Applications of higher harmonic control to hingeless rotor systems

A comprehensive analytical formulation was developed to predict the vibratory hub loads of a helicopter rotor system in forward flight. This analysis is used to calculate the optimal higher harmonic control inputs and associated actuator power required to minimize these hub loads. The present formulation is based on a finite element method in space and time. A nonlinear time domain, unsteady aerodynamic model is used to obtain the airloads, and the rotor induced inflow is calculated using a nonuniform inflow model. Predicted vibratory hub loads are correlated with experimental data from a scale model rotor. Results of a parametric study on a hindgeless rotor show that blade flap, lag and torsion vibration characteristics, offset of blade center of mass from elastic axis, offset of elastic axis from quarter-chord axis, and blade thrust greatly affect the higher harmonic control actuator power requirement

Optimization techniques for satellites proximity maneuvers

The main topic of this dissertation is the control optimization problem for satellites Rendezvous and Docking. Saving resources is almost as important as the mission safeness and effectiveness. Three different numerical approaches are developed. The first two techniques deal with realtime and sub-optimal control, generating a reliable control sequence for a chaser spacecraft which eventually docks to a target. The first approach uses dynamic programming to quickly generate a sub-optimal control sequence on a predetermined path to be followed by one of the two vehicles involved into the docking operations. The second method presents a fast direct optimization technique, which was previously validated on real aircraft for trajectory optimization. The third approach aims to take into account the limitations of space qualified hardware, in particular thrusters. The new technique fuses the use of a set of low thrust on-off engines with impulsive-high-thrust engines. The hybrid method here developed combines and customizes different techniques. The relative motion in the above mentioned control strategies is represented by a linear dynamic model. As secondary topic of this dissertation, the use of a genetic algorithm optimizer to find possible conditions under which spacecraft relative motion can be periodic, or at least bounded, is presented. This analysis takes into account the J2 gravity perturbation and some drag effects. The importance of the obtained results directly apply to the problem of formation keeping, as natural dynamics can be exploited to reduce the amount of active control preventing the spacecrafts to drift apart along tim

On some impulsive fractional differential equations in Banach spaces

This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of $PC$-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration

Orbit control of asteroids in libration point orbits for resource exploitation

The fascinating idea of shepherding asteroids for science and resource utilisation is being considered as a very credible concept in a not too distant future. Past studies have identified asteroids which could be injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system, by means of a low-cost manoeuvre. However, the periodic orbits as well as the manifolds are highly unstable, and small errors in the capture manoeuvre would bring to complete mission failure, with potential danger of collision with the Earth itself. The main source of injection error in position and velocity is the epistemic uncertainty of the asteroid mass, which cannot be measured directly. For this reason, asteroid orbit control will be a strict requirement for such mission. This paper investigates the controllability of some asteroids during the transfer and along the period orbits, assuming the use of a solar-electric low-thrust engine. The control scheme is based on a linear quadratic regulator. A stochastic simulation with a Monte Carlo approach is used to simulate a range of different perturbed initial conditions. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets

Optimization techniques for satellites proximity maneuvers

The main topic of this dissertation is the control optimization problem for satellites Rendezvous and Docking. Saving resources is almost as important as the mission safeness and effectiveness. Three different numerical approaches are developed. The first two techniques deal with realtime and sub-optimal control, generating a reliable control sequence for a chaser spacecraft which eventually docks to a target. The first approach uses dynamic programming to quickly generate a sub-optimal control sequence on a predetermined path to be followed by one of the two vehicles involved into the docking operations. The second method presents a fast direct optimization technique, which was previously validated on real aircraft for trajectory optimization. The third approach aims to take into account the limitations of space qualified hardware, in particular thrusters. The new technique fuses the use of a set of low thrust on-off engines with impulsive-high-thrust engines. The hybrid method here developed combines and customizes different techniques. The relative motion in the above mentioned control strategies is represented by a linear dynamic model. As secondary topic of this dissertation, the use of a genetic algorithm optimizer to find possible conditions under which spacecraft relative motion can be periodic, or at least bounded, is presented. This analysis takes into account the J2 gravity perturbation and some drag effects. The importance of the obtained results directly apply to the problem of formation keeping, as natural dynamics can be exploited to reduce the amount of active control preventing the spacecrafts to drift apart along tim

Pareto-efficient biological pest control enable high efficacy at small costs

Biological pest control is increasingly used in agriculture as a an alternative to traditional chemical pest control. In many cases, this involves a one-off or periodic release of entomopathogens. As the interaction between the entomopathogen and the pest is complex and the production of entomopathogens potentially expensive, it is not surprising that both the efficacy and economic viability of biological pest control are debated. Here, we investigate the performance of very simple control strategies. In particular, we show how Pareto-efficient one-off or periodic release strategies, which optimally trade off between efficacy and economic viability, can be devised and used to enable high efficacy for small economic costs. We demonstrate our method on a pest-pathogen-crop model with a tunable immigration rate of pests. By analyzing this model, we demonstrate that simple Pareto-efficient one-off release strategies are typically efficacious and simultaneously have average profits that are close to the theoretical maximum obtained by less efficacious and complicated profit-optimizing strategies. The only exception occurs for high pest-immigration rates, in which case periodic release is preferable. The methods presented here can be extended to more complex scenarios and thus be used to identify promising biological pest control strategies in many circumstances

Easily retrievable objects among the NEO population

Asteroids and comets are of strategic importance for science in an effort to understand the formation, evolution and composition of the Solar System. Near-Earth Objects (NEOs) are of particular interest because of their accessibility from Earth, but also because of their speculated wealth of material resources. The exploitation of these resources has long been discussed as a means to lower the cost of future space endeavours. In this paper, we consider the currently known NEO population and define a family of so-called Easily Retrievable Objects (EROs), objects that can be transported from accessible heliocentric orbits into the Earth’s neighbourhood at affordable costs. The asteroid retrieval transfers are sought from the continuum of low energy transfers enabled by the dynamics of invariant manifolds; specifically, the retrieval transfers target planar, vertical Lyapunov and halo orbit families associated with the collinear equilibrium points of the Sun-Earth Circular Restricted Three Body problem. The judicious use of these dynamical features provides the best opportunity to find extremely low energy Earth transfers for asteroid material. A catalogue of asteroid retrieval candidates is then presented. Despite the highly incomplete census of very small asteroids, the ERO catalogue can already be populated with 12 different objects retrievable with less than 500 m/s of Δv. Moreover, the approach proposed represents a robust search and ranking methodology for future retrieval candidates that can be automatically applied to the growing survey of NEOs