Analysis on the effect of stiffness on mass measurement using a relay feedback of velocity

This paper treats a relay-feedback mass measurement system that uses a relay with hysteresis and feeds back the velocity of the object. The efficacy of the proposed method has been already confirmed experimentally. In actual measurement, however, a spring-like element must be added for avoiding the drift of the object. The effect of this spring on mass estimation has not been investigated analytically. In this paper, an estimating equation including this effect is derived. The derived equation indicates that the estimated mass is smaller than the actual value when the conventional estimating equation is used. The experiments carried out in the fabricated apparatus support well the validity of the derived estimating equation.