Purpose

Hermes Flight 2 failed due to aerodynamic forces at approximately 7s into flight. It is speculated that pitch-roll coupling ('coning') contributed to the demise of Hermes 2. Coning could have contributed to the fin load exceedance by increasing the angle of attack the vehicle was able to hold relative to the air stream, significantly increasing the load on the fins. Many other high performance, high altitude rockets have empirically displayed coning behavior in flight. 

To mitigate pitch roll coupling it is necessary to maintain a frequency separation between the pitch and roll modes. Hermes 2 dynamics reveal a pitch mode ranging from 1.5-4 Hz, and roll modes ranging from 0-2.8 hz. Pitch modes are energetic and stochastic depending on winds at liftoff, rail angle, vehicle parameters, and more. Roll modes depend mostly on fin attachment precision. 

Non-active control mitigations for roll mode control are limited to rollerons, and very high tolerance fin attachment. Given the entirely manual assembly, sanding, and painting process of the fin can it is highly unlikely that we will produce a fin can which does not induce some roll on the vehicle. A spin stabilized vehicle is less difficult to produce, although the centripetal forces increase fin load, the fins permanent angle of attack increases fin stress, and the high rotation rate makes video and telemetry very difficult to obtain.

Another option is available in the form of actively controlled mechanisms. Reaction wheels are simply a high moment of inertia disk mounted to a motor. As a controller (likely Pyxida) senses a roll rate, the motor is spun to a velocity which will counteract the vehicle’s roll rate. Reaction wheels are straightforward mechanically and dynamically. The team has limited experience with reaction wheels and already has significant amounts of hardware from Hermes 1.

Requirements

The following requirements are self imposed

Design

Hardware

Pyxida will send I2C commands to a Teensy 3.5 which will PWM Control 60A Hobbyking ESC units that drive Quantum MT motors. The system is powered by a 4s LiPo battery.

Controller

The controller that drives the wheel is incredibly straight-forward. Because we have no position requirement, only a simple physical relationship between the inertias of the rocket and the reaction wheel define the proportional speed of the wheel to the rocket. This can be calculated with very high degree of certainty, and compared to measured values obtained with a bifilar pendulum test. The rocket’s roll rate can be derived either directly from the gyros or be received from the Kalman filter (or other filter). To determine the cumulative set of effects on the 6-DoF dynamics (although they are expected to be minimal) an OpenRocket plugin has been developed to allow for the stabilizing effect of the wheel and the additional angular momentum to be incorporated into pre-flight models. This plugin adds the flywheel assembly as a additional mass and inertia located at the center of mass of the given OpenRocket model. It models both the flywheel as an inertial mass and the brushless motor as an electrical circuit to accurately simulate the effects of torque drop-off at higher speeds with electric motors. From initial simulations using an L2-scale minimum diameter rocket. We were able to use a 300g mass to reduce the maximum roll rate of the rocket from ~6 rad/s at motor burnout to ~1 rad/s at motor burnout. Graphs showing this result can be found below:

The capability of the flywheel will scale well to a larger rocket because the larger tube diameter allows for the flywheel radius to be increased which increases the inertia of the wheel by the square of the radius. larger inertia allows us to exert more torque authority before the brush-less motor saturates at its maximum speed.

Failure Mode Analysis

The worst-case scenario would be a sudden liberation of the reaction wheel from the motor and support bearing. Ignoring what could cause this to happen (one of the bulkheads would need to deform by over a quarter of an inch) we can demonstrate that the composite tube will contain the failure with no damage to other systems. A moderate failure would be the seizing of the wheel during flight, after it was already spinning. If this occurs, the roll rate would be exactly the same as not having flown the reaction wheel at all. This is still a net benefit though as the vehicle is likely higher in altitude so the aerodynamic forces on the fins/nose cone if the vehicle did eventually cone would be lower.

This system is highly testable, and can be fully demonstrated before flight, using straightforward analysis tools.

Another moderate risk would be a runaway reaction wheel. If the wheel immediately spun up to its maximum RPM, the vehicle will have a roll rate of approximately 7 hz, equivalent to a minor spin stabilization system. This would still have a positive effect on stability, although it would have a negative impact on video and telemetry. This negative impact can be characterized on the ground. A ‘dead-man switch’ could also be implemented to allow Pyxida to deactivate the ESC if it detected undesirable behavior such as this.

Conclusion

Flying this system on Hermes 3 allows the team to build experience with control systems, which will be needed in the future for more ambitious projects. The reaction wheel system mitigates a significant risk, which has been empirically demonstrated on both team flights and on flights by vehicles similar to what we want to fly in the future. The majority of the risk remaining to this ECR is schedule risk. The design analysis is already complete. CAD is already complete. 4 parts need fabrication, but they use easy to obtain materials and simple manufacturing processes. Room for future improvements include a custom PCB to clean up the hand-wiring, a more sophisticated wheel design allowing for a slightly lighter system, and design of a suspended test rig. The group of students working on this system are well poised for a PDR in September, one where we could present simulation and test data in addition to hardware. MIT has many world class faculty in controls research. A control system design review, even if we ultimately decide not to fly it, will help us engage with the department and bring in external expertise, such as Hall, How, Sertac, and Roy.