Delayed Feedback Control Schemes for Vibration Suppression and Energy Harvesting with Piezoelectric Resonators

Time delays in feedback control systems have intrigued researchers especially over the past five decades. Some recent studies have discovered that deliberate introduction of delays within certain control laws yields favorable results. This work follows the same philosophy and stems from a pedigree of research where delays are viewed as a tool, and their unique features are exploited. Delayed Resonators use the destabilizing effect of delays to induce resonance in an active vibration absorber, providing complete vibration suppression against time varying tonal disturbances. Inspired by these developments, this work embarks on another exploration on systems that harvest energy from mechanical vibrations. In this research, an analytical framework is developed on generic active mechanical vibration absorbers with delayed feedback control. The interplay between the generated and consumed energy is investigated from a physics viewpoint. It is shown that energy harvesting capacity can be significantly enhanced by introducing a properly designed time-delayed feedback. A critical feature in this work is the use of piezoelectric materials. Considerable research has been devoted to the use of piezoelectric components for both vibration control and energy harvesting. Piezoelectricity provides a bi-directional coupling between mechanical strain and electrical fields. This allows the use of resistive-inductive electrical circuits, which are reconfigured to serve as resonators for mechanical structures. In this work, time-delayed control laws are devised for such systems, primarily to serve two purposes: (a) effective vibration suppression and (b) increased energy harvesting. The essence of the scientific contribution lies at the point that the electrical circuit is actively sensitized to replace a conventional proof-mass absorber (or harvester). This idea could evolve into a design mechanism which has many advantages, such as compactness, reduced weight, and deployment practicality. An experimental setup, consisting of a cantilever beam with piezoelectric patches connected to a shunt circuit, is constructed to demonstrate the core concepts in this effort. Delayed proportional control is applied within the electrical circuit to test the analytical findings. As expected, many practical issues are encountered and addressed during this effort. Favorable experimental results on vibration control and energy harvesting are presented and discussed in detail.