Optimized Active Multidimensional Control Strategy for Nonlinear Vibration Control of Engineering Systems

振动在工业中广泛存在，大多数振动都是不需要的，因为它们可能会对工程系统产生有害影响，并显著缩短其使用寿命。特别是，非线性振动在自然界中是不可预测的，可能会产生复杂的混乱运动，这在几乎所有情况下都是不需要的。这种振动需要适当地控制或减少。然而，准确、可靠地控制这些振动仍然是研究人员和工程技术人员在实践中面临的挑战。主动振动控制方法以其自适应能力和高效性引起了研究人员和工程技术人员的兴趣。然而，大多数活跃的方法是在控制线性振动的基础上发展起来的。在现实中，可以更广泛地观察到非线性振动。尽管非线性振动的重要性很大，但在过去的几十年里，只有少数几种主动非线性振动控制方法被开发出来。此外，现有的大多数主动非线性振动控制方法只能应用于一维形式的系统。*在非线性振动控制应用研究的基础上，提出的研究方案旨在发展和进一步扩展多维非线性振动主动控制。建议的研究结合了模糊逻辑方法，以更好地减少抖振和应对不确定性。为了适应多维方法对非线性振动高效控制的要求，提出了一种优化的主动多维控制策略。此外，申请人介绍的用于诊断非线性系统特性的P-R方法将进一步发展，以适应所提出的方案的要求。此外，还将在所提出的振动控制策略的框架下对申请人开发的P-T方法进行修改，以便对多维系统进行高精度和可靠的数值模拟。为了验证和确保所提出的控制方法的适用性，还将进行带有传感器、执行器和其他电气控制装置的小悬臂梁的实验。将为工业应用建立的优化的多维主动非线性振动控制方法将大大促进当前对非线性振动的理解，为开发有效的振动控制方法和技术提供有用的工具，并为准确和有效地控制和稳定工程领域中广泛存在的非线性振动提供指导。考虑到仅在加拿大每年与振动有关的数十亿美元的损失，拟议的研究对经济的影响是相当大的。

Vibrations exist extensively in industries, and most of the vibrations are unwanted as they may have deleterious effects on engineering systems and significantly reduce their operational life. In particular, nonlinear vibrations are unpredictable in nature and may generate complex chaotic motions that are unwanted for almost all the cases. Such vibrations need to be properly controlled or reduced. However, accurate and reliable control of these vibrations is still a challenge facing researchers and engineers in practice.******Active vibration control methodologies have drawn interest from researchers and engineers for their self-adaptive feature and high efficiency. However, most active methodologies are developed on the basis of controlling linear vibrations. In reality, nonlinear vibrations are much more extensively observed. Despite the significance of nonlinear vibrations, only a handful of active nonlinear vibration control methodologies have been developed in the past decades. Furthermore, most of the existing active nonlinear vibration control methodologies can only be applied to systems expressible in a single dimensional form.******Based on the research of the applicant in nonlinear vibration control, the proposed research program aims at developing and further expanding active multidimensional nonlinear vibration control. The proposed research incorporates a fuzzy logic approach to better reduce chattering and cope with uncertainties. An Optimized Active Multidimensional Control strategy is to be developed to fit with the requirements of the multidimensional approach for nonlinear vibration control with high effectiveness. In addition, the P-R method introduced by the applicant for diagnosing the characteristics of nonlinear systems will be further developed to fit with requirements of the proposed program. Moreover, the numerical method named P-T method developed by the applicant is to be modified under the framework of the proposed vibration control strategy to carry out highly accurate and reliable numerical simulations for multidimensional systems. Experiments of a small-scale cantilever beam with sensors, actuators and other electrical control devices are also to be performed to validate and assure the applicability of the proposed control methodology.******The optimized active multidimensional nonlinear vibration control methodology to be established for industrial applications will significantly advance current understanding of nonlinear vibrations, foster useful tools for developing effective vibration control methodologies and techniques, and provide guidance for accurately and effectively controlling and stabilizing the nonlinear vibrations widely seen in engineering fields. In considering the vibration related loss of billions of dollars each year in Canada alone, the economic impact of the proposed research is substantially large.