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

振动在工业中广泛存在，大多数振动都是不必要的，因为它们可能对工程系统产生有害影响，并显着降低其使用寿命。特别是，非线性振动在本质上是不可预测的，并且可能产生复杂的混沌运动，这在几乎所有情况下都是不希望的。这种振动需要适当地控制或减少。然而，在实践中，如何准确可靠地控制这些振动仍然是研究人员和工程师面临的挑战。******主动振动控制方法以其自适应和高效率的特点引起了研究人员和工程师的兴趣。然而，大多数主动方法都是在控制线性振动的基础上发展起来的。在现实中，非线性振动被更广泛地观察到。尽管非线性振动具有重要意义，但在过去的几十年中，只有少数主动非线性振动控制方法得到了发展。此外，大多数现有的主动非线性振动控制方法只能应用于以单维形式表示的系统。******基于申请人在非线性振动控制方面的研究，提出的研究计划旨在发展和进一步扩展主动多维非线性振动控制。本文提出的研究采用模糊逻辑方法，以更好地减少抖振和应对不确定性。为了适应非线性振动的多维控制要求，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征的P-R方法将进一步发展，以适应所提出的方案的要求。此外，申请人开发的名为P-T方法的数值方法将在提出的振动控制策略框架下进行修改，以对多维系统进行高精度和可靠的数值模拟。还将对带有传感器、致动器和其他电气控制装置的小型悬臂梁进行实验，以验证和确保所提出的控制方法的适用性。******为工业应用而建立的优化主动多维非线性振动控制方法将显著推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，并为准确有效地控制和稳定工程领域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相关的数十亿美元的损失，拟议研究的经济影响是相当大的。

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.