Aspects in inferential iterative learning control : a 2D systems analysis

Increasing performance requirements lead to a situation where performance variables need to be explicitly distinguished from measured variables. The performance variables are not available for 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 to reveal potential problems in combining ILC and feedback control for this scenario, and to propose a solution. The time-trial dynamics of a common ILC algorithm with dynamic learning filters are cast into discrete linear repetitive processes, a class of 2D systems. Appropriate 2D stability notions are connected to well-known conditions on the ILC algorithm. The analysis reveals that there are important cases where the ILC and feedback combination is not stable in a 2D sense. A solution to deal with such cases is proposed. The analysis is supported with a simulation example of medium positioning drive in a printing system.