Thomas F. Edgar

Efficient data reconciliation and estimation for dynamic processes using nonlinear programming techniques

Abstract Through the use of data reconciliation techniques, the level of process variable corruption due to measurement noise can be reduced and both process knowledge and control system performance can be improved. Process data from systems governed by dynamic equations are typically reconciled using the Kalman filter or the extended Kalman filter. Unfortunately, chemical engineering systems often operate dynamically in highly nonlinear regions where the extended Kalman filter may be inaccurate. In addition, the Kalman filter may not be adequate in the presence of inequality constraint Thus, a more robust means for reronciling process measurements for nonlinear dynamic systems is desirable. In this paper, a new method for nonlinear dynamic data reconciliation (NDDR) using nonlinear programming is proposed. Through the use of enhanced simultaneous optimization and solution techniques the algorithm provides a general framework within which efficient state and parameter estimation can be performed. Extensions for the treatment of biased measurements are also discussed. We demonstrate the use of NDDR and its extensions on a reactor example.

Survey Automatic control in microelectronics manufacturing: Practices, challenges, and possibilities

Advances in modeling and control will be required to meet future technical challenges in microelectronics manufacturing. The implementation of closed-loop control on key unit operations has been limited due to a dearth of suitable in situ measurements, variations in process equipment and wafer properties, limited process understanding, non-automated operational practices, and lack of trained personnel. This paper reviews the state-of-the-art for process control in semiconductor processing, and covers the key unit operations of lithography, plasma etching, thin film deposition, rapid thermal processing, and chemical-mechanical planarization. The relationship of process (equipment) models to control strategies is elaborated because recently there has been a considerable level of activity in model development in industry and academia. A proposed control framework for integrating factory control and equipment scheduling, supervisory control, feedback control, statistical process control, and fault detection/diagnosis in microelectronics manufacturing is presented and discussed.

An improved method for nonlinear model reduction using balancing of empirical gramians

Abstract Nonlinear model predictive control has become increasingly popular in the chemical process industry. Highly accurate models can now be simulated with modern dynamic simulators combined with powerful optimization algorithms. However, computational requirements grow with the complexity of the models. Many rigorous dynamic models require too much computation time to be useful for real-time model based controllers. One possible solution to this is the application of model reduction techniques. The method introduced here reduces nonlinear systems while retaining most of the input–output properties of the original system. The technique is based on empirical gramians that capture the nonlinear behavior of the system near an operating point. The gramians are then balanced and the less important states reduced via a Galerkin projection which is performed onto the remaining states. This method has the advantage that it only requires linear matrix computations while being applicable to nonlinear systems.

Nonlinear model predictive control

Abstract Nonlinear Model Predictive Control (NMPC), a strategy for constrained, feedback control of nonlinear processes, has been developed. The algorithm uses a simultaneous solution and optimization approach to determine the open-loop optimal manipulated variable trajectory at each sampling instant. Feedback is incorporated via an estimator, which uses process measurements to infer unmeasured state and disturbance values. These are used by the controller to determine the future optimal control policy. This scheme can be used to control processes described by different kinds of models, such as nonlinear ordinary differential/algebraic equations, partial differential/algebraic equations, integra-differential equations and delay equations. The advantages of the proposed NMPC scheme are demonstrated with the start-up of a non-isothermal, non-adiabatic CSTR with an irreversible, first-order reaction. The set-point corresponds to an open-loop unstable steady state. Comparisons have been made with controllers ...

Fuzzy model predictive control

A fuzzy model predictive control (FMPC) approach is introduced to design a control system for a highly nonlinear process. In this approach, a process system is described by a fuzzy convolution model that consists of a number of quasi-linear fuzzy implications. In controller design, prediction errors and control energy are minimized through a two-layered iterative optimization process. At the lower layer, optimal local control policies are identified to minimize prediction errors in each subsystem. A near optimum is then identified through coordinating the subsystems to reach an overall minimum prediction error at the upper layer. The two-layered computing scheme avoids extensive online nonlinear optimization and permits the design of a controller based on linear control theory. The efficacy of the FMPC approach is demonstrated through three examples.

Optimal control via collocation and non-linear programming

The collocation method meshed with non-linear programming techniques provides an efficient strategy for the numerical solution of optimal control problems. Good accuracy can be obtained for the state and the control trajectories as well as for the value of the objective function. In addition, the control strategy can be quite flexible in form. However, it is necessary to select the appropriate number of collocation points and number of parameters in the approximating functions with care.

Just-in-time adaptive disturbance estimation for run-to-run control of semiconductor processes

Run-to-run control is the term used for the application of discrete parts manufacturing control as practiced in the semiconductor industry. This paper presents a new algorithm for use in run-to-run control that has been designed to address some of the challenging issues unique to batch-type manufacturing. Just-in-time adaptive disturbance estimation (JADE) uses recursive weighted least squares parameter estimation to identify the contributions to variation that are dependent upon manufacturing context. The strengths and weaknesses of the JADE algorithm are demonstrated in a series of test cases developed to separate the various disturbances and processing issues a control system would be expected to encounter

Kinetic model reduction using genetic algorithms

Large reaction networks pose difficulties in simulation and control when computation time is restricted. We present a novel approach to simplification of reaction networks that formulates the model reduction problem as an optimization problem and solves it using a genetic algorithm (GA). Two formulations of kinetic model reduction and their encodings are considered, one involving the elimination of reactions and the other the elimination of species. The GA approach is applied to reduce an 18-reaction, 10-species network, and the quality of solutions returned is evaluated by comparison with global solutions found using complete enumeration. The two formulations are also solved for a 32-reaction, 18-species network.

A sequential error-in-variables method for nonlinear dynamic systems

Abstract For nonlinear dynamic systems, a sequential optimization and solution strategy for data reconciliation and parameter estimation has been investigated. Specifically, numerical integration nested within a nonlinear programming algorithm was employed within the proposed nonlinear dynamic error-in-variables method (NDEVM) for on-line and off-line parameter estimation. NDEVM provided improved estimates over conventional least-squares techniques for both on-line and off-line applications. In addition, NDEVM was able to provide reliable estimates even in the presence of measurement bias under certain conditions. Finally, the use of orthogonal collocation as an alternative solution method is discussed.

The future of open- and closed-loop insulin delivery systems

We have analysed several aspects of insulin‐dependent diabetes mellitus, including the glucose metabolic system, diabetes complications, and previous and ongoing research aimed at controlling glucose in diabetic patients. An expert review of various models and control algorithms developed for the glucose homeostasis system is presented, along with an analysis of research towards the development of a polymeric insulin infusion system. Recommendations for future directions in creating a true closed‐loop glucose control system are presented, including the development of multivariable models and control systems to more accurately describe and control the multi‐metabolite, multi‐hormonal system, as well as in‐vivo assessments of implicit closed‐loop control systems.