Tracking Control of Nonlinear Maneuverable Re-Entry Vehicles Using a Fluid-Flow Newton-Raphson Controller
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Olsen, Mark
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Abstract
The objective of this thesis is to apply a previously developed novel controller, based
upon a fluid-flow implementation of the Newton-Raphson method for solving algebraic
equations, to the problem of maneuvering re-entry vehicles modeled by state equations.
This research is motivated by a resurgence in the area of maneuverable aerospace vehicles
spurred by shifting geopolitical landscapes and renewed interest in space exploration. Both
thrust-free and thrust-enabled vehicles are modelled to overcome reachability constraints
and enable understanding of an oscillation phenomenon that was observed in simulations.
Over the recent years, due to advances in controls and rocket technology, the need for atmospheric re-entry vehicles (RVs) capable of following a precise trajectory as they re-enter a planetary body has become paramount in the aerospace industry. Gone are the days of rocket boosters considered disposable, and astronaut re-entry vehicles (e.g. soyuz), targeting vast areas of impact. No longer is the goal of atmospheric re-entry simply to slow the vehicle to a safe speed for landing, protect it from thermal heating, and ensure ablation does not result in destruction or implosion. Rather, RVs capable of a controlled descent accurately tracking a predefined trajectory are needed. This need for precise RVs, along with advances in the mechanical systems used to maneuver vehicles, has caused a need for robust and computationally efficient algorithms capable of keeping a vehicle along the specified path. This thesis focuses on applying a novel control law to Maneuverable Re-entry Vehicles (MaRVs) to ensure the tracking of a predefined trajectory with no a priori knowledge of the reference.
Primarily, this thesis focuses on contributing to the body of knowledge through application of a new and novel control algorithm to nonlinear aerospace vehicles. The control scheme is not the novel contribution, as that was formulated by other authors, but its application to aerospace vehicles along with subsequent experimentation and troubleshooting is the focused contribution of this work.
The tracking controller was successfully applied to different vehicle models and tracking was achieved in each one. A reachability issue was discovered and overcome through the implementation of thrust. However, another way to overcome reachability issues could be to implement tracking of a reference which does not have time as the independent variable. Rather, position or energy could be used as the independent variable.
One of the primary discoveries in applying the novel tracking controller to the aerospace vehicles in this text was the presence of oscillations in the positional tracking errors. Although initially perplexing, this was eventually solved through the use of a continuous reference. This was further confirmed by changing the simulation time step in application of the Forward Euler method for solving the differential equations to generate the discrete reference. Results and figures from these simulations were not included for brevity of the text, but the reference's time step is inversely proportional to the oscillatory positional error.
Initial transients were common across all of the vehicle models used, and a high sensitivity to initial conditions was observed. Small perturbations in initial conditions could cause large transients and overshoot. Further, if initial conditions moved far enough away from the reference then stability would be lost. These issues were not addressed in this thesis, other than a few simple simulations involving saturation not presented in the text, but are an area of further research. Using splines to modify the reference or more sophisticated methods such as Control Barrier Functions (CBFs) are methods to be considered.
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Date
2023-07-25
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Dissertation