Mass measurement using relay feedback of velocity and restoring force compensation is investigated for determining the mass of an object under weightless conditions. In the measurement system, the velocity of the object is fed back through a relay with hysteresis and the force acting on the object is switched from a positive value to a negative value when the velocity reaches a positive threshold and vice versa. As a result, a limit cycle is induced in the measurement system and the mass is estimated based on the period of the limit cycle. In addition, restoring force compensation with a spring is introduced to avoid the drift of the trajectory. This compensation makes the static equilibrium state unique. However, the trajectory still drifts slightly. It causes some error in measurement when a simple formula of estimating mass is applied. To eliminate such an error, a new formula is derived to estimate the mass independently of the position of the trajectory that is determined by the switching positions in the relay actions. When the switching positions deflect from the origin at which the spring is in the natural length, the trajectory is not at the center and becomes asymmetric. It is analytically shown that the period of the limit cycle is minimum when the switching positions are at the origin. It indicates that mass is overestimated with the simple estimation formula when the trajectory is not at the center. The validity of the modified formula and the analytical results are confirmed experimentally.
A mass measurement system with a relay feedback of velocity has been developed to achieve measurement without gravity. In this system, mass is estimated from the periods of oscillation in the relay-feedback system. Originally, the velocity of the object was solely fed back, which caused the orbit of the object to drift easily. A restoring force compensation by a spring was introduced to avoid such drift. However, a slight drift still occurs in spite of the restoring force element. A new estimation formula has been derived which can estimate mass regardless of the position of the closed orbit. An analytical study on this formula shows that mass is overestimated when the restoring force is neglected in the estimation. Several experimental results show that the estimated mass is slightly larger than the actual value even though the new formula is used in estimation. In the measurement, the periods of oscillation are measured with a digital oscilloscope. A delay in the period measurement is expected to cause such overestimation. To reduce the error due to delay in measuring periods, a new device for rapid period measurement is developed, which uses the edge detecting function of a micro-computer. It is experimentally demonstrated that the measurement error is reduced by the developed measurement device.
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