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Satellite Boundary Observer and Attitude Controller Design Considering Fluid Fuel Sloshing

Jokar, Meysam | 2023

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 57099 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Salarieh, Hassan; Nejat Pishkenari, Hossein
  7. Abstract:
  8. Fuel sloshing plays a direct and pivotal role in the tracking control tasks of liquid-propellant satellites. To address this problem, existing works have considered some simplifying assumptions on fuel motion, such as fuel rigidity and potential ideal fluid. On the other hand, most studies have used the ODE discretized model-based control schemes to stabilize the infinite-dimensional satellite-fuel system, which can cause spillover instability and lead to a significant loss of accuracy. To overcome these issues, we generally solve the PDE-based control problem for rigid bodies with partially liquid cavities. In this regard and based on the governing PDEs of the liquid motion, the dissertation falls into two parts. The liquid dynamics model is given by the Navier-Stokes equations (NSEs) in the first part and by the Saint-Venant equations (SVEs) in the second one. The latter equations were firstly derived for shallow-water sloshing description. Despite being partial, the SVEs have less order, complexity, and nonlinearity than NSEs. However, the SVEs -as a different case study- show the efficacy of our proposed methodology. The dissertation’s main objective is to design innovative boundary feedback controllers to deal with rigid body attitude/trajectory tracking errors and sloshing cancellation. To this end, we derive the nonlinear PDE-ODE cascades governing the attitude/trajectory dynamics of the rigid bodies containing liquids using Hamilton’s principle. Then, we construct boundary feedback laws (BFLs), which simply require measurements of (i) rigid body information, and (ii) liquid boundary parameters. Indeed, the main complexity lies in the fact that no sensor can be implemented in the liquid domain. We show that adding the boundary feedback terms to the controller effectively improves the closed-loop transient response quality. The obtained improvement is a direct consequence of sensing from the liquid boundary that provides the controller with the liquid information including the boundary forces and torque. We further develop innovative Luenberger-type boundary observers to cope with requirements on the infinite number of unmeasurable boundary states. The proposed scheme has two limitations to reaching the goals: (i) it only guarantees the asymptotic stability of the closed-loop system, and (ii) it is not applicable for PDE-ODE cascades in which the effect of the PDE part on the ODE part contains nonlinear terms. To get around these limitations and only based on the SVEs, we construct two BFLs with exponential convergence: a static feedback law and a dynamic feedback law (state feedback law augmented with full-order and reduced-order boundary observers). We prove the stability of the resulting closed-loop systems utilizing the control Lyapunov function methodology and demonstrate the feasibility of the designed controllers through simulations
  9. Keywords:
  10. Satellite ; Slosh Dynamics ; Lyapunov Function ; Navier-Stokes Equation ; Boundary Feedback Controller ; Saint-Venant Equations ; Boundary Observer ; Satellite Attitude Control

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