A wide variety of processes in microelectronics industries are characterized by events that take place at disparate time and length scales. Such processes, which also occur in many chemical, biological and material process systems, are modeled by multiscale systems and pose significant challenges both from analysis and control point of view [4]. These difficulties can be attributed in part to the unavailability of closed form models to describe the microscopic process evolution. One example relevant to the microelectronics industry where multiscale models would be employed is thin film deposition process. Driven by a competitive global market and reduced profit margins recent focus has been towards tighter quality control of thin films. Motivated by this, a significant amount of research has been focused on the design of feedback controllers for controlling thin film microstructure, during thin film deposition. One of the proposed approaches is to identify a closed form model based on stochastic partial differential equations [7]. This approach however assumes specific structure to the nonlinear stochastic terms. Another approach [3] directly calculates the quantities needed for design of linear or nonlinear controllers from appropriately initialized microscopic simulations. A shortcoming of this method is that it is limited to stabilization and involves closed loop eigenvalue assignment constraints. A different approach is to use the so called hybrid multiscale scheme [1,2] where continuum laws which are applicable at the macroscopic level have been combined with computationally expensive microscopic laws (Monte-Carlo (MC) / Kinetic-Monte-Carlo (KMC) or Molecular dynamics (MD)) to get the “coarse” process behavior. Using the “coarse” variables nonlinear process models are identified offline through a series of nonlinear programs. Subsequently the identified models were used to design an output feedback controller. The methodology used in this approach is computationally intensive and involves offline process identification.

The objective of the present work is to build upon the approach of [1, 2] and develop a computationally tractable online process model identification which takes into account the change in the underlying process dynamics as process traverses different regions in the variable state space. We develop a computationally tractable online system-identification scheme based on subspace-system identification (SSI) [5] to address the above mentioned problems. SSI algorithms, such as N4SID are traditionally used to identify linear systems. Recently, this algorithm was also extended for identification of bilinear systems excited by white inputs. A modification for bilinear systems excited by general inputs was also proposed [6]. We extended the applicability of SSI algorithm to identify a nonlinear process model and subsequently designed an output feedback robust controller based on the identified model. This approach updates the process model as the system evolves, to better approximate the microscopic process evolution. We illustrate the applicability of the proposed identification scheme on a KMC realization of a simplified surface reaction scheme for the dynamics of NO oxidation by H2 on Pt and Rh surfaces [3]. The system is characterized by two “coarse” stable stationary states. We designed an output feedback controller to successfully switch the process from one stationary state to the other.

REFERENCES:

[1] A Armaou, “Output feedback control of dissipative distributed process via microscopic simulations”, Computers &Chemical Engineering., 29, 771-782, 2005.

[2] A. Varshney, A Armaou, “Multiscale Optimization using hybrid PDE /KMC process systems with applications to thin film growth”, Chemical Engineering Science., 60, 6780-6794, 2005.

[3] C.I Siettos, I. G Kevrekidis, “An Equation-Free Approach to Nonlinear Control: Coarse Feedback Linearization With Pole-Placement” International Journal of Bifurcation and Chaos., 16, 2029-2041, 2006.

[4] P. D Christofides, A Armaou , “Control of Multiscale and Distributed process systems-preface,” Computers &Chemical Engineering., 29,687-688, 2005.

[5] W. Favoreel, B. D Moor and P. V. Overschee, “Subspace state space system identification for industrial processes,” Journal of Process Control., 10, 149-155, 2000.

[6] W. Favoreel, “Subspace methods for identification and control of linear and bilinear systems,” PhD thesis, Katholieke Universiteit Leuven, Belgium.

[7] Y Lou, P. D Christofides, “Nonlinear Feedback Control of Surface Roughness Using a Stochastic PDE: Design and Application to a Sputtering Process,” Industrial & Engineering Chemistry Research., 45, 7177-7189, 2006.