The work deals with composite iterative learning model predictive control (CILMPC) for uncertain batch processes via a two dimensional Fornasini–Marchesini (2D-FM) model. A novel equivalent error system is first presented which is composed of state error and tracking error. Then an iterative learning predictive updating law is constructed by 2D state feedback control and the ‘worst’ case linear quadratic function is also designed. Besides, the update controller considering the input and output constraint will be optimized using the worst-case objective function along the infinite moving horizon. The solvable conditions that can be optimized online in real time are constructed using linear matrix inequalities (LMIs). The stability of the proposed control scheme can be achieved with the feasibility of the optimization problem. Compared with robust traditional MPC using one-dimensional models, the presented control approach can guarantee more degrees of tuning to achieve faster convergence of tracking error, which is of more significance since uncertainties exist inevitably in industrial batch processes. Finally, an injection molding process and a three-tank are introduced as two cases to demonstrate the feasibility and superiority of the proposed MPC strategy.

该工作通过二维Fornasini-Marchesini（2D-FM）模型处理不确定批次过程的复合迭代学习模型预测控制（CILMPC）。首先提出了一种新颖的等效误差系统，该系统由状态误差和跟踪误差组成。然后，通过2D状态反馈控制构造迭代学习预测更新定律，并设计“最坏”情况的线性二次函数。此外，将使用沿无限移动范围的最坏情况目标函数来优化考虑输入和输出约束的更新控制器。可使用线性矩阵不等式（LMI）构造可实时在线优化的可解条件。所提出的控制方案的稳定性可以通过优化问题的可行性来实现。与使用一维模型的鲁棒传统MPC相比，所提出的控制方法可以保证更大程度的调整，以实现跟踪误差的更快收敛，因为工业批处理过程中不可避免地存在不确定性，因此具有更重要的意义。最后，介绍了两种情况下的注塑工艺和三罐工艺，以证明所提出的MPC策略的可行性和优越性。