Iterative Learning Control for waferstage positioning based on orthogonal projection

In this paper, design and analysis of Iterative Learning Control (ILC) based on partial information from previous cycles is developed. Typically, in a discrete-time repetitive process, ILC schemes use error from the entire previous cycle for updating the control input in the current cycle. Partial information of error from the previous cycle can be modeled as a projection onto a lower dimensional subspace. By appropriate choice of the subspace, noise and other non- repetitive disturbances in the error can be suppressed, leading to cleaner learning signals. In particular, two aspects of the orthogonal projection-based ILC schemes are investigated. First, conditions on stability of the projection-based ILC scheme are developed. Second, given a stable ILC scheme which uses the full error vector, the possible choices of projection subspaces is discussed. Implementation of the projection-based ILC scheme in precision positioning of a waferstage is presented. The major sources of repetitive error in precision tracking are phase- mismatch and force ripple. These effects are mathematically modeled and the subspace spanned by them is obtained from initial experimentation. A standard P-type ILC scheme based on the proposed projection method is then used in control of a prototype one DOF waferstage to effectively reject the error caused by these disturbances, thereby verifying the effectiveness of the proposed projection ILC scheme.