Average dwell time-based optimal iterative learning control for multi-phase batch processes

• The multi-phase batch process with different dimensions is considered and designed as a switching system.
• The exponential stability of switching system and its shortest running time are studied.
• Using the average dwell time method, the exponential stability condition of the system is obtained, and the minimum running time is calculated.

Multi-phase batch process plays an important role in modern industry, especially for processes with different dimensional phases. As the different phases may interact with each others deeply, when and how to perform the transfer between adjacent phases highly affect the control performance and product quality. Meanwhile, the running time in different phases influence the production efficiency. Therefore it is of crucial importance to study the control of multi-phase batch processes with time constraints. Take the injection molding process as an example, a multi-phase batch process can be regarded as a switched system with different-dimensional subsystems in each batch. In this paper, the multi-phase batch process is converted to an equivalent two-dimensional (2D) switched system and the repetitive and 2D nature of batch processes is explored. Within the framework of 2D system theory, both the exponential stability and the shortest running time are considered. Meanwhile, a compound 2D controller with optimal performance is designed. The contributions of this paper are as follows: (1) the batch process studied is with different dimensions in each phase. (2) using the average dwell time method, a sufficient condition ensuring the exponential stability is obtained, meanwhile, the minimum running time of each subsystem, i.e., the running time of each phase can be calculated. Finally, the proposed method is illustrated with an injection molding process to show the effectiveness.