PI gain tuning for pressure-based MFCs with Gaussian mixture model

A vast number of mass flow controllers (MFCs) are used in semiconductor industry. For the stable supply, an efficient production method of MFC is required. The gain tuning of the proportional-integral (PI) control to realize a setting flow rate is essential for efficient mass production. The gains are tuned to meet the specifications required for evaluation indices of response time and overshoot amount in a step response waveform. The tuning is complicated especially for the case of pressure-based MFCs. In this paper, we propose a simple method for the PI gain tuning using the Gaussian mixture model (GMM) and the direct inverse analysis applicable to the pressure-based MFCs' production. The relationship between the gains and evaluation indices for a standard unit of the MFC is modeled as the GMM. The direct inverse analysis calculates the difference between the standard and a test unit. Under the assumption that the difference can be compensated by a simple shift, gains likely to meet the specifications for the test unit are searched. We applied the method to seven test units. The result showed that the gains of all the test units were tuned within only a few iterations whose numbers were much less than the conventional manual tuning method, and there was no untunable unit.