Abstract: In view of the strong nonlinearity, the uncertainties of model and the existence of path constraints and terminal constraints, a multi-stage nonlinear model predictive control method is applied to the design of the batch polymerization reaction controller. The method uses a tree of discrete scenarios to represent the effect of uncertainties on the system, which means the future control input depends on the realization of the previous uncertainty, so as to form a robust closed-loop control method. In order to improve the efficiency, simultaneous method based on orthogonal collocation on finite element is used to solve the dynamic optimization problem. Selecting appropriate radau configuration points to discretize the control variables and the state variables simultaneously, the dynamic optimization problem is transformed into NLP problem, which is solved by internal point solver IPOPT. The validity of the proposed method is verified by the semi-batch reaction model provided by BASF SE.

Key words: multi-stage Nonlinear Model Predictive Control（NMPC）, Orthogonal Collocation on Finite Element（OCFE）, radau, polymerization reaction, semi-batch

摘要： 针对半间歇聚合反应强非线性，模型参数的不确定性以及过程存在路径约束和终端约束等特点，将多阶非线性模型预测控制方法应用于半间歇聚合反应控制器的设计。该方法使用离散的场景树表示不确定量对系统的影响，使得未来的控制输入取决于先前的不确定量实现，从而构成闭环的鲁棒性控制方法。为了提高求解效率，使用基于有限元正交配置的联立法对问题求解，通过选取合适的radau配置点对控制变量和状态变量同时离散化，将动态优化问题转化为NLP问题，并使用内点法求解器IPOPT求解。在BASF SE公司提供的半间歇聚合反应模型上验证了提出方法的有效性。

关键词: 多阶模型预测控制, 有限元正交配置, radau, 聚合反应, 半间歇