Performance analysis of active dynamic vibration absorber controlled by homogeneous control Lyapunov functions

Active dynamic vibration absorbers are widely known as vibration control device exhibiting good performance for disturbance signal with various frequencies. Linear quadratic (LQ) control is often used in active dynamic vibration absorbers. We show that nonlinear control laws provide vibration control performance higher than the LQ controller by designing homogeneous control Lyapunov function (CLF) controllers guaranteed convergence rates and high robustness. In this paper, we design homogeneous exponential stabilization controllers based on Riccati solutions of LQ controllers and finite-time stabilization controllers for vibration control device using fixed surface and confirm that designing convergence rates are quite effective for vibration control performance. Moreover, the effectiveness of our controllers is verified by the analysis of transient and steady-state frequency responses for hybrid dynamic vibration absorbers with numerical simulation.