Multivariable Experiment Design with Application to a Wafer Stage: a Sequential Relaxation Approach for Dealing with Element-Wise Constraints

Abstract

Optimal Experiment Design (OED) is an essential aspect in accurate Frequency Response Function (FRF) identification of complex systems. The aim of this paper is to optimally design experiments for FRF identification of multivariable motion systems subject to element-wise power constraints. This design problem involves solving a non-convex and generally NP-hard optimization problem. An algorithm to solving this problem approximately is presented based on sequential semi-definite relaxations. Experimental results on a wafer stage show an improvement of the FRF quality using the proposed techniques over traditional excitation design methods.