Asymptotic behavior of sampling zero dynamics for a 3-DOF tandem-rotor model helicopter

This paper derives an approximate discrete-time model for a nonlinear 3-DOF (degree-of-freedom) tandem-rotor model helicopter in the case of the multirate input and hold, which is accurate to some order in the sampling period. More importantly, the proposed model has more accurate than the classic Euler approximation. We also show how a particular strategy can be used to approximate the system outputs and its derivatives in such a way as to obtain a local truncation errors, between the outputs of the resulting sampled-data model and the true continuous-time system outputs, of order T⁵, where T is the sampling period. An insight interpretation of the obtained sampled-data model can be made in terms of sampling zero dynamics, and their explicit characterization are also given. Moreover, we show a condition which assures the stability of the sampling zero dynamics for the resulting model helicopter.