On integral resonant vibration control and the negative direct feedthrough term of a piezoelectric bimorph beam

Abstract

Integral resonant control (IRC) is a vibration control method that measures the displacement of a flexible structure and positively feeds back the force generated by integrating the displacement. In the case of vibration control with IRC, the DC gain and the direct feedthrough term of the transfer function of a flexible structure have important roles for modeling and analysis. In the case of a piezoelectric bimorph beam, we experimentally found that the direct feedthrough term, which should have a positive value in the conventional model, has a negative value. This paper proposes a model in which the direct term is negative, considering the electrical coupling caused by the structure of a piezoelectric bimorph beam. In addition, the stability of the control system is shown based on the negative imaginariness, and the IRC is shown to be applicable to a control object with a negative direct feedthrough term.