Predictions Using OLOP

As discussed previously, OLOP is used to determine the PIO susceptibility from RLEs. Results are based upon observation of the position of the so-called ‘Open-Loop Onset Point’ on a Nichols chart. The following bullet points describe how OLOP is applied to a simulation model.

•Apply a sinusoidal control signal to the open-loop system. Any control system feedback

elements are not included. It is assumed that the sinusoidal stick input should be of maximum amplitude (i.e. worst case scenario).

•Determine the onset frequencies of any rate limiting elements in the system, by ob-

serving the frequency when rate limits will be triggered in the system.

tuned through the observation of the Phase Margin at 0dB. This should be kept consis- tent throughout.

•Plot the frequency response of the closed-loop system, without rate limits active, on a

Nichols Chart, displaying the Gain and Phase of the system. On the same figure, plot the onset point determined.

•Observe where the onset point lies in relation to OLOP boundaries. If the point is

above the boundary, then the configuration is deemed susceptible to Rate Limited PIO.

The OLOP method was performed on both the lateral and longitudinal axes of the BO105 aircraft, at three speeds (0knots, 60knots, 80knots). Five Rate Limits (RLs) were applied to each condition. Results are shown in Figures 3.7a to 3.7f. All plots display the two OLOP boundaries found in the literature. ‘OLOP’ was the original boundary determined for use with the OLOP criteria. However, in later developments, it was suggested that this boundary was too conservative, and that a boundary such as ‘OLOP 2’ should be used. Despite this suggestion, no further validation of ‘OLOP 2’ was presented, and therefore in this investigation both were used to observe PIO potential. Markers display OLOP results, with the numbers beside them displaying the system rate limit (in deg/s). OLOP above the boundary denotes a configuration that is deemed to be susceptible to Rate Limited PIO, whilst those points below should be free from PIO.

As shown, for the BO105 simulation model, aRL= 15deg/swas always found to be prone to PIO, when using the ‘OLOP’ boundaries. However, when using the ‘OLOP2’ boundaries this RL was never found prone to PIO. For all but one of configurations and speeds, RLs found to be prone to PIO using ‘OLOP’ boundaries were found to be PIO robust when using ‘OLOP2’ boundaries. The large differences in predictions made it challenging to ascertain the PIO susceptibility of the vehicle models. OLOP boundaries have seen only limited use in rotary-winged campaigns [27, 44]. In one previous study [44], is was suggested that that the OLOP boundary for rotorcraft should be placed between ‘OLOP’ and ‘OLOP2’. However, this was supported only by limited results.

Figures 3.8a and 3.8b display OLOP results for the FGR model, for both SAS- ON and SAS-OFF configurations. For this aircraft model, the susceptibility to Rate Limiting was found to be similar with and without the SAS engaged. Using the original OLOP boundaries,RL= 20deg/s and 10deg/s were found to be susceptible to PIO.

Tables 3.2 and 3.3 show the predictions made using OLOP, for both the BO105 and FGR models. ‘Tick’ symbols display cases where OLOP has predicted PIOs due

(a) Roll Axis, Hover Condition. (b) Roll Axis, 60 knots.

(c) Roll Axis, 80 knots. (d) Pitch Axis, Hover Condition.

(e) Pitch Axis, 60 knots. (f) Pitch Axis, 80 knots.

(a) Pitch Axis, SAS-ON. (b) Pitch Axis, SAS-OFF.

Figure 3.8: OLOP results for the FGR simulation model for various RL settings.

Table 3.2: OLOP predictions for lateral axis BO105

Bound. Speed (Kts) Rate Limit, deg/s

20 15 10 5 2.5 0 7 3 3 3 3 OLOP 60 7 3 3 3 3 80 3 3 3 3 3 0 7 7 7 7 3 OLOP2 60 7 7 7 7 7 80 7 7 7 7 7 0 7 7 7 3 3 Mid-point 60 7 7 3 3 3 80 7 7 3 3 3

to RLEs, and ‘cross’ elements show the cases where no PIO is predicted.

As shown by results, with boundaries not currently standardised, it is difficult to determine the susceptibility using OLOP. For this reason, it could not be used directly to determine rate limits to be used in the investigations. During this investigation, a boundary mid-way between ‘OLOP’ and ‘OLOP2’ (mid-point) was selected, as it was thought to offer a good compromise for the assessment of RLEs. This was a recommendation from results discussed in Ref. [44]. Therefore, this boundary was used when selecting rate limits, and was used to determine OLOP predictions when used for comparisons in the subsequent sections. Both the OLOP, and BPD boundaries could be used to set experimental conditions before the simulation test campaigns, in order to obtain a good balance between PIO prone and PIO robust vehicle models.

Table 3.3: OLOP predictions for longitudinal axis BO105

Bound. Speed (Kts) Rate Limit, deg/s

20 15 10 5 2.5 0 7 3 3 3 3 OLOP 60 7 3 3 3 3 80 7 3 3 3 3 0 7 7 7 7 3 OLOP2 60 7 7 7 7 3 80 7 7 7 3 3 0 7 7 7 3 3 Mid-point 60 7 7 7 3 3 80 7 7 7 3 3

Table 3.4: OLOP predictions for longitudinal axis FGR

Bound. Configuration Rate Limit, deg/s

50 30 20 10 OLOP SAS-ON 7 7 3 3 SAS-OFF - 7 3 3 OLOP2 SAS-ON 7 7 7 7 SAS-OFF - 7 7 7 Mid-point SAS-ON 7 7 7 3 SAS-OFF - 7 7 3