Active Compensation of Position Dependent Flexible Dynamics in High-Precision Mechatronics

TL;DR

The paper addresses position-dependent flexible dynamics in high-precision mechatronics by extending rigid-body control with an output-based modal observer and a structured flexible-mode feedback. It introduces position-dependent weighting to realize a real-time modal observer and designs a CT modal feedback that actively tunes modal stiffness and damping. Experimental validation on an EUV wafer stage shows substantial resonance suppression (≈18 dB) and improved position-tracking performance across multiple axes, enabling higher closed-loop bandwidth. The approach offers a practical pathway to meet stringent lithography throughput and precision requirements in semiconductor manufacturing.

Abstract

Growing demands in the semiconductor industry necessitate increasingly stringent requirements on throughput and positioning accuracy of lithographic equipment. Meeting these demands involves employing highly aggressive motion profiles, which introduce position-dependent flexible dynamics, thus compromising achievable position tracking performance. This paper introduces a control approach enabling active compensation of position-dependent flexible dynamics by extending the conventional rigid-body control structure to include active control of flexible dynamics. To facilitate real-time implementation of the control algorithm, appropriate position-dependent weighting functions are introduced, ensuring computationally efficient execution of the proposed approach. The efficacy of the proposed control design approach is demonstrated through experiments conducted on a state-of-the-art extreme ultraviolet (EUV) wafer stage.

Figures (7)

• Figure 1: Proposed extension of the rigid-body control interconnection to allow for active regulation of position dependent flexible dynamics.
• Figure 2: Block interconnection of proposed position dependent observer implementation for the estimation of a single position dependent flexible mode, where the modal states are approximated through a weighted sum of the outputs of the set of local observers $\lbrace O_i \rbrace_{i=1}^n$.
• Figure 3: State-of-the-art EUV wafer stage system.
• Figure 4: Local FRF measurements of the equivalent mechanics$\mathcal{P}$ of the transfer in $x$-direction ($u_{\mathrm{RB}}^x \rightarrow y_{\mathrm{RB}}^x$), where the blue graph corresponds to local FRF measurements of the conventional rigid body control loop. The red graph denotes to FRF measurements for which the proposed active damping loop is closed.
• Figure 5: Five motion profiles that are considered to evaluate improvement of position tracking performance using the proposed control approach.