Enhancing Controllability and Observability in Underactuated and Undersensed Systems Through Switching: Application to Vibration Control

Many dynamical systems use transducers that can function both as actuators and sensors. It is possible to continuously switch the functionality of the transducer elements in such systems and effectively use each element both as an actuator and a sensor. This provides the scope for significantly reducing the number of transducer elements required for complete controllability and observability of the system and hence reduce the hardware required for controlled system operation. In this paper we advocate underactuation and undersensing in dynamical systems with the objective of reducing cost, weight, and system complexity. To this end, we first illustrate the role of switching in enhancing controllability and observability in underactuated and undersensed linear time-invariant systems and determine the switching requirement for observer-based control designs. For a proof of principle, we consider the problem of vibration suppression in a flexible beam instrumented with piezoelectric transducers. Using simulation and experiments, we demonstrate feasibility of switching the piezoelectric elements between actuator and sensor modalities and establish the merit of introducing underactuation and undersensing deliberately.