器[J].电工技术学报,2013,28(11):118-123.Zheng Zedong,Wang Kui,Li Yongdong,et al.Current controller for AC motors using model predictive control[J].Transactions of China Electrotechnical Society,2013,28(11):118-123(in Chinese).
[11]Lim C S,Levi E,Jones M,et al.A comparative study of synchronous current control schemes based on FCS-MPCand PI-PWM for a two-motor three-phase drive[J].IEEETransactions on Industrial Electronics,2014,61(8):3867-3878.
[12]Rojas C A,Rodriguez J,Villarroel F,et al.Predictive torque and flux control without weighting factors[J].IEEETransactions on Industrial Electronics,2013,60(2):681-690.
[13]Miranda H,Cortés P,Yuz J I,et al.Predictive torque control of induction machines based on state-space models[J].IEEE Transactions on Industrial Electronics,2009,56(6):1916-1924.
[14]Cortés P,Kouro S,La Rocca B,et al.Guidelines for weighting factors design in model predictive control of power converters and drives[C]//IEEE International Conference on Industrial Technology.Gippsland,VIC,Australia:IEEE,2009:1-7.
[15]夏长亮,仇旭东,王志强,等.基于矢量作用时间的新型预测转矩控制[J].中国电机工程学报,2016,36(11):3045-3053.Xia Changliang,Qiu Xudong,Wang Zhiqiang,et al.Predictive torque control based on optimal operating time of vector[J].Proceedings of the CSEE,2016,36(11):3045-3053(in Chinese).
[16]Davari S A,Khaburi D A,Kennel R.An improved FCS-MPC algorithm for an induction motor with an imposed optimized weighting factor[J].IEEE Transactions on Power Electronics,2012,27(3):1540-1551.
[17]Mahmoudi H,Lesani M J.Online fuzzy tuning of weighting factor in model predictive control of PMSM[C]//IEEE 13th Iranian Conference on Fuzzy Systems.Qazvin,Iran:IEEE,2013:1-5.
[18]Davari S A,Khaburi D A,Kennel R.Using a weighting factor table for FCS-MPC of induction motors with extended prediction horizon[C]//38th Annual Conference on IEEE Industrial Electronics Society.Montreal,QC,Canada:IEEE,2012:2086-2091.
[19]Ahmed A A,Koh B K,Park H S,et al.Finite-control set model predictive control method for torque control of induction motors using a state tracking cost index[J].IEEE Transactions on Industrial Electronics,2017,64(3):1916-1928.
[20]Aristidou P,Fabozzi D,Van Cutsem T.Dynamic simulation of large-scale power systems using a parallel Schur-complement-based decomposition method[J].IEEETransactions on Parallel and Distributed Systems,2014,25(10):2561-2570.