Thomas A. Badgwell

An Overview of Nonlinear Model Predictive Control Applications

This paper provides an overview of nonlinear model predictive control (NMPC) applications in industry, focusing primarily on recent applications reported by NMPC vendors. A brief summary of NMPC theory is presented to highlight issues pertinent to NMPC applications. Five industrial NMPC implementations are then discussed with reference to modeling, control, optimization, and implementation issues. Results from several industrial applications are presented to illustrate the benefits possible with NMPC technology. A discussion of future needs in NMPC theory and practice is provided to conclude the paper.

Modeling and control of microelectronics materials processing

Abstract Major advances in modeling and control will be required to meet future technical challenges in microelectronics manufacturing. This paper reviews the recent applications of fundamental mathematical modeling to unit operations such as crystal growth, lithography, chemical vapor deposition and plasma etching, where there have been some notable successes. Important characteristics of these processes are identified, and the evolution of the standard multiwafer reactor to single wafer reactors processing larger wafers is discussed. The implementation of closed-loop control on key unit operations in microelectronics manufacturing has been extremely limited due to a lack of suitable on-line measurements. There remains considerable promise for application of modern control and optimization techniques in manufacture of integrated circuits.

Modeling the Wafer Temperature Profile in a Multiwafer LPCVD Furnace

A mathematical model has been developed to predict wafer temperatures within a hot-wall multiwafer low pressure chemical vapor deposition (LPCVD) reactor. The model predicts both axial (wafer-to-wafer) and radial (across-wafer) temperature profiles. Model predictions compare favorably with in situ wafer temperature measurements described in an earlier paper. Measured axial and radial temperature nonuniformities are explained in terms of radiative heat-transfer effects. A simulation study demonstrates how changes in the outer tube temperature profile and reactor geometry affect wafer temperatures. Reactor design changes which could improve the wafer temperature profile are discussed.

A robust model predictive control algorithm for stable linear plants

This paper presents a new robust model predictive control (MPG) algorithm for stable, linear plants that is a direct generalization of the nominally stabilizing regulator presented by Rawlings and Muske (1993). Model uncertainty is parameterized by a list of possible plants. Robust stability is achieved through the addition of constraints that prevent the sequence of optimal controller costs from increasing for the true plant. Asymptotic stability is demonstrated through a Lyapunov argument. Simulation experiments demonstrate the performance of the algorithm for a continuous stirred tank reactor (CSTR) process.

Robust stability conditions for SISO model predictive control algorithms

Abstract This paper presents a new method for deriving robust stability conditions for single-input/single-output (SISO) model predictive control algorithms, based on an application of Jurys dominant coefficient lemma. Model uncertainty is parameterized by a range of possible plant impulse responses. The method is illustrated by deriving robust stability conditions for the extended-horizon predictive control algorithms EHPC1 and EHPC2, as well as for a prototypical model predictive controller presented originally by Garcia and Morari.

Robust control of stable linear systems with continuous uncertainty

Abstract This paper presents a robust model predictive control (MPC) algorithm for stable, linear plants described by a state-space model. Model uncertainty is parameterized by an infinite-dimensional set of possible plants. Robust stability is achieved by adding cost function constraints that prevent the sequence of optimal controller costs from increasing for the true plant. The optimal input is re-computed at each time step by solving a convex semi-infinite program. The solution is Lipschitz continuous in the state at the origin; as a result the closed loop system is exponentially stable and asymptotically decaying disturbances can be rejected. Simulation results illustrate performance of the algorithm relative to other methods when the elements of the input matrix lie in an elliptical uncertainty region.

Experimental Verification of a Fundamental Model for Multiwafer Low‐pressure Chemical Vapor Deposition of Polysilicon

A fundamental model for multiwafer low‐pressure chemical vapor deposition of polysilicon has been developed and evaluated in terms of its ability to predict experimental data from two widely differing reactors. The model can predict the main features of polysilicon deposition in a small research reactor, even though the model parameters were estimated using data taken from a much larger industrial system. It is demonstrated that the assumption of thermal variations within the reactor can greatly improve model predictions.

A Robust Model Predictive Control Algorithm for Stable Nonlinear Plants

Abstract This paper presents a Model Predictive Control (MPC) algorithm that is robustly stabilizing for a large class of stable nonlinear processes. Model uncertainty is parameterized by a list of possible plants. Robust stability is achieved through addition of constraints that prevent the controller cost function from increasing for every plant in the uncertainty description. Robust stability is proven via a Lyapunov function argument.

Modeling diamond chemical vapor deposition in a rotating disk reactor

Abstract A theoretical model for diamond chemical vapor deposition has been developed by combining mass, momentum and energy balance equations for the gas flow with detailed chemical mechanisms for the appropriate gas phase and surface chemistry. The model equations were solved numerically to determine the gas phase composition profile for representative hot filament and d.c. arc jet conditions. The model was then used to investigate the potential benefits of activating the gas phase chemically with chlorine atoms and injecting methane through the substrate. Combining the two modifications may allow growth of a porous diamond film at 1200 μm h−1, using an order of magnititude less energy per carat than a conventional d.c. arc jet reactor.

Analysis of process modifications for efficient diamond chemical vapor deposition

Abstract A theoretical model has been developed to investigate transport phenomena and chemical kinetics in a rotating disk diamond chemical vapor deposition (CVD) reactor. The model combines mass, momentum and energy balances for the gas flow with detailed gas and surface chemical kinetics for diamond formation. The model equations are solved numerically to determine gas phase composition profiles and diamond film growth rates for hot-filament and d.c. arc-jet systems. The model is then used to investigate the potential benefits of two process modifications which may increase the efficiency of diamond CVD reactors. The first involves lowering the energy requirements by dissociating hydrogen chemically with chlorine. The second involves increasing the growth rate by injecting methane through the substrate. Combining the two modifications may allow growth of a porous diamond film at 1200 μ h −1 , using an order of magnitude less energy per carat than a conventional d.c. arc-jet reactor.