A 2D-FM model-based robust iterative learning model predictive control for batch processes

Abstract

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.