Rozprawy doktorskie na temat „Flutter Prediction”

The flutter is a dangerous aeroelastic instability that can cause dramatic failures. It is important to evaluate in which conditions it can occur to ensure the safety of the pilots and the passengers. As flight tests are very expensive and hazardous, the need for efficient and trustworthy numerical tools becomes essential. This report focuses on two methods to predict the flutter conditions in the transonic domain. To evaluate the accuracy of these tools, their results are compared to experimental data gathered during a wind-tunnel test. The influence of the Mach number and the angle of attack on the flutter conditions is studied and physical explanations are put forward.

Flutter analyses and tests are the major items in flight certification efforts required when a new air vehicle is developed or when a new external store is developed for an existing aircraft. The flight envelope of a new aircraft as well as the influence of aircraft modifications on an existing flight envelope can be safely determined only by flutter tests. In such tests, the aircraft is instrumented by accelerometers and exciters. Vibrations of the aircraft at specific dynamic pressures are measured and transmitted to a ground station via telemetry systems during flutter tests. These vibration data are analyzed online by using a flutter test software with various methods implemented in order to predict the safety margin with respect to flutter. Tests are performed at incrementally increasing dynamic pressures and safety regions of the flight envelope are determined step by step. Since flutter is a very destructive instability, tests are performed without getting too close to the flutter speed and estimations are performed by extrapolation. In this study, pretest analyses and flutter prediction methods that can be used in various flight conditions are investigated. Existing methods are improved and their applications are demonstrated with experiments. A novel method to predict limit cycle oscillations that are encountered in some modern fighter aircraft is developed. The prediction method developed in this study can effectively be used in cases where the nonlinearities in aircraft dynamics and air flow reduce the applicability of the classical prediction methods. Some further methods to reduce the adverse effects of these nonlinearities on the predictions are also developed.

This dissertation deals with the instability, known as flutter, of the lifting and control surfaces of aircraft of advanced design at high altitudes and speeds. A simple model is used to represent the aerodynamics for flutter analysis of a two-degree-of-freedom airfoil system. Flutter solutions of this airfoil system are shown to be algebraically homomorphic in that solutions about different elastic axes can be found by mapping them to those about the mid-chord. Algebraic expressions for the flutter speed and frequency are thus obtained. For the prediction of flutter of a wing at transonic speeds, an accurate and efficient computer code is developed. The unique features of this code are the capability of accepting a steady mean flow regardless of its origin, a time dependent perturbation boundary condition for describing wing deformations on the mean surface, and a locally applied three-dimensional far-field boundary condition for minimizing wave reflections from numerical boundaries. Results for various test cases obtained using this code show good agreement with the experiments and other theories.

Recent design trends in steam turbines strive for high aerodynamic loading and high aspect ratio to meet the demand of higher efficiency. These design trends together with the low structural frequency in last stage steam turbines increase the susceptibility of the turbine blades to flutter. Flutter is the self-excited and self-sustained aeroelastic instability phenomenon, which can result in rapid growth of blade vibration amplitude and eventually blade failure in a short period of time unless adequately damped. To prevent the occurrences of flutter before the operation of new steam turbines, a compromise between aeroelastic stability and stage efficiency has to be made in the steam turbine design process. Due to the high uncertainty in present flutter prediction methods, engineers use large safety margins in predicting flutter which can rule out designs with higher efficiency. The ability to predict flutter more accurately will allow engineers to push the design envelope with greater confidence and possibly create more efficient steam turbines. The present work aims to investigate the influence of tip clearance flow on the prediction of steam turbine flutter characteristics. Tip clearance flow effect is one of the critical factors in flutter analysis for the majority of aerodynamic work is done near the blade tip. Analysis of the impact of tip clearance flow on steam turbine flutter characteristics is therefore needed to formulate a more accurate aeroelastic stability prediction method in the design phase.Besides the tip leakage vortex, the induced vortices in the tip clearance flow can also influence blade flutter characteristics. However, the spatial distribution of the induced vortices cannot be resolved by URANS method for the limitation of turbulence models. The Detached-Eddy Simulation (DES) calculation is thus applied on a realistic-scale last stage steam turbine model to analyze the structure of induced vortices in the tip region. The influence of the tip leakage vortex and the induced vortices on flutter prediction are analyzed separately. The KTH Steam Turbine Flutter Test Case is used in the flutter analysis as a typical realistic-scale last stage steam turbine model. The energy method based on 3D unsteady CFD calculation is applied in the flutter analysis. Two CFD solvers, an in-house code LUFT and a commercial software ANSYS CFX, are used in the flutter analysis as verification of each other. The influence of tip leakage vortex on the steam turbine flutter prediction is analyzed by comparing the aeroelastic stability of two models: one with the tip gap and the other without the tip gap. Comparison between the flutter characteristics predicted by URANS and DES approaches is analyzed to investigate the influence of the induced vortices on blade flutter characteristics. The multiple induced vortices and their relative rotation around the tip leakage vortex in the KTH Steam Turbine Flutter Test Case are resolved by DES but not by URANS simulations. Both tip leakage vortex and induced vortices have an influence on blade loading on the rear half of the suction side near the blade tip. The flutter analysis results suggest that the tip clearance flow has a significant influence on blade aerodynamic damping at the least stable interblade phase angle (IBPA), while its influence on the overall shape of the damping curve is minor. At the least stable IBPA, the tip leakage vortex shows a stabilization effect on rotor aeroelastic stabilities while the induced vortices show a destabilization effect on it. Meanwhile, a non-linear unsteady flow behavior is observed due to the streamwise motion of induced vortices during blade oscillation, which phenomenon is only resolved in DES results.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2018.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 121-141) and index.
Novel commercial transport aircraft concepts feature large wing spans to increase their fuel efficiency; these wings are more flexible, leading to more potential aeroelastic problems. Furthermore, these aircraft fly in the transonic flow regime, where utter prediction is difficult. The goals for this thesis are to devise a method to reduce the computational burden of including transonic utter constraints in conceptual design tools, and to offer a potential solution for mitigating utter problems through the use of additive manufacturing techniques, specically focusing on a design methodology for lattice structures. To reduce the computational expense of considering transonic utter in conceptual aircraft design, a physics-based low-order method for transonic utter prediction is developed, which is based on small unsteady disturbances about a known steady flow solution. The states of the model are the circulation and doublet perturbations, and their evolution equation coefficients are calibrated using off-line unsteady two-dimensional flow simulations. The model is formulated for swept high-aspect ratio wings through strip theory and 3D corrections. The resulting low-order unsteady flow model is coupled to a typical-section structural model (for airfoils) or a beam model (for wings) to accurately predict utter of airfoils and wings. The method is fast enough to permit incorporation of transonic utter constraints in conceptual aircraft design calculations, as it only involves solving for the eigenvalues of small state-space systems. This model is used to describe the influence of transonic utter on next generation aircraft configurations, where it was found that transonic utter constraints can limit the eciency gains seen by better material technology. As a potential approach for mitigating utter, additively manufactured lattice structures are aeroelastically tailored to increase the flutter margin of wings. Adaptive meshing techniques are used to design the topology of the lattice to align with the load direction while adhering to manufacturing constraints, and the lattice is optimized to minimize the structural weight and to improve the flutter margin. The internal structure of a wing is aeroelastically tailored using this design strategy to increase the flutter margin, which only adds minimal weight to the structure due to the large design freedom the lattice structure offers.
by Max Maria Jacques Opgenoord.
Ph. D.

The turbomachinery related industry relies heavily on numerical tools for the design and development of modern turbomachines. In order to be competitive turbomachines ought to be highly efficient and robust. This has lead engineers to develop more aggressive designs, which often leads to lower margins of structural reliability.  One of the strongest threats to turbomachines are high cycle fatigue problems which arise from aeroelastic phenomena such as flutter. According to Kielb R. (2013) many of such problems are detected at developing testing stage. This implies that the prediction capabilities for aeroelastic phenomena are in need of further development and/or tuning. This is especially evident for unsteady flow phenomena at transonic regimes. A very important step for the improvement of unsteady aerodynamic solvers is the validation and comparison of such solvers. The present thesis concerns with the validation and comparison of a non-linear time marching (ANSYS CFX) and the GKN’s in-house linearised solvers used for flutter analysis. The former has recently implemented a new feature called Transient Blade Row TBR, which drastically reduces the simulation domain to a maximum of two blades.  In order to be included in the deign process, such tool need to be validated. In the same way, the recently launched in-house code LINNEA needs to be validated in order to be considered as a design tool. Experimental data from the aeroelastic standard configuration 4, and the FUTURE project were used for the validation purposes. The validation process showed that the solvers agreed very well between them for the standard configuration. Such agreement was less clear for the FUTURE compressor; nonetheless, the solutions still sit within the bulk of solutions provided from the different FUTURE partners. The validation showed that these tools provide with similar results as the state of the art tools from different companies. This indicates that they can be used in the design process. At the same time it was observed that there is room for improvement in the solvers, as these still present some considerable differences with the experimental results.

Although flutter analysis is a relatively old problem in aviation, it is still challenging, particularly with the advent of composite materials and requirements for high-speed light airframes. The main challenge for this problem is at the transonic flow region. The transonic flow, being non-linear, poses a great challenge over traditional linear theories which fail to predict the aerodynamic properties accurately. Aerospace has been one of the primary areas of applications to take advantage of composite materials with the aim to reduce the total mass and improve control effectiveness. This work takes advantage of CFD methods advancement as the main flow solver for non-linear governing equations. In order to investigate the dynamic behaviour of composite aircraft wings, the dynamic stiffness method (DSM) for bending-torsion composite beam is used to compute the free vibration natural modes. The main objective of this work is coupling the dynamic stiffness method (DSM) with high fidelity computational fluid dynamics models in order to predict the transonic flutter of composite aircraft wings accurately and efficiently. In addressing the main aim of this study, Euler fluid flow solvers of an open source CFD code called OpenFOAM has been coupled with elastic composite wing, represented by the free vibration modes computed by DSM. The first part of this study is devoted to investigating the free vibration characteristics of two types of aircraft, namely sailplane type and transport airliner type. Two models of each type have been analysed and contrasted, which revealed the significance of the natural modes of aircraft wings and how these modes inherently capture the essential characteristics of the system. Then to validate the CFD code, two pitching and self-sustained two degrees of freedom airfoils under different flow condition have been modelled. The results have been compared against experimental measurements and numerical data from the literature which showed good agreement for the predicted force coefficients. Finally, the model has been extended to study a complete aircraft wing. Both metallic and composite Goland wings have been investigated under a wide range of flow conditions. The composite wing has been investigated using different material coupling values to show their effect on its aeroelastic behaviour. The results showed the significant influence of the material coupling on the aeroelastic characteristics of composite wings.

Les ensembles disque-aubes des turbomachines modernes sont amenés à satisfaire des critères stricts en termes de stabilité aéroélastique et de réponse forcée. L'objectif de cette thèse est d'utiliser et de développer des techniques de modélisation, capables de prédire le phénomène de flottement et de quantifier les amplitudes de résonance des aubages de turbomachine. Pour le flottement, deux méthodes d'analyse aéroélastique sont considérées: la méthode énergétique (approche fluidestructure non-couplée) et le schéma de couplage modal (approche fluide-structure couplée). Ces modèles ont été installés dans le code de calcul STRUFLO qui offre des outils d'interface performants pour coupler divers codes de calcul. Des méthodes spécifiques sont utilisées afin de combiner plusieurs types d'analyses fluide et structure, et ainsi de progresser dans le sens d'un traitement général des interactions fluide-structure. A cet effet, le schéma de couplage modal est adapté pour être compatible avec des analyses modales d'aube seule ainsi que des analyses modales d'ensemble disque-aubes avec ou sans symétrie cyclique. Un maillage d'interface est utilisé pour résoudre les problèmes liés à l'incompatibilité des maillages fluide et structure à l'interface et une méthode d'interpolation/extrapolation permet de transférer les modes de vibration d'aube et les champs de pression instationnaire, du maillage structure au maillage aérodynamique et vice versa. Le désaccordage structure est l'une des caractéristiques pouvant considérablement modifier la stabilité aéroélastique et les amplitudes de résonance des aubages. A cet effet, deux méthodes de réduction ont été étudiées afin d'autoriser des analyses modales et de réponse forcée d'ensemble disque-aubes complet. Les techniques développées sont appliquées à l'étude des comportements dynamiques, aérodynamiques et aéroélastiques du fan transonique NASA Rotor 67, d'un fan transonique avec nageoires et d'un fan subsonique à large corde
The lightweight, high performance bladed-disks used in today's aeroengines must meet strict standards in terms of aeroelastic stability and resonant response characteristics. The research presented in this thesis is directed toward improved prediction and understanding of blade flutters and forced response problems in turbomachines. To address the blade flutter problem, two aeroelastic analysis methods are considered: the energy method (fluid-structure uncoupled approach) and the modal aeroelastic coupling scheme (fluid-structure coupled approach). The two methods have been implemented in the STRUFLO master code which is designed to provide fluid-structure interfaces for a library of structural and flow solvers. Especially tailored methods are used to couple or interface a wide range of structural and aerodynamic analyses. First, the modal aeroelastic coupling scheme is extended to deal with single blade, cyclic symmetric and full assembly modal analyses as weil as single and multiple blade passage unsteady aerodynamic analyses. Second, an interfacing grid technique is proposed to circumvent problems due to the presence of non-conforming fluid and structural grids at the interface. Finally, a grid-to-grid interpolation/extrapolation scheme is used to transfer blade mode shapes and blade surface unsteady pressures from the structural grid to the aerodynamic grid and vice versa. One structural characteristic of bladed-disks that can significantly impact bath on the aeroelastic stability and the resonant response is that of structural mistuning. With this respect, two reduction methods have been developed to perform full assembly modal analyses and forced response analyses. Various numerical applications are proposed to illustrate the applicability of the above mentioned methods including structural dynamic, aerodynamic and aeroelastic analyses of the NASA Rotor 67 unshrouded transonic fan, a shrouded transonic fan and a subsonic wide chard fan

碩士
中原大學
土木工程研究所
92
This investigation develops an artificial neural network (ANN) algorithm to identify aeroelastic parameters of cable-supported bridge section models in smooth flow and turbulent flow in a wind tunnel test. The ANN approach method uses observed dynamic responses to train a back-propagation (BP) neural network frame. The characteristic parameters of the section model for various wind velocities are estimated using weight matrices in the neural network. The eight flutter derivatives can then be determined precisely. The procedure can be applied to process experimental data obtained from wind tunnel tests involving flat plate section models given various width/depth (B/D) ratios. Finally, the flutter characteristics of various bluff bodies are examined, as they are very sensitive to geometry and structural dynamics.

As flight flutter testing on an airplane progresses to high dynamic pressures and high Mach number region, it becomes very difficult for engineers to predict the level of the remaining stability in a flutter-prone mode and flutter-prone mechanism when response data is infested with uncertainty. Uncertainty and ensuing scatter in modal data trends always leads to diminished confidence amidst the possibility of sudden decrease in modal damping of a flutter-prone mode. Since the safety of the instrumented prototype and the crew cannot be compromised, a large number of test-points are planned, which eventually results in increased development time and associated costs. There has been a constant demand from the flight test community to improve understanding of the con-ventional methods and develop new methods that could enable ground-station engineers to make better decision with regard to flutter susceptibility of structural components on the airframe. An extensive literature survey has been done for many years to take due cognizance of the ground realities, historical developments, and the state of the art. Besides, discussion on the results of a survey carried on occurrences of flutter among general aviation airplanes has been provided at the very outset. Data for research comprises results of Computational Aero elasticity Analysis (CAA) and limited Flight Flutter Tests (FFTs) on two slightly different structural designs of the airframe of a supersonic fixed-wing airplane. Detail discussion has been provided with regard to the nature of the data, the certification requirements for an airplane to be flutter-free in the flight-envelope, and the adopted process of flight flutter testing. Four flutter-prone modes - with two modes forming a symmetric bending-pitching flutter mechanism and the other two forming an anti-symmetric bending-pitching mechanism have been identified based on the analysis of computational data. CAA and FFT raw data of these low frequency flutter modes have been provided followed by discussion on its quality and flutter susceptibility of the critical mechanisms. Certain flight-conditions, at constant altitude line and constant Mach number lines, have been chosen on the basis of availability of FFT data near the same flight conditions. Modal damping is often a highly non-linear function of airspeed and scatter in such trends of modal damping can be very misleading. Flutter margin (FM) parameter, a measure of the remaining stability in a binary flutter mechanism, exhibits smooth and gradual variation with dynamic pressure. First, this thesis brings out the established knowledge of the flutter margin method and marks the continuing knowledge-gaps, especially about the applicable form of the flutter margin prediction equation in transonic region. Further theoretical developments revealed that the coefficients of this equation are flight condition depended to a large extent and the equation should be only used in small ‘windows’ of the flight-envelope by making the real-time flutter susceptibility assessment ‘progressive’ in nature. Firstly, it is brought out that lift curve slope should not be treated as a constant while using the prediction equation at constant altitudes on an airplane capable of transonic flight. Secondly, it was realized that the effect of shift in aerodynamic canter must be considered as it causes a ‘transonic-hump’. Since the quadratic form of flutter margin prediction equation developed 47 years ago, does not provide a valid explanation in that region, a general equation has been derived. Furthermore, flight test data from only supersonic region must be used for making acceptable predictions in supersonic region. The ‘ameliorated’ flutter margin prediction equation too provides bad predictions in transonic region. This has been attributed to the non-validity of quasi-steady approximation of aerodynamic loads and other additional non-linear effects. Although the equation with effect of changing lift curve slope provides inconsistent predictions inside and near the region of transonic-hump, the errors have been acceptable in most cases. No consistent congruency was discovered to some earlier reports that FM trend is mostly parabolic in subsonic region and linear in supersonic region. It was also found that the large scatter in modal frequencies of the constituent modes can lead to scatter in flutter margin values which can render flutter margin method as ineffective as the polynomial fitting of modal damping ratios. If the modal parameters at a repeated test-point exhibit Gaussian spread, the distribution in FM is non-Gaussian but close to gamma-type. Fifteen uncertainty factors that cause scatter in modal data during FFT and factor that cause modelling error in a computational model have been enumerated. Since scatter in modal data is ineluctable, it was realized that a new predictive tool is needed in which the probable uncertainty can be incorporated proactively. Given the recent shortcomings of NASA’s flutter meter, the neural network based approach was recognized as the most suitable one. MLP neural network have been used successfully in such scenarios for function approximation through input-output mapping provided the domains of the two are remain finite. A neural network requires ample data for good learning and some relevant testing data for the evaluation of its performance. It was established that additional data can be generated by perturbing modal mass matrix in the computational model within a symmetric bound. Since FFT is essentially an experimental process, it was realized that such bound should be obtained from experimental data only, as the full effects of uncertainty factors manifest only during flight tests. The ‘validation FFT program’, a flight test procedure for establishing such bound from repeated tests at five diverse test-points in safe region has been devised after careful evaluation of guide-lines and international practice. A simple statistical methodology has been devised to calculate the bound-of-uncertainty when modal parameters from repeated tests show Gaussian distribution. Since no repeated tests were conducted on the applicable airframe, a hypothetical example with compatible data was considered to explain the procedure. Some key assumptions have been made and discussion regarding their plausibility has been provided. Since no updated computational model was made available, the next best option of causing random variation in nominal values of CAA data was exercised to generate additional data for arriving at the final form of neural network architecture and making predictions of damping ratios and FM values. The problem of progressive flutter susceptibility assessment was formulated such that the CAA data from four previous test-points were considered as input vectors and CAA data from the next test-point was the corresponding output. General heuristics for an optimal learning performance has been developed. Although, obtaining an optimal set of network parameters has been relatively easy, there was no single set of network parameters that would lead to consistently good predictions. Therefore some fine-tuning, of network parameters about the optimal set was often needed to achieve good generalization. It was found that data from the four already flown test-points tend to dominate network prediction and the availability of flight-test data from these previous test-points within the bound about nominal is absolutely important for good predictions. The performance improves when all the five test-points are closer. If above requirements were met, the predictive performance of neural network has been much more consistent in flutter margin values than in modal damping ratios. A new algorithm for training MLP network, called Particle Swarm Optimization (PSO) has also been tested. It was found that the gradient descent based algorithm is much more suitable than PSO in terms of training time, predictive performance, and real-time applicability. In summary, the main intellectual contributions of this thesis are as follows: • Realization of that the fact that secondary causes lead incidences of flutter on airplanes than primary causes. • Completion of theoretical understanding of data-based flutter margin method and flutter margin prediction equation for all ranges of flight Mach number, including the transonic region. • Vindication of the fact that including lift-curve slope in the flutter margin pre-diction equation leads to improved predictions of flutter margins in subsonic and supersonic regions and progressive flutter susceptibility assessment is the best way of reaping benefits of data-based methods. • Explanation of a plausible recommended process for evaluation of uncertainty in modal damping and flutter margin parameter. • Realization of the fact that a MLP neural network, which treats a flutter mechanism as a stochastic non-linear system, is a indeed a promising approach for real-time flutter susceptibility assessment.

To be able to harness more power from the wind, wind turbine blades are getting longer. As they get longer, they get more flexible. This creates issues that have until recently not been of concern. Long flexible wind turbine blades can lose their stability to flow induced instabilities such as coupled-mode flutter. This type of flutter occurs when increasing wind speed causes a coupling of a bending and a torsional mode, which create limit cycle oscillations that can lead to blade failure. To be able to make the design of larger blades possible, it is important to be able to predict the critical flutter and post critical flutter behaviors of wind turbine blades. Most numerical research concerning coupled-mode wind turbine is focused on predicting the critical flutter point, and less focused on the post critical behavior. This is because of the mathematical complexities associated with the coupled, nonlinear wind turbine blade systems. Here, a numerical model is presented that predicts the critical flutter velocity and post critical flutter behavior for 3D airfoils with third order structural nonlinearities. The numerical model can account for the attached flow and separated flow region by using the ONERA dynamic stall model. By retaining higher-order structural nonlinearities, lateral and torsional displacements can be predicted, which makes it possible to use this model in the future to control wind turbine blade flutter. Furthermore, by using a dynamic stall model to simulate the flow, the solver is able to predict accurate limit cycle oscillations when the effective angle of attack is larger than the stall angle. The coupled, nonlinear equations of motion are two coupled nonlinear PDEs and are determined using Hamilton’s principle. In order to solve the equations of motion, they are discretized using the Galerkin technique into a set of ODEs. The motion of the airfoil is used as an input to ONERA. The airfoil is sectioned with the lateral position and angle of attack known as well as the velocity and acceleration of the section at an instance of time. This information is used by ONERA to calculate lift and moment coefficients for each section which are then used to calculate the total lift and moment forces of the airfoil. Then, a Fortran code solves the system by using Houbolt’s finite difference method. A theoretical NACA 0012 airfoil has been designed to define the parameters used by the equations of motion. Third bending and first torsional coupling occurs after the critical flutter point and dynamic lift and moment coefficients were observed. Dynamic stall was also observed at wind velocities farther away from the bifurcation point. Bifurcation diagrams, time histories, and phase planes have been created that represent the flutter behavior.

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.