Nonlinear Aircraft Trim Using A Newton-Raphson Based Whale Optimization Algorithm

Determining the trim point of an aircraft is essential for designing control law and plays a key role in analyzing flight mechanics and overall performance. This point is obtained by solving a set of nonlinear algebraic equations that define the aircraft’s steady-state conditions. Due to various nonlinearities, the trim problem, formulated as a constrained optimization problem, may not be solved or yield multiple solutions. The Newton-Raphson (NR) method, a widely used approach for solving such nonlinear equations, is highly sensitive to initial conditions and may not converge if the starting point is distant from the actual solution. To address this limitation, a hybrid method combining the NR technique with the Whale Optimization Algorithm (WOA), a modern swarm-based meta-heuristic, is proposed and tailored for aircraft trim analysis in this study. A nonlinear aircraft model of an F-16 was developed in the MATLAB/Simulink environment. The model was first trimmed using the NR method and, then, with the proposed hybrid method under different trim conditions. The results show that the hybrid algorithm successfully finds the trim point in cases where the NR method fails to converge to an accurate solution.