On Newton-type methods with cubic convergence
Journal of Computational and Applied Mathematics
Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations
Journal of Computational Physics
On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations
Journal of Computational Physics
Conjugate direction particle swarm optimization solving systems of nonlinear equations
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Helicopter trimming and tracking control using direct neural dynamic programming
IEEE Transactions on Neural Networks
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A key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim, particularly when free wake models are used. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero. An appropriate initial estimate of the trim state is needed for successful helicopter trim. This study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed. It is found that the basins of attraction can have fractal boundaries.