Process adjustment with an asymmetric quality loss function

Controlling an engineering process usually focuses on maintaining the process output on-target with minimum variation. Conventionally, the quality loss incurred by the deviation from the nominal values is assumed symmetric. However, in some engineering processes, the penalties incurred by positive and negative deviations of the quality variables are different. In such cases, we need to redesign the controller so that the overall quality loss is minimized. In this work, motivated by a real ingot growing process, a new controller is proposed for an asymmetric quality loss function. Its performance and stability are studied via numerical simulation. The effectiveness of the method is also demonstrated in the real engineering process.