Towed System Research Articles

Research on the trajectory tracking method of aircraft towing systems based on nonlinear control

Abstract In this paper, for the towing problem of wheeled aircraft, an automatic control method is proposed based on the nonlinear control theory, which realizes the trajectory tracking of the aircraft by controlling the velocity of the towing point of the aircraft, so as to realize the aircraft’s outbound and inbound operations. Firstly, based on the nonholonomic constraint theory, the mathematical model of the aircraft towing system is established, and the kinematic relationship between the aircraft towing point and the aircraft is obtained. Then, a controller is designed based on the nonlinear control theory, and the stability analysis is carried out using the Lyapunov method to realize the trajectory tracking of the aircraft traction system. Finally, the effectiveness and accuracy of the control method are verified by the combination of MATLAB simulation analysis and scaled-down model experiment. The results show that the proposed control method can realize the trajectory control of the aircraft towing system.

Alternative Solution for Towing Systems Used in the Automotive Industry

This paper aims, in the context of the need to reduce the weight and price of vehicles, to present theoretical and experimental results regarding towing systems made of alternative materials (fibrous composite materials and aluminum alloys). The study of the main element of the whole system, namely towbar research, was stressed, presenting comparative results. The FEM will be used to obtain the stress and strain field in the towball and the towing system. The experimental tests validate the theoretical results obtained. This paper studies five towing systems made by different materials and finally presents a series of practical recommendations, useful in the industry, regarding the improvement of the analyzed models.

Nonlinear wave model of towed system and numerical method for its calculation

Towed systems have found wide practical applications. Notable underwater systems for the long-distance extraction of minerals (concretions) from the ocean floor extend over 5-10 km. The existing mathematical models for solving dynamic problems of such systems in various environments are not entirely accurate regarding the diversity of wave processes. This necessitates the development of refined wave models. This article presents a new quasi-linear mathematical model describing the nonlinear four-mode dynamics of a towed system in a spatially inhomogeneous field of mass and surface forces. It is described by a nonlinear system of twelve first-order partial differential equations. The principles of boundedness and hyperbolicity are satisfied. The validation of the two-mode reduction of the model is based on the numerical solution of the problem of the propagation of two waves: longitudinal and configurational. Using a numerical algorithm and a program based on the finite difference method, a comparison of two difference schemes – Crank-Nicolson and Euler – was conducted. The main limitations for applying the finite difference method used for numerical modeling of wave propagation and reflection in a towed system are the peculiarities of the defining quasi-linear equations, which are related to the necessity of simultaneous computation of variables responsible for fast and slow processes. For such systems of equations, the term "singularly perturbed system of equations" is used. These perturbations result from the significant differences in the propagation speeds of longitudinal and configurational waves at the physical level. Consequently, it is necessary to employ special time-stepping regularization and filtering methods for numerical results. This imposes certain restrictions on the ability to model real processes and on the accuracy of the obtained results, necessitating the use of implicit difference schemes and high-frequency filtering.

Cable length prediction for towing models of reverse towing systems based on the cable deployment process

Given the dynamic depth changes of the underwater support vessel in the reverse towing system, the vessel needs to continuously adjust the cable length by reeling in or out to ensure that the towed body is stably towed at the designated position. Therefore, this paper considers the impact of the cable deployment process on cable length prediction and proposes a model that can dynamically predict the required cable length for the towed body at the designated position. A floating tow experiment was conducted in a towing tank, and the predicted and experimental cable length data were compared to verify the accuracy of the dynamic cable length prediction algorithm. The lift height of the towed body was compared between the proposed model and the traditional model to verify the validity of the model. The relative error between the predicted cable lengths and the experimental data was 3.8%. The relative error in the lift height between the proposed model and the traditional model was 7.2%. The proposed model can continuously and accurately predict cable length, allowing the underwater support vessel to continuously adjust the cable length, thereby ensuring the stable operation of the towed body at the designated operational position.

Model predictive control with real-time variable weight for civil aircraft towing taxi-out control systems

Unlike the traditional method of taxying, where civil aircraft reach the runway by relying on their engines, the new mode of towing taxi-out may become preferred because of its lower energy consumption, lower emissions, and higher efficiency. To improve the tracking accuracy and lateral stability of the towing system, this study used a two-level time-varying weight control method (RMPC) based on model predictive control (MPC) and fuzzy control. The tractor speed and front wheel angle were set as the control variables in the MPC controller, and the real-time lateral displacement error and yaw angle error of the tractor were set as the fuzzy control inputs. The influence of the weight matrix on the accuracy and stability of path tracking was coordinated by online optimization of the MPC objective function weight. The simulations of multiple working conditions were performed using TruckSim software in Simulink, which showed that the proposed control method can limit the lateral displacement error of the tractor and aircraft within 0.4 m, which can be reduced by 70.83% and 77.4% compared with the single MPC, respectively. Additionally, the maximum yaw angle errors of the tractor and aircraft are reduced by 76.11% and 51.31% compared with the single MPC, respectively. Furthermore, the yaw angle error of tractors can be limited to 4° and that of aircraft can be limited to 6.5°, which is an improvement of the lateral stability and driving safety for the civil aircraft towing system. The new controller may provide technical insights and support for the practical development and safe application of the towing taxi-out mode.

Use of New and Light Materials in Automotive Engineering for Towing System

Towing systems are an important component in the automobile industry, having to meet specific quality and resistance conditions. In most cases, the towbar is made of steel. Decreases in vehicle weight and manufacturing price mean that, in this field, research is also being conducted in order to replace the materials that make up the towbar and replace the steel with composite materials or aluminum alloys. In this paper, research was performed on towing systems built from other materials, and the obtained results were compared with those of steel systems. Theoretical calculations and experimental results made it possible to obtain a database and recommendations for the use of new and composite materials. The experimental tests validated the theoretical results obtained. Five towing systems made of different materials were studied. The results of the research are emphasized through recommendations regarding the manufacturing of towing systems.

Numerical analysis of dynamic behaviors of underwater towed system with hydrofoil manipulations

This paper addresses the dynamic characteristics of an underwater towed system under manipulations of synchronous hydrofoils, considering the coupling of instantaneous fluid forces on the complete systems and hydrofoil control, which is usually difficult to solve with existing methods. A hydrodynamic model coupled with hydrofoil control algorithms is presented, wherein the hydrodynamic forces on the hydrofoils and Underwater Towed Vehicle (UTV) are simulated using the Computational Fluid Dynamics (CFD) method, and the fluid forces on the Towing Cable (TC) are described using a flexible cable dynamic model. The dynamic behaviors of the underwater towed system under depth-undulating, depth-tracking, and depth-keeping controls of hydrofoils are analyzed using the proposed model. The results show that the towing speed has a significant effect on the control efficiency of the hydrofoils. The dynamic responses of the underwater towed system increase or decrease more significantly in submerged depth control operations than in freely towing operations. The hydrofoils can achieve satisfactory effects in submerged depth control for the UTV at an appropriate towing speed, whereas it fails at a lower towing speed and noticeable dynamic response oscillations occur simultaneously. This study is expected to provide guidance on both hydrodynamic and control issues of underwater towed systems.

Motion Response of the Submersible Underwater Towed System as Cable Length Changes

Submersible underwater towed systems usually need to transition from steady-state motion to maneuvering motion during operation while dynamically adjusting the length of the towed cable. The lumped mass approach was employed to convert the dragged cable into a model with a concentrated mass. Analyzed utilizing a computational simulation tool, the motion response of the towed system was examined for both simple and composite maneuvering motions. By comparing the changes in tension at the end of the towed cable and the depth of the towed body motion under different motion states and cable retraction and deployment speeds, the motion response law of the system when the length of the towed cable changes during the submarine maneuver motion is obtained. The maximum tension value occurred at 1.0 m/s during the acceleration maneuver when the velocity change of the submersible ended at the same time as the cable length change. After the deployment maneuver in a circular rotating motion, the range of tension fluctuations decreased by 93%, greatly improving the stability of the towed system. An analysis was conducted to examine the impact of various motion and structural parameters on the motion response. The study revealed that the buoyancy-to-gravity ratio of the towed body, the acceleration time of the accelerated motion, and the rotational speed of the circular rotational motion had a notable influence on the outcomes. When the buoyancy-to-gravity ratio of the towed body is 1.0, the maximum tension value of the towed cable is minimized, and the depth change of the towed body is closer to 0 m.

Event-Triggered Neural Adaptive Distributed Cooperative Control for the Multi-Tug Towing of Unactuated Offshore Platform with Uncertainties and Unknown Disturbances

An event-triggered neural adaptive cooperative control is proposed for the towing system (TS) with model parameter uncertainties and unknown disturbances. Different from ordinary multi-vessel formation control, the tugs and unactuated offshore platform in the TS are connected together by towlines, and the resultant tension of the towlines serves as the actual drag force for the platform. Initially, based on the radial basis function neural network (RBFNN), an adaptive RBFNN is designed to compensate unknown disturbances and model parameter uncertainties of the TS, and we use minimal learning parameter (MLP) algorithm to reduce the online learning parameters of adaptive RBFNN. Combined with dynamic surface technology and event-triggered control (ETC) mechanism, an event-triggered neural adaptive virtual controller is designed to obtain the desired drag force of the platform. According to the quadratic programming algorithm, the desired drag force is allocated as the desired tensions of towlines. Subsequently, the desired towline length and the desired position information of the tugs are obtained sequentially through the towline model and the position relationship between the tugs and the platform. Then, according to the desired positions of tugs, an event-triggered neural adaptive distributed cooperative controller is designed for achieving the multi-tug towing of the offshore platform. The ETC mechanism is introduced to reduce the communication burden within the TS and the execution frequency of the tugs’ thrusters. Finally, the stability of the closed-loop system is proven using the Lyapunov theory, and the ETC mechanism proves that no Zeno behavior occurs. The effectiveness of the ETC mechanism and the MLP-based adaptive RBFNN on the controllers of TS is verified through simulations and comparison analysis.

Intelligent towing and pushing system for unmanned tugboats under wind and wave disturbances

ABSTRACT Intelligent unmanned tugboats have the potential to significantly improve the efficiency of barge manipulation. This paper investigates the kinetic modelling, optimal force distribution, and cooperative control within the unmanned tugboat towing and pushing system. A practical kinetic model for the towing and pushing system has been developed, precisely taking into account factors like physical cable forces and disturbances caused by wind and waves in turbulent sea conditions. Following this, an optimal force allocation approach is investigated to allocate the desired force and determine the towing and pushing angles. Furthermore, a cooperative model predicted control strategy is proposed for the dual unmanned tugboats' towing and pushing systems. This strategy aims to ensure the barge quickly reaches its designated location, maintaining the desired heading and velocity. Simulation results indicate that unmanned tugboats can collaboratively tow and push the unpowered barge to the specified location with the desired heading and speed.

Influence of Vehicle Wake on the Control of Towed Systems

Influence of Vehicle Wake on the Control of Towed Systems

Investigation on the induced electrical wakes generated by underwater vehicles

The induced electrical wake generated by underwater vehicles in the conductive seawater subject to the geomagnetic field can offer significant information for non-acoustic detection. However, the crucial demand in actual detection requires the sophisticated detection technology to capture the variations in the wake, which has not been experimentally explored. In this paper, an underwater measurement platform, which is capable of accurately capturing the weak electrical signature, is developed to verify the detectability of the induced electric field in the wake. Besides, a towing system is designed and established to generate the wake driving the motion of the conducting seawater in the current experiment. The results indicate that the induced electric field distributions in the wake demonstrate prominent peak characteristics. The detectable intensity of the measured electric signatures in the wake can range from 1 to 3 μV/m, primarily concentrated within the extremely low frequency band below 1 Hz. Additionally, the induced electric field intensity is positively correlated with the towing velocity and demonstrates a similar evolutionary trend. Subsequently, the numerical simulations are performed to not only cross-validate the measurement results but also further demonstrate the detailed distribution of the electrical wake evolution. These findings illustrate the feasibility of detection based on the induced electric field disturbance signal in the wake, which holds potential for non-acoustic detection and tracking of underwater targets.

Анализ показателей эффективности подводных буксируемых комплексов по параметрам устойчивости и управляемости

В работе рассмотрен системный подход анализа и синтеза показателей носителя нейтральной плавучести универсального многоцелевого буксируемого геофизического подводного комплекса. В основу системного подхода предложены показатели энергоэффективности, статической и динамической устойчивости. Статическая устойчивость определяется соотношением параметров веса, размерами и геометрией отсеков плавучести лёгкого корпуса. Форма и центровка блоков плавучести лёгкого корпуса с учётом присоединённых масс связаны с величинами скорости буксировки и угла наклона буксирной линии. Достижение статической устойчивости определяется набором альтернатив обтекаемых или необтекаемых форм, а также размеров и соотношение геометрических размеров носителя нейтральной плавучести, обеспечивающих требуемые показатели назначения. Динамическая устойчивость связана с параметрами статической и определяет достижимые параметры качества динамики при буксировке на заданной глубине хода универсального многоцелевого буксируемого комплекса. Выбор и проработка комплекса учитывает изменение параметров плотности воды в зависимости от глубины хода, рыскания и боковой и курсовой устойчивости. Определены соотношения длины, ширины и высоты носителя нейтральной плавучести, а также варианты получения необходимых параметров устройством гидродинамических профилей, крыльев, пластин. Динамическая устойчивость связана с временем стабилизации носителя нейтральной плавучести при изменении высоты хода над донной поверхностью, а также чувствительности на изменение скорости буксировки и изменения длины и угла буксирной линии. Системный анализ, построенный на показателях энергоэффективности, статической и динамической устойчивости в достижимых альтернативах определяет качественную и количественную меру параметров в величинах размерности, веса и запаса плавучести. In the paper considers a systematic approach to the analysis and synthesis of indicators of the neutral buoyancy carrier of a universal multi-purpose towed geophysical underwater complex. The indicators of energy efficiency, static and dynamic stability are proposed as the basis of the systematic approach. Static stability is determined by the ratio of weight parameters, dimensions and geometry of the buoyancy compartments of the lightweight hull. The shape and alignment of the buoyancy blocks of the light hull, taking into account the attached masses, are related to the values of the towing speed and the angle of inclination of the tow line. The achievement of static stability is determined by a set of alternatives to streamlined or non-streamlined shapes, as well as the dimensions and ratio of geometric dimensions of the neutral buoyancy carrier, which provide the required destination indicators. Dynamic stability is related to the parameters of static stability and determines the achievable parameters of the quality of dynamics when towing at a given stroke depth of a universal multi-purpose towed complex. The selection and development of the complex takes into account the change in water density parameters depending on the depth of travel, yaw and lateral and directional stability. The ratios of the length, width and height of the neutral buoyancy carrier are determined, as well as options for obtaining the necessary parameters by the device of hydrodynamic profiles, wings, plates. Dynamic stability is related to the stabilization time of the neutral buoyancy carrier when the stroke height above the bottom surface changes, as well as sensitivity to changes in towing speed and changes in the length and angle of the tow line. A system analysis based on indicators of energy efficiency, static and dynamic stability in achievable alternatives determines the qualitative and quantitative measure of parameters in terms of dimension, weight and buoyancy reserve.

Structural Strength Analysis and Optimization of Commercial Aircraft Nose Landing Gear under Towing Taxi-Out Conditions Using Finite Element Simulation and Modal Testing

In the field of civil aviation, the nose landing gear is a critical component that is prone to damage during taxiing. With the advent of new technologies such as towing taxi-out and hub motors, the nose landing gear faces increasingly complex operational environments, thereby imposing higher performance demands. Ensuring the structural safety of the nose landing gear is fundamental for the successful application of these technologies. However, current research on aircraft nose landing gear under these new conditions is somewhat lacking, particularly in terms of reliable analysis models for real-world scenarios. This study focuses on a typical Class C aircraft, specifically the B-727 model, for which a finite element model of the nose landing gear is developed. Modal testing of the aircraft’s nose landing gear is conducted using the impact hammer method, and the results are compared with those from the simulations. The experimental data indicate that the error range for the first seven natural frequencies is between 0.23% and 9.27%, confirming the high accuracy of the developed landing gear model. Furthermore, with towing taxi-out as the primary scenario, a dynamic model of the aircraft towing system is established, and an analysis on the structural strength and topological optimization of the nose landing gear under various conditions, including high speeds and heavy loads, is performed. The results show that the developed model can effectively support the analysis and prediction of the mechanical behavior of the nose landing gear. Under high-speed, heavy-load conditions, the nose landing gear experiences significantly increased loads, with the maximum deformation primarily occurring at the lower section of the shock strut’s outer cylinder. However, no damage occurred. Additionally, under these conditions, an optimized structural design for the landing gear was identified, which, while ensuring structural strength, achieves a 22.32% reduction in the mass of the outer cylinder, also ensuring safety in towing taxi-out conditions.

Study on the steady state position of ocean towing cables

A study is conducted on the static equilibrium posture of the towing cable in water under a constant speed state in the towing system. Firstly, the underwater force state of the towing body is calculated and then the posture and tension of the towing cable are analyzed and calculated. As the cable is divided into two states which are above water and below water, a differential equation system is established as the boundary. The initial value of the equation can be transformed by the drag and gravity values of the towing body. The program solves the differential equations using the fourth-order Runge Kutta method and draws the attitude curve. Finally, it verifies the theoretical calculation results through experiments.

A Flow Structure Interaction Method for Towed Cable System

Abstract: The ocean towed cable system is a classic example of fluid-structure interaction (FSI). This interaction can exhibit stability or oscillation between a highly deformable moving cable and the surrounding turbulent flow. However, in dynamic simulations of towed cable systems, a constant drag coefficient for an infinite circular cylinder is often used based on experimental data. An innovative fluid-structure interaction method is introduced to obtain accurate drag distribution along cable to couple with towed system dynamics. A modified nodal position finite element method (NPFEM) coupled with Reynolds-averaged Navier-Stokes (RANS) approach has been utilized to predict hydrodynamic forces along the cable. A data exchange algorithm has been developed specifically for fluid-structure interaction within the towed cable system where the cable profile is transferred to construct the flow domain while hydrodynamics is interpolated for NPFEM analysis. A topology partition around cable is applied. A multiblock grid is generated around cable. The simulation results of the fluid-structure interaction of the towing system are verified. This FSI scheme reveals how strongly hydrodynamics determine cable dynamics and induce vortex structure vibrations around a towed cable system. Parametrically controlled structured grid generation and their applicability for complex flow fields have also been discussed. Detailed descriptions of boundary layer separation evolution around spatially distributed cable are provided. This FSI scheme reveals a real strongly hydrodynamic determined cable dynamics and vortex structure induced vibrations around a towed cable system. The proposed method enhances predictive accuracy of the towed system dynamics response.

Automated zooplankton detection from in situ imagery for forward scattering predictions

Ocean midwaters—the vast region between the sunlit surface layers and seafloor—comprise the largest habitat on Earth but are among the least understood marine environments. This project aims to combine concurrently collected imaging and acoustic measurements in the epi and mesopelagic environment to interpret zooplankton scattering from mixed assemblages and determine in situ zooplankton distributions within their local environments. We have trained a machine learning model for the automated detection of 13 zooplankton functional groups from a 1000m rated towed shadowgraph imaging system. The zooplankton detection model currently achieves 80% F1 scores on our validation image set and was trained using adversarial methods. We have derived biometric measurements from the zooplankton image data necessary to generate forward scattering predictions. We compare the distributions of scattering layers detected acoustically with zooplankton distributions from the imagery. We will compare forward scattering predictions derived from sparse geometric representations of the zooplankton and full 3D model volumes using the distance transform of the zooplankton images. This work will further enable the use of optical techniques for midwater surveys and the interpretation of acoustic scattering returns from mixed zooplankton populations.

The ONR three octave research array at Penn State

A new, large diameter towed research array has been built to support the experimental efforts of the Office of Naval Research (ONR) Ocean Acoustics Program. Array development was a collaborative effort between the Centre for Maritime Research and Experimentation (CMRE) in La Spezia, Italy, and the Penn State Applied Research Laboratory (PSU). PSU chose the array specifications based on discussions within the underwater acoustics community, prior measurement experience, cost efficiency, and flexibility in scientific measurements, while CMRE designed and assembled the array. The design includes three, forward-nested acoustic apertures cut for 1, 2, and 4 kHz, and hence, has been dubbed the Three Octave Research Array (THORA) in deference to its predecessor, the Five Octave Research Array (FORA). However, this system has a modular design to allow addition of acoustic apertures if scientific interest and sponsor support warrant. The array currently consists of a 50 m acoustic module and a 25 m vibration isolation module to help isolate the acoustic module from cable strum. This ship towed system has nearly 1 km of tow cable and a maximum measurement depth of 500 m. The array’s design, its use in the ONR NESMA23 Pilot experiment, and data quality will be discussed.

Dynamic analysis of aircraft towing slip-out system considering vertical wheel constraints

Abstract To analyze the vertical dynamic characteristics of the aircraft towing system under different constraints on the nose landing gear wheels of the aircraft during the towing slip-out mode, a dynamic model of the towing system considering the constraints between the clamping mechanism and the aircraft nose landing gear wheels was established based on the general towing system dynamic model. On this basis, an analysis was conducted to determine whether considering the aircraft wheel constraints affects the vertical vibration acceleration of the towing vehicle and the nose landing gear in low-speed (10 km/h) and high-speed (40 km/h) operating conditions. With the consideration of constraints at both ends of the aircraft wheels, the vertical acceleration of the towing vehicle's center of mass increased by 153% and 172% at low speed and high speed, respectively, compared to not considering the aircraft wheel constraints. Additionally, with the consideration of constraints at both ends of the aircraft wheels, the vertical acceleration of the nose landing gear's center of mass decreased to 20% and 57% at low speed and high speed, respectively, compared to not considering the aircraft wheel constraints. An analysis of the vertical vibration acceleration of the towing vehicle under different wheel constraint conditions found that the RMS value of the vertical vibration acceleration of the towing vehicle's center of mass was minimized when the clamping angles of the clamping mechanism to the nose landing gear wheels were 63° and 64°, respectively. Under this clamping angle, the influence of the clamping forces at both ends of the clamping mechanism on the vertical vibration acceleration of the towing vehicle was minimal. The research results provide valuable reference for the direct constraints between the clamping mechanism and the nose landing gear wheels in the aircraft towing slip-out system.

Development of a mathematical model of underwater towing, based on single- and double-link rod models of towing lines

This paper develops a mathematical model of underwater towing by the example of a complex fishing complex "vessel - vaer - trawl" by calculating its traction and speed characteristics.
 The tow line is an important factor when towing an underwater object because it can affect the stability and maneuverability of the towing vessel. If the shaft is too long, it can create a lot of drag and make it difficult to move the boat. On the other hand, if the shaft is too short, it may cause the towed object to sink too deeply and potentially damage the object or towing equipment. Consequently, it is critical to select the proper towing system settings based on the size and weight of the object being towed, the depth of the stroke, and the environmental conditions.
 Existing methods for writing models of tug - towing object systems, namely, methods based on stationary and non-stationary nature of the vaer selection process are investigated.
 The paper presents a comparative analysis of single-link and two-link rod models of towing lines. The main errors in the construction of trajectories of towed objects using these types of towing lines are revealed.
 In particular, one of the results of the study is, building a model of the system "ship - vaer - towed object", which has a similar accuracy index to the more complex two- and three-link lines.