Minimizing conflict quantity with speed control

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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
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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
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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
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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
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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
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Conflict indicator

• Local
• Around intersections of the flight paths
• For aircraft having close altitudes
• Depending on time gap between aircraft at this
  point
• Global

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Mathematical formulation

• Dependent on the state of the traffic at time
• Boundary
  condition for flight f
• Arrival times optimized through inter-beacon
  travel times

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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

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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

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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

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Travel time control with speed changes

• 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.

Predicted temporal separation
Arrival time uncertainty
t2
Time
t1
Minimum temporal separation
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Travel time control with an optimal control
technique

• Optimal control techniques developed to control
  industrial processes.

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.

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Travel time control with an optimal control
technique

• Speed variations on cruise phase only

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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 control
actions
Constraints on speed, acceleration, deceleration
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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(n1), u(n2), , u(nh2)
• At time sample n1, u(n1) is applied and D(n1)
  is minimised to get u(n2).

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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).

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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
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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.

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Example

• Three phases
• Speed goes down to increase travel time,
• Speed keeps at lower bound,
• Speed goes up to nominal cruise speed

True airspeed and ground speed as a function of
time
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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.

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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

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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