Yakıt çalkalanmalı uzay araçları için stabilite kontrol problemi

Sloshing is caused by any disturbance of free liquid surface in a partially filled tank. Depending on the peak accelerations in any direction or the shape of container, the free surface of liquid can be subjected to different types of motion either symmetric or asymmetric. These types of motion have significant influence on vehicles which have liquid fuel in their tanks. Owing to the fact that fuel sloshing plays a crucial role in the stability of the vehicles, many diversified engineering departments give considerable attention to this problem. To prevent structural damages for vehicles with liquid fuel such as trucks on highways, cars, ships, space vehicles, new designs of tanks are evaluated and loss of the stability due to sloshing is tried to minimise. To prevent sloshing effects, physical barriers are placed into the fuel tank such as baffles or containers are designed by using bladders. Main purpose of these designes is to limit the movement of liquid fuel. But these techniques increase both the mission cost and the weight of the tank of spacecraft. The natural frequency of motion of liquid is related to two main factors (i) the shape of tank and (ii) the acceleration of gravity or the axial acceleration of vehicle. A liquid's motion contains an infinite number of natural frequencies, however the lowest few modes of frequencies are the most important for vehicle. When the natural frequency of liquid fuel coincides with the frequency of the vehicle, this situation generates resonance and damages the structure. Near resonance, the fluid's motion loses linearity and nonlinear representation starts to be valid. An analytical approach to sloshing has some limits to obtain a solution. Factors like tank shape, existence of external forces etc. have a great importance to design a model for sloshing phenomena. By taking into consideration the factors, to use an equivalent mechanical model becomes a realistic approach to liquid dynamics in closed tanks. Primal parameters of liquid are qualified and by utilizing these parameters, equivalent mechanical models are designed. Some rules must be followed before equivalent mechanical models are created. Firstly, passing from the liquid material to rigid masses, the change of masses and moments of inertia must be preserved. Then, center of gravity must be unchangeable. The equivalent models produce the same frequency range as liquid model does. Lastly, the system must come up with the results which is equivalent to real material. Having regard to these conditions, physical parameters must be determined, then the system is designed. The major objective of this thesis is to investigate the case of sloshing in space vehicles by utilizing equivalent mechanical models. Mass-spring system is one of the models, and for small oscillations, it becomes the most appropriate model. It replaces the liquid fuel by becoming inner-rigid-masses corresponding to first few slosh modes. As a result of axial and transverse accelerations of space vehicle, the inner-masses begin to oscillate and have a great impression on the stability of vehicle. After designing an acceptable model, to investigate the stability, optimal feedback law and Lyapunov-based control law are utilized. Firstly, the model is designed with two-inner-masses and the results of simulations are demonstrated. Then, the model with four-inner-masses are designed and same steps are applied to it in order to show the stability of the spacecraft. When large-amplitude oscillations occur, mass-spring system is no longer sufficient to demonstrate the change in the stability of spacecraft. In such a case, simple-pendulum model accommodates to the circumstances and describes relatively large motions. For sloshing due to a nonplanar or rotational motion, simple-pendulum model fits to real life cases excellently. The main purpose is to derive the equations of motion of spacecraft by means of these two model. Utilizing the mass-spring-system and simple-pendulum model, the motion of vehicle in a specific time and plane can be estimated. Moreover, the stability of the space vehicle can be investigated by taking advantages of Linear Quadratic Regulator and Lyapunov-based control laws. Apart from these two cases, space vehicle is investigated under lateral and pitching excitations. The equations of motion are derived by using the same parameters and they are compared to each other. In previous models, it is assumed that there are no external forces or moments. But in these models, important thing is the change of force and moment equations for either mass-spring system or simple-pendulum system under excitations. Moreover, in these systems, gravitational effects are not neglected.