FUNCTIONAL STABILITY OF THE INVERTED PENDULUM AND ITS RELATION TO UNCREWED AERIAL VEHICLE WINGS THROUGH SYSTEM MATHEMATICAL MODELING AND SIMULATION

Abstract

The flight instability of an uncrewed aerial vehicle (UAV) can be considered critical, and investigations of stability can be compared to the study of the stabilization of an inverted pendulum. This study investigated the stability of two dynamic systems, represented by an inverted pendulum and a simple approximation of an aircraft wing surface exposed to aerodynamic forces. This study illustrates the advantages of time-domain simulation for solving the differential equation of motion. The simulation used the Euler integration approach for various system parameters. Essentially, an aircraft in flight must constantly maintain pitch stability, which, in practical considerations, can be compared to the mechanism of a rotary motion represented by the up-swinging motion of an inverted pendulum. The pendulum may conserve the same concept as an aircraft’s acceleration, as both are affected by the same gravity and acceleration forces, in which the longitudinal stability of the aircraft must be ensured immediately upon takeoff. An inverted pendulum and a UAV aircraft system simulation were developed with basic MATLAB software. The inverted pendulum simulation showed that as the value of the spring’s stiffness at the limit of stability (klim) increased, the system became more convergent and, as a result, more stable. The stiffness of the spring at the limit of stability, klim = 32.69 N m-1 (i.e., equivalent to an initial angular rotation θ = 5 °), and the system’s stability were observed up to the value of klim = 179.79 N m-1, which resulted in an unstable short initial period. In addition, for the aircraft’s wing, the damping coefficient (clim) value was in the range of clim ≥ 10,000 N s m-1. Therefore, with the damping ratio ζ being equal to zero, the system vibrated consistently at its natural frequency (wn), never deviating drastically to become unstable.