(39e) Investigating Model Predictive Control for a Wafer Etch Temperature Control System Using Computational Fluid Dynamics Simulations

Model predictive control [1] has been extensively utilized in the process industries for decades, and in the academic literature it has typically been investigated for industrially-relevant processes using ordinary differential equations or their discrete-time equivalents. A relatively new trend in the process systems engineering literature has been exploring control of process systems using computational fluid dynamics (CFD) or finite element analysis (FEA) simulations. For example, [2] performed closed-loop simulations of a steam methane reforming reactor under proportional-integral control and under an optimization-based strategy. [3] expanded this work and used a model predictive controller considering a linear dynamic model. Recent work [4] has modulated the temperature at the wall of a 1-m version of a steam methane reforming reactor and simulated not only the impacts of the modulated input on process variables, but also on the maximum equivalent stress in the reforming tube walls. [5] has shown the impacts of run-to-run control on the performance of a plasma-enhanced chemical vapor deposition process. These works have shown the value of using CFD simulation to evaluate the performance of complex process systems under various control concepts or operating policies.

Given the successes in using CFD for control evaluation above, we evaluate another complex process with many interacting variables using CFD simulation. In this case, we focus on a temperature control system for a silicon wafer etching process, where heat is removed from two tanks and flows leaving these tanks are either diverted back to the tanks or mixed together to maintain the temperature at the inlet to a wafer etching process electrostatic chuck (ESC) at a required specification. The fluid leaving the ESC is then returned to the tanks. The manipulated inputs are valve positions for valves that return fluid to the tanks; this causes the temperatures observed throughout the system to be coupled so that designing a model predictive control algorithm for this system would be expected to be beneficial for dealing with the interactions between variables, as well as constraints such as the cooling tank heat removal rate limits. Though ordinary differential equations could be developed to describe this system, they do not permit the impacts of different control actions on the details of heat rate and flow profiles in the system to be examined. Therefore, we develop a CFD model of this full system, using several simplifications such as not explicitly modeling the valves or wafer etching process and instead incorporating their effects on the system transport profiles via user defined functions that set flow rate boundary conditions out of each diverter valve and into the next set of piping, or using an assumed rate of heat added to the cooling fluid by the outlet of the ESC.

We use the CFD simulations to develop first-order-plus-dead-time models for capturing input-output relationships throughout the system (e.g., relationships between estimated average temperatures or flow rates and the measured values, and relationships between valve positions and flow rates) and then use these to develop an ordinary differential equation model for tuning baseline proportional-integral-derivative (PID) controllers for the full system, which are then simulated in the CFD environment. Mesh and time independence tests are used to validate the transient simulation behavior and to simulate the system under the baseline control design consisting of several PID type controllers used for manipulating rates of heat removal at the cooling tanks and valve positions throughout the system. Subsequently, the first-order-plus-dead-time models are used in the design of a model predictive controller for the system. This controller is then implemented on the full CFD temperature control system, and the details of the transport profiles different under the different control strategies are compared.

References:

[1] Qin, S. J., & Badgwell, T. A. (2003). A survey of industrial model predictive control technology. Control Engineering Practice, 11, 733-764.
[2] Lao, L., Aguirre, A., Tran, A., Wu, Z., Durand, H., & Christofides, P. D. (2016). CFD modeling and control of a steam methane reforming reactor. Chemical Engineering Science, 148, 78-92.
[3] Wu, Z., Aguirre, A., Tran, A., Durand, H., Ni, D., & Christofides, P. D. (2017). Model predictive control of a steam methane reforming reactor described by a computational fluid dynamics model. Industrial & Engineering Chemistry Research, 56, 6002-6011.
[4] Nieman, K., D. Messina, M. Wegener and H. Durand, “Cybersecurity and Dynamic operation in Practice: Equipment Impacts and Safety Guarantees,” Journal of Loss Prevention in the Process Industries, submitted.
[5] Crose, M., Zhang, W., Tran, A., Orkoulas, G., & Christofides, P. D. (2018). Run-to-Run Control of Film Thickness in PECVD: Application to a Multiscale CFD Model of Amorphous Silicon Deposition. In Computer Aided Chemical Engineering (Vol. 44, pp. 511-516). Elsevier.