Optimal Design of Multiple Robust Control Systems

鲁棒控制理论是一种分析和设计反馈控制系统的工具，它明确地考虑了对象动态变化，如参数值和操作条件的变化。在鲁棒控制中，对象动态变化的大小越大，可达到的鲁棒性能就越差。尽管在设计、制造和建模阶段都在努力减少动态变化，但这种变化通常不可能完全消除。在需要高控制性能的应用中，有必要克服不可避免的动态变化所带来的性能限制。多重鲁棒控制方法将变差空间划分为若干个子区域，每个子区域分配一个鲁棒控制器，是克服现有理论局限性的一种很有前途的方法。 该计划的目标是发展多鲁棒控制系统的优化设计方法。该方案的新奇之处在于控制性能的最优性。对于广泛的适用性，在这个程序中开发的方法，各种情况下被认为是植物动态变化的类型（时不变或时变，确定性或随机），控制器的类型（线性时不变或线性参数变化，全阶或固定结构），性能指标（频域或时域），和子区域的形状（矩形或一般多面体）。 所发展的多鲁棒控制系统的优化方法具有重要的应用价值，例如，其中需要极高的控制精度和控制速度，或者其中在设备操作期间设备动态变化很大。在本计划中，该方法将被应用到汽车发动机控制和风力涡轮机控制问题，以证明其对机电和能源系统的影响。预计该计划的成果将对机械，电气，航空航天，化学和生物医学工程领域的控制应用产生重大影响，通过提供一种方法来提高这些领域的控制系统的性能。

Robust control theory is a tool to analyze and design feedback control systems by explicitly taking into account plant dynamics variations, such as changes of parameter values and operating conditions. In robust control, the larger the size of plant dynamics variations is, the worse the achievable robust performance becomes. Although efforts to reduce dynamics variations are always made in the design, manufacturing, and modeling stages, such variations are often impossible to eliminate completely. In applications that need high control performance, it is necessary to overcome the performance limitations imposed by the unavoidable dynamics variations. The multiple robust control method, which divides the variation space into subregions and assign one robust controller to each subregion, is a promising approach to overcome the limitations of existing theories. The objective of the proposed program is to develop optimal design methodologies of multiple robust control systems. The novelty of the program is the focus on the optimality of the control performance. For a wide applicability of the methods developed in this program, various situations are considered for the type of plant dynamics variations (time-invariant or time-varying, deterministic or stochastic), the type of controllers (linear time-invariant or linear parameter-varying, full-order or fixed-structure), the performance measures (frequency domain or time domain), and the shape of subregions (rectangles or general polytopes). The developed optimal methodologies of multiple robust control systems are significant in applications, e.g., where extremely high control accuracy and control speed are required, or where plant dynamics vary to a large extent during plant operations. In the present program, the methods will be applied to automotive engine control and wind turbine control problems to demonstrate their impact on mechatronic and energy systems. It is also expected that the outcome of this program will have a great impact on control applications in mechanical, electrical, aerospace, chemical, and biomedical engineering fields, by providing a way to improve performance of control systems in these fields.