多变量线性控制系统解耦与控制方法的仿真
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摘要
随着工业的发展,工业过程控制出现了大量的变量间相互影响的多变量控制系统,因此多变量系统的解耦设计具有举足轻重的作用。
对于关联系统给出了判断耦合程度的方法—相对增益法和逆乃奎斯特列阵法。对于耦合严重,需要进行解耦设计的系统,分别介绍了复频域解耦法和时域解耦法的原理及解耦条件,并对相应的例子进行仿真实验分析。针对前馈补偿器解耦,提出了一种针对线性时不变多变量系统能否使用前馈补偿器解耦的判断方法。该判断方法是基于最小设计的思想,将最小设计问题应用到解耦问题,并通过应用该判断方法得到了前馈补偿器解耦的条件。对于没有必要完全解耦的复杂的高阶系统,介绍了对角优势化,使系统实现近似解耦。
分析对多变量线性系统进行动态矩阵预测控制时的鲁棒性,抗干扰能力,及在保证解耦控制效果的前提下,预测控制参数可变化的范围。将前馈补偿解耦法、状态反馈解耦法和静态解耦法分别与动态矩阵预测控制器相结合,分别对解耦后的多变量线性系统进行仿真实验,分析其解耦后的鲁棒性,抗干扰能力,及在保证解耦控制效果的前提下,预测控制参数可变化的范围。通过分析仿真实例,开环预测解耦有较好的鲁棒性。
With the development of the industry, the multivariable system in which lots of parameters interact appears in industrial process of control. Therefore, the design of decoupling for the multivariable system is most important in the process of control.
For the interacted system, two methods are given in order to judge the coupling degree of the multivariable system, such as relative gain method and Inverse Nyquist Array method. For the strong coupling system which needs to be decoupled, this paper introduces the principle and conditions of complex frequency domain decoupling method and time domain decoupling method .And the corresponding examples are simulated and analyzed. For feed-forward compensator decoupling method, a judgment method is proposed. By using the method, we can know whether the feed-forward compensator decoupling method is appropriate to the multivariable linear system or not. The method is based on minimal design problems. The minimal design problem is applied to the decoupling problem. And the conditions of the feed-forward compensator decoupling are obtained from the method. For the complex high order system, diagonal dominance is introduced. Thus, the high order system achieves approximate decoupling.
The robustness, anti-interference ability and ranges of predictive control parameters to ensure the decoupling control performance of the multivariable linear system are analyzed when the dynamic matrix predictive controller is designed for the system. Feed-forward compensation decoupling method, state feedback decoupling method and static decoupling method are combined with dynamic matrix predictive controller. Simulations of decoupled multivariable linear system are given. Analysis of the robustness, anti-interference ability and ranges of predictive control parameters to ensure the decoupling control performance of the decoupled system are also given. Open-loop predictive decoupling has better robustness from analyzing the simulation experiment.
对于关联系统给出了判断耦合程度的方法—相对增益法和逆乃奎斯特列阵法。对于耦合严重,需要进行解耦设计的系统,分别介绍了复频域解耦法和时域解耦法的原理及解耦条件,并对相应的例子进行仿真实验分析。针对前馈补偿器解耦,提出了一种针对线性时不变多变量系统能否使用前馈补偿器解耦的判断方法。该判断方法是基于最小设计的思想,将最小设计问题应用到解耦问题,并通过应用该判断方法得到了前馈补偿器解耦的条件。对于没有必要完全解耦的复杂的高阶系统,介绍了对角优势化,使系统实现近似解耦。
分析对多变量线性系统进行动态矩阵预测控制时的鲁棒性,抗干扰能力,及在保证解耦控制效果的前提下,预测控制参数可变化的范围。将前馈补偿解耦法、状态反馈解耦法和静态解耦法分别与动态矩阵预测控制器相结合,分别对解耦后的多变量线性系统进行仿真实验,分析其解耦后的鲁棒性,抗干扰能力,及在保证解耦控制效果的前提下,预测控制参数可变化的范围。通过分析仿真实例,开环预测解耦有较好的鲁棒性。
With the development of the industry, the multivariable system in which lots of parameters interact appears in industrial process of control. Therefore, the design of decoupling for the multivariable system is most important in the process of control.
For the interacted system, two methods are given in order to judge the coupling degree of the multivariable system, such as relative gain method and Inverse Nyquist Array method. For the strong coupling system which needs to be decoupled, this paper introduces the principle and conditions of complex frequency domain decoupling method and time domain decoupling method .And the corresponding examples are simulated and analyzed. For feed-forward compensator decoupling method, a judgment method is proposed. By using the method, we can know whether the feed-forward compensator decoupling method is appropriate to the multivariable linear system or not. The method is based on minimal design problems. The minimal design problem is applied to the decoupling problem. And the conditions of the feed-forward compensator decoupling are obtained from the method. For the complex high order system, diagonal dominance is introduced. Thus, the high order system achieves approximate decoupling.
The robustness, anti-interference ability and ranges of predictive control parameters to ensure the decoupling control performance of the multivariable linear system are analyzed when the dynamic matrix predictive controller is designed for the system. Feed-forward compensation decoupling method, state feedback decoupling method and static decoupling method are combined with dynamic matrix predictive controller. Simulations of decoupled multivariable linear system are given. Analysis of the robustness, anti-interference ability and ranges of predictive control parameters to ensure the decoupling control performance of the decoupled system are also given. Open-loop predictive decoupling has better robustness from analyzing the simulation experiment.
引文
[1]马平,杨金芳,崔长春,胡胜坤,解耦控制的现状及发展,控制工程,第12卷第2期,2005年3月
[2]桑保华,薛晓中.多变量解耦控制方法.火力与指挥控制.第32卷第11期,2007年11月
[3]郑大钟,线性系统理论,清华大学出版社,2002.10
[4]胡品慧,袁璞,状态反馈预测控制干扰解耦的研究,控制与决策,第18卷第2期,2003.3
[5] V.Sankaran and M.D.Srinath, Decoupling of linear discrete time systems by state variable feedback, Journal of Mathematical Analysis and Applications, Volume 39, Issue 2, August 1972, Pages 338-345
[6] P. N. Paraskevopoulos and F. N. Koumboulis, A new approach to the decoupling problem of linear time-invariant systems, Journal of the Franklin Institute, Volume 329, Issue 2, March 1992, Pages 347-369
[7] D. Vafiadis and N. Karcanias ,Decoupling and pole assignment of singular systems: A frequency domain approach,Automatica, Volume 33, Issue 8, August 1997, Pages 1555-1560
[8]韩光信,施云贵,孟亚男,王立国,三容系统状态反馈解耦PID控制,吉林化工学院学报,第23卷第3期,2006.6
[9]王军,王雁,邵惠鹤,状态反馈解耦技术在变风量空调系统中的应用,自动化仪表,第26卷第2期,2005.2
[10]张汉年,朱秋,张植保,基于前馈补偿器的无轴承同步磁阻电机解耦控制,东南大学学报,第35卷增刊,2005.11
[11] Cheng Liu, Fu Yu Zhao, Ping Hu, Suxia Hou and Chong Li, P controller with partial feed forward compensation and decoupling control for the steam generator water level, Nuclear Engineering and Design, Volume 240, Issue 1, January 2010, Pages 181-190
[12] Jinsong Wang, Jun Wu, Liping Wang and Zheng You,Dynamic feed-forward control of a parallel kinematic machine , Mechatronics, Volume 19, Issue 3, April 2009, Pages313-324
[13]黄健康,李妍,管永祥,王玗,樊丁,基于PI控制不同解耦补偿控制器的铝合金MIG焊过程MIMO解耦控制仿真,兰州理工大学学报,第34卷第5期,2008,10
[14] Qing-Guo Wang, Decoupling with internal stability for unity output feedback systems, Automatica, Volume 28, Issue 2, March 1992, Pages 411-415
[15] Qing-Guo Wang , Yongsheng Yang,Transfer function matrix approach to decoupling problem with stability ,Systems & Control Letters, Volume 47, Issue 2, 7 October 2002, Pages 103-110
[16] Manolis A. Christodoulou, Decoupling in the design and synthesis of singular systems, Automatica, Volume 22, Issue 2, March 1986, Pages 245-249
[17]刘伟,冯向军,关于多变量PID自适应解耦控制器的设计,<微计算机信息>(测控自动化)2004年第20卷第4期
[18] K. G. Arvanitis, Adaptive decoupling control of linear systems without a persistent excitation requirement, Journal of the Franklin Institute, Volume 332, Issue 6, November 1995, Pages 681-715
[19]焦竹青,屈百达,徐保国,基于RBF神经网络的多变量系统PID解耦控制,系统仿真学报,第20卷第3期,2008年2月
[20]陈娟,陈岳峰,潘立登,曹柳林,多变量时滞系统的解耦模糊内模控制,电机与控制学报,第l0卷第2期,2006年3月
[21]李辉,一种多变量模糊神经网络解耦控制器的设计,控制与决策,第21卷第5期,2006年5月
[22] Peiying Chen,and Weidong Zhang,Improvement on an inverted decoupling technique for a class of stable linear multivariable processes, ISA Transactions, Volume 46, Issue 2, April 2007, Pages 199-210
[23] Ole B. Gj?s?ter and Bjarne A. Foss, On the use of diagonal control versus decoupling for ill-conditioned processes, Automatica, Volume 33, Issue 3, March 1997, Pages 427-432
[24]李华聪,荣立烨,朱玉斌,基于QDRNN网络的航空发动机多变量解耦控制,航空动力学报,第22卷第11期,2007年11月
[25] Xiaoping Liu, A. Jutan and S. Rohani, Almost disturbance decoupling of MIMOnonlinear systems and application to chemical processes, Automatica, Volume 40, Issue 3, March 2004, Pages 465-471
[26]刘贤兴,胡育文,永磁同步电机的神经网络逆动态解耦控制,中国电机工程学报,第27卷第27期,2007年9月
[27] Tsao-Tsung Ma, P–Q decoupled control schemes using fuzzy neural networks for the unified power flow controller , International Journal of Electrical Power & Energy Systems, Volume 29, Issue 10, December 2007, Pages 748-758
[28]曹卫华,吴敏,侯少云,煤气混合加压过程的智能解耦控制方法与应用,中南大学学报(自然科学版),第37卷第4期,2006年8月
[29]王树青,工业过程控制工程,北京:化学工业出版社,2002.12
[30]金以慧,过程控制,清华大学出版社,1993.4
[31]何衍庆,姜捷,江艳君,郑莹,控制系统分析、设计和应用—MATLAB语言的应用,化学工业出版社,2002.12
[32]徐和生,陈锦娣,线性多变量系统的分析与设计,国防工业出版社,1989.8
[33]罗家洪,方卫东,矩阵分析引论,华南理工大学出版社,2006.6
[34]刘豹,现代控制理论,机械工业出版社,2000.5
[35]郑大钟,线性系统理论,清华大学出版社,2002.10
[36]陈启宗,线性系统理论与设计,科学出版社,1988.1
[37] General Decoupling Theory of Multivariable Process Control Systems,Springer Berlin/Heidelerg,1983
[38]王永初,解耦控制系统,四川科学出版社,1985
[39]戴永彬,杨卫东,王少福,张明,多变量预测解耦控制综述,电气自动化,第30卷第6期,2008
[2]桑保华,薛晓中.多变量解耦控制方法.火力与指挥控制.第32卷第11期,2007年11月
[3]郑大钟,线性系统理论,清华大学出版社,2002.10
[4]胡品慧,袁璞,状态反馈预测控制干扰解耦的研究,控制与决策,第18卷第2期,2003.3
[5] V.Sankaran and M.D.Srinath, Decoupling of linear discrete time systems by state variable feedback, Journal of Mathematical Analysis and Applications, Volume 39, Issue 2, August 1972, Pages 338-345
[6] P. N. Paraskevopoulos and F. N. Koumboulis, A new approach to the decoupling problem of linear time-invariant systems, Journal of the Franklin Institute, Volume 329, Issue 2, March 1992, Pages 347-369
[7] D. Vafiadis and N. Karcanias ,Decoupling and pole assignment of singular systems: A frequency domain approach,Automatica, Volume 33, Issue 8, August 1997, Pages 1555-1560
[8]韩光信,施云贵,孟亚男,王立国,三容系统状态反馈解耦PID控制,吉林化工学院学报,第23卷第3期,2006.6
[9]王军,王雁,邵惠鹤,状态反馈解耦技术在变风量空调系统中的应用,自动化仪表,第26卷第2期,2005.2
[10]张汉年,朱秋,张植保,基于前馈补偿器的无轴承同步磁阻电机解耦控制,东南大学学报,第35卷增刊,2005.11
[11] Cheng Liu, Fu Yu Zhao, Ping Hu, Suxia Hou and Chong Li, P controller with partial feed forward compensation and decoupling control for the steam generator water level, Nuclear Engineering and Design, Volume 240, Issue 1, January 2010, Pages 181-190
[12] Jinsong Wang, Jun Wu, Liping Wang and Zheng You,Dynamic feed-forward control of a parallel kinematic machine , Mechatronics, Volume 19, Issue 3, April 2009, Pages313-324
[13]黄健康,李妍,管永祥,王玗,樊丁,基于PI控制不同解耦补偿控制器的铝合金MIG焊过程MIMO解耦控制仿真,兰州理工大学学报,第34卷第5期,2008,10
[14] Qing-Guo Wang, Decoupling with internal stability for unity output feedback systems, Automatica, Volume 28, Issue 2, March 1992, Pages 411-415
[15] Qing-Guo Wang , Yongsheng Yang,Transfer function matrix approach to decoupling problem with stability ,Systems & Control Letters, Volume 47, Issue 2, 7 October 2002, Pages 103-110
[16] Manolis A. Christodoulou, Decoupling in the design and synthesis of singular systems, Automatica, Volume 22, Issue 2, March 1986, Pages 245-249
[17]刘伟,冯向军,关于多变量PID自适应解耦控制器的设计,<微计算机信息>(测控自动化)2004年第20卷第4期
[18] K. G. Arvanitis, Adaptive decoupling control of linear systems without a persistent excitation requirement, Journal of the Franklin Institute, Volume 332, Issue 6, November 1995, Pages 681-715
[19]焦竹青,屈百达,徐保国,基于RBF神经网络的多变量系统PID解耦控制,系统仿真学报,第20卷第3期,2008年2月
[20]陈娟,陈岳峰,潘立登,曹柳林,多变量时滞系统的解耦模糊内模控制,电机与控制学报,第l0卷第2期,2006年3月
[21]李辉,一种多变量模糊神经网络解耦控制器的设计,控制与决策,第21卷第5期,2006年5月
[22] Peiying Chen,and Weidong Zhang,Improvement on an inverted decoupling technique for a class of stable linear multivariable processes, ISA Transactions, Volume 46, Issue 2, April 2007, Pages 199-210
[23] Ole B. Gj?s?ter and Bjarne A. Foss, On the use of diagonal control versus decoupling for ill-conditioned processes, Automatica, Volume 33, Issue 3, March 1997, Pages 427-432
[24]李华聪,荣立烨,朱玉斌,基于QDRNN网络的航空发动机多变量解耦控制,航空动力学报,第22卷第11期,2007年11月
[25] Xiaoping Liu, A. Jutan and S. Rohani, Almost disturbance decoupling of MIMOnonlinear systems and application to chemical processes, Automatica, Volume 40, Issue 3, March 2004, Pages 465-471
[26]刘贤兴,胡育文,永磁同步电机的神经网络逆动态解耦控制,中国电机工程学报,第27卷第27期,2007年9月
[27] Tsao-Tsung Ma, P–Q decoupled control schemes using fuzzy neural networks for the unified power flow controller , International Journal of Electrical Power & Energy Systems, Volume 29, Issue 10, December 2007, Pages 748-758
[28]曹卫华,吴敏,侯少云,煤气混合加压过程的智能解耦控制方法与应用,中南大学学报(自然科学版),第37卷第4期,2006年8月
[29]王树青,工业过程控制工程,北京:化学工业出版社,2002.12
[30]金以慧,过程控制,清华大学出版社,1993.4
[31]何衍庆,姜捷,江艳君,郑莹,控制系统分析、设计和应用—MATLAB语言的应用,化学工业出版社,2002.12
[32]徐和生,陈锦娣,线性多变量系统的分析与设计,国防工业出版社,1989.8
[33]罗家洪,方卫东,矩阵分析引论,华南理工大学出版社,2006.6
[34]刘豹,现代控制理论,机械工业出版社,2000.5
[35]郑大钟,线性系统理论,清华大学出版社,2002.10
[36]陈启宗,线性系统理论与设计,科学出版社,1988.1
[37] General Decoupling Theory of Multivariable Process Control Systems,Springer Berlin/Heidelerg,1983
[38]王永初,解耦控制系统,四川科学出版社,1985
[39]戴永彬,杨卫东,王少福,张明,多变量预测解耦控制综述,电气自动化,第30卷第6期,2008