System studies and re-entry algorithms of a reusable VEGA variant

Abstract

RLV development can be considered as the modern step towards mission design due to financial and strategic decisions. In the past, reusability has been addressed however the level of maturity of the technology, both in terms of hardware and software was not yet reached. There are several aspects to developing a RLV, and these can be categorized into optimization of the LV, optimization of the trajectory, and cost analysis. TO be able to determine the feasibility of the mission, it is not just necessary to develop a suitable configuration, but to also determine the physical feasibility of the trajectory. Several methods exist of which convex optimization is selected. This class of algorithms have risen in popularity in the regime of powered descent guidance, and present a desirable trade-off between performance and computational cost. An already existing algorithm, DESCENDO, for a two-staged vehicle CALLISTO purposed for a mission to a geo-synchronous orbit, is taken as reference. The algorithm is rewritten in YALMIP allowing it to perform more efficiently by saving computation time through creation of multiple controllers based on a discretized burn schedule. A potential candidate for reusability in the future is selected, which is a VEGA variant, considered as a two-staged vehicle with set requirements on the mission and configuration. Through closed-loop simulations, the feasibility of RTLS for a particular mission of this VEGA variant can be studied. The disciplines involved in the study include the launch vehicle optimization, engine sizing, preliminary ascent & descent, and 3-DoF simulations. Previous research at TU Delft on RLV has included the work Rozenmeijer, Vandamme, Van Kesteren, Miranda, and Contant, graduate students of the TU Delft Aerospace Engineering faculty. The work relied on the usage of the TUDAT C++ software environment and based its feasibility or reusability of operations through a cost-analysis. A shift in direction is taken away from cost-analysis to examine at a greater detail the physical feasibility of the trajectory for a nominal candidate RLV. This is done by examining the influence of simulator to guidance algorithm dynamics and guidance algorithm parameters. Moreover, a nominal payload class between 100 and 500 kg is selected to determine the configuration of the vehicle ideal for this mission. To be able to determine feasibility of RTLS, three metrics are considered, which are the final landing velocity, final landing position, and maximumdynamic pressure. The study performs higher fidelity analysis only on the return phase, and as such the starting conditions for descent are determined through a preliminary design process by considering a drag-less ascent. This returns a starting altitude of around 26-30 km, with similar values for starting downrange position, and varying conditions of initial mass and velocity. For the preliminary descent, it is found that the metric of dynamic pressure does not reach more than around 60% of the limit imposed by the VEGA-C, which is similar for other VEGA variants. This coincides with research done with the CALLISTO vehicle. All in all, the best cases for these metrics and one included as an overall best case where candidates for the 400 kg payload class. The selection criteria for best cases of the preliminary descent involved the dynamic pressure, final velocity, and required propellant mass for descent. Moreover, the vehicle optimization results showed that this contained the most variation of vehicle characteristics, and as such it was deemed as a desirable class to work with for its flexibility in design. The best case burnt mass result was selected as the best case velocity required extensive propellant mass to burn for only a less than 7 m/s difference in result, which would not be indicative of what the convex algorithm could achieve due to dynamics involved in the preliminary experiment. This nominal candidate is then tested for various variations of controller tuning parameters combinations, burn schedules, and simulator/guidance frequencies. The results showed a clear desirable region for the final time of just between 300 and 310 seconds for return, favouring shorter burns. The solution envelope for the burn schedule showed gaps in zones of feasibility as well as optimality, suggesting some performance issues with the algorithm due to it failing to find solutions. Nevertheless this envelope is well defined and several feasible solutions existed. The influence of parameter tuning and simulator frequency was studied. It was determined that no set of guidance parameters could give an advantage over the other, but that some values did favour feasibility more. This is somewhat in contrast to the selection of frequencies, as despite the fact there was also a large difference for higher frequency ratios between the Q3 to Q4 and Q0 to Q2, there is a noticeably trend that higher ratios are favoured. Moreover, a local optimal ratio of frequency of 10-1 was also found, and being the same ratio used for the other experiments as well as the CALLISTO study, provides more evidence that this effect is intended. The uncertainties studied are for the initial state variations, errors in reading of position and velocities, and process time delays. It was noted that almost all the errors in the initial state variations shared similar distributions for ranges of values of the metrics. The overall majority returned feasible as well as the large minority of this returned optimal. Of little to no significance was the processing time delay, of which the overwhelming majority returned optimal results, and the rest where outliers whose process time factor where beyond the 3σ limit imposed in the creation of normal random variables. The largest errors arose from the real-time uncertainty in the velocities and position, modelled after pseudo-range errors. Although results showed a high density in the feasible and optimal regions for metrics of final time and position, there was also a high density past the feasible regions. It can be considered that the feasibility of RTLS operations for such a VEGA vehicle is restricted by such errors as expected, but nevertheless results are promising in what can be the main steps to lead to an error analysis study by the use of state estimation techniques and testing various modifications made to the SOCP problem to improve performance.