Evanghelos Zafiriou

Robust Model Predictive Control of Processes with Hard Constraints.

Abstract A significant number of model predictive control algorithms solve on-line an appropriate optimization problem and do so at every sampling point. The major attraction of such algorithms, like the quadratic dynamic matrix control, lies in the fact that they can handle hard constraints on the inputs (manipulated variables) and outputs of a process. The presence of such constraints results in 0 an on-line optimization problem that produces a nonlinear controller, even when the plant and model dynamics are assumed linear. This paper provides a theoretical framework within which the stability and performance properties of such algorithms can be studied. Necessary and/or sufficient conditions for nominal and robust stability are derived and two simple examples are used to demonstrate their effectiveness in capturing the nonlinear characteristics of the system. These conditions are also used to analyze simulation results of a 2 × 2 subsystem of the Shell Standard Control Problem.

Use of neural networks for sensor failure detection in a control system

The use of the back-propagation neural network for sensor failure detection in process control systems is discussed. The back-propagation paradigm and traditional fault detection algorithms such as the finite integral squared-error method and the nearest-neighbor method are discussed. The algorithm is applied to the internal model control structure for a first-order linear time-invariant plant subject to high model uncertainty. Compared with traditional methods, the back-propagation technique is shown to be able to discern accurately the supercritical failures from their subcritical counterparts. The use of online adapted back-propagation fault detection systems in nonlinear plants is also investigated.<<ETX>>

Model reduction for optimization of rapid thermal chemical vapor deposition systems

A model of a three-zone rapid thermal chemical vapor deposition (RTCVD) system is developed to study the effects of spatial wafer temperature patterns on polysilicon deposition uniformity. A sequence of simulated runs is performed, varying the lamp power profiles so that different wafer temperature modes are excited. The dominant spatial wafer thermal modes are extracted via proper orthogonal decomposition and subsequently used as a set of trial functions to represent both the wafer temperature and deposition thickness. A collocation formulation of Galerkins method is used to discretize the original modeling equations, giving a low-order model which loses little of the original, high order models fidelity. We make use of the excellent predictive capabilities of the reduced model to optimize power inputs to the lamp banks to achieve a desired polysilicon deposition thickness at the end of a run with minimal deposition spatial nonuniformity. Since the results illustrate that the optimization procedure benefits from the use of the reduced-order model, our future goal is to integrate the model reduction methodology into real-time and run-to-run control algorithms. While developed in the context of optimizing a specific RTP process, the model reduction techniques presented in this paper are applicable to other materials processing systems.

On-line tuning strategy for model predictive controllers

This paper presents an intuitive on-line tuning strategy for linear Model Predictive Control (MPC) algorithms. The tuning strategy is based on the linear approximation between the closed-loop predicted output and the MPC tuning parameters. By direct utilization of the sensitivity expressions for the closed-loop response with respect to the MPC tuning parameters, new values of the tuning parameters can be found to steer the MPC feedback response inside predefined time-domain performance specifications. Hence, the algorithm is cast as a simple constrained least squares optimization problem which has a straightforward solution. The simplicity of this strategy makes it more practical for on-line implementation. Effectiveness of the proposed strategy is tested on two simulated examples. One is a linear model for a three-product distillation column and the second is a non-linear model for a CSTR. The effectiveness of the proposed tuning method is compared to an exiting offline tuning method and showed superior performance.

Output Constraint Softening for SISO Model Predictive Control

The presence of constraints in the on-line optimization problem solved by Model Predictive Control algorithms results in a nonlinear control system, even if the plant and model dynamics are linear. This is the case both for physical constraints, like saturation constraints, as well for performance or safety constraints on outputs or other variables of the process. Performance constraints can usually be softened by allowing violation if necessary. This is advisable, as hard constraints can lead to stability problems. The determination of the necessary degree of softening is usually a trial-and-error matter. This paper utilizes a theoretical framework that allows to relate hard as well as soft constraints to closed-loop stability. We focus on the special case of output constraints for single-input single-output systems and develop a non-conservative condition. This condition allows the determination of the appropriate amount of softening either numerically or via a suitable Nyquist plot.

Inverse model-based real-time control for temperature uniformity of RTCVD

A reduced-order model describing a rapid thermal chemical vapor deposition (RTCVD) process is utilized for real-time model based control for temperature uniformity across the wafer. Feedback is based on temperature measurements at selected points on the wafer surface. The feedback controller is designed using the internal model control (IMC) structure, especially modified to handle systems described by ordinary differential and algebraic equations. The IMC controller is obtained using optimal control theory on singular arcs extended for multi-input systems. Its performance is also compared with one based on the Hirschorn inverse of the model. The proposed scheme is tested with extensive simulations where the full-order model is used to emulate the process. Several cases of significant uncertainty, including model parameter errors, process disturbances, actuator errors, and measurement noise are used to test the robustness of the controller to real life situations. Both controllers succeed in achieving temperature uniformity well within the desirable bounds, even in cases where several sources of uncertainty are simultaneously present with measurement noise.

A methodology for on-line setpoint modification for batch reactor control in the presence of modeling error

Batch and semi-batch reactors are usually highly nonlinear and involve complex reaction mechanisms. Often, the lack of rapid direct or indirect measurements of the properties to be controlled makes the process control task very difficult. It is the usual practice to follow the prespecified setpoint profiles for process variables for which measurements are available, e.g., temperature, in order to obtain desired product properties. Model error can be the cause of poor performance when these setpoint profiles based on a model are implemented on the actual plant. This paper formulates a state estimation model based algorithm for on-line modification of setpoint profiles utilizing infrequent and delayed measurement information of the properties to be controlled, with the goal of obtaining the desired values of the properties in the minimum batch time. The algorithm modifies the setpoint profile for the remainder of the batch after every such measurement by making one step in the right direction instead of attempting to find a completely new optimal profile. This results in robustness with respect to model error and allows improvement even with infrequent product property measurements. The implementation of the setpoint profiles is made via real-time observer based nonlinear quadratic dynamic matrix control, which has been studied extensively in the literature. The modest additional on-line computational requirements of the proposed method offer promise for the practical on-line implementation. The effectiveness of the algorithm is demonstrated with simulations for bulk polymerization of styrene.

A stochastic model of Escherichia coli AI-2 quorum signal circuit reveals alternative synthesis pathways

Quorum sensing (QS) is an important determinant of bacterial phenotype. Many cell functions are regulated by intricate and multimodal QS signal transduction processes. The LuxS/AI‐2 QS system is highly conserved among Eubacteria and AI‐2 is reported as a ‘universal’ signal molecule. To understand the hierarchical organization of AI‐2 circuitry, a comprehensive approach incorporating stochastic simulations was developed. We investigated the synthesis, uptake, and regulation of AI‐2, developed testable hypotheses, and made several discoveries: (1) the mRNA transcript and protein levels of AI‐2 synthases, Pfs and LuxS, do not contribute to the dramatically increased level of AI‐2 found when cells are grown in the presence of glucose; (2) a concomitant increase in metabolic flux through this synthesis pathway in the presence of glucose only partially accounts for this difference. We predict that ‘high‐flux’ alternative pathways or additional biological steps are involved in AI‐2 synthesis; and (3) experimental results validate this hypothesis. This work demonstrates the utility of linking cell physiology with systems‐based stochastic models that can be assembled de novo with partial knowledge of biochemical pathways.

An approach to run-to-run control for rapid thermal processing

This paper introduces a new approach to run-to-run (RtR) control for semiconductor manufacturing processes. It is based on a technique developed for batch-to-batch operating profile modification for batch chemical processes. It is particularly appropriate for rapid thermal processing (RTP) reactors, where the recipe includes a function of time and the optimization requires the use of dynamic models. Our technique modifies the profile between runs directly, without requiring re-modeling or the adaptation of model parameters. This is accomplished by combining the existing model with process measurement information and obtaining a direction of improvement by utilizing the similarity between iterations in numerical optimization and runs in RtR control. The example that is used to illustrate the method is motivated by an overheating problem that was observed experimentally and reported in the literature. A very simple set of model and plant equations are used to emulate the model-plant mismatch.

Optimization-based Tuning of Nonlinear Model Predictive Control with State Estimation

Abstract Nonlinear model predictive controllers determine appropriate control actions by solving an on-line optimization problem. A nonlinear process model is utilized for on-line prediction, making such algorithms particularly appropriate for the control of chemical reactors. The algorithms presented in this paper incorporates an extended Kalman filter, which allows operations around unstable steady-state points. The paper proposes a formalization of the procedure for tuning the several parameters of the control algorithm. This is accomplished by specifying time-domain performance criteria and using an interactive multi-objective optimization package off-line to determine parameters values that satisfy these criteria. Three reactor examples are used to demonstrate the effectiveness of the proposed on-line algorithm and off-line tuning procedure.