Sliding-Mode Boundary Control of an In-Line Heating System Governed by Coupled PDE/ODE Dynamics

This present article addresses the feedback control design problem of in-line liquid flow heating units used to process silicon wafers in the semiconductor industry. A physics-based model is developed to describe the thermal behavior of the heater and the liquid circulating in it. Under sensible approximations, process dynamics are shown to be governed by a coupled partial differential equation (PDE)/ordinary differential equation (ODE) system. A boundary control law capable of steering the fluid temperature to the desired set-point value while rejecting matched disturbances is developed. The proposed boundary control is sliding-mode-based and makes use of boundary measurements only. The convergence properties of the closed-loop system are formally demonstrated by means of Lyapunov-based analysis. In addition, the input-to-state stability (ISS) properties of the closed-loop system with respect to nonmatching boundary disturbances are investigated. To corroborate the theoretical findings, this article additionally presents the experimental results with the proposed controller implemented in the closed loop on a real in-line heating unit.