Constraint Boundary Effect in Model Predictive Control and Corresponding Solution
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摘要: 约束预测控制(Constrained model predictive control,CMPC)中,因约束的存在,优化过程中最优控制作用可能会在可行域的边界取值,也就是说会 有一个或多个变量饱和,即约束边界效应. 而过程控制中操纵变量饱和是我们不希望出现的. 对此,首先基于稳态模型,对期望值位于可行域内时最优解必在期望值处达到给出证明;同时证明了期望值在可行域外时最优解可转化为期望值到可行域的投影. 其次,针对变量在动态及稳态过程中饱和的情况提出了改善控制性能的措施——调整目标函数;终端约束的加入,为预测控制系统稳定性提供了保障. 通过对包含约束的连续搅拌釜式反应器(Continuous stirred tank reactor,CSTR)系统进行仿真实验,验证了所提方法的正确性,并说明了对目标函数进行适当调整,可有效改善系统的控制性能.Abstract: In constrained predictive control, the optimal control sequence may reach the boundary of the feasible domain during optimization due to the existence of constraints, in other words, one or more variables will be saturated, which is the constraint boundary effect. However, it is undesirable that the manipulated variables get saturated in process control. Therefore, firstly based on a steady-state model, it is proved that the optimal solution will reach the desired value when it is in the feasible domain; it is shown that the optimal solution can be viewed as the projection of the desired value onto the feasible region when the desired value is outside of the feasible region. Secondly, to avoid the saturation of variables when the system is in a transient or steady state, the parameters of the objective function are altered and the control performance is improved. The terminal constraint is imposed to guarantee the stability. Finally, the simulation of a constrained continuous stirred tank reactor (CSTR) model verifies the correctness of the proposed method and the effectiveness of adjustment of objective function.
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[1] Yang Ma-Ying, Yu Li, Zhang Mei-Yu, Chen Guo-Ding. Feasibility and stability in constrained predictive control. Journal of Zhejiang University of Technology, 1999, 27(3): 187-194(杨马英, 俞立, 张美玉, 陈国定. 约束预测控制的可行解与稳定性. 浙江工业大学学报, 1999, 27(3): 187-194) [2] Wang Juan, Xu Guo-Kai, Du Hai-Ying, Liu Zhi-Yuan. Chaotic synchronization of tracking control scheme by the moving horizon H∞. Journal of Dalian Nationalities University, 2012, 14(1): 24-27 (王娟, 徐国凯, 杜海英, 刘志远. 用滚动时域H∞跟踪控制实现的混沌同步化. 大连民族学院学报, 2012, 14(1): 24-27) [3] Feher J D, Erickson K T. Solving the model predictive control problem with soft constraints. In: Proceedings of the 1993 American Control Conference. San Francisco, USA: IEEE, 1993. 377-378 [4] Zheng A, Morari M. Stability of model predictive control with mixed constraints. IEEE Transactions on Automatic Control, 1995, 40(10): 1818-1823 [5] Keerthi S S, Gilbert E G. Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations. Journal of Optimization Theory and Applications, 1988, 57(2): 265-293 [6] Zhang Xi-Ling, Wang Shu-Bin, Luo Xiong-Lin. Feasibility analysis and constraints adjustment of constrained optimal control in chemical process. CIESC Journal, 2011, 62(9): 2546-2554(张惜岭, 王书斌, 罗雄麟. 化工过程约束优化控制的可行性分析及约束处理. 化工学报, 2011, 62(9): 2546-2554) [7] Luo Xiong-Lin, Zhou Xiao-Long, Wang Shu-Bin. Analysis of constrained optimal control with related constraints of input variables. Acta Automatica Sinica, 2013, 39(5): 679-689 (罗雄麟, 周晓龙, 王书斌. 输入变量关联约束对约束优化控制的影响特性分析. 自动化学报, 2013, 39(5): 679-689) [8] Rao C V, Rawlings J B. Steady states and constraints in model predictive control. AIChE Journal, 1999, 45(6): 1266-1278 [9] Wang Bai-Ping, Li Shao-Yuan, Zou Tao. Steady-state objective optimization in model predictive control and its application. Systems Engineering and Electronics, 2009, 31(6): 1429-1431(王柏萍, 李少远, 邹涛. 预测控制中的稳态目标优化策略及其应用. 系统工程与电子技术, 2009, 31(6): 1429-1431) [10] Zou Tao, Wei Feng, Zhang Xiao-Hui. Strategy of centralized optimization and decentralized control for two-layered predictive control in large-scale industrial systems. Acta Automatica Sinica, 2013, 39(8): 1366-1373 (邹涛, 魏峰, 张小辉. 工业大系统双层结构预测控制的集中优化与分散控制策略. 自动化学报, 2013, 39(8): 1366-1373) [11] Zou Tao, Li Hai-Qiang, Ding Bao-Cang, Wang Ding-Ding. Compatibility and uniqueness analyses of steady state solution for multi-variable predictive control systems. Acta Automatica Sinica, 2013, 39(5): 519-529 (邹涛, 李海强, 丁宝苍, 王丁丁. 多变量预测控制系统稳态解的相容性与唯一性分析. 自动化学报, 2013, 39(5): 519-529) [12] Tang Huan-Wen, Qin Xue-Zhi. Practical Methods of Optimization. Dalian: Dalian University of Technology Press, 2004. 153-157(唐焕文, 秦学志. 实用最优化方法. 大连: 大连理工大学出版社, 2004. 153-157) [13] Boyd S, Vandenberghe L. Convex Optimization. Cambridge: Cambridge University Press, 2004 [14] Mayne D Q, Rawlings J B, Rao C V, Scokaert P O M. Constrained model predictive control: stability and optimality. Automatica, 2000, 36(6): 789-814 [15] Zhang Qun-Liang, Xi Yu-Geng. New MPC controller based on a terminal convex set constraint. Control and Decision, 2006, 21(6): 631-635 (张群亮, 席裕庚. 基于终端凸集约束的新MPC控制器. 控制与决策, 2006, 21(6): 631-635) [16] Xi Yu-Geng, Li De-Wei. Fundamental philosophy and status of qualitative synthesis of model predictive control. Acta Automatica Sinica, 2008, 34(10): 1225-1234 (席裕庚, 李德伟. 预测控制定性综合理论的基本思路和研究现状. 自动化学报, 2008, 34(10): 1225-1234) [17] Zhang Zhi-Sheng, Chen Huai-Min, Wu Cheng-Fu, Ma Song-Hui. Design and software realization of the predictive control synthesis strategy. Flight Dynamics, 2011, 29(4): 60-64 (张治生, 陈怀民, 吴成富, 马松辉. 预测控制综合设计算法设计及软件实现. 飞行力学, 2011, 29(4): 60-64) [18] Li Zhi-Jun. Research on Stability and Robustness of Constrained Model Predictive Control [Ph.D. dissertation], North China Electric Power University, China, 2005 (李志军. 约束模型预测控制的稳定性与鲁棒性研究 [博士学位论文], 华北电力大学, 中国, 2005) [19] Wan Z Y, Kothare M V. An efficient off-line formulation of robust model predictive control using linear matrix inequalities. Automatica, 2003, 39(5): 837-846
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