A comparison between mathematical models of stationary configuration of an undewater towed system with experimental validation

The analysis of underwater towed systems attracted the interest of many researchers because of the recent years utilization of remotely-operated underwater vehicle (ROV) and towed array in offshore and military applications. The purpose of this work is to show, by experimental validation, that towed cable configurations may be computed effectively and accurately by discretizing the towing cable rather than using a continuous modeling approach. Two mathematical models have been developed to predict the stationary configuration of an underwater towed system loaded by hydrodynamic forces. The system is composed of a towed inextensible cable, with no bending stiffness, and a depressor that is fixed at the cable free end. This configuration is currently used for underwater remotely-operated vehicle. This work investigates the comparison between continuous and discrete models of the 2D static equations of the steady-state towing problem in a vertical plane at different towing speeds. The results of the models have been validating using experimental trials. In the first part of this paper, a continuous model is presented, which is based on geometric compatibility relations, equilibrium equation. A set of nonlinear differential equations has been derived and solved using Runge-Kutta iterative procedure. In the second part, a discrete rod model is proposed to determinate the cable shape, which is based on a system of nonlinear algebraic equations that are solved numerically. This two models are both suitable for analyzing an underwater towed system having a known top tension and inclination angle obtained from experiments. The third part of the paper describes the experiments, which have been in a towing tank basin (CNR-INSEAN). In the fourth and last part of this study it is demonstrated the effort and cost of numerically integrating the continuous model do not compare favorably with the relative ease and efficiency of solving the discrete model, which yields the same results

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

Aeroelastic dynamic feedback control of a Volterra airfoil

The work aims to develop a novel optimal control algorithm for integral differential equations which includes the first kind Volterra’s integral. An indirect and analytical solution of Pontryagin’s problem for Volterra equations permits to find an explicit feedback control solution here called PI(N). Numerical simulations are performed to validate the proposed algorithm with a classical test case in aerodynamic: the motion control of a moving airfoil modelled with the Wagner time-varying theory. The wings are characterized by memory effects, due to aeroelastic phenomena, which are usually difficult to incorporate in optimal control logics unless quantized numerical solvers are used, which require onerous computational efforts

Experimental valuation of the pressure field around a cylinder at varying towing speed

The purpose of this document is to provide the experimental results performed at the first water tank of the CNR-INSEAN Marine Institute of Rome. The experimental campaign has been developed to evaluate the pressure field around a cylinder towed at different speed and in different configurations

OPTIMAL FEEDBACK CONTROL LAW FOR VISCOELASTIC MATERIALS WITH MEMORY EFFECTS

Viscoelastic materials have excellent properties of absorbing vibrational energy which makes their use very attractive in structural, aerospace and biomechanics engineering applications. The macroscopic dynamical behaviour of such materials depends on the time history, or memory, of the strain. The stress-strain viscoelastic relation can be described by a convolution integral with a memory kernel, according to Boltzmann’s formulation of hereditary elasticity, or by using Caputo or Riemann-Liouville fractional derivatives. In order to emphasize the vibrations damping attitude of these materials, by actively controlling their stress-strain behaviour, novel optimal control logics are required which involve memory effects. This paper deals with a feedback control strategy applied to a structural-dynamic problem described by integral-differential equations. It is shown how to obtain a feedback control, called PD(N), i.e. Proportional-Nth-order-Derivatives control, by using a variational approach. Numerical simulations show how the PD(N) controller is an effective tool to improve the viscoelastic materials performance. © 2020 European Association for Structural Dynamics. All rights reserved

Report ETLAT EDA Project: measurements on drag/towing speed law and dynamical behaviour from video analysis with different types of thin line arrays sensors

The purpose of this document is to provide the experimental results performed at the first water tank of the CNR-INSEAN Marine Institute of Rome. The experimental campaign has been developed in order to evaluate the dynamical behaviour of the tested TLA. Two kind of experimental trials have been performed in parallel: the value of drag force of the TLA at varying towing speed and the reconstruction of TLA dynamical behaviour by a video analysis

Report on ETLAT EDA Project: Test of Dummy Sensors in Water Tank

The goal of the \u27Test of dummy sensors in water tank\u27 report is to get data to validate the fluid-dynamic numerical models on the thin line array dynamic behaviour. All the partners, involved in the project, have to realize the dummy sensors (3 diameters, length > 5 m) and measurement of the speed and pressure fields around the sensors with water speed up to 5 m/s. In the present document the experimental measures of the speed and pressure fields of water flowing around TLA sensors at max 5 m/s are exposed. In the first part, the Test Plan and Interface Specification between dummy sensors and water tank are explained. Instead, the second part reports the measured speed and pressure fields with different types of TLA sensors. Test performed at INSEAN towing tank