Although the design of a RIMP control system is not the intent of this effort, at least a simplified functioning control system is required to manipulate the RIMP environment and assess the sensitivity of various components to uncertainties, errors, and perturbations. A simple RIMP control described below consists of a minimum speed change calculation used as a scaling parameter followed by calculation of the required speed change and associated logic.
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9.5.1
Minimum Required Speed Change
The minimum required speed change is a calculated speed change based on the current estimate of the spacing error and current time-to-go of the reference aircraft. It defines a speed change which if started instantly and applied up to the interval management point, will adjust the spacing interval by the time the reference aircraft arrives at the interval management point. This provides for the longest duration allowed for the speed change to adjust the interval time. As expected, when the aircraft is far from the spacing point, the calculated minimum speed change will be very small. As the aircraft approaches the reference point, the minimum speed change value will increase. Therefore, it can be seen that the minimum speed change is akin to a scaling parameter for the RIMP operation. Instead of using the distance to the reference point, the simplified equations use the TTG of the reference aircraft for this measure.
The along-track distance to go must be flown at either a nominal speed or at the nominal speed plus a speed increment. For this calculation it is assumed that the current aircraft ground speed is the nominal value to fly the rest of the plan.
V V
TTG TTG
TTG V
G
ATD2 measured ownnominal measured min ownnominal (129)
Assuming a general speed trend of faster speed to slower speed during RIMP operation, a simplified but conservative solution can be derived based on the current speed of ownship, time- to-go of the reference aircraft, and the spacing error. This solution is conservative since the current speed used in the above equation is equal or faster than the speed used in the planned trajectory. Therefore, the estimated TTG adjustment is equal or less than what is achievable in the course of the flight.
The simplified equations do not work at the limit when the reference aircraft is very close to the RIMP reference point. However, assuming that
TTGrefA/C TIM
>> 1 second, the followingminimum required speed change can be computed.
refA C IM
ref own IM measured T TTG TTG TTG T V V / min (130)The sign of the required speed change is negative for deceleration and positive for acceleration. This value is significant since it has the longest time to impact the RIMP operation. If no action is taken as the paired aircraft proceed on their flight plans, the magnitude of the minim required speed change will increase. Operationally, once a reasonable threshold value is reached, the minimum required speed change must become the speed change command, and should be used to re-negotiate the flight plan.
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9.5.2
Nominal Speed Change
In the simplified RIMP control model, the nominal speed change is computed as the speed change to resolve the current spacing error in 600 seconds.
600 ref own IM measured nom TTG TTG T V V (131)The required speed change is the larger of the nominal and minimum speed change values.
, min
max * ) ( V V V sign VIM nom nom (132)The resulting speed change is then passed through a speed change logic (described below) to quantize the speed change events. The result is then multiplied by the speed change factor to generate the commanded change in speed, and in this particular case, change in true airspeed of the aircraft. This commanded speed change does not take into account if the aircraft is operating at the specified airspeed limit. The guidance module limits the sum of planned and RIMP commanded airspeed.
9.5.3
Speed Change Logic
To ensure that the RIMP speed command is engaged in a pseudo-discrete sense and to minimize the nuisance occurrence of speed change events the following simplified logic has been implemented. A RIMP speed logic state is defined in the memory. It is currently setup to include two speed-up steps, three slow-down steps and a null step. Figure 51 provides a logic flow diagram for the speed change algorithm.
Figure 51 – Speed Change Logic null -1 -2 -3 +1 +2 V<-1.5 V>+1.5 V>+12.5 V>+5.0 V<-5.0 V<-12.5 V<-22.5
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When the logic state is in the null mode, the speed change command is set to zero. If the “IM speed change” described above becomes greater than 5.0, the logic mode is switched to “+1 Speed-Up”. If the speed change drop below -5.0, the logic mode is switched to “-1 Slow- Down”.
When the logic state is in “+1 Speed-Up” mode if the IM speed change drops below -1.5, the mode is switched to null. If the IM speed change increases past +12.5, the mode is switched to +2 Speed-Up.
When the logic state is in +2 Speed-Up mode if the IM speed change drops below -1.5, the mode is switched to null.
When the logic state is in -1 Slow-Down mode if the IM speed change drops below -12.5, the mode is switched to “-2 Slow-Down”. If the IM speed change increases past +1.5, the mode is switched to null.
When the logic state is in “-2 Slow-Down” mode if the IM speed change drops below -22.5, the mode is switched to “-3 Slow-Down”. If the IM speed change increases past +1.5, the mode is switched to null.
When the logic state is in “-3 Slow-Down” mode if the IM speed change increases past +1.5, the mode is switched to null.
The final RIMP speed command is set equal to the above mode number multiplied by the IM spacing multiplier specified in the “Constants” data file. Nominally, this multiplier is set to equal to 10 Knots. RIMP speed control is disabled when commanded spacing is set to zero, and upon reaching the reference waypoint.