Frequency domain identification for multivariable motion control systems: Applied to a prototype wafer stage

Multivariable parametric models are essential for optimizing the performance of high-tech systems. The main objective of this paper is to develop an identification strategy that provides accurate parametric models for complex multivariable systems. To achieve this, an additive model structure is adopted, offering advantages over traditional black-box model structures when considering physical systems. The introduced method minimizes a weighted least-squares criterion and uses a refined instrumental variable method to solve the estimation problem, achieving local optimality upon convergence. Experimental validation is conducted on a prototype wafer-stage system, featuring a large number of spatially distributed actuators and sensors and exhibiting complex flexible dynamic behavior, to demonstrate the effectiveness of the proposed method.