C-PRE-PAC Method

The C-PRE-PAC model uses the same inner-loop system, but using this method an outer-loop is added to represent the pilot response to a particular task. Rather than applying unforced sinusoidal inputs, the pilot is required to respond to the vehicle motion given through the outer-loop. Therefore, the motion of the vehicle, and the response, is dependent on the characteristics of the vehicle. The typical system is shown in Fig. 5.4.

Figure 5.4: Example of vehicle model used with C-PRE-PAC analysis.

Although C-PRE-PAC has been designed to operate systems similar to that shown in Fig. 5.2, it is not restricted to this structure. It is envisaged that the system model could include, for example, under-slung loads or other relevant external factors. These could be incorporated within models akin to those shown in Fig. 5.2 and Fig. 5.4.

(AG) parameters can be calculated. This is completed in the same way as proposed for

the real-time detection method. Both Φ and AG are calculated with respect to time,

allowing one to observe when PIO incipient conditions exist. As each calculation of parameters is specific to a point in time, for the O-PRE-PAC method, each point can also be related to the known frequency at that time. Therefore, one can observe the PIO tendencies with respect to frequency rather than with respect to time. For the C- PRE-PAC method, results are still desired with respect to time, making the calculation process the same as for the real-time method discussed in Chapter 4.

To determine PIO susceptibility, boundaries developed in Chapter 4 are used to distinguish between PIO incipient and robust cases, and act as predictions. This is true for both PRE-PAC methods, with the boundaries used dependent on both the aircraft condition (speed, etc.) and the axis of interest.

For the C-PRE-PAC analysis, there is both the requirement for a pilot model and for a closed-loop task. In this approach, the PAC algorithm is used to predict the PIO incipience of a certain set of conditions. For this analysis, to demonstrate the initial concept of the method, the McRuer cross-over model has been used, which satisfies Eqn. 5.1. This approach applies for compensatory systems only. In this work, the model has been used due to the ease of application. It is hoped that in follow-up studies, the model may be extended to show predictions for more complex pilot models, for non-compensatory, multi-loop task performance. This would give a more accurate prediction of PIO susceptibility, and increase the confidence in results obtained.

All rotorcraft models investigated within this work feature Rate Command systems. Therefore, the controlled element (i.e. the vehicle) is in the form Kc/s. According to McRuer [3], as the human operator will attempt to control the vehicle to ensure that the open-loop transfer function is given by Eqn. 5.2, the controller dynamics (i.e. of the pilot) will be in the form given in Eqn. 5.3. Therefore, in order for Eqn. 5.2 to be valid,KcKp =ωc. Furthermore, from McRuer’s experiments, τs was identified as 0.14

seconds [3]. YpYc= ωceτs s (5.1) Yp = ωceτs sYc(s) =Kpe−τs (5.2) Yp =Kpe−τs (5.3)

Therefore, the pilot gain (Kp) is tuned to provide a crossover frequency (ωco) that

occurs within an acceptable range. According to McRuer [12], pilot crossover frequency for compensatory tasks can be approximated asωco≈2rad/s. The actualωcowill vary

based upon pilot strategy and task performance. Furthermore, pilots can vary their

ωco based on the situation, whereby a strategy is employed to improve control of the

vehicle through crossover regression.

The C-PRE-PAC method also requires a desired trajectory, based on the task. This task should be both appropriate and realistic for the vehicle model tested. However, the level of aggression demanded is specific to the user’s requirements. Tasks with lower aggression are unlikely to display the full spectrum of PIO tendencies. Conversely, higher aggression tasks may display tendencies that surpass those expected during normal operation of the vehicle. For the C-PRE-PAC analysis, the selection of the task is critical to the results which will be obtained.

Three examples of proposed tasks are shown in Fig. 5.5a to Fig. 5.5c. Figure 5.5a displays the intended trajectory for completion of the Pitch Tracking task detailed in Chapter 4. This task has been shown as suitable for exposing both Cat. I and Cat. II RPCs. These are triggered through the sharp changes in pitch attitude, which force the pilot to apply aggressive control input.

A similar task, shown in Fig. 5.5b, has been used to expose PIOs within the lateral axis, for fixed-wing research campaigns (examples include results presented in [56, 63, 71]). In the same way as the Pitch Tracking task, large changes in attitude are intended to force high pilot aggression, to trigger PIOs. However, due to the low frequency content, it is unlikely to expose Cat. I PIO tendencies in any but the most PIO prone vehicles.

A final example is shown in Fig. 5.5c. This task is used in Ref. [57, 126], and is generated by a series of sinosodial signals. The values ofAi,Ni, and ωi are shown in

Table 5.1. These are used to determine the command signal, given by Eqn. 5.4.

θcommand = ΣAisin(ωit) (5.4)

ωi= 2π

Ni

Table 5.1: Sum-of-sines parameters. i Ai Ni ωi 1 -1.0 2 0.1995 2 1.0 5 0.4987 3 1.0 9 0.8976 4 0.5 14 1.396 5 -0.2 24 2.394 6 0.2 42 4.189 7 -0.08 90 8.976 0 5 10 15 20 25 30 35 40 45 50 −20 −10 0 10 20 Time, sec

Vehicle Attitude, deg

(a) Desired task trajectory for completion of Pitch Track- ing manoeuvre 0 10 20 30 40 50 60 70 80 90 100 −40 −20 0 20 40 Time, sec

Vehicle Attitude, deg

(b) Discrete tracking task used in previous fixed-wing re- search campaigns 0 10 20 30 40 50 60 −10 −5 0 5 10 Time, sec

Vehicle Attitude, deg

(c) Sum-of-Sines Tracking Task.

Figure 5.5: Examples of proposed compensatory tasks.