Designing Learning Control that is Close to Instability for Improved Parameter Identification

Iterative learning control (ILC) uses an iteration in hardware adjusting the input to a system in order to converge to zero tracking error following a desired system output. Convergence is sensitive to model error, and errors that are sufficiently large to cause divergence, produce inputs that particularly excite unmodeled or poorly modeled dynamics, producing experimental data that is focused on what is wrong with the current model. A separate paper studied the overall concept, and specifically addressed issues of model order error. The first purpose of this paper is to develop modified ILC laws that are intentionally non-robust to model errors, as a way to fine tune the use of ILC for identification purposes. And the second purpose is to study the non-robustness with respect to its ability to improve identification of system parameters when the model order is correct. It is demonstrated that in many cases the approach makes the learning particularly sensitive to relatively small parameter errors in the model, but sensitivity is sometimes limited to parameter errors of a specific sign.