基于状态空间模型的轧制鲁棒控制器设计
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摘要
板带材生产过程中,轧制系统是一个典型的多变量、强扰动、高耦合的非线性系统。作为保证带钢出口厚度精度的前提,应保证系统是具有鲁棒稳定性的。所设计的控制器应能抑止扰动对系统的影响,以及在有限系统参数摄动的情况下仍能保持稳定。考虑到系统的复杂性,为了更好地研究轧制过程各个变量之间的关系,建立了液压辊系、电机传动、轧制过程的线性化状态空间模型,考虑到外扰的复杂性,选用H_∞控制策略,并利用MATLAB进行线性矩阵不等式的求解,通过选取适当的性能指标,找到状态反馈控制器。仿真效果表明,其较之常规控制方法有着良好的鲁棒性与性能指标。
For the rolling system, it should be a multi-variable, strong disturbance and coupled nonlinear system. As the precondition of ensuring the precision of strip thickness, it is necessary to ensure that the system is robust. The controller should be able to suppress the disturbance of the system and remain the system stable under the uncertain parameters. Taking into account the complexity of the system, this paper establishes a linear state space model of the hydraulic roller system, motor transmission and rolling process system for the deeper study of the relationship between the variables in the rolling process. Considering the complexity of the external disturbance, this paper chooses the H_∞ control strategy. MATLAB is used to solve the linear matrix inequalities. By selecting the appropriate performance index, the state feedback controller could be found. The simulation result shows that the state feedback control system has better robustness and performance index.
For the rolling system, it should be a multi-variable, strong disturbance and coupled nonlinear system. As the precondition of ensuring the precision of strip thickness, it is necessary to ensure that the system is robust. The controller should be able to suppress the disturbance of the system and remain the system stable under the uncertain parameters. Taking into account the complexity of the system, this paper establishes a linear state space model of the hydraulic roller system, motor transmission and rolling process system for the deeper study of the relationship between the variables in the rolling process. Considering the complexity of the external disturbance, this paper chooses the H_∞ control strategy. MATLAB is used to solve the linear matrix inequalities. By selecting the appropriate performance index, the state feedback controller could be found. The simulation result shows that the state feedback control system has better robustness and performance index.
引文
[1]刘乐,方一鸣,李晓刚.基于Hamilton理论的可逆冷带轧机速度张力系统无张力计控制[J].自动化学报,2015,41(1):165-175.Liu L,Fang Y M,Li X G.Tensiometer-free Control for a Speed and Tension System of Reversible Cold Strip Mill Based on Hamilton Theory[J].Acta Automatica Sinica,2015,41(1):165-175.
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[3]李仲德,杨卫东.冷连轧机厚度和张力系统的多变量解耦鲁棒控制[J].控制理论与应用,2011,28(4):581-586.Li Z D,Yang W D.Multivariable Decoupling Robust Control for the Thickness and Tension System of Tandem Cold Rolling Mill[J].Control Theory and Application,2011,28(4):581-586.
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[8]谭树彬.轧机辊缝控制建模及仿真[J].系统仿真学报,2006,18(6):1 425-1 427.Tan S B.Modeling and Simulation of Rolling Gap Control in Strip Mills[J].Journal of System Simulation,2006,18(6):1 425-1 427.
[9]任新意.1420冷连轧机板形板厚控制数理建模与仿真[D].秦皇岛:燕山大学,2012.Ren X Y.Mathematical Modeling and Simulation of Strip Shape and Gauge Controlling in 1420 Cold Tandem Mills[D].Qinhuangdao:Yanshan University,2012.
[10]焦玺晓.虚拟轧机的建模与仿真[D].沈阳:东北大学,2014.Jiao X X.Modeling and Simulation of Virtual Rolling Mill[D].Shenyang:Northeastern University,2014.
[11]孙一康.带钢冷连轧计算机控制[M].北京:冶金工业出版社,2010:212-214.Sun Y K.Computer Control of Cold Rolling Mill[M].Beijing:Metallurgical Industry Press,2010:212-214.
[12]申铁龙.H∞控制理论及应用[M].北京:清华大学出版社,1996:75-78.Shen T L.H∞Control Theory and Its Application[M].Beijing:Tsinghua University Press,1996:75-78.
[13]屈百达,张玉军,廖建庆.一类不确定线性时变时滞系统的鲁棒H∞控制[J].控制工程,2016,23(1):91-96.Qu B D,Zhang Y J,Liao J Q.Robust H∞Controller Design for a Class of Uncertain Linear Systems with Time-varying and Control Delay[J].Control Engineering of China,2016,23(1):91-96.
[14]俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京:清华大学出版社,2002:42-45.Yu L.Robust Control Linear Matrix Inequality Approach[M].Beijing:Tsinghua University Press,2002:42-45.
[2]李丽,恒庆海.鲁棒控制在热连轧AGC中的应用[J].北京信息科技大学学报(自然科学版),2015,30(3):90-94.Li L,Heng Q H.Robust Control for Automatic Gauge Control in Hot Strip Milling[J].Journal of Beijing Information Science&Technology University.2015,30(3):90-94.
[3]李仲德,杨卫东.冷连轧机厚度和张力系统的多变量解耦鲁棒控制[J].控制理论与应用,2011,28(4):581-586.Li Z D,Yang W D.Multivariable Decoupling Robust Control for the Thickness and Tension System of Tandem Cold Rolling Mill[J].Control Theory and Application,2011,28(4):581-586.
[4]杨斌虎,杨卫东,陈连贵.基于H∞-H2的多变量约束热轧带钢AGC鲁棒控制[J].信息与控制,2007,36(4):514-518.Yang B H,Yang W D,Chen L A.Multivariable Constrained Agc Rubust Control Based on H∞-H2 for Hot Rolling Strip[J].Information and Control,2007,36(4):514-518.
[5]向丹,邵忠良.铝合金厚板轧制设备电液位置伺服系统建模与分析[J].自动化仪表,2014,35(2):13-15.Xiang D,Shao Z L.Modeling and Analysis of the Electro-hydraulic Position Servo System for Rolling Facilities of Aluminum Alloy Thick Plate[J].Process Automation Instrumentation,2014,35(2):13-15.
[6]刘彬,赵红旭,朱月.基于动态轧制力的冷轧机两自由度垂直振动特性[J].中国机械工程,2014,25(17):2 344-2 350.Liu B,Zhao H X,Zhu Y.Two Degree of Freedom Vertical Vibration Characteristics of Cold Rolling Mill Based on Dynamic Rolling Force[J].China Mechanical Engineering,2014,25(17):2 344-2 350.
[7]张瑞成,童朝南.轧机主传动系统自抗扰控制器设计与应用[J].控制理论与应用,2005,22(6):1 005-1 009.Zhang R C,Tong C N.Design and Application of Active Disturbance Rejection Controller for Main Drive System of Rolling Mill[J].Control Theory and Application,2005,22(6):1 005-1 009.
[8]谭树彬.轧机辊缝控制建模及仿真[J].系统仿真学报,2006,18(6):1 425-1 427.Tan S B.Modeling and Simulation of Rolling Gap Control in Strip Mills[J].Journal of System Simulation,2006,18(6):1 425-1 427.
[9]任新意.1420冷连轧机板形板厚控制数理建模与仿真[D].秦皇岛:燕山大学,2012.Ren X Y.Mathematical Modeling and Simulation of Strip Shape and Gauge Controlling in 1420 Cold Tandem Mills[D].Qinhuangdao:Yanshan University,2012.
[10]焦玺晓.虚拟轧机的建模与仿真[D].沈阳:东北大学,2014.Jiao X X.Modeling and Simulation of Virtual Rolling Mill[D].Shenyang:Northeastern University,2014.
[11]孙一康.带钢冷连轧计算机控制[M].北京:冶金工业出版社,2010:212-214.Sun Y K.Computer Control of Cold Rolling Mill[M].Beijing:Metallurgical Industry Press,2010:212-214.
[12]申铁龙.H∞控制理论及应用[M].北京:清华大学出版社,1996:75-78.Shen T L.H∞Control Theory and Its Application[M].Beijing:Tsinghua University Press,1996:75-78.
[13]屈百达,张玉军,廖建庆.一类不确定线性时变时滞系统的鲁棒H∞控制[J].控制工程,2016,23(1):91-96.Qu B D,Zhang Y J,Liao J Q.Robust H∞Controller Design for a Class of Uncertain Linear Systems with Time-varying and Control Delay[J].Control Engineering of China,2016,23(1):91-96.
[14]俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京:清华大学出版社,2002:42-45.Yu L.Robust Control Linear Matrix Inequality Approach[M].Beijing:Tsinghua University Press,2002:42-45.