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US 2018/0003506 A1Published application
Methods and systems for optimal guidance based on energy state approximation
AssigneeGeneral Electric Company
InventorsReza GHAEMI, Eric Richard WESTERVELT, Mark Lawrence DARNELL
Life of this patent
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Abstract
A system, computer-readable medium, and a method to operate a vehicle in a manner that minimizes a cost to travel from an origin to a destination that includes finding the input to a flight control system that minimizes direct operating cost. The approach described herein employs an energy state approximation (ESA).
Claims18
A method for optimizing vehicle guidance to minimize direct operating cost of a prescribed mission, the method comprising:
- obtaining a mathematical model of a vehicle motion;
- eliminating fast dynamic state variables in the mathematical model;
- deriving a reduced-order mathematical model of the vehicle motion as a set of Differential Algebraic Equations that represent the slow dynamic states and includes mass as a slow state variable;
- determining quasi steady-state operating points within a flight envelope for the prescribed mission by solving the reduced-order model for thrust, drag, and fuel flow at uniform intervals of energy;
- generating a record of the quasi steady-state operating points with energy as an independent input variable and thrust, drag and fuel flow as dependent output variables;
- selecting speed as a control variable and using methods of optimal control to define a Hamiltonian function as direct operating cost per energy unit;
- at uniform intervals of energy, using a numerical method to determine the speed that minimizes the Hamiltonian function for a fixed energy per interval;
- constructing an optimal quasi-steady speed-energy trajectory based on the minimized Hamiltonian function and a corresponding velocity-altitude state trajectory derived therefrom using the reduced-order equations of motion;
- determining an optimal flight path angle to depart from the velocity-altitude state trajectory and terminate at a prescribed target cruise state;
- integrating backward from the target cruise state using an approximate weight and the previously-determined optimal flight path angle to define a departure point where the state trajectory intersects the velocity-altitude state trajectory;
- and
- generating an optimal guidance solution that includes the velocity-altitude state trajectory from a predetermined initial position to the departure point and the state trajectory from the departure point to the target cruise state, which is determined by the target cruise speed and altitude.
9 more elements
A non-transitory computer-readable medium storing processor executable instructions, the medium comprising:
- instructions to obtain a mathematical model of a vehicle motion;
- instructions to eliminate fast dynamic state variables in the mathematical model;
- instructions to derive a reduced-order mathematical model of the vehicle motion as a set of Differential Algebraic Equations that represent the slow dynamic states and includes mass as a slow state variable;
- instructions to determine quasi steady-state operating points within a flight envelope for the prescribed mission by solving the reduced-order model for thrust, drag, and fuel flow at uniform intervals of energy;
- instructions to generate a record of the quasi steady-state operating points with energy as an independent input variable and thrust, drag and fuel flow as dependent output variables;
- instructions to select speed as a control variable and using methods of optimal control to define a Hamiltonian function as direct operating cost per energy unit and;
- instructions to, at uniform intervals of energy, use a numerical method to determine the speed that minimizes the Hamiltonian function for a fixed energy per interval;
- instructions to construct an optimal quasi-steady speed-energy trajectory based on the minimized Hamiltonian function and a corresponding velocity-altitude state trajectory derived therefrom using the reduced-order equations of motion;
- instructions to determine an optimal flight path angle to depart from the velocity-altitude state trajectory and terminate at a prescribed target cruise state;
- instructions to integrate backward from the target cruise state using an approximate weight and the previously-determined optimal flight path angle to define a departure point where the state trajectory intersects the velocity-altitude state trajectory;
- and
- instructions to generate an optimal guidance solution that includes the velocity-altitude state trajectory from a predetermined initial position to the departure point and the state trajectory from the departure point to the target cruise state, which is determined by the target cruise speed and altitude.
9 more elements
Dependencies are inferred from the claim text.