Control of Nonlinear Dynamical Systems with Time-Periodic Coefficients

具有时间周期系数的非线性动力系统的控制

• 批准号: 0114571
• 负责人: Subhash Sinha
• 金额: $ 16万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-15 至 2007-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0114571&HistoricalAwards=false
• 关键词: Control; Nonlinear; Dynamical; Systems; Time

Project Abstract: Modeling of many mechanical systems leads to a set of nonlinear differential equations with periodic coefficients. The dynamics and control of these systems is a very significant issue due to its impact on reliability, capability of operating under high speeds and longevity. In most instances, the linearized equations are used to design the controllers, which by no means is an efficient or a practical solution. Further, in the case when a system has linearly uncontrollable modes then a linear controller cannot be designed and one must resort to a nonlinear controller. In this study a set of practical and efficient techniques are developed that can be applied to a wide class of control problems encountered in nonlinear systems with periodically varying parameters. The main approach is based on the application of Lyapunov-Floquet transformation and time-dependent normal form theory. For linearly uncontrollable critical cases, bifurcation control is suggested through an application of the center manifold theory. Backstepping and Lyapunov's second methods are also employed to synthesize controllers. The practical significance of this study is demonstrated through applications (via computer simulations) to some typical problems including the controller designs for an asymmetric magnetic rotor-baring system, helicopter blades and structures subjected to periodic loads. As an application to cardiac dynamics, a control system is designed to change an irregular heat beat to a desired periodic rhythm.

项目摘要：许多机械系统的建模会导致一组具有周期系数的非线性微分方程。 这些系统的动态和控制是一个非常重要的问题，因为它对可靠性，高速和寿命下运行能力的影响。 在大多数情况下，线性化方程用于设计控制器，这绝不是有效的或实用的解决方案。 此外，如果系统具有线性不可控制的模式，则无法设计线性控制器，并且必须诉诸于非线性控制器。 在这项研究中，开发了一套实用和高效的技术，可以应用于具有定期不同参数的非线性系统中遇到的广泛控制问题。 主要方法是基于Lyapunov-Floquet转换和时间依赖的正常形式理论的应用。对于线性不可控制的关键案例，通过应用中心歧管理论提出分叉控制。还采用了BackStepping和Lyapunov的第二种方法来合成控制器。 这项研究的实际意义是通过应用（通过计算机模拟）来证明了一些典型问题，包括用于不对称磁转子式托架系统的控制器设计，直升机叶片和遭受周期性载荷的结构。作为对心脏动力学的应用，控制系统旨在将不规则的热节拍更改为所需的周期性节奏。