多变量大时滞系统的内模解耦控制
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摘要
在工业控制领域中,被控对象往往存在很多难以控制的因素,如非线性、强耦合、大时滞、非最小相位特性等,导致系统超调量变大,调节时间加长,有些甚至出现振荡、发散,系统的动态品质明显下降。大多数已有的控制方法也很难应用于这样的过程,所以多变量大时滞过程的解耦控制问题一直是控制领域中的一大难题。本文针对多变量系统强耦合和大时滞的特点,将当前迅速发展的内模控制方法应用于多变量大时滞系统的解耦中。并对非方形系统的解耦控制问题进行了初步的研究。本文的主要工作如下:
(1)根据内模控制原理和解耦控制理论推导内模解耦控制器矩阵,分析时滞和非最小相位零点对控制器的影响。
(2)采用遗传算法对模型进行降阶处理,简化设计过程;并且在此基础上对模型进行最小相位和非最小相位分离,然后根据解耦后闭环回路和控制器对角元素应该满足的时滞和RHP零点的条件设计内模解耦控制器,并且在反馈回路中添加低通滤波器,滤波器参数的选择兼顾了系统的稳定性和鲁棒性。
(3)基于Matlab/Simulink平台,对内模解耦控制器的控制效果进行了研究。分别对系统的解耦性能、鲁棒稳定性以及在干扰和参数摄动下对工艺指标的控制效果进行了仿真实验研究。
(4)创新地把多元统计中建立最优回归方程的理论应用到耦合度分析中,根据系统的输入输出数据建立回归模型,通过建立最优回归方程来确定系统输入和输出之间的最佳配对关系,达到了弱化系统耦合的效果。仿真实验证明了方法的可行性。
In the industrial control field, many uncontrollable factors exist in the controlled object, such as nonlinear, strong coupling, large time-delay, non-minimum phase characteristics etc, the factors lead to large quantitative overshoot, settling time longer, and even, some even appear to flap and dissipation,so the system dynamic quality significantly decreased.It is difficult to use most of the control methods in the control system, so decoupling control in the multi-variable big time-delay process has been a major problem in the control area. According to the characteristics of strong coupling and large time-delay of the multivariable system, the internal model control method, developed rapid at present, is applied to the decoupling of the multi-variable big time-delay system. And make a preliminary study for the decoupling control issues of non-square system.The main contents of this paper are as follows:
(1) According to the internal model control principle and decoupling control theory, the decoupling controller matrix is derived and the influence of the time-delay and non-minimum phase zero for the controller is analyzed.
(2) The reduction of time-delay model is processed with genetic algorithm, and the design process is simplified, the minimum phase and the non-minimum phase are separated based on the model reduction, then design the internal model decoupling controller based on the diagonal elements of the decoupled closed-loop transfer function and the controller should meet the requirements of the time-delay and RHP zero. And then low-pass filter is added in the feedback loop, Both the system stability and robustness are considered to choose the filter parameters.
(3) Based on platform of Matlab / Simulink, the control effects of internal model decoupling controller was studied.Decoupling performance of the system, robust stability ,disturbance and parameter perturbation performance are tested in the Matlab / Simulink platform.
(4) The theory, which the optimal regression equation is established in the multivariate statistics, is innovatively applied to coupling analysis. According to input and output data of the system, regression model is established, the optimal matching relation is determined between input and output of the system by establishing the optimal regression equation, reach to the effect of weakening the system coupling, the simulation results show that the method is feasible.
(1)根据内模控制原理和解耦控制理论推导内模解耦控制器矩阵,分析时滞和非最小相位零点对控制器的影响。
(2)采用遗传算法对模型进行降阶处理,简化设计过程;并且在此基础上对模型进行最小相位和非最小相位分离,然后根据解耦后闭环回路和控制器对角元素应该满足的时滞和RHP零点的条件设计内模解耦控制器,并且在反馈回路中添加低通滤波器,滤波器参数的选择兼顾了系统的稳定性和鲁棒性。
(3)基于Matlab/Simulink平台,对内模解耦控制器的控制效果进行了研究。分别对系统的解耦性能、鲁棒稳定性以及在干扰和参数摄动下对工艺指标的控制效果进行了仿真实验研究。
(4)创新地把多元统计中建立最优回归方程的理论应用到耦合度分析中,根据系统的输入输出数据建立回归模型,通过建立最优回归方程来确定系统输入和输出之间的最佳配对关系,达到了弱化系统耦合的效果。仿真实验证明了方法的可行性。
In the industrial control field, many uncontrollable factors exist in the controlled object, such as nonlinear, strong coupling, large time-delay, non-minimum phase characteristics etc, the factors lead to large quantitative overshoot, settling time longer, and even, some even appear to flap and dissipation,so the system dynamic quality significantly decreased.It is difficult to use most of the control methods in the control system, so decoupling control in the multi-variable big time-delay process has been a major problem in the control area. According to the characteristics of strong coupling and large time-delay of the multivariable system, the internal model control method, developed rapid at present, is applied to the decoupling of the multi-variable big time-delay system. And make a preliminary study for the decoupling control issues of non-square system.The main contents of this paper are as follows:
(1) According to the internal model control principle and decoupling control theory, the decoupling controller matrix is derived and the influence of the time-delay and non-minimum phase zero for the controller is analyzed.
(2) The reduction of time-delay model is processed with genetic algorithm, and the design process is simplified, the minimum phase and the non-minimum phase are separated based on the model reduction, then design the internal model decoupling controller based on the diagonal elements of the decoupled closed-loop transfer function and the controller should meet the requirements of the time-delay and RHP zero. And then low-pass filter is added in the feedback loop, Both the system stability and robustness are considered to choose the filter parameters.
(3) Based on platform of Matlab / Simulink, the control effects of internal model decoupling controller was studied.Decoupling performance of the system, robust stability ,disturbance and parameter perturbation performance are tested in the Matlab / Simulink platform.
(4) The theory, which the optimal regression equation is established in the multivariate statistics, is innovatively applied to coupling analysis. According to input and output data of the system, regression model is established, the optimal matching relation is determined between input and output of the system by establishing the optimal regression equation, reach to the effect of weakening the system coupling, the simulation results show that the method is feasible.
引文
[1]刘涛,张卫东,顾诞英,蔡云泽.化工多变量时滞过程的频域解耦控制设计的研究进展.自动化学报,2006,32(1):73～83
[2]林光辉.方形系统多变量内模控制方法的研究:[硕士学位论文].北京:北京化工大学,2010.1～4
[3] Xue Fuzheng,Pang Guozhong,Hu Jinghua.Multivariable control for beer fermentation temperature.Acta Automatic Sinica,2002,28(1):150～154
[4] Li Ning,Li Shaoyuan,Xi Yugeng.Multiple model predictive control for MIMO systems.Acta automatic Sinica,2003,29(4):516～523
[5]潘峰,常娥,马兵胜.时变大时滞系统的一种智能控制策略.电气技术,2009,(7):19～22
[6]陶睿,肖术骏,王秀.基于内模PID控制器在大时滞过程中的应用研究.控制理论与应用,2009,28(8):8～10
[7]程启明,杜许峰,郭润清等.汽包锅炉燃烧PID型神经网络解耦控制系统仿真研究.上海电力学院学报,2008,24(1):26～31
[8]姚培,郑恩让.内模解耦单神经元自适应PID仿真研究.计算机仿真,2008,25(7):155～157
[9] Hovd , M ., Skogestad , S . Sequential design of decentralized controllers.Automatic,1994,30(10):1601～1607
[10] Shiu,S.J.,Hwang,S.H.Sequential design method for multivariable decoupling and multi-loop PID controllers.Ind.Eng.Chem.Res.1998,37(1):107～119
[11] Hiu,M.S.,Arkun,Y.Methodology for sequential design of robust decentralized control systems,Automatic.1992,28(5):997～1001
[12] Hinskey,F.G.,Process Control System,forth ed.,McGraw-Hill,New Y- ork,1996
[13]黄玉清,李磊民.大时滞系统的自校正控制.西南工学院学报,1997,12(2):8～13
[14]张卫东,孙优贤.Smith预估器的一种工程实现方法及其整定.控制与决策,1996,11(增刊):213～316
[15] Alevisakis,G.and Seborg,D.E.An extension of the Smith Predictor method to multivariable linear systems containing time delays.Int.J.Control,1973,17(3):541～551
[16] Ogunnaike,B.A.and Ray,W.H.Multivariable controller design for linear systems having multiple time delays.AIChE J,1979,25(6):1043～1057
[17]何衍庆,陈积玉,姜捷.时滞对象的预估校正控制.华东理工大学学报, 2002,26(2):534～538
[18] Jerome,N.F.and Ray,W.H.High-performance multivariable control strategies for systems having time delays.AIChE J,1986,32(6):914～931
[19] Wang,Q.G.,Zou,B.and Zhang,Y.Decoupling smith predictor design for multivariable systems with multiple time delays.Trans.IChemE.,Part A,2000,78(4):565～572
[20] Huang,H.P.and Lin,F.Y.Decoupling multivariable control with two degrees of freedom.Ind.Eng Chem Res.,2006,45(9):3161～3173
[21] Kaya1 IMC based automatic tuning method for PID controllers in a Smith predictor configuration.Computers & Chemical Engineering,2004,28(l):281～290
[22]黄言.多变量内模-PID控制:[硕士学位论文].北京:北京化工大学,2008,2～4
[23]赵曜.内模控制发展综述.信息与控制,2000,29(6):526～531
[24] Wang Q G,Zhang Y,Chiu M S.Decoupling internal model control for multivariable systems with multiple time delays . Chemical Engineering Science,2002,57(1):115～124
[25] Liu T,Zhang W D,Gu D Y.New IMC-based control strategy for open-loop unstable cascade processes.Industrial and Engineering Chemistry Research,2005,44(4):900～909
[26] Wang Q G,Hang C C,Yang X P.IMC-based controller design for MIMOsystem.Journal of Chemical Engineering of Japan,1993,35(12):1231～1243
[27] Liu Tao,Zhang Weidong,Gu Danying,Cai Yunze.Research progress of frequency domain decoupling control design for chemical and industrial multivariable processes with time delays.Acta Automatic Sinica,2006,32(1):73～83
[28] Sebastain E.Feedback control for optimal process operation Journal of Process Control,2007,17(3):203～219
[29]周平,柴天佑,陈通文.工业过程运行的解耦内模控制方法.自动化学报,2009,35(10):1362～1368
[30]汤伟,施颂椒,王孟效.大时滞过程双自由度自整定内模控制.上海交通大学学报,2003,37(4):494～498
[31] Huang,H.P.and Lin,F.Y.Decoupling multivariable control with two degrees of freedom.Ind.Eng.Chem.Res.,2006,45(9):3161～3173
[32]王薇,赵文仓,葛艳.一类非线性时滞系统的解耦控制.信息与控制,2006,35(5):564～567
[33]要艳静,王晶,潘立登.多变量多时滞非方系统的解耦内模控制.化工学报,2008,59(7):1737～1742
[34]靳其兵,袁琴.双输入双输出过程解耦内模控制.控制工程,2009,16(1):5～11
[35] Chu,C.C.,H∞-Optimization and Robust Multivariable Control,Ph.D.Thesis,University of Minnesota,Minneapolis,MN,1985
[36] Wang,Q.G.Decoupling Control; Springer:Berlin,2003
[37] Niculescu,S.I.,Gu,K.Q.Advances in Time-Delay Systems,LNCS E,Springer-Verlag:Berlin,2004
[38] Zhang,W.D.,Lin,C,Ou,L.L.Algebraic Solution to H2 Control Problems.II.The Multivariable Decoupling Case.Ind.Eng.Chem. Res.2006,45(21):7163～7176
[39]尹美兰.多变量内模解耦控制的研究:[硕士学位论文].北京:北京化工大学,2006.14~20
[40] Skogestad S,Postlethwaite I.Multivariable Feedback Control:Analysis and Design .New York:John Wiley and Sons,1996
[41] Nash J C,Walker-Smith M.Nonlinear Parameter Estimation.New York :Marcel Dekker.Inc,1987
[42]黄樟灿,陈思多,金庭枝.基于遗传算法的传递函数的模型降阶.武汉汽车工业大学学报,2000,22(2):26～29
[43] Kuo B C.Automatic Control Systems.Englewood Cliffs:Prentice-Hall,1991
[44] Sebastian E.Feedback control for optimal process operation.Journal of process control,2007,17(3):203～219
[45]丛琳,刘兴高.基于内模控制的内部热耦合精馏策略.化工学报,2010, 61(8):2067～2071
[46]刘涛,张卫东,顾诞英.多变量时滞过程的解耦控制设计.自动化学报,2005,31(6):881～889
[47]陈培颖,欧林林,孙敬等.改进的内模控制方法及其在非方系统中的应用.控制与决策,2008,23(5):581～584
[48]靳其兵,袁琴.双输入双输出过程解耦内模控制.控制工程,2009,16(1):5～11
[49] Ramasamy M,Narayanan S S ,Rao Ch D P.Control of ball mill grinding circuit using model predictive control scheme.Journal of Process Control, 2005,15(3):273～283
[50]谢克明,杨博,谢刚.一种基于概率统计算法的耦合度分析.太原理工大学学报,1999,30(2):111～114
[51]王微微,耿艳峰,黄志尧.基于逐步回归方法和电容分布辨识油气两相流流型.化工自动化及仪表,2007,34(2):63～65
[52]唐家德.应用MATLAB统计工具箱进行教学评价.大学数学,2009,25(5):148～153
[2]林光辉.方形系统多变量内模控制方法的研究:[硕士学位论文].北京:北京化工大学,2010.1～4
[3] Xue Fuzheng,Pang Guozhong,Hu Jinghua.Multivariable control for beer fermentation temperature.Acta Automatic Sinica,2002,28(1):150～154
[4] Li Ning,Li Shaoyuan,Xi Yugeng.Multiple model predictive control for MIMO systems.Acta automatic Sinica,2003,29(4):516～523
[5]潘峰,常娥,马兵胜.时变大时滞系统的一种智能控制策略.电气技术,2009,(7):19～22
[6]陶睿,肖术骏,王秀.基于内模PID控制器在大时滞过程中的应用研究.控制理论与应用,2009,28(8):8～10
[7]程启明,杜许峰,郭润清等.汽包锅炉燃烧PID型神经网络解耦控制系统仿真研究.上海电力学院学报,2008,24(1):26～31
[8]姚培,郑恩让.内模解耦单神经元自适应PID仿真研究.计算机仿真,2008,25(7):155～157
[9] Hovd , M ., Skogestad , S . Sequential design of decentralized controllers.Automatic,1994,30(10):1601～1607
[10] Shiu,S.J.,Hwang,S.H.Sequential design method for multivariable decoupling and multi-loop PID controllers.Ind.Eng.Chem.Res.1998,37(1):107～119
[11] Hiu,M.S.,Arkun,Y.Methodology for sequential design of robust decentralized control systems,Automatic.1992,28(5):997～1001
[12] Hinskey,F.G.,Process Control System,forth ed.,McGraw-Hill,New Y- ork,1996
[13]黄玉清,李磊民.大时滞系统的自校正控制.西南工学院学报,1997,12(2):8～13
[14]张卫东,孙优贤.Smith预估器的一种工程实现方法及其整定.控制与决策,1996,11(增刊):213～316
[15] Alevisakis,G.and Seborg,D.E.An extension of the Smith Predictor method to multivariable linear systems containing time delays.Int.J.Control,1973,17(3):541～551
[16] Ogunnaike,B.A.and Ray,W.H.Multivariable controller design for linear systems having multiple time delays.AIChE J,1979,25(6):1043～1057
[17]何衍庆,陈积玉,姜捷.时滞对象的预估校正控制.华东理工大学学报, 2002,26(2):534～538
[18] Jerome,N.F.and Ray,W.H.High-performance multivariable control strategies for systems having time delays.AIChE J,1986,32(6):914～931
[19] Wang,Q.G.,Zou,B.and Zhang,Y.Decoupling smith predictor design for multivariable systems with multiple time delays.Trans.IChemE.,Part A,2000,78(4):565～572
[20] Huang,H.P.and Lin,F.Y.Decoupling multivariable control with two degrees of freedom.Ind.Eng Chem Res.,2006,45(9):3161～3173
[21] Kaya1 IMC based automatic tuning method for PID controllers in a Smith predictor configuration.Computers & Chemical Engineering,2004,28(l):281～290
[22]黄言.多变量内模-PID控制:[硕士学位论文].北京:北京化工大学,2008,2～4
[23]赵曜.内模控制发展综述.信息与控制,2000,29(6):526～531
[24] Wang Q G,Zhang Y,Chiu M S.Decoupling internal model control for multivariable systems with multiple time delays . Chemical Engineering Science,2002,57(1):115～124
[25] Liu T,Zhang W D,Gu D Y.New IMC-based control strategy for open-loop unstable cascade processes.Industrial and Engineering Chemistry Research,2005,44(4):900～909
[26] Wang Q G,Hang C C,Yang X P.IMC-based controller design for MIMOsystem.Journal of Chemical Engineering of Japan,1993,35(12):1231～1243
[27] Liu Tao,Zhang Weidong,Gu Danying,Cai Yunze.Research progress of frequency domain decoupling control design for chemical and industrial multivariable processes with time delays.Acta Automatic Sinica,2006,32(1):73～83
[28] Sebastain E.Feedback control for optimal process operation Journal of Process Control,2007,17(3):203～219
[29]周平,柴天佑,陈通文.工业过程运行的解耦内模控制方法.自动化学报,2009,35(10):1362～1368
[30]汤伟,施颂椒,王孟效.大时滞过程双自由度自整定内模控制.上海交通大学学报,2003,37(4):494～498
[31] Huang,H.P.and Lin,F.Y.Decoupling multivariable control with two degrees of freedom.Ind.Eng.Chem.Res.,2006,45(9):3161～3173
[32]王薇,赵文仓,葛艳.一类非线性时滞系统的解耦控制.信息与控制,2006,35(5):564～567
[33]要艳静,王晶,潘立登.多变量多时滞非方系统的解耦内模控制.化工学报,2008,59(7):1737～1742
[34]靳其兵,袁琴.双输入双输出过程解耦内模控制.控制工程,2009,16(1):5～11
[35] Chu,C.C.,H∞-Optimization and Robust Multivariable Control,Ph.D.Thesis,University of Minnesota,Minneapolis,MN,1985
[36] Wang,Q.G.Decoupling Control; Springer:Berlin,2003
[37] Niculescu,S.I.,Gu,K.Q.Advances in Time-Delay Systems,LNCS E,Springer-Verlag:Berlin,2004
[38] Zhang,W.D.,Lin,C,Ou,L.L.Algebraic Solution to H2 Control Problems.II.The Multivariable Decoupling Case.Ind.Eng.Chem. Res.2006,45(21):7163～7176
[39]尹美兰.多变量内模解耦控制的研究:[硕士学位论文].北京:北京化工大学,2006.14~20
[40] Skogestad S,Postlethwaite I.Multivariable Feedback Control:Analysis and Design .New York:John Wiley and Sons,1996
[41] Nash J C,Walker-Smith M.Nonlinear Parameter Estimation.New York :Marcel Dekker.Inc,1987
[42]黄樟灿,陈思多,金庭枝.基于遗传算法的传递函数的模型降阶.武汉汽车工业大学学报,2000,22(2):26～29
[43] Kuo B C.Automatic Control Systems.Englewood Cliffs:Prentice-Hall,1991
[44] Sebastian E.Feedback control for optimal process operation.Journal of process control,2007,17(3):203～219
[45]丛琳,刘兴高.基于内模控制的内部热耦合精馏策略.化工学报,2010, 61(8):2067～2071
[46]刘涛,张卫东,顾诞英.多变量时滞过程的解耦控制设计.自动化学报,2005,31(6):881～889
[47]陈培颖,欧林林,孙敬等.改进的内模控制方法及其在非方系统中的应用.控制与决策,2008,23(5):581～584
[48]靳其兵,袁琴.双输入双输出过程解耦内模控制.控制工程,2009,16(1):5～11
[49] Ramasamy M,Narayanan S S ,Rao Ch D P.Control of ball mill grinding circuit using model predictive control scheme.Journal of Process Control, 2005,15(3):273～283
[50]谢克明,杨博,谢刚.一种基于概率统计算法的耦合度分析.太原理工大学学报,1999,30(2):111～114
[51]王微微,耿艳峰,黄志尧.基于逐步回归方法和电容分布辨识油气两相流流型.化工自动化及仪表,2007,34(2):63～65
[52]唐家德.应用MATLAB统计工具箱进行教学评价.大学数学,2009,25(5):148～153