多变量预测函数控制及应用研究
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摘要
模型预测控制(MPC)是一类计算机控制算法，它通过预测系统未来的行为，对目标函数进行滚动优化和模型误差补偿，得到系统当前及未来时刻的控制量。其结合了工业生产的实际要求，具有控制效果好，鲁棒性强等优点。而预测函数控制(PFC)是在模型预测控制原理的基础上提出的，并且将控制规律进行了结构化设计。该控制算法认为控制输入是事先选定的基函数的线性组合，因此具有控制规律明确，在线计算量小，动态跟踪效果好等优点。本文在前人研究工作的基础上，从实际出发，对预测函数控制的若干问题进行了较为深入的研究，其中包括：
(1)综述了模型预测控制技术和预测函数控制技术的基本原理、发展现状，以及其商业化软件产品。
(2)针对2输入／2输出一阶加纯滞后系统，提出了一种多变量预测函数控制算法。通过滚动优化目标函数，得到控制量的显式解析表达式。采用内模原理分析了该多变量预测函数控制系统的稳定性和鲁棒性。最后通过计算机仿真和物理实验，证明了该控制算法的有效性。
(3)针对3输入／3输出一阶加纯滞后系统，提出了一种多变量预测函数控制算法，并将该算法推广到n输入／m输出系统。采用Smith预估思想，推导得到控制量的显式解析表达式。最后针对Shell公司的重油催化裂化分馏塔装置，进行计算机仿真，并与单变量预测函数控制效果进行比较。比较结果表明，该多变量预测函数控制算法具有较好的控制品质。
(4)通过机理分析，建立了塑料熔化过程料筒温度对象的数学模型结构，采用带遗忘因子的递推最小二乘辨识技术在线辨识模型参数。利用该模型，设计了以预测函数控制算法为核心的先进控制系统。应用结果表明，该先进控制系统比模糊控制系统具有更好的控制效果。
最后是全文的总结和展望。
Model predictive control (MPC) refers to a class of computer control algorithms. At eachcontrol interval an MPC algorithm predicts the future response of a process, and attemptsto optimize future process behavior by computing a sequence of future manipulatedvariables. Because this kind of control algorithm has taken into consideration of theindustrial requirements, the control system under MPC has good performance and strongrobustness. Predictive functional control (PFC) is a branch of the MPC family. The maindistinguishing feature of the PFC algorithm over other MPC algorithms is the constructionof the manipulated variables. Usually, the manipulated variables can be represented as asum of pre-determined basis functions, which achieves computational simplicity and goodperformance of tracking set-point without steady-state error. Some problems of predictivefunctional control are researched in this thesis, and the main research works are as follows:
(1) An overview of MPC and PFC technology is given.
(2) A multivariable predictive functional control algorithm based on a two-inputs/two-outputs system with the transfer function model is presented in this section. A simpleand explicit solution of manipulated variables of the control system can be obtained byoptimizing the objective function. The stability and robustness analysis of this kind ofmultivariable predictive functional control algorithm is given. Finally, simulations andexperiment of the system applying this control algorithm are provided, showing that thepresented algorithm is feasible.
(3) A multivariable predictive functional control algorithm, on the basis of a three-inputs/three-outputs system with the transfer function model is presented, which has beenpromoted into the n-inputs/m-outputs system. The explicit solution of manipulatedvariables is obtained by using the idea of Smith predictor. In the end, some simulationexamples are presented by using Shell Oil's heavy-oil fractionator model. The result ofcomparing with single-variable predictive functional control is shown in the simulation,which displays that this multivariable predictive functional control algorithm has goodcontrol performance.
(4) Based on the mechanism of plastic melting, the energy conservation mathematicalmodel is proposed. The parameters of this model are obtained by identification online,which ensures the robustness and disturbance rejection. An advanced control system has been established which based on the model and the predictive functional control algorithm.The good result of experiment is shown in the last part, approving the validity of thecontroller.
The last part is summary and perspective.
(1)综述了模型预测控制技术和预测函数控制技术的基本原理、发展现状，以及其商业化软件产品。
(2)针对2输入／2输出一阶加纯滞后系统，提出了一种多变量预测函数控制算法。通过滚动优化目标函数，得到控制量的显式解析表达式。采用内模原理分析了该多变量预测函数控制系统的稳定性和鲁棒性。最后通过计算机仿真和物理实验，证明了该控制算法的有效性。
(3)针对3输入／3输出一阶加纯滞后系统，提出了一种多变量预测函数控制算法，并将该算法推广到n输入／m输出系统。采用Smith预估思想，推导得到控制量的显式解析表达式。最后针对Shell公司的重油催化裂化分馏塔装置，进行计算机仿真，并与单变量预测函数控制效果进行比较。比较结果表明，该多变量预测函数控制算法具有较好的控制品质。
(4)通过机理分析，建立了塑料熔化过程料筒温度对象的数学模型结构，采用带遗忘因子的递推最小二乘辨识技术在线辨识模型参数。利用该模型，设计了以预测函数控制算法为核心的先进控制系统。应用结果表明，该先进控制系统比模糊控制系统具有更好的控制效果。
最后是全文的总结和展望。
Model predictive control (MPC) refers to a class of computer control algorithms. At eachcontrol interval an MPC algorithm predicts the future response of a process, and attemptsto optimize future process behavior by computing a sequence of future manipulatedvariables. Because this kind of control algorithm has taken into consideration of theindustrial requirements, the control system under MPC has good performance and strongrobustness. Predictive functional control (PFC) is a branch of the MPC family. The maindistinguishing feature of the PFC algorithm over other MPC algorithms is the constructionof the manipulated variables. Usually, the manipulated variables can be represented as asum of pre-determined basis functions, which achieves computational simplicity and goodperformance of tracking set-point without steady-state error. Some problems of predictivefunctional control are researched in this thesis, and the main research works are as follows:
(1) An overview of MPC and PFC technology is given.
(2) A multivariable predictive functional control algorithm based on a two-inputs/two-outputs system with the transfer function model is presented in this section. A simpleand explicit solution of manipulated variables of the control system can be obtained byoptimizing the objective function. The stability and robustness analysis of this kind ofmultivariable predictive functional control algorithm is given. Finally, simulations andexperiment of the system applying this control algorithm are provided, showing that thepresented algorithm is feasible.
(3) A multivariable predictive functional control algorithm, on the basis of a three-inputs/three-outputs system with the transfer function model is presented, which has beenpromoted into the n-inputs/m-outputs system. The explicit solution of manipulatedvariables is obtained by using the idea of Smith predictor. In the end, some simulationexamples are presented by using Shell Oil's heavy-oil fractionator model. The result ofcomparing with single-variable predictive functional control is shown in the simulation,which displays that this multivariable predictive functional control algorithm has goodcontrol performance.
(4) Based on the mechanism of plastic melting, the energy conservation mathematicalmodel is proposed. The parameters of this model are obtained by identification online,which ensures the robustness and disturbance rejection. An advanced control system has been established which based on the model and the predictive functional control algorithm.The good result of experiment is shown in the last part, approving the validity of thecontroller.
The last part is summary and perspective.
引文
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[5] Seki H, Ogawa M, Ooyama S, Akamatsu K, etc. Industrial application of a nonlinear model predictive control to polymerization reactors [J]. Control Engineering Practice, 2001, 9(8): 819-828.
[6] Havlena V, Findejs J. Application of model predictive control to advanced combustion control [J]. Control Engineering Practice, 2005, 13(6): 671-680.
[7] Kim Y H, Kwon W H. An application of min-max generalized predictive control to sintering processes [J]. Control Engineering Practice, 1998, 6(8): 999-1007.
[8] Shang H, Forbes J F, Guay M. Computationally efficient model predictive control for convection dominated parabolic systems [J]. Journal of Process Control, 2007, 17(4): 379-386.
[9] Kawohl M, Heine T, King R. A new approach for robust model predictive control of biological production processes [J]. Chemical Engineering Science, In Press, Corrected Proof, Available online 24 January 2007.
[10] Na M G, Upadhyaya B R. Application of model predictive control strategy based on fuzzy identification to an SP-100 space reactor [J]. Annals of Nuclear Energy, 2006, 33(17-18):1467-1478.
[11] Qin S J, Badgwell T A. A survey of industrial model predictive control technology [J]. Control Engineering Practice, 2003, 11 (7): 733-764.
[12] Shaikh N I, Prabhu V. Model predictive controller for cryogenic tunnel freezers [J]. Journal of Food Engineering, 2007, 80(2): 711-718.
[13] Sandoz D J, Desforges M J, Lennox B, Goulding P R. Algorithms for industrial model predictive control [J]. Computing & Control Engineering Journal, 2000, 11(3): 125-134.
[14] Sandoz D J, Lennox B, Goulding P R, etc.. Innovation in industrial model predictive control [J]. Computing & Control Engineering Journal, 1999, 10(5): 189-197.
[15] Nagy Z K, Mahn B, Franke R, Allgower F. Evaluation study of an efficient output feedback nonlinear model predictive control for temperature tracking in an industrial batch reactor [J]. Control Engineering Practice, 2007, 15(7): 839-850.
[16] Bleris L G, Kothare M V. Real-time implementation of model predictive control [A]. American Control Conference [C], 2005, 6: 4166-4171.
[17] 席裕庚，耿晓军，陈虹．预测控制性能研究的新进展[J]．控制理论与应用，2000，17(4)：469-475．
[18] Alpbaz M, Karacan S, Cabbar Y, Hapoglu H. Application of model predictive control and dynamic analysis to a pilot distillation column and experimental verification [J]. Chemical Engineering Journal, 2002, 88(1-3): 163-174.
[19] Rouhani R, Mehra R K. Model algorithmic control (MAC); basic theoretical properties [J]. Automatica, 1982, 18(4): 401-414.
[20] Culter C R, Ramaker B L. Dynamic matrix control-a computer control algorithm [A]. Proceedings of the American Control Conference [C], San Francisco, WP5-B, 1980.
[21] Clarke D W, Mohtadi C, Tuffs, P S. Generalized predictive control-part 1. basic algorithm [J]. Automatica, 1987, 23(2): 137-148.
[22] Clarke D W, Mohtadi C, Tuffs P S. Generalized predictive control-part 2. extensions and interpretations [J]. Automatica, 1987, 23(2): 149-160.
[23] Garcia C E, Morari M. Internal model control, 1.—a unifying review and some new results [J]. IEC Process, 1982, 21(2): 308-323.
[24] Kuntze H B, Jacubasch A, Richalet J, Arber C. On the predictive functional control of an elastic industrial robot [A]. Proc. 25th CDC [C], Athens, Greece, 1986:1877-1881
[25] Dougherty D, Cooper D. A practical multiple model adaptive strategy for multivariable model predictive control [J]. Control Engineering Practice, 2003, 11 (6): 649-664.
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