Stability and Robustness Analysis of Switched Vibrational Control

Abstract

Vibrational control stabilizes an unstable nominal system by injecting high-frequency dither signals. However, high-frequency dithers consume much energy, and demand high power and high bandwidth control actuators. To alleviate the energy consumption issue, we propose to switch off the dither injection in a periodic manner - introducing a switched dither signal. By tuning the period of the switching appropriately, system stability can be guaranteed. Moreover, the closed loop system's stability properties are robust with respect to a class of additive disturbances. A simulation of an inverted pendulum system illustrates the theory, and shows that the control energy is significantly reduced wi..