On the inherent stabilization of a bio-inspired mono-wing rotorcraft

Abstract

The intricate concept of inherent stabilization of a mono-wing aerial vehicle, as a Nonlinear Time-Periodic (NLTP) system is investigated in this research. Stability analysis has been performed based on the dynamic characteristics of the system by using the most appropriate approaches, including Floquet theory, averaging theory, and kinetic energy integration. To achieve stable flight performance, specifying the admissible range of the aerodynamic coefficients and system parameters has been proposed. Using Floquet analysis, the system has initially been linearized around the periodic orbit that was found by numerical techniques. The stability condition of the linear model has been studied by evaluating the eigenvalues of the Monodromy matrix. Instability of the orbit has also been determined owing to the eigenvalues-greater-than-one rule. In averaging approach, time averaging is conducted over the fast time scale, transforming the NLTP system into the Nonlinear Time-Invariant (NLTI) one. Here, the new system is linearized around the trim condition, where two natural modes have been identified. The stable mode indicates coupling between the components of the linear and angular velocities, and the unstable mode appears due to the coupling of the yaw angle, the downward velocity, and the yaw rate. Furthermore, the cause of undesirable dynamic behavior has been investigated using kinetic energy time-history data. The proposed mono-wing exhibits instability with initial design condition that necessitates optimization of aerodynamic coefficients and geometric and inertia parameters. It is shown that the inherent stability of such NLTP system can be significantly improved by careful alteration of these parameters to achieve an optimal design.