Design of Optimal Hybrid Controller for Multi-Phase Batch Processes With Interval Time Varying Delay

Concerning two dimensional (2D) multi-phase batch processes, a delay-range-dependent optimal hybrid iterative learning control (2D-OILC) scheme is presented. Firstly, the process is converted into a 2D-FM time delay switched system in different dimensions by introduction of state errors and system output tracking errors among batches. According to this model, hybrid iterative learning control is combined with feedback control and a 2D optimal hybrid controller is designed. Secondly, the average dwell time method is adopted to give sufficient conditions for system robust stability in terms of linear matrix inequalities and the upper bound for system's optimal performance index is provided. Besides, the issue of optimal controller design is presented to draw the minimum upper limit of the closed-loop system performance index. The presented control law not only can make the closed-loop system preserving good tracking performance but also ensures its $H_{\infty }$ performance. Last but not least, the validity of the above strategies is proved by the simulation on an injection molding process.