Optimal control of coning motion of spinning missiles

Coning motion has been detected in flight experiments of many spinning projectiles for decades and the stability analysis of this motion has been extensively studied recently. In this paper, a novel optimal control algorithm based on stability analyses is developed to suppress the coning motion. A Lagrangian functional is built to compute the optimal control that minimizes the coning motion for a given control cost. Then a linearized approach, which produces accurate enough control within the range of parameters considered, is proposed to reduce the computational cost. It is analytically presented that the optimal solution of this linearized optimization is unique at any given values of control cost. The analytical analysis also indicates that there exists a direct solution of the control that approaches the linearized optimal control when the control cost is small enough and that this direct solution can be obtained much more efficiently than the linearized optimal control. The controllability problem associated with this optimal control algorithm is also discussed and the results shed lights on the choice of numerical parameters in the optimization. These optimal control algorithms are implemented to calculate the optimal control that minimizes the coning motion induced by initial disturbances to a wrap-around-fin missile.