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

通过切换提高欠驱动/欠感知系统的可控性和可观测性：在振动控制中的应用摘要许多动态系统使用既可用作执行器又可用作传感器的换能器，本研究的目的是研究此类系统中的欠驱动和欠感知，以减少控制系统硬件。与传统方法相比，传感器被用作专用的执行器和传感器，我们建议在执行器和传感器模式之间不断切换传感器元件的功能，以便每个元件有效地同时充当执行器和传感器。这为显著减少换能器和相关硬件的数量提供了空间，而不会损失任何可控性或可观测性。我们建议开发开关、控制和传感算法以优化系统性能，但由于这些算法将取决于换能器类型，因此我们将重点讨论使用电容式压电换能器抑制振动的具体问题。具体地说，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，但不是同时使用，(B)确定换能器到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颠倒，(C)设计用于在每次切换时基于反馈而不是使用固定分区将换能器划分为致动器和传感器的规则，(D)确定最佳切换间隔、最佳控制器和观测器增益、以及最佳切换次数，(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测性的增强，调查引入欠驱动和欠感知的优点，解决实施切换算法的挑战，并验证理论结果。在执行器和传感器模式之间切换传感器的概念虽然简单，但很新颖，以前还没有人探索过。这项研究将提供显著减少控制系统硬件的范围，尽管这里建议将其用于压电式换能器，但它可以扩展到其他类型的换能器，并有益地应用于许多其他动力系统，如主动磁轴承、MEMS谐振器和热电制冷设备。

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.