積分制御によるvan der Pol型自励発振カンチレバー(<特集>D&D2009)

Abstract

We propose a van der Pol-type self-excited cantilever beam by positive velocity feedback and nonlinear feedback. Self-excited oscillation keeps the resonant condition independent of the modulation of system parameters and the resonance characteristic of self-excited oscillation is suitable to realize auto-resonance machines such as AFM micro-cantilever proble. Because the amplitude of self-excited oscillation grows with time, a special control method is required for the amplitude control. To this end, we propose the application of the nonlinear dynamics of van der Pol oscillator. Making use of the characteristic of a stacked-type piezoelectric actuator, we demonstrate that the amplitude control of a cantilever beam by using only integral controller without differential controller. We show the equation of motion in which the nonlinear effect is taken into account and the averaged equation which is derived by applying the method of multiple scales. The bifurcation diagram is theoretically described. Then, it is clarified that the amplitude of the cantilever beam can be controlled by setting the nonlinear feedback gain. Furthermore, a van der Pol-type self-excited cantilever beam is realized by using a simple apparatus and the validity of amplitude control method by integral control is experimentally confirmed.