Multivariable iterative learning control: analysis and designs for engineering applications

Iterative Learning Control (ILC) enables high control performance through learning from measured data, using limited model knowledge, typically in the form of a nominal parametric model. Robust stability requires robustness to modeling errors, often due to deliberate undermodeling. The aim of this chapter is to outline a range of design approaches for multivariable ILC that is suited for engineering applications, with specific attention to addressing interaction using limited model knowledge. The proposed methods either address the interaction in the nominal model, or as uncertainty, i.e., through robust stability. The result is a range of techniques, including the use of the structured singular value (SSV) and Gershgorin bounds, that provide a different trade-off between modeling requirements, i.e., modeling effort and cost, and achievable performance. This allows control engineers to select the approach that fits best the modeling budget and control requirements. This trade-off is demonstrated in case studies on industrial printers. Additionally, two learning approaches are presented that are compatible with, and provide extensions to, the developed multivariable design framework: model-free iterative learning, and ILC for varying tasks.