Flight Guidance Optimization via Energy State Approximation
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Solution Overview
Problem
Current Flight Management Systems (FMS) rely on simplifying assumptions to determine flight speeds and altitudes, resulting in suboptimal performance and compromised fuel savings, as they do not fully optimize all phases of flight without numerical methods.
Innovation Solution
The optimization problem is reformulated using modern numerical methods to derive a reduced-order mathematical model of vehicle motion as Differential Algebraic Equations, selecting speed as a control variable and employing optimal control to define a Hamiltonian function, which generates an optimal quasi-steady speed-energy trajectory and corresponding velocity-altitude state trajectory to minimize direct operating cost.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If simplifying assumptions are used to determine constant climb, cruise, and descent speeds, then the system implementation becomes practical and simple, but the optimization performance deteriorates and fuel savings are compromised
Solution Approach 1:
The patent transforms the optimization problem by changing the independent variable from time to energy state. This parameter transformation allows the system to avoid complex numerical methods while achieving superior optimization results. The energy state variable encapsulates multiple flight parameters (speed, altitude, weight) into a single governing variable, simplifying the control logic while improving fuel efficiency beyond traditional constant-speed approaches
Solution Approach 2:
The patent extracts and eliminates fast dynamic state variables from the mathematical model, retaining only the slow dynamic states. This model reduction technique simplifies the computational complexity while preserving the essential optimization characteristics. By separating fast and slow dynamics, the system achieves practical implementation feasibility without sacrificing optimization performance
2Manufacturing precision
If numerical methods are used to solve the optimization problem without simplifying assumptions, then the guidance accuracy improves, but the computational complexity increases
Solution Approach 1:
The patent changes the fundamental parameter used for optimization from time-based to energy-state-based. This transformation converts a complex numerical optimization problem into a more tractable form that can be solved with reduced computational effort. The energy state variable naturally incorporates the effects of multiple flight phases and constraints, eliminating the need for complex numerical methods while maintaining high guidance accuracy
Solution Approach 2:
The patent segments the flight trajectory into distinct phases (climb, cruise, descent) with different optimal energy state relationships. By dividing the continuous flight path into these segments, each with its own optimization characteristics, the system achieves high accuracy without requiring complex numerical solutions for the entire trajectory simultaneously. This segmentation allows for simpler computational approaches in each phase
3Ease of operation
If constant thrust for climb and idle thrust for descent are assumed, then the system becomes practical to implement, but the fuel efficiency deteriorates
Solution Approach 1:
The patent transitions from static thrust assumptions (constant thrust for climb, idle for descent) to dynamic thrust optimization based on energy state. The system continuously adjusts thrust levels according to the optimal energy state relationships derived for each flight phase. This dynamic approach allows thrust to vary optimally throughout the flight, improving fuel efficiency while maintaining system practicality through the simplified energy-state framework
Solution Approach 2:
The patent changes the control parameter from fixed thrust settings to energy-state-dependent thrust optimization. By using energy state as the governing variable, the system can determine optimal thrust levels for each phase without complex real-time calculations. The energy state parameter naturally captures the trade-offs between thrust, speed, and altitude, enabling improved fuel efficiency while keeping the control logic practical and implementable
Data Source
AI summary
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).