带有不确定性的多电机卷绕系统的分散最优保性能控制
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摘要
针对具有参数不确定、强耦合的多电机卷绕系统,提出一种分散最优保性能控制方法.首先,将多电机卷绕系统看成由若干动态区间子系统组成的综合系统,引入区间矩阵以处理子系统模型中的设定值改变和不确定参数;在此基础上设计基于状态反馈的分散最优保性能控制器,得到控制器存在的线性矩阵不等式(LMI)充分条件;最后以三电机卷绕系统为研究对象,对所设计的控制器进行仿真和平台实验,实验结果表明,所提出的分散最优保性能控制能有效降低控制代价,增强系统的抗干扰能力,保证张力和速度的控制精度.
For the multi-motor winding system with parametric uncertainties and strong coupling, a decentralized optimal guaranteed cost control method is proposed. Firstly, a multi-motor winding system is regarded as a synthetic system with several dynamic interval subsystems. To describe the modifications of set point and the uncertain parameters, a interval matrix is introduced. Then, a decentralized optimal guaranteed cost controller is designed based on state feedback, and a sufficient condition for the existence of this controller is derived in terms of the linear matrix inequalities(LMIs). Finally,some simulation and experimental tests are conducted on a three-motor winding system. The experimental results show that the proposed decentralized optimal guaranteed cost controller can efficiently reduce control cost, strengthen the anti-jamming capability of the system, and ensure control precision of the tension and velocity.
For the multi-motor winding system with parametric uncertainties and strong coupling, a decentralized optimal guaranteed cost control method is proposed. Firstly, a multi-motor winding system is regarded as a synthetic system with several dynamic interval subsystems. To describe the modifications of set point and the uncertain parameters, a interval matrix is introduced. Then, a decentralized optimal guaranteed cost controller is designed based on state feedback, and a sufficient condition for the existence of this controller is derived in terms of the linear matrix inequalities(LMIs). Finally,some simulation and experimental tests are conducted on a three-motor winding system. The experimental results show that the proposed decentralized optimal guaranteed cost controller can efficiently reduce control cost, strengthen the anti-jamming capability of the system, and ensure control precision of the tension and velocity.
引文
[1] Hou H L, Nian X H, Xiong H Y, et al. Robust decentralized coordinated control of a multi-motor web-winding System[J]. IEEE Trans on Control Systems Technology,2016, 24(4):1495-1503.
[2] Claveau F, Chevrel P, Knittel K. A 2DOF gain-scheduled controller design methodology for a multi-motor web transport system[J]. Control Engineering Practice,2008,16(5):609-622.
[3] He J J, Yu S Y, Zhong J. Tension-speed decoupling control of temper mill for plate-strip steet[J]. Control and Decision, 2003,18(5):522-526.
[4] Dou X, Wang W. Robust control of multistage printing systems[J]. Control Engineering Practice, 2010, 18(3):219-229.
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[6] Zhang Y F, Chang Y L, Gao Y Y, et al, Fuzzy ADRC applied in gravure press tension control system[J]. J of Xi’an University of Technology, 2015, 31(2):144-149.
[7] Pagilla P R, King E O, Dreinhoefer L H, et al. Robust observer-based control of an aluminum strip processing line[J]. IEEE Trans on Industry Applications, 2000,36(3):865-870.
[8] Hakan Koc, Dominique Knittel, Michel de Mathelin,et al. Modeling and robust control of winding systems for elastic webs[J]. IEEE Trans on Control Systems Technology, 2002, 10(2):197-208.
[9] Knittel D, Laroche E, Gigan D, et al. Tension control for winding system with two-degrees-of controllers[J]. IEEE Trans on Industry Applications, 2003, 39(1):113-120.
[10] Liu L, Fang Y M, Li J X, et al. Dynamic sliding mode decoupling control for speed and tension system of reversible cold strip mill[J]. Control Theory&Applications, 2013, 30(8):581-586.
[11] Deng X, Hu M Y. Application of PID neural network in paper tension control system[J]. Trans of China Pulp and Paper, 2014, 29(1):44-48.
[12] Chen C L, Chang K M, Chang C M. Modeling and control of a web-fed machine[J]. Applied Mathematical Modelling, 2004, 28(10):863-876.
[13] Zhang C F, Wang Y N, He J. GA-NN-integrated sliding mode control system and its application in the printing press[J]. Control Theory&Applications, 2003, 20(2):217-222.
[14] Sun J Q, Lv S, Dai H. Study on optimization of reduction amount and tension in cold rolling mill based on particle swarm optimization[J]. ICIC Express Letters, 2010, 4(4):1385-1392.
[15] Priya N H, Kavitha P, Muthukumar N, et al. Design of PSO-based PI controller for tension control in web transport systems[C]. Int Conf on Soft Computing Systems. India:Springer, 2016:509-516.
[16] Xiao L, Ding Y S, Ren L H, et al. Data-driven cooperative intelligent controller based on the endocrine regulation mechanism[J]. IEEE Trans on Control Systems Technology, 2014, 22(1):94-101.
[17] Chen Y X, Wang Y C. Study on guaranteed cost control for linear motor servo system[J]. Proc of the CSEE, 2006,26(24):174-178.
[18] Hou H L, Nian X H, Peng Z, et al. State feedback robust control for three-motor winding system—LMI approach[J]. Electric Machines and Control, 2016, 20(7):111-118.
[19] Mao W, Chun J. Quadratic stability and stabilization of dynamic interval systems[J]. IEEE Trans on Automatic Control, 2009, 32(3):1007-1012.
[20] Alefeld G, Herzberger J. Introduction to interval Computation[M]. New York:Academic Press, 1983:2-19.
[21] Boyd S, Ghaoui EI L, Feron E, et al. Linear matrix inequalities in system and control theory[M].Philadelphia:SIAM, 1994:43-52.
[22] Petersen I R, McFarlane D C. Optimal guaranteed cost control and filtering for uncertain linear systems[J]. IEEE Trans on Automatic Control, 1994, 39(9):1971-1977.
[23] Hou H L, Nian X H, Xu S Z, et al. Robust decentralized control for large-scale web-winding systems:A linear matrix inequality approach[J]. Trans of the Institute of Measurement and Control, 2017, 39(7):953-964.
[24] Wang Y W, Gong Y Z, Xiao Q, et al. Variable range analysis based on interval computation[J]. J of Beijing University of Post and Telecommunication, 2009, 32(3):36-41.
[2] Claveau F, Chevrel P, Knittel K. A 2DOF gain-scheduled controller design methodology for a multi-motor web transport system[J]. Control Engineering Practice,2008,16(5):609-622.
[3] He J J, Yu S Y, Zhong J. Tension-speed decoupling control of temper mill for plate-strip steet[J]. Control and Decision, 2003,18(5):522-526.
[4] Dou X, Wang W. Robust control of multistage printing systems[J]. Control Engineering Practice, 2010, 18(3):219-229.
[5] Raul P R, Manyan S G, Pagilla P R, et al. Output regulation of nonlinear systems with application to roll-to-roll manufacturing system[J]. IEEE-ASME Trans on Mechatronics, 2015, 20(3):1089-1098.
[6] Zhang Y F, Chang Y L, Gao Y Y, et al, Fuzzy ADRC applied in gravure press tension control system[J]. J of Xi’an University of Technology, 2015, 31(2):144-149.
[7] Pagilla P R, King E O, Dreinhoefer L H, et al. Robust observer-based control of an aluminum strip processing line[J]. IEEE Trans on Industry Applications, 2000,36(3):865-870.
[8] Hakan Koc, Dominique Knittel, Michel de Mathelin,et al. Modeling and robust control of winding systems for elastic webs[J]. IEEE Trans on Control Systems Technology, 2002, 10(2):197-208.
[9] Knittel D, Laroche E, Gigan D, et al. Tension control for winding system with two-degrees-of controllers[J]. IEEE Trans on Industry Applications, 2003, 39(1):113-120.
[10] Liu L, Fang Y M, Li J X, et al. Dynamic sliding mode decoupling control for speed and tension system of reversible cold strip mill[J]. Control Theory&Applications, 2013, 30(8):581-586.
[11] Deng X, Hu M Y. Application of PID neural network in paper tension control system[J]. Trans of China Pulp and Paper, 2014, 29(1):44-48.
[12] Chen C L, Chang K M, Chang C M. Modeling and control of a web-fed machine[J]. Applied Mathematical Modelling, 2004, 28(10):863-876.
[13] Zhang C F, Wang Y N, He J. GA-NN-integrated sliding mode control system and its application in the printing press[J]. Control Theory&Applications, 2003, 20(2):217-222.
[14] Sun J Q, Lv S, Dai H. Study on optimization of reduction amount and tension in cold rolling mill based on particle swarm optimization[J]. ICIC Express Letters, 2010, 4(4):1385-1392.
[15] Priya N H, Kavitha P, Muthukumar N, et al. Design of PSO-based PI controller for tension control in web transport systems[C]. Int Conf on Soft Computing Systems. India:Springer, 2016:509-516.
[16] Xiao L, Ding Y S, Ren L H, et al. Data-driven cooperative intelligent controller based on the endocrine regulation mechanism[J]. IEEE Trans on Control Systems Technology, 2014, 22(1):94-101.
[17] Chen Y X, Wang Y C. Study on guaranteed cost control for linear motor servo system[J]. Proc of the CSEE, 2006,26(24):174-178.
[18] Hou H L, Nian X H, Peng Z, et al. State feedback robust control for three-motor winding system—LMI approach[J]. Electric Machines and Control, 2016, 20(7):111-118.
[19] Mao W, Chun J. Quadratic stability and stabilization of dynamic interval systems[J]. IEEE Trans on Automatic Control, 2009, 32(3):1007-1012.
[20] Alefeld G, Herzberger J. Introduction to interval Computation[M]. New York:Academic Press, 1983:2-19.
[21] Boyd S, Ghaoui EI L, Feron E, et al. Linear matrix inequalities in system and control theory[M].Philadelphia:SIAM, 1994:43-52.
[22] Petersen I R, McFarlane D C. Optimal guaranteed cost control and filtering for uncertain linear systems[J]. IEEE Trans on Automatic Control, 1994, 39(9):1971-1977.
[23] Hou H L, Nian X H, Xu S Z, et al. Robust decentralized control for large-scale web-winding systems:A linear matrix inequality approach[J]. Trans of the Institute of Measurement and Control, 2017, 39(7):953-964.
[24] Wang Y W, Gong Y Z, Xiao Q, et al. Variable range analysis based on interval computation[J]. J of Beijing University of Post and Telecommunication, 2009, 32(3):36-41.