Research Interests

For the past 15 years, Dr. Beale's research activity has focused on robust control theory, primarily in the areas of simultaneous stabilization and reconfigurable control. Simultaneous stabilization is concerned with the problem of determining a single compensator which stabilizes each system in a finite collection of system models. The different models can represent linearizations of a nonlinear system evaluated at various operating points, perturbations to a nominal model due to failures or drifting parameter values, perturbations due to unmodeled dynamics, etc. The research has focused on determining the existence of a simultaneously stabilizing controller under various scenarios.
An application of this theory has also been applied to the design and implementation of a controller for a nonlinear process model which arises when low-loss ceramic materials are heated by microwave energy. That research, entitled "Development of Process Control for Microwave Joining of Ceramics", was funded by the National Science Foundation. A brief description of the research with several figures and the list of publications are presented for that work.
The possibility of using multiple simultaneously stabilizing compensators with reconfigurable control is currently being studied. The particular application is ship control where the various controllers are designed for different operating and/or fault conditions. Each of the controllers simultaneously stabilizes all the system models but is designed to provide specified performance for its "nominal" model. Fault detection and classification techniques are used to switch between the compensators. A simple example of two systems, each of which has its own bounded domain of stability, is given to illustrate this approach.

Fault detection and classification are crucial steps in the implementation of reconfigurable control. That work has involved the application of the Hotelling T statistic to the detection of major faults in underwater vehicles, such as stern plane and rudder jams and loss of the speed sensor. Principal Component Analysis (PCA) is used to reduce the dimensionality of the data and improve the reliability of the T statistic. Measured data are collected over blocks of time, and a summary value of the T statistic is computed at the end of each block to accomplish the detection. Two methods are being studied for fault classification, namely, Fisher Discriminant Analysis (FDA) and Quantification of Contributing Variables (QCV). Simulation results indicate that these methods are capable of providing rapid and reliable detection and classification for these types of faults.

The most recent work has focused on the development of the reconfigurable control strategy to be followed once the fault detection and classification tasks have been performed. Reconfiguration to mitigate the effects of a stern plane jam in underwater vehicles has been accomplished. The results are very good. Not only can catastrophic behavior be prevented when a stern plane jam occurs, but it has been shown that desired depth and course trajectories can be closely followed as well.

Recent Graduate Students

Recent Publications

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Latest revision on Monday, August 19, 2013 6:41 PM