Optimal trajectory generation framework for inflight

Transcription

1 Optimal trajectory generation framework for inflight applications Rafael Fernandes de Oliveira TCC4 Autonomous Systems, Image & Signal Processing

2 Motivation the work integrates into the CLEANSKY european project, which targets significant reductions in the aviation environmental impact

3 Motivation Average Average fuel fuel burn burn for for new new jet jet aircrafts, aircraft, s seat-km 197s 198s Annual Improvement Period Seat-km T on-km 196s 2.3% 3.6% 197s.6% -.1% 198s 3.5% 2.5% 199s.7%.9% post-2.%.3% ton-km 199s post Year ICCT (29). "Efficiency Trends for New Commercial Jet Aircraft, 196 to 28." 8

4 Background MISSION PLANNING planning & Scheduling resource Allocation sequencing time scale 1 hr PATH PLANNING navigation weather avoidance collision avoidance time scale 1 min TRAJECTORY GENERATION guidance, waypoint navigation time scale 1s TRAJECTORY FOLLOWING control & stabilization time scale.1s

5 Fuel cons. vs speed [knots.kg/s] Background finding optimal trajectories is a well-known problem studied since the beginning of aviation aircraft fuel efficient trajectories can be defined in terms of optimal climb and descent profiles cruise altitude and speed modified for weather and wind conditions Mach Altitude [ft] 4 x 1 4

6 Trajectory planning using optimal control Find the controls and system dynamics that results in the best possible trajectory x t u t = f x t, u t, t while respecting all necessary constraints x lb t < x t < x ub t f x t, u t, t model

7 Flight Planning flight plan is translated into a series of intermediate actions to be fulfilled by the aircraft and a set of rules to be followed ground track take off from RWY 18 cross DF197 fly to DF16 fly to ROSIG fly to DF21 fly to DONAB fly to SOBRA flight profile take off from RWY 18 retract flaps to 1 at F speed retract flaps to at S speed climb to cruise altitude flight rules keep speed below 25 KIAS until FL1 keep speed below Mach.82 keep Mach above buffeting-onset speed keep bank angle under 35 (25 for TO/LD) vertical acceleration under 5ft/s²

8 Altitude [ft] Flight Planning the set of actions and rules is parsed into a multiple phase optimal control problem, and solved using a pseudospectral colocation method Distance [NMI]

9 Aircraft equations of motion full flight vertical plane V cos γ cos ψ φ = R + h s = V cos γ V cos γ λ = h = CR sin ψ sec φ R + h h = CR V = Thrust(Γ) Drag h, V, φ m g sin (γ) V = Thrust(Γ) Drag h, V, φ m ψ = g V Γ = Γ c φ = φ c sin (φ) cos (γ) m = FuelFlow Thrust, V, h g sin (γ) Γ = Γ C m = FuelFlow Thrust, V, h Controls: CR - vertical acceleration Γ c - throttle dot φ c - roll acceleration

10 Aircraft performance config phase C D C D2 C Lmax based on BADA 3.1 data for > 1 aircrafts clean cruise initial climb F take off approach full landing extrapolated from flight data, errors are minimized for operational region C L C D clean 1 1+F 2 full

11 Altitude [ft] Aircraft Performance x Minimum 3.5 thrust is function of altitude fuel flow is function of speed and thrust Mach

12 Cumulative distribution [%] Net Thrust [N] Aircraft Performance v2 neural networks are used to map the cloud of points into a continuously differentiable function Thrust MCR = f Mach, Alt 2.5 x mean =.35% ±.64% Net Thrust Relative Error [%] 5 1 Altitude [m] Mach.4.2

13 Altitude [ft] Altitude [ft] Aircraft Performance v2 3.5 x Minimum x Minimum Mach better representation of fuel consumption Mach

14 Optimization criteria TIME J Time t = t f FUEL J Fuel t, x, u = t f fengine x t, u t dt t NO X t f J NOX t, x, u = EINO X x t t f engine x t, u t dt CO t f J CO t, x, u = EICO x t t f engine x t, u t dt HC t f J HC t, x, u = EIHC x t t f engine x t, u t dt

15 CO [kg/s] HC [kg/s] Fuel Flow [kg/s] NOx [kg/s] Aircraft Emissions Advanced Emission Model 3 (AEM3) from EUROCONTROL AEM3 estimates the emission index, given in grams of pollutant per kilogram of burnt fuel (g/kg), corrected for atmospheric conditions and engine setting Thrust [KN] Thrust [KN] 2 FL 2 FL Thrust [KN] x Thrust [KN] 2 FL 2 FL 4 4

16 Optimization criteria NOISE on station J LAmax t, x t, u t = log 1 1 N i=1 L Amaxi 1 AWAKENINGS N J Noise t, x t, u t = Pop i.87 SEL t, x t, u t 5.5 db 1.79 i=1 from the 1997 study by the Federal Interagency Committee on Aviation Noise (FICAN) models the overall sleep disturbance related to the Indoor Sound Exposure Level (SEL)

17 Aircraft Noise Doc.29 model used to calculate SEL and L A max β l h d

18 Population Dataset 2k population grid converted into 5 clusters Gallego F.J., 21, A population density grid of the European Union, Population and Environment Page 18 October 19th 211

19 Optimization criteria regularization of the solution to avoid bang-bang control inputs and numerical noise t f J t, x t, u t = + α CR CR 2 t f t 2 f dt + α Γ Γc dt + α φ φ t t t c 2 dt

20 Altitude [ft] Results 4 x 14 fixed range: 4 NMI targets: emissions, fuel and time time fuel nox co hc Distance [NMI]

21 TAS [knots] Distance [NMI] Results time fuel nox co hc Distance [NMI] time [s] fuel [kg] NO X [kg] CO [kg] HC [kg] time , 12,3 2,62 fuel ,9 19,6 4,4 NO X ,9 24,5 5,5 CO ,2 1,8 3,72 HC ,9 11,9 2,57

22 Departure from RWY 18C at AMSTERDAM SCHIPHOL 53% reduction in awakenings and 15% higher fuel consumption Hoofddorp Amsterdam Aalsmeer Bussum Uithoorn Nieuw-Vennep Hilversum fuel awakenings

23 EDDF RWY 18 departure 558 A32 departures from RWY 18 over one year period real trajectories recorded from ADS-B tracking

24 EDDF RWY 18 departure Assumptions initial mass estimated from distance to final destination plus extra fuel and 85% PAX occupation iterative inverse dynamics calculation to estimate necessary thrust, yaw and bank angles aircraft configuration based on S and F speeds wind taken from NOTAM reports for time of departure same ground track for optimized trajectories, only optimize vertical profile and speed schedule

25 TAS [knots] Altitude [ft] EDDF RWY 18 departure 15 awakenings NOX fuel savings 11.3% 22.9% 29.4% Distance [NMI] original 25 time fuel 2 NO X awakenings Distance [NMI]

26 TAS [knots] EDDF RWY 18 departure - awakenings original time fuel NO X awakenings sleep disturbance (no. people) original 1819 time 1423 fuel 142 NOX 1286 awakenings Distance [NMI] and then cut thrust while flying over people trajectory climbs faster while far from population clusters

27 EDDF RWY 18 departure mean potential for savings awakenings 33.9% NOX 25.1% fuel 1.2% from an average of 558 flights

28 Conclusions Optimization based approaches have the potential to reduce environmental impact of flying from existing aircrafts Translation of flight problem into an OCP, to be solved using existing optimization tools and framework (GPOPS/SNOPT/WORHP): no need to build custom solver, well-studied problem, continued improvement in solvers Challenges: how to best implement the interface between Pilot/ATM and the trajectory optimization and to integrate a self-defined trajectory into the ATC scenario how to communicate changes and receive updates (the more information we have, the closer to the real optimal we can be) how to certify

29 Thanks for your attention! questions?