The initial step in the O-PRE-PAC process requires the user to specify the vehicle model. The complexity of this model is dependent on user requirements; an aircraft in the early design stage may require only a linear analysis model. However, prior to full scale flight tests, the requirement may be for a full non-linear model, at various conditions and configurations. Figure 5.2 gives an example of a typical rotorcraft model architecture that may be employed.
Figure 5.2: Example of vehicle model used with O-PRE-PAC analysis.
The typical rotorcraft model, assuming rigid body dynamics, contains a number of elements that have an influence on PIO susceptibility. Firstly, the interface between the pilot and the vehicle may have a significant effect on the tendency to induce oscillations. In previous studies, it has been found that static and dynamic inceptor forces can have significant influence over the tendency to induce PIO [122–124]. Secondly, it is important to consider the transfer of pilot command to the vehicle through the swashplate dynamics. Here, one should consider any transport delays, actuator position and rate limits, and non-linearities. It is at this stage that many quasi-linear effects have been previously studied. Thirdly, the transformation from swash plate deflection to vehicle response must be correctly modelled. The rigid body dynamics have perhaps the largest influence on the response characteristics. Finally, consideration must be made for the effects of any Stability Control Augmentation System (SCAS). These systems, now predominantly digital and becoming more common in rotorcraft, have the potential to add both transport delays and non-linearities. Furthermore, system ‘mode switching’ elements could have a significant influence over RPC potential [4].
The O-PRE-PAC model represents the excitation of the open-loop vehicle model by an active pilot. Here, the pilot is said to be applying control inputs regardless of the end vehicle motion. With this in mind, there is no feedback between the vehicle and the pilot. A typical open-loop model is shown in Fig. 5.2. Pilot control is passed through the control inceptor, swashplate, quasi-linear elements, and the rigid body vehicle dynamics, resulting in the motion of the rotorcraft. The model may feature inner-loop closed-loop systems, but the overall system response is open loop.
For O-PRE-PAC, there is no requirement to model the human pilot. Rather than try and replicate the actions of the human pilot, it takes consideration of a number of generic input signals, that adequately describe possible actions of the pilot. There- fore, it is proposed that sinusoidal inputs, of varying magnitudes and frequencies will adequately show at what conditions a PIO will occur. As a result, a ‘pilot model’, is not required. For the analysis, sinusoidal frequency sweeps are proposed, covering the range for which PIOs are known to occur. This is in an attempt to ‘map’ the complete potential response envelope of the vehicle, rather than its response to an individual pilot. If the mapping is conducted for the range of achievable pilot inputs, it can be used to judge at what level of control input pilots will likely enter into a PIO.
During the development of O-PRE-PAC, signals were generated to try and map possible pilot inputs, by varying the amplitude of input and different frequencies [125]. However, this led to a complicated method of application. Instead, it is now proposed that signals of constant amplitude are used, and simulations are run within the allowable range of vehicle safety constraints. An example is shown within Fig. 5.3. Here, input signals are shown with respect to frequency and amplitude as dashed lines. The start and end frequencies for each signal are governed through a number of constraints, representing operational or structural limits of the aircraft. For example, Constraint 1 may govern the structural limits of the vehicle. This relationship is known, and the aircraft should not be operated beyond this limit. Therefore, it should not be necessary to determine PIO potential in this region, as it should never be entered. As another example, Constraint 3 for example could represent the allowable roll attitude excursions of the vehicle. Again, the vehicle should not be operated in this range and therefore, the danger of this region is already known. After accounting for the constraints, the user is left with a region to investigate.
The example shown in Fig. 5.3 suggests nine input signals, with frequencies ranging from 0−10rad/s. In studies, no signals have been defined above this frequency range, because PIOs have historically occurred in the range of 1-8 rad/s [4]. Therefore, at this stage, the criterion does not account for high-frequency events, those termed pilot- assisted oscillations (PAO). However, the authors recognize that such an extension may
0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 Frequency, (rad/s) Amplitude, (−) CONST. 2 CONSTRAINT 1 CONST. 3
Figure 5.3: Input frequency spectrum.
be feasible at a later stage in the development of the criterion.