Identifying Position-Dependent Mechanical Systems: A Modal Approach Applied to a Flexible Wafer Stage

Increasingly stringent performance requirements for motion control necessitate the use of increasingly detailed models of the system behavior. Motion systems inherently move, therefore, spatio-temporal models of the flexible dynamics are essential. In this paper, a two-step approach for the identification of the spatio-temporal behavior of mechanical systems is developed and applied to a lightweight prototype industrial wafer stage. The proposed approach exploits a modal modeling framework and combines recently developed powerful linear time invariant (LTI) identification tools with a spline-based mode-shape interpolation approach to estimate the spatial system behavior. The experimental results for the wafer stage application confirm the suitability of the proposed approach for the identification of complex position-dependent mechanical systems, and its potential for motion control performance improvements

Spatial system identification of a simply supported beam and a trapezoidal cantilever plate

Dynamic models of structural and acoustic systems are usually obtained by means of modal analysis or finite element modelling. To their detriment, both techniques rely on a comprehensive knowledge of the system's physical properties. Experimental data and a nonlinear optimization is often required to refine the model. For the purpose of control, system identification is often employed to estimate the dynamics from disturbance and command inputs to a set of outputs. Such discretization of a spatially distributed system places further unknown weightings on the control objective, in many cases, contradicting the original goal of optimal control. This paper introduces a frequency domain system identification technique aimed at obtaining spatially continuous models for a class of distributed parameter systems. The technique is demonstrated by identifying a simply supported beam and trapezoidal cantilever plate, both with bonded piezoelectric transducers. The plate's dimensions are based on the scaled front elevation of a McDonnell Douglas FA-18 vertical stabilizer