  Motivated by improving performance of a bi-stable vibration energy harvester
(VEH) from the viewpoint of vibration control, the time-delayed feedback
control of displacement and velocity are constructively proposed into an
electromechanical coupled VEH mounted on a rotational automobile tire, which is
subject to colored noise and the periodic excitation. Using the improved
stochastic averaging procedure based on energy-dependent frequency, the
expressions of stationary probability density (SPD) and signal-to-noise ratio
(SNR) are obtained analytically. Then, the efficiency of time-delayed feedback
control on the stationary response and stochastic resonance (SR) for the
delay-controlled VEH is explored in detail theoretically. Results show that
both noise-induced SR and delay-induced SR can occur. Time delay is able to not
only enhance the SR behavior but also weaken it. Furthermore, a larger negative
feedback gain of displacement and a larger positive feedback gain of velocity
are more beneficial for VEH. Interesting finding is that the optimal
combination of time delay in maximizing the harvested performance, such as the
harvest power, the output RMS voltage and the power conversion efficiency, is
almost perfectly consistent with that in maximizing SNR. Compared with the
uncontrolled VEH, the delay-controlled VEH can achieve certain desirable
optimization in harvesting energy by choosing the appropriate combination of
time delays and feedback gains.
