多速率采样预测控制系统的分析与设计
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摘要
本文研究了多速率采样预测控制的若干问题.主要内容分为两部分:第一部分是多速率采样预测控制算法的设计.包括基于极点配置的双速率采样预测控制算法、双速率采样Min-max鲁棒广义预测控制算法和时滞多速率采样预测控制算法三种情形;第二部分研究多速率采样预测控制系统的性能分析.论文的主要结果有: (1)对双速率采样预测控制系统的性能进行了分析.推导双速率采样预测控制系统具有内模结构,研究了双速率采样预测控制系统的鲁棒稳定性和零稳态偏差特性.通过仿真实例说明双速率采样预测控制对比单速率采样预测控制在性能上的优越性. (2)研究了基于极点配置的双速率采样预测控制算法.针对一类输入更新速率是输出采样速率N倍的系统,充分利用该系统存在的自由度,设计状态反馈矩阵,不但能将闭环极点配置到期望位置,而且当系统参数存在不确定性时,能够保证系统的鲁棒稳定性.从而推进了双速率采样预测控制的已有的研究工作. (3)给出了一类新的双速率采样Min-max鲁棒广义预测控制.此算法是针对已有文献中的双速率采样预测控制算法的不足提出来的.通过增加受限输出时域和在性能指标中引入干扰项的方法,设计了鲁棒性较强的控制律,有效的减弱了干扰对系统的影响.在此基础上,对系统的鲁棒稳定性进行了分析. (4)研究了一类时滞双速率采样预测控制问题.针对输入更新速率比输出采样速率慢的双速率采样系统,建立了带有时滞的输入输出预测模型,给出了时滞双速率采样预测控制算法,弥补了已有文献中时滞多速率采样加权最小方差控制的不足,解决了时滞对多速率采样系统带来的影响.利用线性矩阵不等式对闭环系统的鲁棒稳定性进行了分析. (5)对所提出的各类预测控制算法进行了仿真研究,证明了算法的有效性.
This thesis discusses several researches on multi-rate predictive control contenting of two parts. The first part is the algorithm design, which consists of dual-rate predictive control based on the pole placement, dual-rate min-max robust generalized predictive control and dual-rate predictive control for time-delay systems; the second part is the performance analysis of multi-rate predictive control systems.
The main results are: (1) The IMC structure of the dual-rate predictive control system is derived, and its robust stability and zero steady state error characteristics are analyzed. Simulation examples explain the dual-rate predictive control has more superiority than the single-rate predictive control. (2) An algorithm of dual-rate predictive control based on the pole placement is proposed. A class of system that the control is applied at a faster rate than the available measurements of the plant output signal is chosen to illustrate the technique. A state feedback gain matrix is designed, which can not only assign closed loop poles at desiring position but also ensure the system robust stability, though there are some uncertain parameters in the system. This result precedes the former research work. (3) Dual-rate min-max robust generalized predictive control algorithm is proposed, which adds a constraint output horizon to improve the system properties. A controller with strong robustness is derived, which is robust to disturbances by minimizing the cost function while disturbances maximize it. Some robust stability conditions are derived. (4) A class of dual-rate input-output predictive model containing time delays is established. A new dual-rate predictive control algorithm for the time-delay system is presented, which makes up the shortcoming of multi-rate weighted minimum-variance control for time-delays system, and has solved the influence of time delays on the multi-rate system. Furthermore, the robust stability of the closed-loop system is analyzed using linear matrix inequalities (LMI) method. (5) Computer simulations demonstrate the usefulness of the proposed algorithms in this paper.
This thesis discusses several researches on multi-rate predictive control contenting of two parts. The first part is the algorithm design, which consists of dual-rate predictive control based on the pole placement, dual-rate min-max robust generalized predictive control and dual-rate predictive control for time-delay systems; the second part is the performance analysis of multi-rate predictive control systems.
The main results are: (1) The IMC structure of the dual-rate predictive control system is derived, and its robust stability and zero steady state error characteristics are analyzed. Simulation examples explain the dual-rate predictive control has more superiority than the single-rate predictive control. (2) An algorithm of dual-rate predictive control based on the pole placement is proposed. A class of system that the control is applied at a faster rate than the available measurements of the plant output signal is chosen to illustrate the technique. A state feedback gain matrix is designed, which can not only assign closed loop poles at desiring position but also ensure the system robust stability, though there are some uncertain parameters in the system. This result precedes the former research work. (3) Dual-rate min-max robust generalized predictive control algorithm is proposed, which adds a constraint output horizon to improve the system properties. A controller with strong robustness is derived, which is robust to disturbances by minimizing the cost function while disturbances maximize it. Some robust stability conditions are derived. (4) A class of dual-rate input-output predictive model containing time delays is established. A new dual-rate predictive control algorithm for the time-delay system is presented, which makes up the shortcoming of multi-rate weighted minimum-variance control for time-delays system, and has solved the influence of time delays on the multi-rate system. Furthermore, the robust stability of the closed-loop system is analyzed using linear matrix inequalities (LMI) method. (5) Computer simulations demonstrate the usefulness of the proposed algorithms in this paper.
引文
[1] Al-Rahmani H M, Franklin G F. A new optimal multirate control of linear periodic and time-in variant systems [J]. IEEE Transactions on Automatic Control, 1990, 35(4): 404-415.
[2] Al-Rahmani H M, Franklin G F. Multirate control: A new approach [J]. Automatica, 1992, 28(1): 35-44.
[3] Chen T W. On stability robustness of a dual-rate control system [J]. IEEE Transactions on Automatic Control, 1994, 39(1):164-167.
[4] Scattolini R. Self-tuning control of systems with infrequent and delayed output sampling [J]. IEE Proceedings, Part D, Control Theory and Applications, 1988, 135(4): 213-221.
[5] Sheng J, Chen T W, Sirish L. On Stability Robustness of Dual-Rate Generalized Predictive Control Systems [C]. Proc.of 5th American Control Conference, 2001, 3415-3420.
[6] Lee J H. Model Predictive Control of Multirate Sampled-data Systems: A State-space Approach [J]. Int J Control, 1992, 55(1): 153-191.
[7] Ling K V, Lim K W. A State Space GPC with Extensions to Multirate Control [J]. Automatica,1996, 32(7):1087-1071.
[8]Albertos P, Ortega R. On Generalized Predictive Control:Two Alternative Formulations [J]. Automatica, 1989, 35(5): 753-755.
[9] Scattolini R, Schiavoni N. A Multirate Model-based Predictive Controller [J]. IEEE Trans. Automatic Control, 1995, 40: 1093-1097.
[10] Li D, Shah S L , Chen T. Analysis of Dual-rate Inferential Control Systems [J]. Automatica, 2002, 38(6):1053-1059.
[11] Li D, Shah S L, Chen T, Qi K Z. Application of Dual-rate Modeling to CCR Octane Quality Inferential Control [J]. IEEE Transactions on Control Systems Technology, 2003, 11(1): 43-51.
[12] Carini P, Micheli R and Scattolini R. Mutirate Self-tuning Predictive Control with Application to Binary Distillation Column[J]. Int J System and Science, 1990, 21(1) : 51-54.
[13] Masahiro O, Iori H, Hirimu O, Makoto T, Takashi Y and Fumio G. Multirate Multivariable Model Predictive Control and Application in a Polymerization Reactor[J]. Int J Control, 1994, 59(3): 731-742.
[14] Ravi S, Gopinath B, Wayne B, Rob J R, Howard K. Multirate MPC Design for a Nonlinear Drug Infusion Systems[C]. Proceeding of the American Control Conference, Baltlmore, Maryland, 1994.
[15] Ohshima M, Hashimoto I, Takeda M, Yoneyama T, Goto F. Multivariable Model Predictive Control and its Application to a Semi-commercial Polymerization Reactor [C]. Proceeding of the American Control Conferernce, Chicago, USA, 1992, 1576-1581.
[16] Kranc G M. Input-output Analysis of Multirate Feedback System[J]. IRE Trans Automatic Control, 1957, 3: 21-28.
[18] Kalman R E, Bertram J E. A Unified Approach to the Theory of Sampling Systems [J]. J Franklin Inst, 1959, 267(3): 405-436.
[19] Amit N. Optimal Cntrol of Mltirate Dgital Cntrol Sstems. Report SUDAAR#523, Standford University, 1980.
[20] Araki M, Yamamoto K. Multivariable Multirate Sampled-Data Systems: State-space Description, Transfer, Characteristics and Nyquist Criterion [J]. IEEE Trans. Automat. Control, 1986, 31(1): 145-154.
[21] Chen T W, Optimal Sampled-data System [M]. Springer, London, 1995.
[22] Friedland B. Sampled-data Control Systems Containing Periodically Varying Members [C]. Proceedings of the first IFAC congress, 1960.
[23] Kreissemeier G. On Sampling Without Loss of Observability / Controllability [J]. IEEE Trans. Automatic Control, 1999, 44(5): 1021-1025.
[24] Rossiter J A, Chen T W and Shah S L. A Comparison of Lifting and Inferential Control for Multi-rate Systems [C]. Proceeding of the American Control Conference. Denver, Colorado. June 4-6, 2003.
[25] Li D, Shah S L and Chen T W. Analysis of Dual-rate Inferential Control System [J]. Automatica, 2002, 38(6): 1053-1059.
[26] Sheng J, Chen T W and Sirish S L. Generalized Predictive Control for Non-uniformly Sampled Systems [J]. J of Process Control, 2002, 12(3): 875-885.
[27] 查星宇, 董浩, 周立芳, 钱积新. 多频多变量 DMC 预测控制算法[J]. 石油化工自动化, 2000, 6: 30-34.
[28] Gopinath R S, Bequette B W. Multirate Model Predictive Control of Unconstrained Single Input-Single Output Process [C], Proceedings of the American Control Conference,TM8, 2042-2045
[29] Scattolini R. Multirate Self-tuning Predictive Controller for Multivariable System [J]. Int J Systems Sci, 1992, 23(8): 1347-1359.
[30] Lu W P. Multirate Constrained Adaptive Control [J]. Int J Control, 1990, 51(6): 1439-1456.
[31] Mao K Z, Chai T Y. Model Predictive Control Algorithms for Systems with Slow Sampled Outputs [J]. IEE Proc.Control Theory Appl., 1996, 143(6): 551-556.
[32] Cao Y Y, Hu L S, Frank P M. Model Predictive Control via Piecewise Constant Output Feedback for Multirate Sampled-data Systems [C]. Proceeding of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000.
[33] Gopinath R S. Bequette B W. Multirate Model Predictive Control of Constrained SISO Processes. AICHEJ, 1991.
[34] Truman A W. A Subrate Weighted Minimum-variance Control Law [J]. International Journal of control, 1996, 65(1): 93-115.
[35] 诸静. 智能预测控制及其应用 [M]. 杭州: 浙江大学出版社, 2002.
[36] 周立芳. 多变量多频预测控制系统的研究 [博士学位论文]. 杭州: 浙江大学, 1999.
[37] 周立芳, 钱积新. 多变量多频预测控制与单频预测控制方法的比较[J]. 石油化工自动化, 2001, 1: 20-23.
[38] 金元郁, 顾兴源. 自适应密集预测的模型算法控制 [J]. 控制理论与应用, 1991, 8(3): 348-352.
[39] 陆顾新, 黄道平, 王永庆, 朱学峰. 基于不同建模周期的非自衡预测控制研究[J]. 控制工程. 2003, 10(3): 252-255.
[40] 陆顾新, 黄道平. 两种基于不同周期的多变量预测控制研究[J].自动化与仪器仪表, 2003, 4: 7-9.
[41] 张友刚, 肖建. 输入多采样率数字控制系统的鲁棒稳定性[J]. 电机与控制学报, 1999, 3(4): 228-231.
[42] Truman A W, Govan M. Multirate-Sampled Digital Feedback System Design Via APredictive Control Approach [J], IEE Proc Control Theory Appl, 2000, 147(3): 293-302.
[43] Zhou L F, Dong H, Qian J X. Multirate Dynamic Matrix Control for Multivariable Syatems[J]. Proc.of 14th World Congress of IFAC, 1999, 241-246.
[44] Zhou L F, Qian J X. The IMC Structure of Multi-rate Multivariable Predictive Control System and An Improved Algorithm [J]. Chinese J. of Chem. Eng., 2001, 9(3): 273-279.
[45] 周立芳, 钱积新. 改进的多频自校正广义预测控制算法[J]. 石油化工自动化, 1999, 6: 25-27.
[46] Oh J H. Multi-rate Generalized Predictive Control for Multi-variable System [J]. Automatic, 1990, 26(3):377-380.
[47] Zhou L F, Qian J X.. On Stability Analysis of the Multirate Multivariable Predictive Control Systems [C]. Proceeding of the 4th World Congress on Intelligent Control and Automation, 2002: 288-294.
[48] 舒迪前. 预测控制系统及其应用[M]. 北京: 机械工业出版社,1996.
[49] Louis F. Pole Placement Algorithms for Multirate Sampled Linear Systems [J]. 1994, 30(4): 723-727.
[50] Delasen M. Pole-placement in Discrete Systems by Using Single and Multirate Sampling [J]. 1996, 333(5): 721-746.
[51] Valasek M, Olgac N. Efficient Pole Placement Technique for Linear Time Variant SISO Systems [J]. IEE Proc. Theory Appl., 1995, 142 (5): 451-458.
[52] Soylemez M T, Munro N. Robust Pole Assignment in Uncertain Systems [J]. IEE Proc. Control Theory Appl., 1997, 144(3): 217-224.
[53] Soylemez M T, Munro N. A Note on Pole Assignment in Uncertain Systems [J]. Int. J. Control, 1997, 66(4): 487-497.
[54] Ordys A W, Clarke D W. A State-space Description for GPC Controllers [J]. Int. J. Systems and Science, 1993, 24(9): 1727-1744.
[55] 肖建. 多采样率数字控制系统[M]. 北京:科学出版社,2003.
[56] Lall S, Glover K. A Game Theoretic Approach to Moving Horizon Control [M]. Advances in Model-Based Predictive Control, Oxford: Oxford Univ. Press, 1994.
[57] Li D G, Shah S L, Chen T W. System Identification and Long-range Predictive Control of Multirate Systems [J]. Department of Chemical and Materials Engineering, University of Alberta, Edmonton, CANADA T6G 2G6.
[58] Rossiter J A, Sheng J, Chen T W. Interpretations of and Options in Dual-rate Predictive Control [J], Journal of Process Control, 2005, 15(2): 135-148.
[59] 俞立, 陈国定, 杨马英. 不确定系统具有圆盘区域极点约束的鲁棒控制 [J]. 自动化学报, 2000, 26(1): 116-120.
[60] 肖建, 徐志根. 多采样率数字控制系统综述 [J]. 信息与控制, 2003, 32(5): 436-441.
[2] Al-Rahmani H M, Franklin G F. Multirate control: A new approach [J]. Automatica, 1992, 28(1): 35-44.
[3] Chen T W. On stability robustness of a dual-rate control system [J]. IEEE Transactions on Automatic Control, 1994, 39(1):164-167.
[4] Scattolini R. Self-tuning control of systems with infrequent and delayed output sampling [J]. IEE Proceedings, Part D, Control Theory and Applications, 1988, 135(4): 213-221.
[5] Sheng J, Chen T W, Sirish L. On Stability Robustness of Dual-Rate Generalized Predictive Control Systems [C]. Proc.of 5th American Control Conference, 2001, 3415-3420.
[6] Lee J H. Model Predictive Control of Multirate Sampled-data Systems: A State-space Approach [J]. Int J Control, 1992, 55(1): 153-191.
[7] Ling K V, Lim K W. A State Space GPC with Extensions to Multirate Control [J]. Automatica,1996, 32(7):1087-1071.
[8]Albertos P, Ortega R. On Generalized Predictive Control:Two Alternative Formulations [J]. Automatica, 1989, 35(5): 753-755.
[9] Scattolini R, Schiavoni N. A Multirate Model-based Predictive Controller [J]. IEEE Trans. Automatic Control, 1995, 40: 1093-1097.
[10] Li D, Shah S L , Chen T. Analysis of Dual-rate Inferential Control Systems [J]. Automatica, 2002, 38(6):1053-1059.
[11] Li D, Shah S L, Chen T, Qi K Z. Application of Dual-rate Modeling to CCR Octane Quality Inferential Control [J]. IEEE Transactions on Control Systems Technology, 2003, 11(1): 43-51.
[12] Carini P, Micheli R and Scattolini R. Mutirate Self-tuning Predictive Control with Application to Binary Distillation Column[J]. Int J System and Science, 1990, 21(1) : 51-54.
[13] Masahiro O, Iori H, Hirimu O, Makoto T, Takashi Y and Fumio G. Multirate Multivariable Model Predictive Control and Application in a Polymerization Reactor[J]. Int J Control, 1994, 59(3): 731-742.
[14] Ravi S, Gopinath B, Wayne B, Rob J R, Howard K. Multirate MPC Design for a Nonlinear Drug Infusion Systems[C]. Proceeding of the American Control Conference, Baltlmore, Maryland, 1994.
[15] Ohshima M, Hashimoto I, Takeda M, Yoneyama T, Goto F. Multivariable Model Predictive Control and its Application to a Semi-commercial Polymerization Reactor [C]. Proceeding of the American Control Conferernce, Chicago, USA, 1992, 1576-1581.
[16] Kranc G M. Input-output Analysis of Multirate Feedback System[J]. IRE Trans Automatic Control, 1957, 3: 21-28.
[18] Kalman R E, Bertram J E. A Unified Approach to the Theory of Sampling Systems [J]. J Franklin Inst, 1959, 267(3): 405-436.
[19] Amit N. Optimal Cntrol of Mltirate Dgital Cntrol Sstems. Report SUDAAR#523, Standford University, 1980.
[20] Araki M, Yamamoto K. Multivariable Multirate Sampled-Data Systems: State-space Description, Transfer, Characteristics and Nyquist Criterion [J]. IEEE Trans. Automat. Control, 1986, 31(1): 145-154.
[21] Chen T W, Optimal Sampled-data System [M]. Springer, London, 1995.
[22] Friedland B. Sampled-data Control Systems Containing Periodically Varying Members [C]. Proceedings of the first IFAC congress, 1960.
[23] Kreissemeier G. On Sampling Without Loss of Observability / Controllability [J]. IEEE Trans. Automatic Control, 1999, 44(5): 1021-1025.
[24] Rossiter J A, Chen T W and Shah S L. A Comparison of Lifting and Inferential Control for Multi-rate Systems [C]. Proceeding of the American Control Conference. Denver, Colorado. June 4-6, 2003.
[25] Li D, Shah S L and Chen T W. Analysis of Dual-rate Inferential Control System [J]. Automatica, 2002, 38(6): 1053-1059.
[26] Sheng J, Chen T W and Sirish S L. Generalized Predictive Control for Non-uniformly Sampled Systems [J]. J of Process Control, 2002, 12(3): 875-885.
[27] 查星宇, 董浩, 周立芳, 钱积新. 多频多变量 DMC 预测控制算法[J]. 石油化工自动化, 2000, 6: 30-34.
[28] Gopinath R S, Bequette B W. Multirate Model Predictive Control of Unconstrained Single Input-Single Output Process [C], Proceedings of the American Control Conference,TM8, 2042-2045
[29] Scattolini R. Multirate Self-tuning Predictive Controller for Multivariable System [J]. Int J Systems Sci, 1992, 23(8): 1347-1359.
[30] Lu W P. Multirate Constrained Adaptive Control [J]. Int J Control, 1990, 51(6): 1439-1456.
[31] Mao K Z, Chai T Y. Model Predictive Control Algorithms for Systems with Slow Sampled Outputs [J]. IEE Proc.Control Theory Appl., 1996, 143(6): 551-556.
[32] Cao Y Y, Hu L S, Frank P M. Model Predictive Control via Piecewise Constant Output Feedback for Multirate Sampled-data Systems [C]. Proceeding of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000.
[33] Gopinath R S. Bequette B W. Multirate Model Predictive Control of Constrained SISO Processes. AICHEJ, 1991.
[34] Truman A W. A Subrate Weighted Minimum-variance Control Law [J]. International Journal of control, 1996, 65(1): 93-115.
[35] 诸静. 智能预测控制及其应用 [M]. 杭州: 浙江大学出版社, 2002.
[36] 周立芳. 多变量多频预测控制系统的研究 [博士学位论文]. 杭州: 浙江大学, 1999.
[37] 周立芳, 钱积新. 多变量多频预测控制与单频预测控制方法的比较[J]. 石油化工自动化, 2001, 1: 20-23.
[38] 金元郁, 顾兴源. 自适应密集预测的模型算法控制 [J]. 控制理论与应用, 1991, 8(3): 348-352.
[39] 陆顾新, 黄道平, 王永庆, 朱学峰. 基于不同建模周期的非自衡预测控制研究[J]. 控制工程. 2003, 10(3): 252-255.
[40] 陆顾新, 黄道平. 两种基于不同周期的多变量预测控制研究[J].自动化与仪器仪表, 2003, 4: 7-9.
[41] 张友刚, 肖建. 输入多采样率数字控制系统的鲁棒稳定性[J]. 电机与控制学报, 1999, 3(4): 228-231.
[42] Truman A W, Govan M. Multirate-Sampled Digital Feedback System Design Via APredictive Control Approach [J], IEE Proc Control Theory Appl, 2000, 147(3): 293-302.
[43] Zhou L F, Dong H, Qian J X. Multirate Dynamic Matrix Control for Multivariable Syatems[J]. Proc.of 14th World Congress of IFAC, 1999, 241-246.
[44] Zhou L F, Qian J X. The IMC Structure of Multi-rate Multivariable Predictive Control System and An Improved Algorithm [J]. Chinese J. of Chem. Eng., 2001, 9(3): 273-279.
[45] 周立芳, 钱积新. 改进的多频自校正广义预测控制算法[J]. 石油化工自动化, 1999, 6: 25-27.
[46] Oh J H. Multi-rate Generalized Predictive Control for Multi-variable System [J]. Automatic, 1990, 26(3):377-380.
[47] Zhou L F, Qian J X.. On Stability Analysis of the Multirate Multivariable Predictive Control Systems [C]. Proceeding of the 4th World Congress on Intelligent Control and Automation, 2002: 288-294.
[48] 舒迪前. 预测控制系统及其应用[M]. 北京: 机械工业出版社,1996.
[49] Louis F. Pole Placement Algorithms for Multirate Sampled Linear Systems [J]. 1994, 30(4): 723-727.
[50] Delasen M. Pole-placement in Discrete Systems by Using Single and Multirate Sampling [J]. 1996, 333(5): 721-746.
[51] Valasek M, Olgac N. Efficient Pole Placement Technique for Linear Time Variant SISO Systems [J]. IEE Proc. Theory Appl., 1995, 142 (5): 451-458.
[52] Soylemez M T, Munro N. Robust Pole Assignment in Uncertain Systems [J]. IEE Proc. Control Theory Appl., 1997, 144(3): 217-224.
[53] Soylemez M T, Munro N. A Note on Pole Assignment in Uncertain Systems [J]. Int. J. Control, 1997, 66(4): 487-497.
[54] Ordys A W, Clarke D W. A State-space Description for GPC Controllers [J]. Int. J. Systems and Science, 1993, 24(9): 1727-1744.
[55] 肖建. 多采样率数字控制系统[M]. 北京:科学出版社,2003.
[56] Lall S, Glover K. A Game Theoretic Approach to Moving Horizon Control [M]. Advances in Model-Based Predictive Control, Oxford: Oxford Univ. Press, 1994.
[57] Li D G, Shah S L, Chen T W. System Identification and Long-range Predictive Control of Multirate Systems [J]. Department of Chemical and Materials Engineering, University of Alberta, Edmonton, CANADA T6G 2G6.
[58] Rossiter J A, Sheng J, Chen T W. Interpretations of and Options in Dual-rate Predictive Control [J], Journal of Process Control, 2005, 15(2): 135-148.
[59] 俞立, 陈国定, 杨马英. 不确定系统具有圆盘区域极点约束的鲁棒控制 [J]. 自动化学报, 2000, 26(1): 116-120.
[60] 肖建, 徐志根. 多采样率数字控制系统综述 [J]. 信息与控制, 2003, 32(5): 436-441.