Optimal sensor configuring techniques for the compensation of thermo-elastic deformations in high-precision systems

The time dependent thermal behaviour of precision systems and processes in relation to positioning accuracy is an important aspect and often claims a large part of the available position budged. This problem can be dealt with using real-time error-compensation method that combines measured temperatures with knowledge of thermo-elastic properties of the precision system. The thermally induced time varying deformations are calculated real-time by the error compensation model based on measured temperatures. The gained performance depends on the uncertainty of the thermo-mechanical model, the configuration of the temperature sensors and uncertainties in the temperature measurements. In the paper a method is introduced that enables optimization of the sensor configuration and accompanying compensation model based on the modal reduction technique. This method can be used in cases where only little pre-knowledge of heat-loads are available and enables a more optimal sensor placement, thus improving the performance of the error-compensation method.