Enhancing Controllability and Observability in Under-Actuated/Under-Sensed Systems through Switching: Application to Vibration Control

通过切换增强欠驱动/欠传感系统的可控性和可观察性：在振动控制中的应用摘要许多动力系统采用既可以作为致动器又可以作为传感器的换能器，本研究的目的是研究这些系统中的欠驱动和欠传感，以减少控制系统的硬件。与传统方法相比，传感器被用作专用的致动器和传感器，我们建议在致动器和传感器模式之间不断切换传感器元件的功能，这样每个元件都有效地充当致动器和传感器。这提供了显著减少传感器和相关硬件数量的范围，而不会损失可控性或可观察性。我们建议开发开关、控制和传感算法以获得最佳系统性能，但由于这些算法将取决于传感器类型，因此我们将重点关注使用电容式压电传感器抑制振动的具体问题。特别是，我们将(a)确定给定结构中换能器的最佳数量和位置，其中每个换能器既用作致动器又用作传感器，但不能同时使用；(b)确定换能器分为致动器和传感器的“最佳”固定分区，知道它们的角色将随着每次切换而反转；(c)设计一个规则，根据反馈在每次切换时将换能器划分为致动器和传感器，而不是使用固定分区。(d)确定最优切换间隔，最优控制器和观测器增益，以及最优切换数量，(e)研究快速切换的可能性，目的是在不牺牲稳定性的情况下获得配置的好处，以及(f)进行实验以确定可控性和可观察性的增强，研究引入欠驱动和欠感知的优点，解决实现切换算法的挑战。并对理论结果进行验证。在执行器和传感器模式之间切换换能器的概念虽然简单，但却是新颖的，以前没有研究过。这项研究将为控制系统硬件的显著减少提供范围，尽管它是针对压电换能器提出的，但它可以扩展到其他类型的换能器，并有效地应用于许多其他动态系统，如主动磁轴承、MEMS谐振器和热电冷却装置。

Enhancing Controllability and Observability in Under-Actuated/Under-Sensed Systems through Switching: Application to Vibration ControlAbstractMany dynamical systems employ transducers that can function both as actuators and sensors and the objective of this research is to investigate under actuation and under-sensing in such systems for reduction in control system hardware. As compared to the traditional approach, where transducers are used as dedicated actuators and sensors, we propose to continuously switch the functionality of the transducer elements between actuator and sensor modes such that each element effectively serves both as an actuator and sensor. This provides the scope for significant reduction in the number of transducers and associated hardware without any loss in controllability or observability. We propose to develop switching, control, and sensing algorithms for optimal system performance, but since these algorithms will depend on the transducer type we will focus on the specific problem of vibration suppression using capacitive piezoelectric transducers. In particular, we will (a) determine the optimal number and location of transducers in a given structure, wherein each transducer is used both as an actuator and sensor, but not simultaneously, (b) determine the "best" fixed partition of the transducers into actuators and sensors, knowing that their roles will reverse with every switching, (c) design a rule for partitioning the transducers into actuators and sensors at every switching based on feedback, rather than using a fixed partition, (d) determine optimal switching intervals, optimal controller and observer gains, and optimal number of switchings, (e) investigate the possibility of fast switching with the objective of deriving the benefits of collocation without sacrificing stability, and (f) conduct experiments to ascertain enhancement of controllability and observability, investigate the merit of introducing under-actuation and under-sensing, address the challenges of implementing switching algorithms, and validate the theoretical results. The concept of switching transducers between actuator and sensor modes, although simple, is novel and has not been explored earlier. This research will provide the scope for significant reduction in control system hardware and although it is being proposed here for piezoelectric transducers, it can be extended to other transducer types and profitably applied to many other dynamical systems, such as active magnetic bearings, MEMS resonators, and thermoelectric cooling devices.