Necessity of non-rigid body models for launch vehicles

Abstract

In previous research, the necessity of non-rigid body simulators was stated to be a requirement for long, slender bodies. However, it remains unclear for which vehicle design parameters non-rigid body effects become destabilising. A set of 2+N linearly independent equations of motions can be combined in a single matrix to determine the motion of a flexible launch vehicle with N slosh masses. The flexibility of the vehicle is modelled using the method of assumed modes. The sloshing motion is modelled by assuming that the slosh mass behaves like a pendulum. To couple the different motions, a constraint matrix is used. The model is developed in Matlab Simulink. Using non-quiescent starting conditions with no external forces acting on the vehicle except gravity, it was found that the energy of the system remained constant. The flight data from the Stratos III launch vehicle was obtained and compared to the simulated non-rigid body model data. It was found that slosh motion can result in destabilisation when this vehicle experiences a sudden decrease in acceleration. The destabilisation that occurred could not be observed when rigid body equations of motion were used. Based on a sensitivity analysis over a range of vehicle parameters, it is recommended for length over diameter (L/D) ratios above 20 to consider the use of non-rigid body models. From this ratio, the maximum and total flexibility strongly increase. For L/D ratios below 20, flexibility is negligible and sloshing becomes the main perturbing factor. It was found that a PID controller that is designed using a rigid body model is still able to stabilise the non-rigid body during flight. Oscillations occurred in both the rigid and non-rigid body model when a single set of gains was used. For both models, the oscillations were removed by introducing gain scheduling.