Volume 6 (2013) Issue 6 Pages 396-402
The transition time of a hopping machine (HM) as a piecewise linear (PWL) system is estimated by using a wavelet analysis method proposed in previous papers. The HM is a nonlinear system because its equation of motion has a nonlinear drag coefficient term owing to air resistance. The effectiveness of the proposed method for real (nonlinear) systems is verified through instrumental experiments performed on the HM. First, the effect of nonlinearity on the estimation of a transition time is examined. The HM has a discrete transition caused by the nonlinearity in a real system. In addition, two types of discrete transitions are detected from the output data: one caused by the change between discrete free-fall and spring-mass states and the other caused by inversion of the sign of the nonlinear term owing to a change in the velocity of the mass. These transition times are estimated using the proposed method. Finally, the proposed method is compared with a conventional method based on a clustering technique.