Minimizing conflict quantity with speed control

1. Minimizing conflict quantity withspeed control S. Constans, B. Fontaine, R. Fondacci LICIT (Traffic Engineering Lab.) INRETS / ENTPE, FRANCE 4th EEC Innovative Research Workshop Brétigny sur Orge, December 6-8, 2005

2. Objective • Face the continuous increase in air traffic, preserve safety • Ease traffic flow • Lighten the controllers’ workload • Re-organize the traffic • Reduce the number of potential conflicts to be solved by the controllers • Dynamically act on the traffic with a real-time procedure 4th EEC Innovative Research Workshop

3. Proposed method • Optimal control framework • Sliding horizon loop • Treat traffic situations with reduced uncertainty • Successive optimization sub-problems with updated data • Minimize potential conflict quantity • Adjustment of aircraft speeds • Efficient but seldom used by controllers 4th EEC Innovative Research Workshop

4. Optimal control approach Supervisory layer • Distributed hierarchical control process, • Set point decision carried out by an optimisation function, • Speed computed by an optimal control algorithm Set point decision Conflict detection Localised control layer Reference point crossing times Optimal Controllers Speeds System Prediction of reference point crossing times 4th EEC Innovative Research Workshop

5. Optimization sub-problem • Minimize a global conflict indicator • All the greater that the conflict quantity is high • For all the aircraft, airborne or about to take off • According to the actual route network • Taking into account the flight phases • Acting on the travel times • Considering updated current state of traffic 4th EEC Innovative Research Workshop

6. Conflict indicator • Local • Around intersections of the flight paths • For aircraft having close altitudes • Depending on time gapbetween aircraft at this point • Global 4th EEC Innovative Research Workshop

7. Mathematical formulation • Dependent on the state of the traffic at time • : Boundary condition for flight f • Arrival times optimized through inter-beacon travel times 4th EEC Innovative Research Workshop

8. Resolution of a sub-problem • Problem settlement • Conflicting geographical points (beacons + other crossings) • Nominal travel times between conflicting points • Coefficients G • (Many operations can be done once for all at the beginning, when reading the flight plans) • Optimization phase • Impose DT has the same sign as in nominal case • Turn problem into linear formulation and use CPLEX 4th EEC Innovative Research Workshop

9. First tests • 3 traffic situations of a day of September 2003 • Airborne flights + flights taking off in the next 10 min • Parameters: • Ds = 10 NM • Optimized inter-beacon travel times • Within -10% and +5% of nominal ones • If flight is in cruising phase • For the whole trip of all the flights • C++ code, Pentium IV, 3GHz, 2Go RAM 4th EEC Innovative Research Workshop

10. First results • Reasonable computational times even for largest case • Problem settlement 1 min. • Optimization phase 2 min. • Slight cost enhancement for large instances • Improvement possibilities • Reduce the optimization horizon • Reintroduce the absolute values 4th EEC Innovative Research Workshop

11. Consider two aircraft a1 and a2 and a reference point p0 a1 arrival time at p0 is t1 and a2 arrival time at p0 is t2 Aims: Change travel time with speed variations to keep aircraft beyond minimal separation, Get low uncertainty on travel time, Go back to nominal cruise speed at the end of travel time control. Travel time control with speed changes Predicted temporal separation Arrival time uncertainty t2 Time t1 Minimum temporal separation 4th EEC Innovative Research Workshop

12. Optimal control techniques:developed to control industrial processes. Control loop Optimal Controller yp s u System Travel time control with an optimal control technique s: set point, u: optimal controller output, yp: system output. • The output of the optimal controller is computed so that the process output tracks the set point and reject disturbances. 4th EEC Innovative Research Workshop

13. Speed variations on cruise phase only Optimal Controller yp s u System Speed variation Optimal travel time to avoid a conflict Travel time prediction Travel time control with an optimal control technique 4th EEC Innovative Research Workshop

14. Travel time control with an optimal control technique • What can optimal control bring to travel time control? Accuracy, robustness to disturbances (unknown component of wind speed) Low travel time uncertainty Possibility to apply constraints to controlactions Constraints on speed, acceleration, deceleration 4th EEC Innovative Research Workshop

15. Current and future values of reference signal s Quadratic cost function to minimize u ym yp Model Predictive control s: set point, u: predictive controller output, yp: system output, ym: model output. • Quadratic cost function to minimize at time sample n: : output prediction, estimated with the model Minimisation  u(n+1), u(n+2), …, u(n+h2) • At time sample n+1, u(n+1) is applied and D(n+1) is minimised to get u(n+2). 4th EEC Innovative Research Workshop

16. Example • Aircraft: A320, flight level: 390, nominal cruise true airspeed: 447 KTS. • Travel time controlled over a distance d = 140 NM. • Constraints on speed variations, maximum acceleration, maximum deceleration. • Travel time at nominal cruise speed: 1005 s. • We want to increase the travel time to 1125 s. • Optimal control algorithm used to control travel time: Predictive Functional Control  low computational cost (2 ms / iteration / flight). 4th EEC Innovative Research Workshop

17. Example • Wind speed expressed as the sum of average wind speed (54 KTS) and sinusoid (27 KTS amplitude). • Weather forecast  average wind speed of 59 KTS. Wind speed as a function of distance travelled

18. Example Set point and system output estimation • Sampling period: 10s  speed updated every 10s. • Wished travel time: 1125s / actual travel time: 1120s. • Accuracy depends mainly on unknown component of wind.

19. Example True airspeed and ground speed as a function of time • Three phases: • Speed goes down to increase travel time, • Speed keeps at lower bound, • Speed goes up to nominal cruise speed

20. Example • Open loop trial: • New cruise speed is computed once at the beginning of travel time control, • Computation takes aircraft performances into account as well as forecasted wind. True airspeed and ground speed as a function of time • Trial: same one as previously, • Wanted travel time: 1125s / actual travel time: 1140s, •  Accuracy is a bit lower than in closed loop case, some further trials should be carried out with realistic wind models.

21. Conclusion • Minimizing potential conflict quantity • Dynamic sliding horizon loop principle • Optimal control framework • Act on crossing times through travel time control • Encouraging first results • Good computational times • Improvable efficiency of the optimization procedure 4th EEC Innovative Research Workshop

22. Perspectives • Integration of the optimization sub-problem in the control loop • Optimization procedure • Further work on the objective function • Improvement of the algorithm • Smoothing of the set points from one iteration to the next • Extend travel time control to climb and descent 4th EEC Innovative Research Workshop