摘要
多级连续搅拌釜反应器(CSTR)系统广泛应用于化工过程,其多变量耦合和复杂的非线性动态特性给系统控制带来了挑战.为此,提出一种基于深度Koopman算子的建模方法和含三项惩罚函数的模型预测控制(MPC)方法.通过深度Koopman算子将多级CSTR系统的动力学映射到高维线性空间,并在该空间中设计含三项惩罚函数的模型预测控制算法,从而提高多级CSTR系统的控制性能.仿真结果表明,深度Koopman模型在多步预测任务中具有良好的精度,其在浓度和温度状态变量上的相对平均误差均低于0.10%.相比于传统基于扩展动态模态分解的Koopman模型预测控制算法,所提方法的均方根误差显著降低,且约束优化问题平均求解时间明显低于非线性模型预测控制算法.通过引入状态增量惩罚项,所提出的三项MPC方法有效抑制了超调量,且响应速度与两项MPC相近.
The multi-stage continuous stirred tank reactor(CSTR)system is widely used in chemical processes,yet its multivariable coupling and complex nonlinear dynamics pose significant challenges for control.To address this,a modeling approach based on the deep Koopman operator and a model predictive control(MPC)approach with a threeterm objective function are proposed.The deep Koopman operator is employed to map the dynamics of the multi-stage CSTR system into a high-dimensional linear space,within which the MPC algorithm is designed to enhance the control performance.Simulation results demonstrate that the deep Koopman model exhibits high accuracy in multi-step prediction tasks,with the relative mean error of both concentration and temperature states maintained below 0.10%.Compared with the traditional Koopman MPC based on extended dynamic mode decomposition(EDMD),the proposed method significantly reduces the root mean square error and achieves a much lower average computation time than the nonlinear MPC algorithm.Moreover,by incorporating a state increment penalty term,the proposed controller effectively suppresses overshoot while maintaining a comparable response speed to the other two MPC strategies.
作者
耿志强
辛尚华
王孟志
韩永明
GENG Zhi-qiang;XIN Shang-hua;WANG Meng-zhi;HAN Yong-ming(College of Information Science and Technology,Beijing University of Chemical Technology,Beijing 100029,China;Engineering Research Center of Intelligent PSE,Ministry of Education of China,Beijing 100029,China)
出处
《控制与决策》
2026年第3期675-684,共10页
Control and Decision
基金
国家重点研发计划项目(2024YFB4105203)
国家自然科学基金青年基金项目(62422303)
北京市自然科学基金-丰台创新联合基金重点项目(L241015)
工业控制技术全国重点实验室开放课题(ICT2024B33)
中央高校基本科研业务费专项资金项目(buctrc202418)。
