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Certain control applications require that performance variables are explicitly distinguished from measured variables. The performance variables are not available for real-time feedback. Instead, they are often available after a task. This enables the application of batch-to-batch control strategies such as Iterative Learning Control (ILC) to the performance variables. The aim of this paper is first to show that the pre-existing ILC controllers may not be directly implementable in this setting, and second to develop a new approach that enables the use of different variables for feedback and batch-to-batch control. The analysis reveals that by using pre-existing ILC methods, the ILC and feedback controllers may not be stable in an inferential setting. Therefore, the complete closed-loop system is cast in a 2D framework to analyze stability. Several solution strategies are outlined. The analysis is illustrated through an application example in a printing system. Finally, the developed theory also leads to new results for traditional ILC algorithms in the common situation where the feedback controller contains a pure integrator.

Inferential Iterative Learning Control: A 2D-system approach