Observer design for a nonlinear heat equation: Application to semiconductor wafer processing. (November 2022)

• Record Type: Journal Article
• Authors: Schaum, Alexander; Koch, Stefan; Kleindienst, Martin; Reichhartinger, Markus; Meurer, Thomas; Moreno, Jaime A.; Horn, Martin
• Is Part Of: Journal of process control. Volume 119(2022)
• Page Start: 34
• Page End: 43
• Publication Date: 2022-11
• Subjects: Nonlinear heat equation -- Pointwise measurement injection observer -- Input-to-state stability -- Wafer processing; Process control -- Periodicals; Fabrication -- Contrôle -- Périodiques; Process control; Periodicals; Electronic journals; 660.281
• DOI: 10.1016/j.jprocont.2022.09.004
• Languages: English
• ISSNs: 0959-1524

Abstract

Abstract: In this paper, the problem of observer design for a class of 1D nonlinear heat equations with pointwise in-domain temperature measurements is addressed. A pointwise measurement injection observer is designed and the robust convergence of its estimation error in presence of bounded distributed perturbations is established by verifying input-to-state stability. The obtained convergence conditions express the underlying interplay between heat conduction and radiation and include specific dependencies on the sensor locations which are the main degrees of freedom in the design approach. The theoretical results are experimentally validated on a semiconductor wafer processing unit. Highlights: An observer for nonlinear heat equations with pointwise measurements is proposed. Input-to-state stability of the estimation error is proven by Lyapunov techniques. The observer is tested using measurements from a semiconductor processing equipment.