Controlling Multistability in Vibro-Impact Systems: Theory and Experiment

自工业革命以来，英国一直是欧洲的工业强国之一。如今，英国的电力密集型行业面临着一个重大挑战，即如何优化其能源战略，以确保长期可持续的经济增长。工程系统提高能源效率的策略变得至关重要。本项目旨在解决一个实际问题：我们能否通过明智地切换共存状态来提高工程系统的能源效率？该研究旨在为多稳态工程系统开发一种新的控制策略，以保持其性能在一个令人满意的水平，通过实施能量最优转向。这将通过研究一种新的非光滑动力系统，即振动冲击胶囊系统，通过理论发展和实验验证来实现。该项目首次将系统的吸引域（BoA）用于控制目的，并通过利用多稳定性的积极属性来寻求最小能量解决方案。从长远来看，该项目将是实现节能控制的基础，为未来的工程系统提供安全，可靠和高效的运行。在一个为期21个月的项目中实现这一宏伟目标的方法是：（i）研究振动冲击胶囊系统及其BoA的多稳定性数值和实验;（ii）开发一种新的控制策略，用于在不同的共存吸引子之间切换;以及（iii）使用胶囊系统的实验装置实验验证所提出的控制策略。

UK has been one of the industrial powerhouses of Europe from the time of the Industrial Revolution onwards. Today, it is a major challenge for power intensive industries in the UK to optimize their energy strategy in order to ensure long-term sustainable economic growth. Strategies for engineering systems to improve their energy efficiency are to become vital. This project intends to unravel a practical question: can we improve the energy efficiency of engineering systems through judiciously switching between their coexisting states? The proposed research aims to develop a novel control strategy for multistable engineering systems in order to maintain their performance within a satisfactory level by implementing an energy-optimal steering. This will be achieved by studying a novel non-smooth dynamical system, namely the vibro-impact capsule system through both theoretical development and experimental validation. For the first time, the project aims to use the system's basins of attraction (BoA) for control purpose, and seeks the minimum energy solution by exploiting the positive attributes of multistability. In the long term, this project will be fundamental for the realization of energy efficient control, which will provide safe, reliable, and efficient operations for future engineering systems. The approach to realize this ambitious goal in a 21 month project is: (i) to study multistability in the vibro-impact capsule system and its BoA numerically and experimentally; (ii) to develop a new control strategy for switching between different coexisting attractors; and (iii) to verify the proposed control strategy experimentally using the experimental rig of the capsule system.