CAREER: Modeling and Control Methods for Complex and Uncertain Systems

9733043 BeckA高性能控制系统设计的主要挑战是处理系统的非线性和不确定性的影响。 不确定性的例子包括未建模动态、外部干扰和参数变化。 主要的方法来考虑不确定性集成结构化的不确定性描述到系统模型中，导致通常被称为不确定系统。 在过去的十年中，大量的控制研究一直集中在不确定系统的设计和分析，现在有各种各样的技术。 不幸的是，不确定系统的建模和设计过程通常会导致大型复杂的模型。 由于这些模型的复杂性，设计和分析可能非常困难，在某些情况下甚至难以处理。 此外，这些不确定系统的建模过程本身是不明确的，因此这些方法的真实的工程应用相对较少。 因此，尽管不确定系统框架和许多这些相关的设计方法理想地适合于许多应用领域，很少有真实的应用被追求，并且在理论发展的速度和程度与该理论在工程问题上的实际应用之间存在着可弥补的差距。该理论的一个相关但相对未被探索的应用领域是功率的建模和控制系统. 目前，工业界用于电力系统控制设计的方法主要包括围绕最坏情况负载条件的系统线性化，然后是用于分析和设计控制设置的传统线性方法。 这些设计工具依赖于标准的时域和频域分析程序，除了现代状态空间技术。 所得到的控制设计的鲁棒性进行了测试，在一系列的操作条件下，使用许多详细的时域模拟的非线性系统。 这种方法是实用的，并且在很大程度上达到了预期目的，但是，没有系统的程序，也不能保证使用这种方法将满足稳健的稳定性或性能标准。 此外，由于经济和环境因素，电力系统越来越需要在比标准线性化技术所能适应的更大的操作条件范围内表现出鲁棒性。 在过去的十年中，不确定系统的设计和分析技术的发展提供了保证的鲁棒性在不同的操作条件。 生物工程系统的其他应用将继续进行，包括开发不确定和随时间变化的模型，用于在手术期间自动静脉麻醉剂输送，以及描述人体姿势摇摆和平衡控制。拟议研究的主要目标是：（1）发展系统的非线性建模和模型降阶技术，时变和变参数系统，可以纳入现有的不确定系统框架：（2）利用实际应用的发展，强调电力系统;（3）开发用于实现这些方法的计算工具，并应用这些技术以促进这些系统的控制设计过程;以及（4）开发一个通用的教育计划，为研究生和本科生提供线性和非线性的研究机会系统建模和控制，并包含应用和理论方面。 ***

9733043BeckA 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. ***