Intermediate Control for Stable Trajectory in a Relay-Feedback Mass Measurement System

An intermediate control is introduced to mass measurement system using relay feedback of velocity to stabilize the trajectory. In the original system, the velocity of the object was fed back through a relay with hysteresis, and the mass of the object was determined by measuring the period of an induced limit cycle. It could determine the mass of the object rather accurately. However, the trajectory of the object easily drifted because only the velocity was fed back and there was no restoring force. To generate restoring force, a spring element was added. Although the drift became smaller, it still occurred. It caused the trajectory of the object to fluctuate. To eliminate such fluctuation, an intermediate control is introduced to stabilize the trajectory. The operation of the intermediate control is analyzed to prove the convergence of the trajectory.