Optimal turning maneuvers for six-degree-of-freedom high angle-of-attack aircraft models

Abstract

<p>Various Minimum-Time Turning Maneuvers for two high angle-of-attack, six-degree-of-freedom, aircraft models have been investigated. The primary aircraft model is for a nonlinear 6-DOF F-16 fighter aircraft with high angle-of-attack maneuverability. The other model is for a linearized 6-DOF F-18 fighter which also can be flown in the high angle-of-attack range. Standard 6-DOF equations are employed except that the Quaternion attitude representation system is used instead of Euler Angles to avoid the pitch angle singularity of Euler Angles;These Optimal Control problems have been transformed into Nonlinear Programming problems via Parameter Optimization techniques. Different parameterization techniques were tested on the Van der Pol Problem and Soliman's Problem and their variations before applying them on the main turning problems. These techniques include Control Parameterization and State Parameterization (Inverse Dynamics Approach). Also, a novel Control-Integration Method is proposed to find the discontinuous control history of the possible Singular Arc Problems. Different ways to deal with various types of constraints are also discussed. In particular, when dealing with path constraints of the original optimal control problems, an Extreme-Bounds-on-Intervals method was created. However, it has not been actually developed and tested. The resulting sparse Hessian matrix from this method can speed up the calculations if a specially arranged NLP code is used;The Sequential Quadratic Programming method is primarily relied on to search for the optimum. Several different performance indices are utilized, including 3-D minimum-time-to-turn and 3-D minimum-time-to-half-loop. Several new solutions for these maneuvers are obtained. Moreover, since multiple local minima are present, several global optimization schemes have been studied. A Genetic Algorithm, Adaptive Simulated Annealing, and a Hybrid method which combines the merits of both genetic algorithms and sequential quadratic programming have been used to find the global optimum.</p>