Study on the delay of velocity detection and derivation of a correction formula in mass measurement using relay feedback

Abstract

This paper treats a relay-feedback mass measurement system that uses a relay with hysteresis and feeds back the velocity of the object. The measurement system has an on-off relay with hysteresis and switches force acting on the object in relation to its velocity. Such nonlinear control induces a limit cycle. The mass of the object is determined from the period of this cycle. In previous study, the actual trajectory of the limit cycle was different in shape from the theoretical one so that the prerequisites of the estimation formula were not satisfied. The delay of the velocity sensor is a main factor of such degradation. In this paper, the effect of the delay on mass estimation is investigated experimentally and analytically. In addition, an estimating equation including this effect is derived. Experimental result supports the validity of the derived estimating equation.