The optimal control reentry problem for

The optimal control reentry problem for unconstraint heat load is expressed as to determine the state vector and the control vector that chloride channels minimizes the cost function subject to the dynamic constraints of Eqs. (9)–(15), the initial and terminal flight path conditions given in Eq. (21) and Eq. (22), and the path constraints given by Eqs. (23) and (25). The nonlinear optimal control problem is solved using open source Gauss pseudospectral optimization software version 4.0. The program utilizes hp-adaptive Radau pseudospectral method (RPM) for solving optimal control problem. RPM is an orthogonal collocation method where the collocation points are the Legendre-Gauss-Radau points. The number of mesh intervals and the number of collocation points are determined iteratively at the end of iteration. The mesh refinement continues till a solution, which satisfies the error tolerances, is obtained [13]. The details of the hp-adaptive algorithm are given in Refs. [26, 27]. For the current research the maximum number of mesh iterations was set to 12 with 4–10 nodes between the collocation points. The error tolerance was set to 1e-3. The nonlinear programming (NLP) derivatives were computed using finite difference scheme.
Results
Conclusion The footprints of the hypersonic boost-glide missiles for the three configurations were discussed for medium range application. It has been found that the down-range performance and cross range performance of hypersonic boost-glide waverider are 33 percent higher and twice more than as compared to those of hypersonic boost-glide wing-body missile respectively. The integrated heat load experienced by the HBG waverider was found to be approximately an order of magnitude higher than that of a conventional/lifting body configuration and 5 times that of a wing-body configuration. The results further indicate that the maximum down-range for the waverider configuration is obtained corresponding to the burn-out angle of approximately 5°. The optimal burn-out angle for wing-body configuration is 14.8° within the medium range at the constraint heat rate of 4 MW/m2. The normal load factor remains within the limit.
Acknowledgments I would like to acknowledge the Chinese Scholarship Council for supporting the research.
Introduction Fusion welding of AA7075 alloy is difficult due to solidification and liquation cracking. Friction stir welding (FSW) is an energy efficient, environment-friendly solid state welding process. Because of the absence of parent metal melting and related problems, such as brittle dendrite structure, porosity, distortion and residual stresses, this process can be used for joining most of the aluminium alloys [1]. FSW of aluminium alloys offers the advantages of low heat input, reduced distortion, low residual stress and higher mechanical property compared to the conventional fusion welding methods [2]. During FSW the material is subjected to an intense plastic deformation at elevated temperatures due to the stirring action of a rotating tool [3]. Friction stir welding achieves solid phase joining by locally introducing the frictional heat and plastic flow by rotation of the welding tool with resulting local microstructure change in aluminium alloys [6]. The welding temperature in friction stir welding of AA7075 alloys ranges between 425 °C and 480 °C. The friction stir welded joint is divided into four zones: base metal (BM), heat affected zone (HAZ), thermo-mechanically affected zone (TMAZ) and nugget zone (NZ). The welding temperature never exceeds 80% of the melting point temperature of the base alloy and does not cause melting. But the temperature is high enough to cause the dissolution/overaging of strengthening particles in HAZ, TMAZ and NZ, leading to the formation of a softened region with degraded mechanical properties generally in heat affected zone [5,7]. FSW causes grain refinement in the weld zone due to which the tensile strength of the joint increases with little loss of ductility [4].