James B. Rawlings Research Group

The overall objective of any process is to convert certain raw material into desired products using available resources. During its operation, the plant must satisfy serveral requirements imposed by its designers and the general technical, economic and social conditions in the presence of ever-changing external influences. Among such requirements are product specifications, operational constraints and safety and enviromnetal regulations. But the most significant incentive for using automated feedback control is the fact, that under the effect of external disturbances, the system must be operated in such a fashion, that it makes the maximum profit.

In current practice, this incentive is answered by means of the setpoint/target terminology, which is essentially the process control objective translation of the main economic objective. Translation of objectives in this fashion, results in a loss of economic information and the dynamic regulation layer has no information about the original plant economics except for a fixed steady state target.

This work aims at realizing the fact that from a process engineering point of view, the primary purpose of automatic feedback control is not to track setpoints or targets, or to nicely track the dynamic setpoint changes. The primary goal is to operate the plant such that the net return is maximized in the presence of disturbances and uncertainties, exploiting the available measurements. Almost all the literature on automatic control and controller design for chemical processes is concerned with the task to make certain controlled variables track given setpoints or setpoint trajectories while assuming closed loop stability. The work aims at reducing the loss of economic information while solving the dynamic regulation problem, in an attempt to capture higher cumulative profit that is possible with more complete information about the process economics.

More detail is presented in the slides from my prelim presentation.

Figure 1. Steady state optimization loses information about the overall process economics.

Figure 2. Projection of process economics on the state input plane.

Brett's research focuses on the practical implementation of cooperative control for chemical plants. Although there exists a rich theory for cooperative model predictive control, several factors impede its acceptance as a viable control methodology. For instance, the communication structure of cooperative control necessitates each controller receives input trajectories from all other controllers after each optimization iteration. This structure, in some circumstances, is more complex than communication necessary for centralized control. Also the cooperative control algorithm does not currently permit constraints coupled between subsystems, a class of constraints common to chemical plants. Augmenting the cooperative model prective control theory for these cases is a current area of research.

The supply chain may be defined as a system which runs from raw material procurements, through production, inventory and warehousing, distribution and delivery transportation, order fulfillment as well as customer service and demand. The supply chain, is thus, an interconnected system of nodes consisting of the manufacturing facility, the suppliers for raw material for the manufacturing facility, the warehouses and distribution centers for the finished products and the retailers who interact with the customer. Each node, interacts with the other nodes, through material (raw or finished product) flow and information (about orders and demands). These supply chains, will be highly interconnected, for companies that have multiple products, and demands for it over multiple locations.

Traditionally, the supply chain has been viewed as a individual nodes, and all interactions among the nodes as disturbances. This view of supply chains, leads to an sub-optimal performance, as the eventual aim, is to maximize the profit of the entire supply chain.

A systems-oriented approach to supply chains, is one which emphasizes the process, the operation support and the interactions as major components of the supply chain system, which needs to be optimized for better performance.

From a systems viewpoint, the supply chain is a set of nodes which interact with each other, and is driven by the customer demands for the products at one end (where these demands flow towards the manufacturer) and the production at the other end (where the finished goods flow towards the customer). These flows have to be optimized (for a performance objective like maximizing profit), subject to constraints at each node. To achieve this, the systems viewpoint can look at a centralized objective, where the whole supply chain, is considered as one big process, and the internal flows are optimized accordingly. The alternate view, is to consider each node in the chain separately, and make decisions to maximize the performance objective of that node. This is the decentralized operation. However, for most industrial supply chains, neither of the two approaches may yield optimal results. In the first case, the supply chain, may not be completely owned by the same company, and hence, a centralized model may be infeasible. In the second case, the local performance objectives for two nodes may be conflicting each other, thus driving to a sub-optimal performance. This leads to an alternative viewpoint, where each node, takes its local decisions, but information is being shared among the nodes, so that it has a global picture as well. This is the distributed or decentralized approach with information sharing viewpoint.

More recently, Control theory has been suggested as an approach to obtain optimal scheduling policy for supply chains. In this research, applicability of Model Predictive Control and the communication based MPC schemes for Supply chains will be investigated.

State Estimation and Monitoring

Identification of Nonlinear and Stochastic Models

The use of linearized models to represent a nonlinear chemical process is a common practice in process identification and control. However, these models may not accurately represent the dynamics of the real process. The objective of this research is to identify fully nonlinear, stochastic models combining first principles and process operating data. These models will be primarily used to improve the operations of nonlinear Model Predictive Controllers (MPC).

State Estimation of Nonlinear Systems

This work focuses on the critical evaluation and implementation of nonlinear state estimators to chemical processes. The studied estimators include: Moving Horizon Estimators (MHE), Particle Filters (PF), Unscented Kalman Filters (UKF) and Extended Kalman Filters (EKF).

Identifying Disturbance Models from Data

This research has two sub-topics:

Data-based covariance estimation: application of the linear (Rajamani and Rawlings, 2008) and nonlinear (Rajamani et. al., 2007) Autocovariance Least-Squares (ALS) techniques to determine noise covariances from routine operating data. These covariances are used to tune state estimators such as Kalman Filter (KF), Extended Kalman Filter (EKF) and Moving Horizon Estimators (MHE).

Data-based disturbance structure estimation: estimation of the stochastic disturbance structure that affects the states. This structure provides information about the minimum number of independent disturbances entering the data.

The examples of application and their operating data are provided by industrial partners from the TWCCC consortium.

References:

1

Murali R. Rajamani and James B. Rawlings.
Estimation of the disturbance structure from data using semidefinite programming and optimal weighting.
Accepted for publication in Automatica, January, 2008.

2

Murali R. Rajamani, James B. Rawlings, and Tyler A. Soderstrom.
Application of a new data-based covariance estimation technique to a nonlinear industrial blending drum.
Submitted for publication in IEEE Transactions on Control Systems Technology, September, 2007.

Viruses are a serious threat to human existence, causing fatal diseases like SARS and AIDS. Understanding how they reproduce and propagate would enable people to design better anti-viral therapies. During the initial phase of viral infection the number of virus particles are sufficiently small. Even during the complete infection cycle certain species always remain at small numbers. These behaviors require stochasticity in modeling approaches. Simulating a complete stochastic model for all the species during infection cycle is computationally very expensive and often intermediate species produced are not required in simulating the subsequent events. Developing analytical and computational tools that would enable us to get the levels of desired species without actually simulating the whole infection cycle is the motivation of the work.

Octave is an interactive language for numerical computing that is mostly compatible with MATLAB. Originally intended to be companion software for an undergraduate-level textbook on chemical reactor design being written by James B. Rawlings and John G. Ekerdt at the University of Texas, it has become much more than just another courseware package with limited utility beyond the classroom. It is currently in use by thousands of people at educational, commercial, and government sites worldwide.

The Octave interpreter is written in a mixture of C and C++, but most of the numerical methods are handled by standard Fortran libraries such as the BLAS, LAPACK, MINPACK, QUADPACK, ODEPACK, and DASSL. To smoothly interface with the interpreter, the numerical libraries have been packaged in a library of C++ classes.

Though Octave is compatible with MATLAB in many ways, it is not intended to be a clone. Octave adds many interesting new features and extends the language in fundamentally new ways. Because Octave is available in source form, anyone can experiment with adding new features or modifying the language.

In a relatively short period of time, Octave has become a quite capable system for solving many numerical problems, but it is still far from complete. Some long-term goals include adding a programmable graphical graphical user interface, improving the overall efficiency of the language, and automatic generation of C++ code.

Everyone is encouraged to share Octave with others under the terms of the GNU General Public License (GPL) as published by the Free Software Foundation (FSF). The complete source code for Octave and more information about this project is available on the web at www.octave.org.