Damage Mitigating Control of Rotorcraft

Student: Derek O. Bridges, Ph.D. Candidate

Motivation

Modern rotorcraft are complex dynamical systems which, by virtue of their widely varied missions and operating environments, endure an incredible level of wear and tear during their service life. Specifically, the main rotor drive system and dynamic components, including the engines, transmission, and driveshaft undergo large amounts of periodic and random vibration, which result in both high-cycle and low-cycle fatigue damage. As there is currently no analytical method in place to detect and quantify the extent of this fatigue damage, current procedures focus on preventative maintenance (specifically, a regimen of inspection and replacement of components based on time in service rather than their actual condition). Because of this conservative maintenance approach, as well as the relative complexity of the vehicle, operational costs of rotorcraft are significantly higher than those of equivalent fixed-wing aircraft.

Objective

The objective of this work is to investigate the feasibility and potential benefits of implementing a damage mitigating control system on an operational rotorcraft. At the most basic level, the DMC system uses a dynamic gain-scheduled controller. This controller includes parameters to vary the controller with flight condition, as in traditional gain scheduling; however, the controller also includes a parameter (subsequently referred to as the damage weight) that adjusts the level of damage mitigation in the controller. At a higher level of control, the DMC system may be integrated with a Health and Usage Monitoring System (HUMS) in order to monitor damage in real time. As damage begins to accumulate, the level of damage mitigation can be increased, possibly to a level such that handling qualities are diminished, and the aircraft may need to operate in a degraded mode with a restricted flight envelope.

Controller Description

To demonstrate the concept of damage mitigating control, controllers for a military helicopter are developed over its entire speed envelope (hover to 150 knots). These controllers are designed to regulate the heave, pitch, and rotor speed degrees of freedom by providing collective and longitudinal cyclic inputs to the mechanical mixer and an RPM governor input to the engine throttle. A multi-input, multi-output (MIMO) design approach is used, so the controller features integrated flight and fuel controls.

There are a number of objectives in the controller design. First, the controller should track vertical speed and pitch angle commands while regulating main rotor speed. This command tracking with no damage mitigation is designed to meet Level 1 handling qualities for height response and pitch bandwidth, as specified in the ADS-33E standard. For higher levels of damage mitigation, the handling qualities requirements are relaxed to Level 2. Secondly, the controller should also be designed to operate effectively over a range of flight speeds (hover to 150 knots). Lastly, the controller is designed to minimize torque loads to the main transmission based on the damage weight, which acts to reduce the damage to the transmission. In order to achieve these objectives, a gain-scheduled controller is developed using an explicit model-following control scheme.

The architecture of the damage mitigating control system (shown in Fig. 1) is an explicit model-following scheme. Commands in vertical speed and pitch attitude are passed through separate command filters. The command filter parameters are a function of the level of damage mitigation, or damage weight, D. The natural frequency in the pitch response and the time constant in the vertical speed response are designed to exceed Level 1 handling qualities when D = 0. As the value of the damage weight is increased from 0 to 9, a more sluggish response is allowed in pitch and vertical speed. This effectively achieves a tradeoff in terms of flight control performance and damage mitigation, since a more sluggish maneuver is expected to result in smaller transients in torque response. Rotor speed is regulated at a constant set point, so no command filter is required.

Figure 1. Model-Following Control System Schematic.

The feedback portion of the model-following controller is designed using an LQR full-state feedback approach. The feedback compensation is designed to regulate tracking error in vertical speed, pitch attitude, pitch rate, and rotor speed, as well as the integrated tracking errors in vertical speed, pitch, and rotor speed. The controller is designed by first extracting a linear model of the aircraft/engine dynamics, which is then modified to convert the vertical speed from body axes to Earth-fixed axes, and the four engine states are reduced to one, engine torque. The aircraft dynamics are augmented to include the time-integrated state variables for vertical speed, pitch, and rotor speed.

The nonlinear inversion is accomplished by further reducing the order of the aircraft model. The feedback gain takes in all eight aircraft and engine states, but outputs three pseudocontrols corresponding to vertical speed, pitch rate, and rotor speed. With three pseudocontrols and three outputs, the system is square and invertible. The inversion is nonlinear because the inversion state-space matrices vary with airspeed, and because the vertical speed signal is converted from Earth-fixed axes to body axes.

The feedback gains are designed using linear quadratic regulator (LQR) theory to minimize the cost function which includes the state weighting matrix Q and control weighting matrix R. The state weighting matrix includes a performance penalty for the engine torque, which is a function of damage weight. Thus, as damage weight is increased, the feedback controller is designed to minimize fluctuations in engine torque, which is directly related to damage on the engines, transmission, and drive system of the rotorcraft. The resulting LQR gain matrices are a function of both the airspeed of the helicopter (V), to account for the variation of the plant model with airspeed, and damage weight (D) to account for variation in the cost index with damage mitigation.

Damage Model

In order to intelligently adjust the level of damage mitigation, the control system must incorporate either a direct measurement or a model-based prediction of the damage. Furthermore, in order to evaluate the effectiveness of the controller, the simulation should include an analytical model of some representative damage. In this study, the damage is characterized by the length of a crack in the main bevel pinion of the helicopter transmission, shown in schematic form in Figs. 2 and 3, and is predicted using equations for stress on a gear tooth and crack growth.

Simulation Results

The GENHEL simulation code was used to perform a number of maneuvers using the damage mitigating control system. The controller is evaluated by examining its tracking performance, as well as the time history of damage on the aircraft. In addition, the impact of the controller on the handling qualities of the helicopter is measured by using the ADS-33E handling qualities performance specification.

Outer Loop Controller

To produce the simulation results presented below, it is necessary to include an outer loop controller so that aircraft trajectory commands can be translated into the vertical speed and pitch attitude commands required by the damage mitigating control system. The total airspeed (V) command is translated into the pitch attitude command, and a height above ground level (h) command is translated into the vertical speed command. The conversion between the total airspeed and pitch attitude commands is accomplished through the use of a proportional-integral (PI) controller, which was designed using classical control techniques. The conversion from the height above ground level command to the vertical speed command is performed by a proportional-derivative (PD) controller. The vertical speed commands are limited, both in climb (so the continuous engine torque limit is not exceeded) and in descent (so that engine torque does not reach zero). These limits are scheduled with airspeed. This controller was also designed using classical control techniques; however, due to the variation of the vertical speed command filter with damage weight, the proportional term of the controller also varies with damage weight. The outer loop controller can be interpreted as a model of a human pilot for a piloted rotorcraft or an outer loop autopilot and guidance system for a UAV.

Time History Results

The time history results, shown in Figs. 2-4, are terrain-following maneuvers for damage weights of 2, 5, and 8. The maneuvers are flown over terrain generated by FlightGear, an open-source flight simulation program that interfaces with GENHEL. The maneuvers consist of three circuits around a predefined course flying at a constant airspeed of 75 knots and a constant height above ground level command of 750 feet; since the terrain and flight dynamics are essentially the same for each circuit, the time histories in Fig. 2 represent only one circuit. In this figure, it is difficult to observe the effect of damage weight on altitude tracking performance. Figure 3 shows a shorter 50-second segment of the maneuver, where steep terrain requires the helicopter to switch rapidly between descent and climb. This shorter time segment shows that, once again, lower damage weight allows for better altitude tracking performance in exchange for larger transients in rotor speed and engine torque. In Fig. 4, crack length results are presented for the all three circuits of the maneuver. As the figures show, tracking performance can be traded for damage mitigation by using a greater damage weight value. Figure 4 also better illustrates the nonlinear relation between damage weight and crack length; as the crack length values diverge due to damage weight effects, the nonlinear crack growth causes further divergence.

Figure 2. Terrain-Following Maneuver Altitude Results (One Circuit).

Figure 3. Terrain-Following Maneuver Altitude Results (1050-1100 Seconds).

Figure 4. Terrain-Following Maneuver Crack Length Results (Three Circuits).

Handling Qualities Results

While the helicopter possesses acceptable command tracking performance, even for high damage weights, it is important to understand how the damage mitigating controller affects the aircraft's handling qualities. In order to quantify these effects, the controller was evaluated against the U.S. Army's ADS-33E handling qualities specification; in particular, the controller was tested using the height response (Section 3.3.10.1) and pitch bandwidth (Section 3.4.1.1) portions of the specification.

Figure 5 shows the height response characteristics of the controller at 40 knots for damage weights of 0, 3, 6, and 9. For damage weights from 0 to 6, the aircraft has Level 1, or excellent, handling qualities. For damage weights above 6, the aircraft has Level 2, or adequate, handling qualities. These results match closely with the vertical speed time constant in Eq. (4). Pitch bandwidth characteristics at 40 knots, shown in Fig. 6, also vary with damage weight; in this case, the results for each damage weight fall within Level 1. As damage weight increases, the pitch bandwidth characteristics move closer to the Level 2 boundary.

Figure 5. Height Response Plot (V = 40 Knots).

Figure 6. Pitch Bandwidth Plot (V = 40 Knots).