Active Thermal Management for Precision Positioning

Precision positioning systems are inevitably subject to various thermal disturbances including heating from motors, friction between components, and ambient temperature fluctuations. Thermal disturbances cause unwanted thermal expansion and contraction; the resulting distortion of the components in the positioning system could lead to degraded positioning accuracy. This paper explores the application of estimation and control techniques to address thermally-induced positioning error. A simplified planar system, motivated by linear stages used in semiconductor manufacturing, is considered as a case study. The goal is to estimate the displacements of the locations of interest at the top of the stage and control their positions within an acceptable error bound from the preset target positions. A linear time-invariant model is first identified from the numerical simulation of the system model. Kalman filter is applied for state estimator design and the optimal error covariance is used to guide the temperature sensor placement. It is found that the estimator performance does not significantly improve beyond a small number of well chosen temperature sensors. For the active heating control, an offset is introduced to allow for two-way (both positive and negative) control action. The linear-quadratic-Gaussian design is used for both actuator location selection as well as closed loop active heating control. It is found that the assumed boundary condition between different portions of the stage drastically affect the controllability of the locations of interest. Locations of interest far from the constrained points are well regulated, while those near the constrained points show limited improvement.