Feedback Control of Vibration Generator's Load to Maintain the Vibrating Body's Oscillation Amplitude at a Reference Value

Abstract

This paper considers the problem of controlling a vibrating body's amplitude by varying the load of the vibration generator. We propose a feedback control system for a variable load whose command is the output signal of a proportional integral (PI) controller, which is driven by the deviation between the reference value and the estimated oscillation amplitude. The amplitude is estimated by using the absolute value function and a low-pass filter (LPF). An experiment is carried out with a mass-spring-damper system, which indicates the validity of the proposed method by showing that the closed-loop system becomes stable when PI gains (K_P , K_I) are appropriately chosen. Furthermore, this paper provides a theoretical guarantee of the closed-loop stability of the proposed system by assuming second- and forth-order plant models. The stability conditions are derived using linear approximation of the nonlinear system around the equilibrium point. The validity of the stability conditions are shown by numerical simulations. The stability condition is consistent with the experimental results: the boundary line on the K_P −K_I plane has a positive slope and a positive segment K_I > 0 at K_P =0.