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，它显式地考虑了对象的动态变化，如参数值和运行条件的变化。在鲁棒控制中，被控对象的动态变化越大，可实现的鲁棒性能越差。尽管总是在设计、制造和建模阶段努力减少动力学差异，但这种差异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带来的性能限制。多重鲁棒控制方法将变差空间划分为子区域，并为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。 该方案的目标是发展多个鲁棒控制系统的优化设计方法。该方案的创新之处在于关注控制性能的最佳性。为了使本程序开发的方法具有广泛的适用性，考虑了对象动态变化的类型(时不变或时变、确定性或随机)、控制器类型(线性时不变或线性参数变化、全阶或固定结构)、性能度量(频域或时间域)以及子区域的形状(矩形或一般多面体)的各种情况。 所开发的多鲁棒控制系统的最优方法在应用中具有重要意义，例如，在要求极高的控制精度和控制速度的情况下，或在工厂运行期间对象动态变化很大的情况下。在本计划中，这些方法将应用于汽车发动机控制和风力涡轮机控制问题，以展示它们对机电系统和能源系统的影响。预计该计划的结果将对机械、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，为这些领域的控制系统提供一种改进性能的方法。

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.