Vinay Prasad

Product property and production rate control of styrene polymerization

Abstract A multivariable multi-rate nonlinear model predictive control (NMPC) strategy is applied to styrene polymerization. The NMPC algorithm incorporates a multi-rate Extended Kalman Filter (EKF) to handle state variable and parameter estimation. A fundamental model is developed for the styrene polymerization CSTR, and control of polymer properties such as number average molecular weight (NAMW) and polydispersity is considered. These properties characterize the final polymer distribution and are strong indicators of the polymer qualities of interest. Production rate control is also demonstrated. Temperature measurements are available frequently while laboratory measurements of concentration and molecular weight distribution are available infrequently with substantial time delays between sampling and analysis. Observability analysis of the augmented system provides guidelines for the design of the augmented disturbance model for use in estimation using the multi-rate EKF. The observability analysis links measurement sets and corresponding observable disturbance models, and shows that measurements of moments of the polymer distribution are essential for good estimation and control. The CSTR is operated at an open-loop unstable steady state. Control simulations are performed under conditions of plant-model structural mismatch and in the presence of parameter uncertainty and disturbances, and the proposed multi-rate NMPC algorithm is shown to provide superior performance compared to linear multi-rate and nonlinear single-rate MPC algorithms. The major contributions of this work are the development of the multi-rate estimator and the measurement design study based on the observability analysis.

Nonlinear system identification and model reduction using artificial neural networks

Abstract We present a technique for nonlinear system identification and model reduction using artificial neural networks (ANNs). The ANN is used to model plant input–output data, with the states of the model being represented by the outputs of an intermediate hidden layer of the ANN. Model reduction is achieved by applying a singular value decomposition (SVD)-based technique to the weight matrices of the ANN. The sequence of state values is used to convert the model to a form that is useful for state and parameter estimation. Examples of chemical systems (batch and continuous reactors and distillation columns) are presented to demonstrate the performance of the ANN-based system identification and model reduction technique.

A model predictive formulation for control of open-loop unstable cascade systems

Abstract Cascade control is commonly used in the operation of chemical processes to reject disturbances that have a rapid effect on a secondary measured state, before the primary measured variable is affected. In this paper, we develop a state estimation-based model predictive control approach that has the same general philosophy of cascade control (taking advantage of secondary measurements to aid disturbance rejection), with the additional advantage of the constraint handling capability of model predictive control (MPC). State estimation is achieved by using a Kalman filter and appending modeled disturbances as augmented states to the original system model. The example application is an open-loop unstable jacketed exothermic chemical reactor, where the jacket temperature is used as a secondary measurement in order to infer disturbances in jacket feed temperature and/or reactor feed flow rate. The MPC-based cascade strategy yields significantly better performance than classical cascade control when operating close to constraints on the jacket flow rate.

Modeling and simulation of atomic layer deposition at the feature scale

We present a transient Boltzmann equation based transport and reaction model for atomic layer deposition (ALD) at the feature scale. The transport model has no adjustable parameters. In this article, we focus on the reaction step and the postreaction purge steps of ALD. The heterogeneous chemistry model consists of reversible adsorption of a reactant on a single site, and irreversible reaction of a second gaseous reactant with the adsorbed reactant. We conduct studies on the effect of the kinetic rate parameter associated with the reaction. We provide results for number densities of gaseous species, fluxes to the surface of the feature, and surface coverage of the adsorbing reactant as functions of time. For reasonable reaction rate parameter values, the time scale for gas transport is much smaller than that for reaction and desorption. For these cases, an analytic expression for the time evolution of the surface coverage of the adsorbing reactant provides a good approximation to the solution obtained fro...

Predictive modeling of atomic layer deposition on the feature scale

Abstract A feature scale simulator for atomic layer deposition (ALD) is presented that combines a Boltzmann equation transport model with chemistry models. A simple but instructive chemistry is considered; one reactant species adsorbs onto the surface, and a second reactant reacts with it from the gas phase (Eley–Rideal). This work includes potential desorption of the adsorbed species during purge steps, which may or may not play a role in any given ALD system. Three sets (cases) of rate parameters are chosen to compare chemical rates with transport rates. The duration of the ALD pulses and the geometry of the representative feature are the same for each case. Simulation results are presented for all four steps in one ALD cycle, adsorption, post-adsorption purge, reaction, and post-reaction purge. The results are extended to multiple ALD cycles, and the monolayers per cycle are estimated. We highlight the potential trade-off between pulse durations and deposition rate (wafer throughput); e.g. the time penalty required to increase the amount adsorbed during the adsorption step. The simulation methodology we present can be used to determine the pulse durations that maximize throughput for a given chemistry and chemical rate parameters. One overall observation is that transport is fast relative to chemical reactions, for reasonable kinetic parameters.

A comparison of fundamental model-based and multiple model predictive control

A multiple model strategy is implemented in a model predictive control framework. The model bank design requires minimal plant knowledge based on the ranges of gains, dominant time constants and time delays. The application example is the isothermal Van de Vusse reaction in a continuous stirred tank reactor, which exhibits challenging input multiplicity behavior. Disturbances include additive input and output noises and changes in system parameters. Results are compared with an extended Kalman filter (EKF)-based model predictive controller that uses a fundamental model with a disturbance parameter estimated online. The multiple model predictive controller performance is comparable to that demonstrated by the EKF-based model predictive controller.

Nonlinear Model Predictive Control of A Styrene Polymerization Reactor

In this paper we apply a multivariable nonlinear quadratic dynamic matrix control (NL-QDMC) strategy to the control of a styrene polymerization reactor. NL-QDMC is an extension of a well-known technique for handling constrained processes based on linear models (QDMC) to nonlinear models. The NL-QDMC algorithm incorporates an Extended Kalman Filter (EKF) to handle state variable and parameter estimation; also included is an integrated white noise disturbance model. We consider (through simulations) the control of polymer properties such as number average molecular weight (NAMW) and polydispersity or branching. Temperature and volume measurements are available frequently while concentration and molecular weight distribution measurements are only available every 30 minutes with a delay of 30 minutes. There will always be both parametric and structural uncertainty in any model-based estimation and control scheme. We illustrate the effect of model structure uncertainty by using a simplified model for the control strategy, and a more complex model for the “plant” (incorporating the “gel effect”, for example).

Study of the step coverage and contact resistance by using two-step TiN barrier and evolve simulation

Device aspect ratios and dimensions at the contact and via levels for old and new technologies are driving PVD/WCVD-based metallization to its full limit at integrated circuits (ICs) fabrication sites (Wilson et al., 1993). Contact and via This work describes the work performed at ST Microelectronics regarding the TiN barrier film properties with respect to process variables. Single-step and dual-step TiN barrier processes were studied for contact and via step coverage profiles used for aluminum and tungsten plug technologies. Electrical contact resistance values were evaluated using single and dual step TiN barrier processes. EVOLVE, a topography simulation program was used to study the step coverages and deposited film profiles for single and dual steps TiN barrier processes. In this work we prove that dual step TiN barrier process is superior to single step TiN barrier process in terms of step coverage, current leakage, film stress and contact resistance values.

Modeling and simulation of plasma enhanced processing for integrated circuit fabrication

Plasma processes are used extensively in deposition and etching operations used in the fabrication of integrated circuits (ICs). Modeling and simulation studies have helped improve our understanding and process design of several plasma enhanced processes. We use three examples to show that simple chemical and transport models can help with process understanding and process development. Calibration of these simple engineering models is needed, but the approach can provide timely information for engineering level decisions. In the first example we show that simple models for plasma enhanced chemical vapor deposition (PECVD) of silicon dioxide from tetraethoxysilane (TEOS) were useful for several different process designs. Reactive ion etching (RIE) is another common IC fabrication process, and our second example shows how modeling revealed that one potential reason for aspect ratio dependent etching is the interaction between chemistry and transport. Finally, we show how modeling was used in support of process integration to help decide between two proposed process sequences involving deposition, etching and reflow processes.

Model predictive control of open-loop unstable cascade systems

In this paper we develop a novel state estimation-based model predictive control approach that has the same general philosophy of cascade control (taking advantage of secondary measurements to aid disturbance rejection). The model predictive control formulation can be applied to open-loop unstable cascade systems and has the additional advantage of being able to explicitly handle constraints. Traditional cascade control strategies are designed for open-loop stable systems, and there is no set procedure to tune cascade controllers for these systems. The example application is a jacketed exothermic chemical reactor, where jacket temperature is used as a secondary measurement in order to infer disturbances in jacket feed temperature and/or reactor feed flow rate. The MPC-based cascade strategy yields significantly better performance than classical cascade control when operating close to constraints on the jacket flow rate.