分散式MPC经济性能评估
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摘要
近年来,学术界对集中式模型预测控制(Model predictive control,MPC)性能评估进行了广泛的研究.对于大规模化工过程,工业现场通常采用分散式MPC的控制结构.由于各子系统间存在复杂的耦合关系,针对集中式MPC的性能评估方法不能客观反映分散式MPC的性能.本文基于线性矩阵不等式(Linear matrix inequality,LMI)的方法对分散式MPC进行经济性能评估.首先提出了一种迭代方法求解分散式线性二次型调节器(Linear quadratic regulator,LQR)问题,该方法显著降低了已有求解方法的保守性.再利用LQR基准建立了一组随机优化命题对MPC进行经济性能评估,评估方法对集中式MPC与分散式MPC均适用,评估结果可以指导MPC参数调整,也可以为集中式与分散式MPC结构选择提供重要参考.通过对重油分馏塔控制问题的仿真验证了本文方法的有效性与应用价值.
In recent years,performance assessment of centralized model predictive control(MPC) has attracted a lot of academic interest.In fact,large-scale complex chemical processes are usually controlled by decentralized MPC in the industrial field.Due to the complex interactions between subsystems,most performance assessment methods regarding centralized control structure cannot be applied to the performance assessment of decentralized MPC.In this paper,a linear matrix inequality(LMI) based approach is proposed to assess the economic performance of decentralized MPC.First,an iterative method is proposed to obtain the decentralized linear quadratic regulator(LQR) benchmark.A probabilistic optimization problem is then formulated to assess the economic performance of MPC.The proposed approach can be applied to assessment of both centralized MPC and decentralized MPC.The assessment result provides guidance for parameter tuning as well as control structure selection.The simulation result of Shell control problem shows the effectiveness of the proposed method.
In recent years,performance assessment of centralized model predictive control(MPC) has attracted a lot of academic interest.In fact,large-scale complex chemical processes are usually controlled by decentralized MPC in the industrial field.Due to the complex interactions between subsystems,most performance assessment methods regarding centralized control structure cannot be applied to the performance assessment of decentralized MPC.In this paper,a linear matrix inequality(LMI) based approach is proposed to assess the economic performance of decentralized MPC.First,an iterative method is proposed to obtain the decentralized linear quadratic regulator(LQR) benchmark.A probabilistic optimization problem is then formulated to assess the economic performance of MPC.The proposed approach can be applied to assessment of both centralized MPC and decentralized MPC.The assessment result provides guidance for parameter tuning as well as control structure selection.The simulation result of Shell control problem shows the effectiveness of the proposed method.
引文
1Cui H,Jacobsen E W.Performance limitations in decentral-ized control.Journal of Process Control,2002,12(4):485-494
2Scattolini R.Architectures for distributed and hierarchical model predictive control—a review.Journal of Process Control,2009,19(5):723-731
3Stewart B T,Venkat A N,Rawlings J B,Wright S J,Pan-nocchia G.Cooperative distributed model predictive con-trol.Systems&Control Letters,2010,59(8):460-469
4Harris T J.Assessment of control loop performance.The Canadian Journal of Chemical Engineering,1989,67(5):856-861
5Huang B,Kadali R.Dynamic Modeling,Predictive Control and Performance Monitoring:A Data-driven Subspace Ap-proach.Vol.374.New York:Springer Verlag,2008
6Gao J P,Patwardhan R,Akamatsu K,Hashimoto Y,Emoto G,Shah S L,Huang B.Performance evaluation of two indus-trial MPC controllers.Control Engineering Practice,2003,11(12):1371-1387
7Yang M Y,Jin X M,Chen F.Performance assessment of model predictive control in industrial distillation column.In:Proceedings of the5th World Congress on Intelligent Control and Automation.Hangzhou,China:IEEE,2004.637-641
8Huang B,Shah S L.Performance Assessment of Control Loops:Theory and Applications.New York:Springer Ver-lag,1999
9Shah S L,Patwardhan R,Huang B.Multivariate controller performance analysis:methods,applications and challenges.AIChE Symposium Series,New York,USA,2002.190-207
10Shah S L,Mitchell W,Shook D.Challenges in the detection,diagnosis and visualisation of controller performance data.Computing and Control Engineering Journal,2005,16(4):30-34
11Patwardhan R S,Shah S L,Qi K Z.Assessing the perfor-mance of model predictive controllers.The Canadian Jour-nal of Chemical Engineering,2002,80(5):954-966
12Jain M,Lakshminarayanan S.Estimating performance enhancement with alternate control strategies for multi-loop control systems.Chemical Engineering Science,2007,62(17):4644-4658
13Kariwala V,Forbes J F,Meadows E S.Minimum variance benchmark for decentralized controllers.In:Proceedings of the2005American Control Conference.Portland,OR,USA:IEEE,2005.1437-1442
14Kariwala V.Fundamental limitation on achievable decen-tralized performance.Automatica,2007,43(10):1849-1854
15De Oliveira M C,Geromel J C,Bernussou J.Extended H2and H∞norm characterizations and controller parametriza-tions for discrete-time systems.International Journal of Control,2002,75(9):666-679
16Geromel J C,Peres P L D.Decentralized load-frequency control.IEE Proceedings D(Control Theory and Applica-tions),1985,132(5):225-230
17Geromel J C,Bernussou J,Peres P L D.Decentralized control through parameter space optimization.Automatica,1994,30(10):1565-1578
18Zhao C,Zhao Y,Su H Y,Huang B.Economic performance assessment of advanced process control with LQG bench-marking.Journal of Process Control,2009,19(4):557-569
19Zhao C,Su H Y,Gu Y,Chu J.A pragmatic approach for assessing the economic performance of model predictive con-trol systems and its industrial application.Chinese Journal of Chemical Engineering,2009,17(2):241-250
20Xu Q L,Zhao C,Zhang D F,An A M,Zhang C.Data-driven LQG benchmarking for economic performance assess-ment of advanced process control system.In:Proceedings of the2011American Control Conference.San Francisco,CA,USA:AACC,2011.5085-5090
21Xu F W,Huang B,Akande S.Performance assessment of model predictive control for variability and constraint tun-ing.Industrial and Engineering Chemistry Research,2007,46(4):1208-1219
22Ying,C M,Joseph B.Performance and stability analysis of LP-MPC and QP-MPC cascade control systems.AIChE Journal,1999,45(7):1521-1534
2Scattolini R.Architectures for distributed and hierarchical model predictive control—a review.Journal of Process Control,2009,19(5):723-731
3Stewart B T,Venkat A N,Rawlings J B,Wright S J,Pan-nocchia G.Cooperative distributed model predictive con-trol.Systems&Control Letters,2010,59(8):460-469
4Harris T J.Assessment of control loop performance.The Canadian Journal of Chemical Engineering,1989,67(5):856-861
5Huang B,Kadali R.Dynamic Modeling,Predictive Control and Performance Monitoring:A Data-driven Subspace Ap-proach.Vol.374.New York:Springer Verlag,2008
6Gao J P,Patwardhan R,Akamatsu K,Hashimoto Y,Emoto G,Shah S L,Huang B.Performance evaluation of two indus-trial MPC controllers.Control Engineering Practice,2003,11(12):1371-1387
7Yang M Y,Jin X M,Chen F.Performance assessment of model predictive control in industrial distillation column.In:Proceedings of the5th World Congress on Intelligent Control and Automation.Hangzhou,China:IEEE,2004.637-641
8Huang B,Shah S L.Performance Assessment of Control Loops:Theory and Applications.New York:Springer Ver-lag,1999
9Shah S L,Patwardhan R,Huang B.Multivariate controller performance analysis:methods,applications and challenges.AIChE Symposium Series,New York,USA,2002.190-207
10Shah S L,Mitchell W,Shook D.Challenges in the detection,diagnosis and visualisation of controller performance data.Computing and Control Engineering Journal,2005,16(4):30-34
11Patwardhan R S,Shah S L,Qi K Z.Assessing the perfor-mance of model predictive controllers.The Canadian Jour-nal of Chemical Engineering,2002,80(5):954-966
12Jain M,Lakshminarayanan S.Estimating performance enhancement with alternate control strategies for multi-loop control systems.Chemical Engineering Science,2007,62(17):4644-4658
13Kariwala V,Forbes J F,Meadows E S.Minimum variance benchmark for decentralized controllers.In:Proceedings of the2005American Control Conference.Portland,OR,USA:IEEE,2005.1437-1442
14Kariwala V.Fundamental limitation on achievable decen-tralized performance.Automatica,2007,43(10):1849-1854
15De Oliveira M C,Geromel J C,Bernussou J.Extended H2and H∞norm characterizations and controller parametriza-tions for discrete-time systems.International Journal of Control,2002,75(9):666-679
16Geromel J C,Peres P L D.Decentralized load-frequency control.IEE Proceedings D(Control Theory and Applica-tions),1985,132(5):225-230
17Geromel J C,Bernussou J,Peres P L D.Decentralized control through parameter space optimization.Automatica,1994,30(10):1565-1578
18Zhao C,Zhao Y,Su H Y,Huang B.Economic performance assessment of advanced process control with LQG bench-marking.Journal of Process Control,2009,19(4):557-569
19Zhao C,Su H Y,Gu Y,Chu J.A pragmatic approach for assessing the economic performance of model predictive con-trol systems and its industrial application.Chinese Journal of Chemical Engineering,2009,17(2):241-250
20Xu Q L,Zhao C,Zhang D F,An A M,Zhang C.Data-driven LQG benchmarking for economic performance assess-ment of advanced process control system.In:Proceedings of the2011American Control Conference.San Francisco,CA,USA:AACC,2011.5085-5090
21Xu F W,Huang B,Akande S.Performance assessment of model predictive control for variability and constraint tun-ing.Industrial and Engineering Chemistry Research,2007,46(4):1208-1219
22Ying,C M,Joseph B.Performance and stability analysis of LP-MPC and QP-MPC cascade control systems.AIChE Journal,1999,45(7):1521-1534