Periodic Neighboring Optimum Regulator Applied to a Hypersonic Scramjet Cruiser

For a reasonable model of a hypersonic scramjet cruiser, the optimum fuel cruise trajectories are determined. Two local minimums are obtained which give nearly the same fuel consumption. One local minimum is periodic which has amplitude variations of about 25,000 feet and a mean of about 100,000 feet. The other local minimum is a static path where the maximum thrust is just equal to the aerodynamic drag. This static path seems to be unobtainable except possibly asymptotically. However, for the periodic path which is realizable, a periodic neighboring optimum regulator is derived. This regulator includes variations in the control variables of lift coefficient and thrust switch times. Furthermore, the mass change of the vehicle which is tacitly assumed negligible in producing the nominal path is included explicitly in this regulator. The performance of this regualtor due to variations both in initial conditions and mass of the vehicle is very impressive.