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

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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.