A hybrid 2D fault-tolerant controller design for multi-phase batch processes with time delay

Considering inevitable time delays, actuator faults and other issues in practical industrial batch processes, a two dimensional (2D) robust iterative learning fault-tolerant controller design is presented. The design consists of two parts. First, combining the state error and output error, the iterative learning control is incorporated into the established process model. Second, a switching control law is derived using switching system theory and the limited running time of batch processes. Based on the above two merits, the control law is designed using the sufficient condition that the system is robust stable where the switching control law will meet a lower bound. The advantages of the proposed method lie in the fact that time delay is incorporated in the batch direction during system modeling and traditional 1D problem has been extended to the 2D case, which provides the new idea for research on time delay systems. Moreover, it is shown that the lower bound of the switching control law is directly related to the convergence index in both time and batch directions, and a feasible design algorithm is offered in theory. Compared with the traditional 1D control that considers only the time direction, the system under the proposed 2D control law has a series of advantages such as fast convergence speed, good tracking performance and short running time. Finally, the validity of the proposed method is tested on the injection molding process in comparison with traditional 1D methods.