Passivity Based Control and Optimization of a Silicon Process

Abstract

Abstract:In this paper we develop a Real Time Optimization (RTO) strategy for a silicon reactor. The reactor dynamics are described using parabolic partial differential equations with countercurrent liquid, gas and solid flow with chemical reaction. The model equations are converted to a system of differential algebraic equations using the method of lines and up-winding approximation for the spatial derivatives. The model parameters are matched to industrial data by minimizing a quadratic objective function using a novel interior point SQP method. The dynamic response has been verified and we have shown that passivity based inventory control can be used to stabilize the process at its optimal operating point

Passivity based control of transport reaction systems

“…Full developments are given by Ruszkowski (2003). 27 We see that the system is stable since k is positive. The main objective of the section is to look at a range of feedback control structures that can be used to control the inventory.…”

“…In this section we illustrate the application of inventory control to a TRP described by the equation 27 apply the inventory control method to more complex examples.…”

“…27 The second point ensures that all states (controlled and uncontrolled) reach a stable stationary point.…”

“…This condition fails close to maximum conversion point for component B in reaction scheme A 3 B 3 C. A further discussion is provided by Ruszkowski at al (2005). 27 There are many examples of control that at are strictly input passive.…”

“…A description of this approach and its application to finite dimensional systems with and without input constraints is given by Farschman et al (1998). 5 Ydstie and Jiao (2004) 26 applies inventory and flow control to a float glass production system and Ruszkowski et al (2005) 27 applied inventory and flow control to real-time optimization of a silicon furnace.…”