Optimal control of systems with memory

The “Optimal Control of Systems with memory” is a PhD project that is borne from the collaboration between the Department of Mechanical and Aerospace Engineering of Sapienza University of Rome and CNR-INM the Institute for Marine Engineering of the National Research Council of Italy (ex INSEAN). This project is part of a larger EDA (European Defence Agency) project called ETLAT: Evaluation of State of the Art Thin Line Array Technology. ETLAT is aimed at improving the scientific and technical knowledge of potential performance of current Thin Line Towed Array (TLA) technologies (element sensors and arrays) in view of Underwater Surveillance applications. A towed sonar array has been widely employed as an important tool for naval defence, ocean exploitation and ocean research. Two main operative limitations costrain the TLA design such as: a fixed immersion depth and the stabilization of its horizontal trim. The system is composed by a towed vehicle and a towed line sonar array (TLA). The two subsystems are towed by a towing cable attached to the moving boat. The role of the vehicle is to guarantee a TLA’s constant depth of navigation and the reduction of the entire system oscillations. The vehicle is also called "depressor" and its motion generates memory effects that influence the proper operation of the TLA. The dynamic of underwater towed system is affected by memory effects induced by the fluid-structure interaction, namely: vortex shedding and added damping due to the presence of a free surface in the fluid. In time domain, memory effects are represented by convolution integral between special kernel functions and the state of the system. The mathematical formulation of the underwater system, implies the use of integral-differential equations in the time domain, that requires a nonstandard optimal control strategy. The goal of this PhD work is to developed a new optimal control strategy for mechanical systems affected by memory effects and described by integral-differential equations. The innovative control method presented in this thesis, is an extension of the Pontryagin optimal solution which is normally applied to differential equations. The control is based on the variational control theory implying a feedback formulation, via model predictive control. This work introduces a novel formulation for the control of the vehicle and cable oscillations that can include in the optimal control integral terms besides the more conventional differential ones. The innovative method produces very interesting results, that show how even widely applied control methods (LQR) fail, while the present formulation exhibits the advantage of the optimal control theory based on integral-differential equations of motion

Modeling, identification, estimation and adaptation for the control of power-generating kites

Large-scale kites, flying high-force crosswind trajectories, have been proposed for wind power generation. A two phase operational cycle generates net positive power using a ground-based motor/generator. In the traction phase the kite flies a high-force trajectory while reeling out the generator-connected tethers. A low-force retraction phase reels in the tethers and returns the kite to the start of the cycle. Highly variable conditions and significant uncertainty in the dynamics pose challenges to autonomous, well-controlled flight. The control task is divided into trajectory generation and tracking components and the most uncertain parameters in the model are identified online. The control structure uses these parameters in a robust framework resulting in an experimentally verified adaptive control scheme

A Hybrid Control Approach for the Swing Free Transportation of a Double Pendulum with a Quadrotor

In this article, a control strategy approach is proposed for a system consisting of a quadrotor transporting a double pendulum. In our case, we attempt to achieve a swing free transportation of the pendulum, while the quadrotor closely follows a specific trajectory. This dynamic system is highly nonlinear, therefore, the fulfillment of this complex task represents a demanding challenge. Moreover, achieving dampening of the double pendulum oscillations while following a precise trajectory are conflicting goals. We apply a proportional derivative (PD) and a model predictive control (MPC) controllers for this task. Transportation of a multiple pendulum with an aerial robot is a step forward in the state of art towards the study of the transportation of loads with complex dynamics. We provide the modeling of the quadrotor and the double pendulum. For MPC we define the cost function that has to be minimized to achieve optimal control. We report encouraging positive results on a simulated environmentcomparing the performance of our MPC-PD control circuit against a PD-PD configuration, achieving a three fold reduction of the double pendulum maximum swinging angle.This work has been partially supported by FEDER funds through MINECO project TIN2017-85827-P, and project KK-202000044 of the Elkartek 2020 funding program of the Basque Government. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 777720

Tracking sperm whales using passive acoustics and particle filters

Passive acoustics provides a powerful tool for marine mammal research and mitigation of the risk posed by high energy anthropogenic acoustic activities through monitoring animal positions. Animal vocalisations can be detected and utilised in poor visibility conditions and while animals are dived. Marine mammal research is often conducted on restricted financial budgets by non-government organisations and academic institutions from boats or ships towing hydrophone arrays often comprising only two elements. The arrival time-delay of the acoustic wavefront from the vocalising animals across the array aperture is computed, often using freely available software, and typically regarded as the bearing of the animal to the array. This methodology is limited as it provides no ranging information and, until a boat manoeuvre is performed, whether the animal is to the left or right of the array remains ambiguous. Methods of determining range that have been suggested either negate the fact the animal is moving, rely on robust detection of acoustic reflections, rely on accurate equipment calibration and knowledge of the animal’s orientation or require modification of hydrophone equipment. There is a clear need to develop an improved method of estimating animal position as relative bearing, range and elevation to a hydrophone array or boat based on time-delay measurements. To avoid the costs of upgrading hydrophone arrays, and potentially the size of the vessels required to tow them, a software solution is desirable. This thesis proposes that the source location be modelled as a probability density function and that the source location is estimated as the mean. This is developed into a practical method using particle filters to track sperm whales. Sperm whales are the ideal subject species for this kind of development because the high sound pressure levels of their impulsive vocalisations (up to 236 dB re 1 ?Pa) makes them relatively simple to detect. Simulation tracking results demonstrate particle filters are capable of tracking a manoeuvring target using time-delay measurements. Tracking results for real data are presented and compared to the pseudotrack reconstructed from a tag equipped with accelerometers, magnetometers, a depth sensor and an acoustic recorder placed on the subject animal. For the majority of datasets the animal is tracked to a position relatively close to the surface sighting position. Sperm whales are typically encountered in groups, therefore a viable tracking solution needs to be capable of tracking multiple animals. A multiple hypothesis tracking method is proposed and tested for associating received vocalisations with animals, whereby vocalisations are correctly associated for periods exceeding 15 minute

Sensor Array Processing with Manifold Uncertainty

<p>The spatial spectrum, also known as a field directionality map, is a description of the spatial distribution of energy in a wavefield. By sampling the wavefield at discrete locations in space, an estimate of the spatial spectrum can be derived using basic wave propagation models. The observable data space corresponding to physically realizable source locations for a given array configuration is referred to as the array manifold. In this thesis, array manifold ambiguities for linear arrays of omni-directional sensors in non-dispersive fields are considered. </p><p>First, the problem of underwater a hydrophone array towed behind a maneuvering platform is considered. The array consists of many hydrophones mounted to a flexible cable that is pulled behind a ship. The towed cable will bend or distort as the ship performs maneuvers. The motion of the cable through the turn can be used to resolve ambiguities that are inherent to nominally linear arrays. The first significant contribution is a method to estimate the spatial spectrum using a time-varying array shape in a dynamic field and broadband temporal data. Knowledge of the temporal spectral shape is shown to enhance detection performance. The field is approximated as a sum of uncorrelated planewaves located at uniform locations in angle, forming a gridded map on which a maximum likelihood estimate for broadband source power is derived. Uniform linear arrays also suffer from spatial aliasing when the inter-element spacing exceeds a half-wavelength. Broadband temporal knowledge is shown to significantly reduce aliasing and thus, in simulation, enhance target detection in interference dominated environments. </p><p>As an extension, the problem of towed array shape estimation is considered when the number and location of sources are unknown. A maximum likelihood estimate of the array shape using the field directionality map is derived. An acoustic-based array shape estimate that exploits the full 360$^\circ$ field via field directionality mapping is the second significant contribution. Towed hydrophone arrays have heading sensors in order to estimate array shape, but these sensors can malfunction during sharp turns. An array shape model is described that allows the heading sensor data to be statistically fused with heading sensor. The third significant contribution is method to exploit dynamical motion models for sharp turns for a robust array shape estimate that combines acoustic and heading data. The proposed array shape model works well for both acoustic and heading data and is valid for arbitrary continuous array shapes.</p><p>Finally, the problem of array manifold ambiguities for static under-sampled linear arrays is considered. Under-sampled arrays are non-uniformly sampled with average spacing greater than a half-wavelength. While spatial aliasing only occurs in uniformly sampled arrays with spacing greater than a half-wavelength, under-sampled arrays have increased spatial resolution at the cost of high sidelobes compared to half-wavelength sampled arrays with the same number of sensors. Additionally, non-uniformly sampled arrays suffer from rank deficient array manifolds that cause traditional subspace based techniques to fail. A class of fully agumentable arrays, minimally redundant linear arrays, is considered where the received data statistics of a uniformly spaced array of the same length can be reconstructed in wide sense stationary fields at the cost of increased variance. The forth significant contribution is a reduced rank processing method for fully augmentable arrays to reduce the variance from augmentation with limited snapshots. Array gain for reduced rank adaptive processing with diagonal loading for snapshot deficient scenarios is analytically derived using asymptotic results from random matrix theory for a set ratio of sensors to snapshots. Additionally, the problem of near-field sources is considered and a method to reduce the variance from augmentation is proposed. In simulation, these methods result in significant average and median array gains with limited snapshots.</p>Dissertatio

Multi-Channel Ground-Penetrating Radar for the Continuous Quantification of Snow and Firn Density, Depth, and Accumulation

A priority of ice sheet surface mass balance (SMB) prediction is ascertaining the surface density and annual snow accumulation. These forcing data are inputs for firn density models and can be used to inform remotely sensed ice sheet surface processes and to assess Regional Climate Model (RCM) skill. The Greenland Traverse for Accumulation and Climate Studies (GreenTrACS) retrieved 16 shallow firn cores and dug 42 snow pits along the Western percolation zone of the Greenland Ice Sheet (GrIS) during May and June of 2016 and 2017. I deployed and maintained a multi-channel 500 MHz ground-penetrating radar in a multi-offset configuration throughout the two traverse campaigns. The multi-channel radar technique accurately and independently estimates density, depth, and annual snow accumulation -- between the firn core and snow pit sites -- by horizon velocity analysis of common midpoint radar reflections from the snow and shallow firn. I analyzed a 45 km section of the traverse in a high accumulation zone, known as the GreenTrACS Core 15 Western Spur. Deviations in surface density up to +- 15 kg/m3 from the transect mean correlate with surface elevation and surface slope angle. Spatial variation in mean annual accumulation of ~0.175 m w.e. ɑ-1 occurs across a trough in the surface topography ~5 km wide. The reported variability of density and accumulation demonstrates that RCMs must be down-scaled to resolutions within 5 km to assess subtle yet significant contributions to the GrIS SMB

Nonlinear dynamics and control of electrodynamic tether for deorbiting space debris

The ever increasing population of space debris poses a great threat to the sustainable development of space industry. Electrodynamic tether has been recognized as a promising technology for the active removal of space debris from overpopulated orbital regions. A typical electrodynamic tether system consists of two end-bodies connected by a conductive tether in space. The electric current flowing in the tether will interact with the magnetic field of the Earth to generate the Lorentz force, by which the system can be deorbited almost without expending propellant. The dynamics and control of any electrodynamic tether system is highly nonlinear by nature and have two critical aspects for practical application: the deployment of electrodynamic tether and the attitude stability during the deorbiting process. This paper summarizes some recent efforts made to address these two issues by the authors’ research team in Nanjing University of Aeronautics and Astronautics. Moreover, some open problems deserving future investigation are discussed

The development and use of off-shore mineral exploration techniques

Imperial Users onl

Hydrodynamic profile of young swimmers: changes over a competitive season

The aim of this study was to analyze the changes in the hydrodynamic profile of young swimmers over a competitive season and to compare the variations according to a well-designed training periodization. Twenty-five swimmers (13 boys and 12 girls) were evaluated in (a) October (M1); (b) March (M2); and (c) June (M3). Inertial and anthropometrical measures included body mass, swimmer’s added water mass, height, and trunk transverse surface area. Swimming efficiency was estimated by the speed fluctuation, stroke index, and approximate entropy. Active drag was estimated with the velocity perturbation method and the passive drag with the gliding decay method. Hydrodynamic dimen- sionless numbers (Froude and Reynolds numbers) and hull velocity (i.e., speed at Froude number = 0.42) were also calculated. No variable presented a significant gender effect. Anthropometrics and inertial parameters plus dimensionless numbers increased over time. Swimming efficiency improved between M1 and M3. There was a trend for both passive and active drag increase from M1 to M2, but being lower at M3 than at M1. Intra-individual changes between evaluation moments suggest high between- and within-subject variations. Therefore, hydrodynamic changes over a season occur in a non-linear fashion way, where the interplay between growth and training periodization explain the unique path flow selected by each young swimmer