Analysis of poles and zeros for tapered link designs
Girvin, Douglas L.
Book, Wayne John
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This chapter analyzes the pole and zero locations of a linearly-tapered Euler-Bernoulli beam pinned at one end and free at the other end. Of particular interest is the location of zeros of the transfer function from torque applied at the pin to displacement of the free end. When tapered beams are used as the links of light-weight robots, the existence of non minimum phase (right half plane) zeros complicates the robot control problem. Tapering the beam gives the robot designer an additional design parameter when establishing the flexible dynamics. The pole and zero locations are determined from a transfer matrix model which is the exact solution for a uniform beam. The approximate results for a tapered model result from segmentation of the beam into segments of different but constant cross sections. The relative position of poles and zeros varies significantly as the rate of taper changes, which will have consequences on feedback stability and noncausal effects in inverse dynamics.