多变量预测控制系统模型失配评价方法研究
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摘要
由于实际工况漂移、过程非线性及系统外部干扰等因素,模型预测控制系统在运行一段时间后其控制性能可能下降甚至失效。如果不及时修复控制器以改善控制品质,将降低预测控制系统所能获得的经济效益。作为基于模型的优化控制算法,如果模型预测控制算法的预测模型与实际对象的失配程度很严重,则仅靠整定控制器参数将难以改善控制器性能。模型失配是预测控制中普遍存在的问题,是导致预测控制器性能下降的重要原因。因此迫切需要建立一种有效评估模型质量的方法,为预测控制系统的整定与维护提供重要指导。
本文首先对模型失配问题进行了归类和定义,对一种已有的基于状态空间描述模型预测控制系统的模型失配评估方法进行了分析。在此基础上,针对工业过程常用的非参数模型描述的动态矩阵控制算法,推导了模型失配问题与模型输出误差的关系,证明了预测误差和干扰增量这一时间序列信号对可用于完全表征模型失配信息。然后应用统计推断方法,提出了一种基于信号白色性检验的模型失配评估算法,并将其推广为实时在线模型失配评估算法。
对于多变量系统,模型失配问题需对影响被控变量的各输入通道的失配情况进行评估。为更准确地定位失配通道,提出一种基于时间序列偏相关分析的模型失配评价方法,该方法可消除闭环系统下各输入变量间的耦合,分离出各通道的失配信息,同时定义了一个新的模型失配指数,可对模型失配程度进行量化分析。仿真研究证明,该方法不仅能够有效检测出各种模型失配情况,而且可适用于非平稳随机干扰情形。
The performance of model predictive controller may decline and even invalid because the work point of processes may drift to another one and the actual processes are always non-linear and several other unknown external disturbances will also influent the processes. If the performance of model predictive controller is not improved in time, the model predictive controller will not increase the economic efficiency as much as it can. As a model-based control algorithm, the performance of controller will be hard to be improved only by re-tuning the parameters of controller if there is serious mismatch between model and plant. Model mismatch is a common problem in model predictive control, as well as one of the most important reasons of bad performance. As a result, it is important and urgent to assess model quality and provide guidance to the maintenance of model predictive controller.
In this paper, the model plant mismatch problem is classified and defined. An existed method of model plant mismatches assessment formulated in terms of discrete time state space model is introduced. Then a method of model plant mismatch assessment in terms of non-parameter model is proposed. The relationship between model plant mismatch and model output residues is analyzed and a pair of time series sequences which contains mismatch information is found. A new method based on whiteness test of a time series sequence using statistical inference is presented and it is promoted to on line control performance monitoring.
The mismatch of each channel needs to be evaluated in multivariate process. To mine model mismatch of each channel of multivariate model predictive controllers much correctly, another new scheme based on partial correlation analysis is demonstrated. This method can depart the coupling between process variables and isolate model mismatch information of each channel. A new model mismatch index is defined to express the mismatch quantity exactly. Numerical simulation examples have shown that it can detect model mismatch of each channel effectively. What's more, this new method can deal with non stationary disturbance as well.
本文首先对模型失配问题进行了归类和定义,对一种已有的基于状态空间描述模型预测控制系统的模型失配评估方法进行了分析。在此基础上,针对工业过程常用的非参数模型描述的动态矩阵控制算法,推导了模型失配问题与模型输出误差的关系,证明了预测误差和干扰增量这一时间序列信号对可用于完全表征模型失配信息。然后应用统计推断方法,提出了一种基于信号白色性检验的模型失配评估算法,并将其推广为实时在线模型失配评估算法。
对于多变量系统,模型失配问题需对影响被控变量的各输入通道的失配情况进行评估。为更准确地定位失配通道,提出一种基于时间序列偏相关分析的模型失配评价方法,该方法可消除闭环系统下各输入变量间的耦合,分离出各通道的失配信息,同时定义了一个新的模型失配指数,可对模型失配程度进行量化分析。仿真研究证明,该方法不仅能够有效检测出各种模型失配情况,而且可适用于非平稳随机干扰情形。
The performance of model predictive controller may decline and even invalid because the work point of processes may drift to another one and the actual processes are always non-linear and several other unknown external disturbances will also influent the processes. If the performance of model predictive controller is not improved in time, the model predictive controller will not increase the economic efficiency as much as it can. As a model-based control algorithm, the performance of controller will be hard to be improved only by re-tuning the parameters of controller if there is serious mismatch between model and plant. Model mismatch is a common problem in model predictive control, as well as one of the most important reasons of bad performance. As a result, it is important and urgent to assess model quality and provide guidance to the maintenance of model predictive controller.
In this paper, the model plant mismatch problem is classified and defined. An existed method of model plant mismatches assessment formulated in terms of discrete time state space model is introduced. Then a method of model plant mismatch assessment in terms of non-parameter model is proposed. The relationship between model plant mismatch and model output residues is analyzed and a pair of time series sequences which contains mismatch information is found. A new method based on whiteness test of a time series sequence using statistical inference is presented and it is promoted to on line control performance monitoring.
The mismatch of each channel needs to be evaluated in multivariate process. To mine model mismatch of each channel of multivariate model predictive controllers much correctly, another new scheme based on partial correlation analysis is demonstrated. This method can depart the coupling between process variables and isolate model mismatch information of each channel. A new model mismatch index is defined to express the mismatch quantity exactly. Numerical simulation examples have shown that it can detect model mismatch of each channel effectively. What's more, this new method can deal with non stationary disturbance as well.
引文
[1]Richalet,J.and A.Rault,"Predictive Heuristic Control:Application to Industrial Process".Automatica,1978.14(5):p.413-428.
[2]Rotthani,R.and R.K.Mehra,"Model Algorithmic Control(MAC),Basic Theoretical Properties".Automatica,1982.18(4):p.401-414.
[3]Cutler,C.R.and B.L.Ramaker.Dynamic Matrix Control-A Computer Control Algorithm.in Proc.JACC.1980.SanFranciso.
[4]Keyser,R.D.and A.V.Cauwenberghe.Extended Prediction Self-adaptive Control.in Barker H A,Young P C eds,Identification and System Parameter Estimation.1985.Oxford:Pergamon Press.
[5]Clarke,D.,C.Mohtadi,and P.Tuffs,"Generalized Predictive Control".Automatic,1987.23(2):p.137-162.
[6]Harris,T.J.,"Assessment of Control Loop Performance".Canadian journal of chemical engineering 1989.67:p.856-861.
[7]Desborough,L.and T.Harris,"Performance assessment measures for univariate feedforward/feedback control".The Canadian Journal of Chemical Engineering,1993.71(44):p.605-616.
[8]Stanfelj,N.,T.E.Marlin,and J.F.MacGregor,"Monitoring and diagnosing process control performance:the single loop case".Ind.Eng.Chem.Res.,1993.32 p.301-314.
[9]Vishnubhotla,A.,S.L.Shah,and B.Huang.Feedback and feedforward performance analysis of the shell industrial closed loop data set.in Proceedings of IFAC ADCHEM Conference.1997.Banff,Alta.
[10]Harris,T.J.,F.Boudreau,and J.F.MacGregor,"Performance assessment of multivariable feedback controllers".Automatica,1996.32:p.1505-1518.
[11]Harris,T.J.,C.T.Seppala,and L.D.Desborough,"A review of performance monitoring and assessment techniques for univariate and multivariate control systems".Journal of Process Control,1999.9:p.1-17.
[12]Qin,S.J.,"Control Performance Monitoring-A Review and Assessment".Computers an Chemical Engineering,1998.23:p.173-186.
[13]Harris,T.J.and C.T.Seppala.Recent developments in controller performance monitoring and assessment techniques,in CPC-Ⅵ.2001.Tucson,AZ.
[14]Huang,B.and S.L.Shah,Performance Assessment of Control Loops:Theory and Applications.1999,Berlin:Springer-Verlag.
[15]Horch,A.,Condition Monitoring of Control Loops,in Signals,Sensors and Systems.2000:Stockholm.
[16]Horch,A.and A.Isaksson,"A Modified Index for Control Performance assessment".Journal of Process Control,1999.9(6):p.475-483.
[17]Swanda,A.and D.Seborg,Controller Performance Assessment Based on Setpoint Response Data,in Proc.of the ACC.1999:San Diego.
[18]Jamsa-Jounela,S.L.,R.Pokonen,and K.Halmevaara.Evaluation of Level Control Performance.in Proc.of the 15~(th)IFAC World Congress.2002.Barcelona.
[19]Grimble,M.J.PID Control of Multiple Model Systems and Benchmarking.in Int.Conf.Process Control and Instrumentation.2000. Glasgow,Scotland,UK.
[20]Uduehi,D.,A.Ordis,and M.J.Grimble.,A Generalized Predictive Control Benchmark Index for MIMO Systems.in Proc.of the IEEE lnt.Conf,on Control.Application.2002.Glasgow,Scotland,UK,.
[21]Huang,B.and S.Shah,Performance Assessment of Control Loops.1999:Springer.
[22]Ko,B.-S.and T.E Edgar,"Performance assessment of multivariable feedback control systems".,Automatica,2001(37):p.899-905.
[23]McNabb,C.A.and S.J.Qin,"Projection based MIMO control performance monitoring:I-covariance monitoring in state space".Journal of Process Control,2003.13:p.739-757.
[24]Huang,B.,S.L.Shah,and K.Y.Kwok,"Good,bad or optimal?Performance assessment of MIMO processes".,Automatica,1997.33(6):p.1175-1183.
[25]Huang,B.,Multivariate Statistical Methods For Control Loop Performance,Assessment.1997,University of Alberta.
[26]Shah,S.L.,R.Patwardhan,and B.Huang.Multivariate Controller Performance,Analysis:Methods,,Applications and Challenges.in Proceedings of CPC Ⅵ.2001.Tuscon,AZ
[27]金以慧,过程控制.1993,北京:清华大学出版社.
[28]王树青,工业过程控制工程.2003:化学工业出版社.
[29]Tyler,M.L.and M.Morari.Performance assessment for unstable and nonminimum-phades systems,in Preprints IFAC Workshop on On-line Fault Detection and Supervision in the Chemical Process Industries.1995.U.K.
[30]Julien,R.H.,M.W.Foley,and W.R.Cluett,"Performance assessment using a model predictive control benchmark".Journal of Process Control,2004.14(4):p.441-456.
[31]Raich,A.and A.Cinar,"Statistical process monitoring and disturbance diagnosis in multivariable continuous processes".AIChE Journal,1996.42(4):p.995-1009.
[32]ZHANG,Q.and S.LI,"Performance Monitoring and Diagnosis of Multivariable Model Predictive Control Using Statistical Analysis".Chinese Journal of Chemical Engineering,2006.14(2):p.207-215.
[33]Huang,B.,Bayesian Methods for Control Loop Monitoring and Diagnosis,in 8th International IFAC Symposium on Dynamics and Control of Process Systems 2007:Cancún,Mexico.
[34]Agarwal,N.and B.Huang,"Assessing Model Prediction Control(MPC)Performance.1.Probabilistic Approach for Constraint Analysis ".Ind.Eng.Chem.Res.,2007.46(24):p.8101-8111.
[35]Agarwal,N.and B.Huang,"Assessing Model Prediction Control(MPC)Performance.2.Bayesian Approach for Constraint Tuning".Ind.Eng.Chem.Res.,2007.46(24):p.8112-8119.
[36]Hadjiski,M.,et al.On-line control performance monitor with robust properties,in Industrial Technology,IEEE International Conference.2003.
[37]D.Leung,J.R.,"Real-time MPC supervisory system".Computers &Chemical Engineering 2000.24(2-7):p.285-290
[38]Patwardhan,R.S.,Studies in the synthesis and analysis of model predictive controllers,in Dept.of Chemical and Materials Engng.1999,University of Alberta:Edmonton.
[39]Patwardhan,P.and S.L.Shah,"Performance diagnostics of modelbased controllers".J.Process Control 2002.12:p.413-427.
[40]Patwardhan,R.S.,S.L.Shah,and K.Z.Qi,"Assessing the Performance of Model Predictive Controllers".The Canadian Journal of Chemical Engineering,2002.80:p.954-966.
[41]Kendra,S.J.and A.Cinar,"Controller performance assessment by frequency domain techniques".Journal of Process Control,1997.7(3):p.181-194.
[42]Patwardhan,R.S.and S.L.Shah,"Issues in performance diagnostics of model-based controllers".Journal of Process Control 2002.12(3):p.413-427
[43]Jiang,H.,W.Li,and S.L.Shah,Detection and isolation of model-plant mismatch for multivariate dynamic systems,in 6~(th)IFAC Symposium on Fault Detection,Supervision and Safety of Technical Processes.2006:Beijing,China.p.1396-1401.
[44]Kammer,L.C.,D.Gorinevsky,and GA.Dumont,"Semi-Intrusive Multivariable Model Invalidation[j]".Automatica,2003.39:p.1461-1467.
[45]Ding,X.,L.Guo,and T.Jeinsch,"A characterization of parity space and its application to robust fault detection".IEEE,Transactions on Automatic Control,1999.44:p.337-343.
[46]Chow,E.and A.Willsky,"Analytical redundancy and the design of robust failure detection system".IEEE Transactions on,Automatic Control,1984.29:p.603-614.
[47]Johnson,R.and D.Wichern,Applied Multivariate Statistical,Analysis.1998:Prentice-Hall Inc.
[48]席裕庚,预测控制[M].1993,北京:国防工业出版社.
[49]方崇智and萧德云,过程辨识.2004,北京:清华大学出版社.
[50]盛骤,谢式千,and潘承毅,概率论与数理统计.2001:高等教育出版社.
[51]沈元隆and周井泉,信号与系统.2003:人民邮电出版社.
[2]Rotthani,R.and R.K.Mehra,"Model Algorithmic Control(MAC),Basic Theoretical Properties".Automatica,1982.18(4):p.401-414.
[3]Cutler,C.R.and B.L.Ramaker.Dynamic Matrix Control-A Computer Control Algorithm.in Proc.JACC.1980.SanFranciso.
[4]Keyser,R.D.and A.V.Cauwenberghe.Extended Prediction Self-adaptive Control.in Barker H A,Young P C eds,Identification and System Parameter Estimation.1985.Oxford:Pergamon Press.
[5]Clarke,D.,C.Mohtadi,and P.Tuffs,"Generalized Predictive Control".Automatic,1987.23(2):p.137-162.
[6]Harris,T.J.,"Assessment of Control Loop Performance".Canadian journal of chemical engineering 1989.67:p.856-861.
[7]Desborough,L.and T.Harris,"Performance assessment measures for univariate feedforward/feedback control".The Canadian Journal of Chemical Engineering,1993.71(44):p.605-616.
[8]Stanfelj,N.,T.E.Marlin,and J.F.MacGregor,"Monitoring and diagnosing process control performance:the single loop case".Ind.Eng.Chem.Res.,1993.32 p.301-314.
[9]Vishnubhotla,A.,S.L.Shah,and B.Huang.Feedback and feedforward performance analysis of the shell industrial closed loop data set.in Proceedings of IFAC ADCHEM Conference.1997.Banff,Alta.
[10]Harris,T.J.,F.Boudreau,and J.F.MacGregor,"Performance assessment of multivariable feedback controllers".Automatica,1996.32:p.1505-1518.
[11]Harris,T.J.,C.T.Seppala,and L.D.Desborough,"A review of performance monitoring and assessment techniques for univariate and multivariate control systems".Journal of Process Control,1999.9:p.1-17.
[12]Qin,S.J.,"Control Performance Monitoring-A Review and Assessment".Computers an Chemical Engineering,1998.23:p.173-186.
[13]Harris,T.J.and C.T.Seppala.Recent developments in controller performance monitoring and assessment techniques,in CPC-Ⅵ.2001.Tucson,AZ.
[14]Huang,B.and S.L.Shah,Performance Assessment of Control Loops:Theory and Applications.1999,Berlin:Springer-Verlag.
[15]Horch,A.,Condition Monitoring of Control Loops,in Signals,Sensors and Systems.2000:Stockholm.
[16]Horch,A.and A.Isaksson,"A Modified Index for Control Performance assessment".Journal of Process Control,1999.9(6):p.475-483.
[17]Swanda,A.and D.Seborg,Controller Performance Assessment Based on Setpoint Response Data,in Proc.of the ACC.1999:San Diego.
[18]Jamsa-Jounela,S.L.,R.Pokonen,and K.Halmevaara.Evaluation of Level Control Performance.in Proc.of the 15~(th)IFAC World Congress.2002.Barcelona.
[19]Grimble,M.J.PID Control of Multiple Model Systems and Benchmarking.in Int.Conf.Process Control and Instrumentation.2000. Glasgow,Scotland,UK.
[20]Uduehi,D.,A.Ordis,and M.J.Grimble.,A Generalized Predictive Control Benchmark Index for MIMO Systems.in Proc.of the IEEE lnt.Conf,on Control.Application.2002.Glasgow,Scotland,UK,.
[21]Huang,B.and S.Shah,Performance Assessment of Control Loops.1999:Springer.
[22]Ko,B.-S.and T.E Edgar,"Performance assessment of multivariable feedback control systems".,Automatica,2001(37):p.899-905.
[23]McNabb,C.A.and S.J.Qin,"Projection based MIMO control performance monitoring:I-covariance monitoring in state space".Journal of Process Control,2003.13:p.739-757.
[24]Huang,B.,S.L.Shah,and K.Y.Kwok,"Good,bad or optimal?Performance assessment of MIMO processes".,Automatica,1997.33(6):p.1175-1183.
[25]Huang,B.,Multivariate Statistical Methods For Control Loop Performance,Assessment.1997,University of Alberta.
[26]Shah,S.L.,R.Patwardhan,and B.Huang.Multivariate Controller Performance,Analysis:Methods,,Applications and Challenges.in Proceedings of CPC Ⅵ.2001.Tuscon,AZ
[27]金以慧,过程控制.1993,北京:清华大学出版社.
[28]王树青,工业过程控制工程.2003:化学工业出版社.
[29]Tyler,M.L.and M.Morari.Performance assessment for unstable and nonminimum-phades systems,in Preprints IFAC Workshop on On-line Fault Detection and Supervision in the Chemical Process Industries.1995.U.K.
[30]Julien,R.H.,M.W.Foley,and W.R.Cluett,"Performance assessment using a model predictive control benchmark".Journal of Process Control,2004.14(4):p.441-456.
[31]Raich,A.and A.Cinar,"Statistical process monitoring and disturbance diagnosis in multivariable continuous processes".AIChE Journal,1996.42(4):p.995-1009.
[32]ZHANG,Q.and S.LI,"Performance Monitoring and Diagnosis of Multivariable Model Predictive Control Using Statistical Analysis".Chinese Journal of Chemical Engineering,2006.14(2):p.207-215.
[33]Huang,B.,Bayesian Methods for Control Loop Monitoring and Diagnosis,in 8th International IFAC Symposium on Dynamics and Control of Process Systems 2007:Cancún,Mexico.
[34]Agarwal,N.and B.Huang,"Assessing Model Prediction Control(MPC)Performance.1.Probabilistic Approach for Constraint Analysis ".Ind.Eng.Chem.Res.,2007.46(24):p.8101-8111.
[35]Agarwal,N.and B.Huang,"Assessing Model Prediction Control(MPC)Performance.2.Bayesian Approach for Constraint Tuning".Ind.Eng.Chem.Res.,2007.46(24):p.8112-8119.
[36]Hadjiski,M.,et al.On-line control performance monitor with robust properties,in Industrial Technology,IEEE International Conference.2003.
[37]D.Leung,J.R.,"Real-time MPC supervisory system".Computers &Chemical Engineering 2000.24(2-7):p.285-290
[38]Patwardhan,R.S.,Studies in the synthesis and analysis of model predictive controllers,in Dept.of Chemical and Materials Engng.1999,University of Alberta:Edmonton.
[39]Patwardhan,P.and S.L.Shah,"Performance diagnostics of modelbased controllers".J.Process Control 2002.12:p.413-427.
[40]Patwardhan,R.S.,S.L.Shah,and K.Z.Qi,"Assessing the Performance of Model Predictive Controllers".The Canadian Journal of Chemical Engineering,2002.80:p.954-966.
[41]Kendra,S.J.and A.Cinar,"Controller performance assessment by frequency domain techniques".Journal of Process Control,1997.7(3):p.181-194.
[42]Patwardhan,R.S.and S.L.Shah,"Issues in performance diagnostics of model-based controllers".Journal of Process Control 2002.12(3):p.413-427
[43]Jiang,H.,W.Li,and S.L.Shah,Detection and isolation of model-plant mismatch for multivariate dynamic systems,in 6~(th)IFAC Symposium on Fault Detection,Supervision and Safety of Technical Processes.2006:Beijing,China.p.1396-1401.
[44]Kammer,L.C.,D.Gorinevsky,and GA.Dumont,"Semi-Intrusive Multivariable Model Invalidation[j]".Automatica,2003.39:p.1461-1467.
[45]Ding,X.,L.Guo,and T.Jeinsch,"A characterization of parity space and its application to robust fault detection".IEEE,Transactions on Automatic Control,1999.44:p.337-343.
[46]Chow,E.and A.Willsky,"Analytical redundancy and the design of robust failure detection system".IEEE Transactions on,Automatic Control,1984.29:p.603-614.
[47]Johnson,R.and D.Wichern,Applied Multivariate Statistical,Analysis.1998:Prentice-Hall Inc.
[48]席裕庚,预测控制[M].1993,北京:国防工业出版社.
[49]方崇智and萧德云,过程辨识.2004,北京:清华大学出版社.
[50]盛骤,谢式千,and潘承毅,概率论与数理统计.2001:高等教育出版社.
[51]沈元隆and周井泉,信号与系统.2003:人民邮电出版社.