The problem of reorienting a spacecraft to acquire a moving target is investigated. The spacecraft is modeled as a rigid body with N axisymmetric wheels controlled by axial torques, and the kinematics are represented by Modified Rodriques Parameters. The trajectory, denoted the reference trajectory, is one generated by a virtual spacecraft that is identical to the actual spacecraft. The open-loop reference attitude, angular velocity, and angular acceleration tracking commands are constructed so that the solar panel vector is perpendicular to the sun vector during the tracking maneuver. We develop a nonlinear feedback tracking control law, derived from Lyapunov stability and control theory, to provide the control torques for target tracking. The controller makes the body frame asymptotically track the reference motion when there are initial errors in the attitude and angular velocity. A spacecraft model, based on the X-ray Timing Explorer spacecraft, is used to demonstrate the effectiveness of the Lyapunov controller in tracking a given target. / Master of Science

This thesis develops Lyapunov-based control techniques for nonlinear process systems subject to input constraints and stochastic uncertainty. The problems considered include those which focus on the null-controllable region (NCR) for unstable systems. The NCR is the set of states in the state-space from where controllability to desired equilibrium point is possible. For unstable systems, the presence of input constraints induces bounds on the NCR and thereby limits the ability of any controller to steer the system at will. Common approaches for applying control to such systems utilize Control Lyapunov Functions (CLFs) . Such functions can be used for both designing controllers and also preforming closed--loop stability analysis. Existing CLF-based controllers result in closed--loop stability regions that are subsets of the NCR and do not guarantee closed--loop stability from the entire NCR. In effort to mitigate this shortcoming, we introduce a special type of CLF known as a Constrained Control Lyapunov Function (CCLF) which accounts for the presence of input constraints in its definition. CCLFs result in closed--loop stability regions which correspond to the NCR. We demonstrate how CCLFs can be constructed using a function defined by the NCR boundary trajectories for varying values of the available control capacity. We first consider linear systems and utilize available explicit characterization of the NCR to construct CCLFs. We then develop a Model Predictive Control (MPC) design which utilizes this CCLF to achieve stability from the entire NCR for linear anti-stable systems. We then consider the problem of nonlinear systems where explicit characterizations of the NCR boundary are not available. To do so, the problem of boundary construction is considered and an algorithm which is computationally tractable is developed and results in the construction of the boundary trajectories. This algorithm utilizes properties of the boundary pertaining to control equilibrium points to initialize the controllability minimum principle. We then turn to the problem of closed--loop stabilization from the entire NCR for nonlinear systems. Following a similar development as the CCLF construction for linear systems, we establish the validity of the use of the NCR as a CCLF for nonlinear systems. This development involves relaxing the conditions which define a classical CLF and results in CCLF-based control achieving stability to an to an equilibrium manifold. To achieve stabilization from the entire NCR, the CCLF-based control design is coupled with a classical CLF-based controller in a hybrid control framework. In the final part of this thesis, we consider nonlinear systems subject to stochastic uncertainty. Here we design a Lyapunov-based model predictive controller (LMPC) which provides an explicitly characterized region from where stability can be probabilistically obtained. The design exploits the constraint-handling ability of model predictive controllers in order to inherent the stabilization in probability characterization of a Lyapunov-based feedback controller. All the proposed control designs along with the NCR boundary computation are illustrated using simulation results. / Thesis / Doctor of Philosophy (PhD)

Analytical solutions to complex trajectory design problems are scarce, since only a few specific cases allow for closed-form solutions. The main purpose of this dissertation is to design simple algorithms for trajectory design using continuous thrust, with a focus on low-thrust applications. By “simple” here we seek to achieve algorithms that either admit an analytical solution, or require minimal input by the user and minimal computation time. The three main contributions of this dissertation are: designing Lyapunov-based closed-loop guidance laws for orbit transfers, finding semi-analytical solutions using a constant magnitude thrust, and perturbation theory for approximate solutions to low-thrust problems. The technical aspect that these problems share in common is that they all use, fully or partially, a thrusting model in which the energy of the system is kept constant. Many orbit transfer problems are shown to be solved with this thrusting protocol. / text

The author develops a nonlinear longitudinal model of an aircraft modeled by rigid fuselage, tail, and wing, where the wing is attached to the fuselage with a torsional spring. The main focus of this research is to retain the full nonlinearities associated with the system and to perform gust load alleviation for the model by comparing the impact of a proportional-integral- lter nonzero setpoint linear controller with control rate weighting and a nonlinear Lyapunov-based controller. The four degree of freedom longitudinal system under consideration includes the traditional longitudinal three degree of freedom aircraft model and one additional degree of freedom due to the torsion from the wing attachment. Computational simulations are performed to show the aeroelastic response of the aircraft due to a gust load disturbance with and without control. Results presented in this thesis show that the linear model fails to capture the true nonlinear response of the system and the linear controller based on the linear model does not stabilize the nonlinear system. The results from the Lyapunov-based control demonstrate the ability to stabilize the nonlinear response, including the presence of an LCO, and emphasize the importance of examining the fully nonlinear system with a nonlinear controller.

This work addresses the design and real-time implementation of adaptive control strategies on the parabolic solar collector to enhance the production efficiency under varying working conditions. For example, the unpredictable variations of the solar irradiance and thermal losses, these factors can be a major problem in the control design. The control objective is to force the outlet temperature of the collector fluid, to track a predefined reference temperature regardless of the environmental changes. In this work, two control strategies have been designed and analyzed. First, an intelligent proportional-integral feedback control, which combines the proportionalintegral feedback control with an ultra-local model is proposed. This strategy uses a transfer function model that has been derived and identified from real-time data and used to test the controller performance. Second, an adaptive nonlinear control using Lyapunov stability theory combined with the phenomenological representation of the system is introduced. This strategy uses a bilinear model derived from the heat transfer equation. Both control strategies showed good performance in the simulations with respect to the convergence time and tracking accuracy. Besides, the conventional proportional-integral controller has been successfully implemented in the real system.

Quick and reliable computational methods for optimized orbital transfers are crucial for projects at preliminary stages. They enable an initial, realistic sizing of the propulsion subsystem, one of the major components of satellite design. This thesis work, conducted at ReOrbit Oy, presents a minimum-time optimal trajectory for the orbit raising of a micro-satellite from GTO to GEO, assuming continuous firing by electric propulsion. The Delta-v requirements resulting from this simulation lead to the selection of an appropriate electric propulsion system, elaborating on the design of its configuration in terms of fuel and thrust requirements. This is done by taking into account, other than the major contribution given by the orbit raising, additions due to in-orbit maneuvers performed twice a day over a 10-year lifetime, like station-keeping corrections and reaction wheels desaturation. The optimization method is a direct-indirect hybrid for low-thrust orbital maneuvers, employing Pontryagin’s Minimum Principle for the transcription into a nonlinear programming problem. The initial guess required to start the optimizer is obtained with Lyapunov control theory. An orbital averaging technique is implemented, enabling fast computation of multiple trajectories during the optimization. Disturbances from the J2 zonal harmonic, solar radiation pressure, third-body effects of the Sun and Moon, and atmospheric drag up to 1500 km of altitude are included in the dynamic model. Eclipse conditions are assessed with a cylindrical shadow model, as the solar electric propulsion experiences a zero thrust period when in Earth’s shadow. The electric propulsion system configuration is determined with trade-off studies and comparisons between different suppliers. The chosen outline includes 4 Xenon thrusters, with complementary power processing units and propellant management systems, resulting in a total transfer time of less than 4 months. The same propulsion system is employed both for the transfer trajectory and the in-orbit maneuvers, by changing the thruster’s configuration once in GEO. / Snabba och pålitliga beräkningsmetoder för optimerade växlingar mellan omloppsbanor är avgörande för projekt i preliminära skeden. De möjliggör en initial, realistisk dimensionering av framdrivningssystemet, ett av huvudkomponenterna i satellitdesign. Detta examensarbete, utfört vid ReOrbit Oy, presenterar en tidsoptimerad bana för en mikrosatellits banhöjning från GTO till GEO, förutsatt kontinuerlig avfyring med elektrisk framdrivning. Simuleringens resulterande Delta-v-krav leder till valet av ett lämpligt elektriskt framdrivningssystem, med utarbetande av dess konfiguration vad gäller bränsle- och drivkraftskrav. Detta uppnås genom att ta hänsyn till (förutom bidraget från växlingen av omloppsbanan) tillägg från manövrar i omloppsbana som utförs två gånger om dagen under en 10-årig livstid, som t.ex. korrigeringar för stationshållning och avmättning av svänghjul. Optimeringsmetoden är en direkt-indirekt hybrid för manövrar i omloppsbanor med låg drivkraft, som använder Pontryagins minimiprincip för omskrivning till ett icke-linjärt programmeringsproblem. Den första gissningen som krävs för att starta optimeraren erhålls med Lyapunovs reglerteori. En teknik for omloppsutjämning implementeras, vilket möjliggör snabb beräkning av flera banor under optimeringen. Störningar från zonövertonen J2, solstrålningstryck, tredjekroppseffekter från solen och månen och luftmotstånd upp till 1500 km höjd ingår i den dynamiska modellen. Förmörkelseförhållanden uppskattas med en cylindrisk skuggmodell, då den elektriska solframdrivningen undergår ett skede utan drivkraft inom jordens skugga. Det elektriska framdrivningssystemets konfiguration bestäms med avvägningsundersökningar och jämförelser mellan olika leverantörer. Förslaget på utformning inkluderar 4 Xenon raketmotorer, med kompletterande kraftbearbetningsenheter och drivmedelshanteringssystem, vilket resulterar i en total överföringstid på mindre än 4 månader. Samma framdrivningssystem används både för överföringsbanan och manövrarna inom omloppsbanorna, genom att ändra motorns konfiguration när satelliten är i GEO.