A major challenge in the design of high performance control systems is dealing with the effects of system nonlinearities and uncertainty. Examples of uncertainty include unmodeled dynamics, external disturbances, and parameter variations. The main methodology used to account for uncertainty integrates structured uncertainty descriptions into the system models, resulting in what are commonly referred to as uncertain systems. During the last decade, a large body of control research has been focused on uncertain system design and analysis, and a variety of techniques are now available. Unfortunately, both the modeling and design processes for uncertain systems typically result in large complicated models. Due to the complexity of these models, design and analysis can be extremely difficult and in some cases intractable. Furthermore, the modeling process itself for these uncertain systems is ill-defined; as a result there have been relatively few real engineering applications of these methods. Thus, although the uncertain systems framework and many of these associated design methods are ideally suited for a number of applications areas, very few real applications have been pursued and a noticable gap has developed between both the pace and extent of the theoretical development and the practical use of this theory on engineering problems.
One relevant but relatively unexplored application area for this theory is modeling and control of power systems. Currently, the methods used by industry for power systems control design consist mainly of system linearization around worst-case loading conditions followed by conventional linear methods for analysis and design of the control settings. These design tools rely on standard time domain and frequency domain analysis procedures, in addition to modern state-space techniques. The resulting control designs are tested for robustness over a range of operating conditions using numerous detailed time domain simulations of the nonlinear system. This approach is practical, and has for the most part served the intended purpose, however, there are no systematic procedures and no guarantee that either robust stability or performance criteria will be met using this approach. Furthermore, due to economic and environmental factors, there is an increasing need for power systems to behave robustly over a larger range of operating conditions than standard linearization techniques can accommodate. The design and analysis techniques developed over the last decade for uncertain systems provide for guaranteed robustness over varying operating conditions. Additional applications in bioengineering systems will be pursued including the development of uncertain and time-varying models for automating intravenous anesthetic delivery during surgery and for describing human postural sway and balance control.
The principle objectives of the proposed research are: (1) to develop systematic modeling and model reduction techniques for nonlinear, time-varying and parameter-varying systems which can be incorporated into the existing uncertain systems framework; (2) to utilize practical applications for this development, emphasizing power systems; (3) to develop computational tools for implementing these methods, and to apply the techniques in order to facilitate the control design process for these systems; and (4) to develop a general educational program that provides research opportunities for both graduate and undergraduate students in linear and nonlinear systems modeling and control, and which contains both applied and theoretical aspects. ***
