Extrapolation of optimal lifted system ILC solution, with application to a waferstage

The optimal solution from the lifted system design methods presented by Tousain (2001) has many advantages over classic iterative learning control (ILC) design methods, with one drawback: the ILC solution has to be recalculated for every trajectory of a different length. This paper shows that it is very well possible to avoid this by expressing the solution for the lifted system ILC as a finite time function of the plant parameters. This solution will be referred to as an extrapolated solution since the solution can be used for a trajectory of any length without recalculating the solution. This low order extrapolated solution has been compared to a high order lifted system optimal control (Q-)ILC solution in the application to an industrial grade wafer stage, showing the value of this extrapolated solution.