Trajectory Optimization and Guidance Law Development for National Aerospace Plane Applications

The problem of on-board trajectory optimization for an airbreathing, single-stage-to-orbit vehicle is examined. A simple model representative of the aerospace plane concept, including a dual-mode propulsion system composed of SCRAMJET and rocket engines, is presented. Consideration is restricted to hypersonic flight within the atmosphere. An energy state approximation is employed in a four-state model for flight of a point mass in a vertical plane. Trajectory constraints, including those of dynamic pressure and aerodynamic heating, are initially ignored. Singular perturbation methods are applied in solving the optimal control problem of minimum fuel climb. The resulting reduced solution for the energy state dynamics provides an optimal altitude profil1e dependent on energy level and control for rocket thrust. A boundary-layer analysis produces an approximate lift control solution in feedback form and accounts for altitude and flight path angle dynamics. The reduced solution optimal climb path is presented for the unconstrained case and the case for which a maximum dynamic pressure constraint is enforced.

[1]  Arthur E. Bryson,et al.  Energy-state approximation in performance optimization of supersonic aircraft , 1969 .

[2]  Anthony J. Calise,et al.  Optimal guidance and propulsion control for transatmospheric vehicles , 1989 .

[3]  A. Calise.  SINGULAR PERTURBATION TECHNIQUES FOR ON-LINE OPTIMAL FLIGHT PATH CONTROL* , 1981 .

[4]  J. A. Martin.  An evaluation of composite propulsion for single-stage-to-orbit vehicles designed for horizontal take-off , 1977 .

[5]  N. Rajan,et al.  Separation of time scales in aircraft trajectory optimization , 1983 .

[6]  R. Brockett.  Nonlinear systems and differential geometry , 1976, Proceedings of the IEEE.

[7]  R. Stevenson,et al.  Program to Optimize Simulated Trajectories (POST). Volume 2: Utilization manual , 1975 .

[8]  D. Jacobson,et al.  New necessary conditions of optimality for control problems with state-variable inequality constraints , 1971 .

[9]  D. B. Price,et al.  Altitude/Path-Angle Transitions in Fuel-Optimal Problems for Transport Aircraft , 1983, 1983 American Control Conference.

[10]  Mark D. Ardema,et al.  Nonlinear singularly perturbed optimal control problems with singular arcs , 1980, Autom..

[11]  J. Eric Corban.  Real-time guidance and propulsion control for single-stage-to-orbit airbreathing vehicles , 1989 .

[12]  R. L. Schultz,et al.  Aircraft performance optimization. , 1972 .

[13]  W. J. Small,et al.  Scramjet nozzle design and analysis as applied to a highly integrated hypersonic research airplane , 1974 .

[14]  Anthony J. Calise,et al.  Trajectory optimization and guidance law development for transatmospheric vehicles , 1989, Proceedings. ICCON IEEE International Conference on Control and Applications.

[15]  A. Calise.  Optimal Thrust Control with Proportional Navigation Guidance , 1980 .

[16]  Bernard Etkin,et al.  Dynamics of Atmospheric Flight , 1972 .

[17]  Eugene M. Cliff,et al.  Energy state revisited , 1986 .

[18]  R. M. Williams,et al.  National Aero-Space Plane : Technology for America's Future , 1986 .

[19]  D. Jacobson,et al.  A transformation technique for optimal control problems with a state variable inequality constraint , 1969 .

[20]  Kenneth D. Mease,et al.  Aerospace Plane Guidance using Geometric Control Theory , 1990, 1990 American Control Conference.

[21]  J. R. Thibodeau,et al.  Space Shuttle ascent guidance, navigation, and control , 1979 .

[22]  L. E. Clark,et al.  Aerodynamic characteristics at Mach 6 of a hypersonic research airplane concept having a 70 deg swept delta wing , 1977 .

[23]  T. Edelbaum,et al.  Energy climbs, energy turns, and asymptotic expansions , 1970 .

[24]  A. Calise.  A new boundary layer matching procedure for singularly perturbed system , 1978 .

[25]  Ulrich Michael Schoettle.  Performance analysis of rocket-ramjet propelled SSTO-vehicles , 1985, STOC 1985.

[26]  T. E. Bullock,et al.  State constraints and singular solutions to penalty function optimization problems. , 1972 .

[27]  John V. Breakwell,et al.  Optimal Flight-Path-Angle Transitions in Minimum-Time Airplane Climbs , 1977 .

[28]  A. Bryson,et al.  Optimal programming problems with a bounded state space. , 1968 .

[29]  L. Hunt,et al.  Global transformations of nonlinear systems , 1983 .

[30]  A. Sigalla,et al.  Aeronautical technology 2000 - A projection of advanced vehicle concepts , 1984 .

[31]  Mark D. Ardema,et al.  Interior transition layers in flight-path optimization , 1988 .

[32]  Michael J. Piehler,et al.  Guidance requirements for future launch vehicles , 1987 .

[33]  Jack L. Kerrebrock,et al.  Aircraft Engines and Gas Turbines , 1977 .

[34]  B.D.O. Anderson,et al.  Singular optimal control problems , 1975, Proceedings of the IEEE.

[35]  A. Calise.  On the use of singular perturbation methods in the solution of variational problems , 1973 .

[36]  A. Calise.  Singular perturbation methods for variational problems in aircraft flight , 1976 .

[37]  A. J. Calise,et al.  Singular perturbation techniques for real time aircraft trajectory optimization and control , 1982 .

[38]  J. A. Penland,et al.  Aerodynamic characteristics of a hypersonic research airplane concept having a 70 degree swept double delta wing at Mach numbers from 1.50 to 2.86 , 1975 .

[39]  J. Mcintyre,et al.  On Optimal Control with Bounded State Variables , 1967 .

[40]  Gene P. Menees,et al.  Aerothermodynamics of transatmospheric vehicles , 1986 .

[41]  P. Zweifel.  Advanced Mathematical Methods for Scientists and Engineers , 1980 .

[42]  Anthony J. Calise,et al.  Extended Energy Management Methods for Flight Performance Optimization , 1975 .

[43]  John W. Hardtla,et al.  An adaptive guidance algorithm for aerospace vehicles , 1985 .