Method and system for controlling the inclination of a rocking structure

Abstract

The invention relates to various methods and systems for controlling the inclination of a rocking structure. One method concerns adjusting a force applied by an electric machine to a mass coupled to the rocking structure. The method is based on executing a control that uses a dynamic model and indicative parameters of the position of the mass and of an angle of inclination of the rocking structure to adjust the force applied by the electric machine to the mass. The invention also relates to a system for carrying out the method. Another method relates to adjusting the transmission ratio between a mass coupled to the structure and a rotor of an electric machine. A further method relates to adjusting the curvature of a guide for mechanically coupling a body to the rocking structure.

Description

[0001]P231106EN METHOD AND SYSTEM FOR CONTROLLING THE INCLINATION OF AN OSCILLATING STRUCTURE DESCRIPTION TECHNICAL SECTOR The present invention corresponds to the area of ​​physical technology, and more specifically to control. In particular, it concerns a method and system for controlling the inclination of an oscillating structure. The invention can be applied in, among others, sectors of activity in which the inclination of a structure or installation subject to internal and / or external disturbances of any type is controlled, such as installations for the extraction and / or production and distribution of energy products (oil / gas platforms, floating platforms for offshore wind turbines, onshore and offshore wind turbines on the seabed, etc.), as well as in the fishing sector, maritime transport and, in general, economic activities developed based on the use of structures subject to the force of the sea.It can also be applied in, among others, the construction sector to stabilize structures (bridges, buildings, etc.) subject to disturbances (wind, tectonic movements, etc.). BACKGROUND OF THE INVENTION There are various devices designed to correct or fix the inclination of a structure subject to disturbances. Those considered to be most relevant are mentioned below. Document US3557735 by Dreyfus et al. (1968) introduces a cylindrical mobile mass that can move in a trajectory confined by stops and whose movement is damped by a liquid of high and variable density. The idea is to control, through the density and / or volume of the liquid, the dissipation of the kinetic energy of the mobile mass in order to obtain the correct phase of the movement of the mass with respect to the list of a ship, and thus achieve the stabilization of the structure. This document does not indicate how to adjust the density and / or volume of the liquid.The document “Development of hybrid anti-rolling device for ships and test at sea” by Koike et al. (1996), previously published in 1994 in Japanese, describes the design and installation of a hybrid (active and passive) control device based on a 3.5-tonne moving mass on the deck of a 190-tonne vessel. An optimal LQ (linear quadratic) control is used to minimise the vessel's heeling. Very good results were achieved with these devices in Tokyo Bay when drifting in beam seas (1 / 3 attenuation) and, especially, with low-speed quarter waves (1 / 2 attenuation), a situation in which systems based on anti-rolling tanks are counterproductive. The document. reduce the roll motion of a ship”, Treakle et al. (2000) studies, through numerical simulations, the potential of moving masses to reduce the roll motion of a vessel and shows that the use of a mass corresponding to less than 1% of the vessel's displacement can be sufficient to largely eliminate (85-95%) its roll. This study uses a hybrid moving mass system, since it applies an active force to the mass, but also a spring and a damper. It has the advantage of using a simple active control law. However, it requires the heuristic adjustment of several parameters so that the movement of the mass within the vessel is “physically reasonable”. As the authors themselves state, the study was initially intended to analyze the potential of commonly used anti-heeling tanks, but they end up proposing moving masses as a stabilization system with great potential in themselves. Finally,They mention that the fact that the natural frequency of the hybrid servomechanism does not generally coincide with the heeling frequency causes irregular movements of the mass and the vessel, when both frequencies are mixed. Document US6019056 by Maeda et al. (2000) refers to an anti-heeling system for floating structures subjected to the force of waves. In this case, the authors propose that, in the face of a periodic heeling motion, the movement of the mass coupled to the structure must have the same period and a given phase shift (90 sexagesimal degrees of delay) with the first in order to obtain optimal results in stabilization. The adjustment of said period is proposed, as well as the confinement of the mass, by different mechanical methods: springs, curved trajectories, stops, pulleys, pistons and magnetic flux dampers,the latter being the easiest to adjust depending on the characteristics of the list at any given time by altering the relative position of the permanent magnets used for this purpose. The use of an electromagnet in the magnetic flux damper of the moving mass is even mentioned in order to dynamically alter the damping coefficient by means of an electric current. Document US6349660 by Chaix (2002) proposes a relatively complex mechanical device for moving a certain number of concatenated masses inside the structure in an attempt to stabilize it. However,It is limited to the design of the P231106ES device and says nothing about how to move the masses to achieve the aforementioned stabilization. Document US2010 / 0307401A1 by Bereznitski et al. (2008) proposes a system based on a moving mass to correct the list of a vessel due to the work of a crane during its operation for cargo movements. The mass is moved by means of a system of pulleys and cables. The system is therefore not designed to correct the list due to the force of the waves, but rather that due to a temporary imbalance of the apparent load. The document “The effectiveness of moving masses in reducing the roll motion of floating vessels” by Montazeri et al. (2010) takes into account that the dynamic behavior of vessels is nonlinear when the list reaches large values. In that sense,uses second-order damping modeling and a fifth-order righting moment to study the system consisting of the vessel and a moving mass with a spring and damper. It shows that, with optimal tuning of these passive elements, up to 80% of the heel can be eliminated, using only a mass equivalent to 0.5% of the vessel's displacement. However, this is a passive control that must be readjusted for each type of swell. Documents US9150291B2 (2015) and US11427287B1 (2022) by E. Dollar are based on a moving-mass system that allows the heel (and pitch) angle of a vessel to be set at will depending on the circumstances. In this case, the objective is to optimize the interaction of the hull with the water surface to achieve the creation of a passing wake with certain shape characteristics.slope and symmetry. The system proposes moving the masses on rails and a mechanical system connected to an electric motor that the human operator moves at will. Finally, the work carried out on the motion control of buildings subject to external disturbances, especially wind and earthquakes, is also of interest. It is very extensive and can be well summarized in the document "Review of vibration control strategies of high-rise buildings" by El Ouni et al. (2022) where you can find a good summary of the contributions that use active control through AMD (Active Mass Damper) based on auxiliary mobile masses whose oscillation / pendulum can be adjusted in various ways. In summary, the systems described use masses whose movement can be controlled passively (by adjusting the parameters of springs and dampers), actively (by applying force through an actuator) or hybrid (both methods simultaneously). As described,In some cases, the objectives of such control have been set using various, more or less sophisticated methods. The problem arises when trying to determine how to alter the motion of the structure based on the changing circumstances associated with the disturbances caused by the motion. The state-of-the-art methods proposed for determining the motion of the masses (stops, springs, dampers, etc.) are not easy to adjust to these circumstances in a sufficiently flexible and / or rapid manner. Furthermore, as the circumstances, and therefore the motion of the structure, change, it is impossible to describe explicitly and in detail how the mass should move to achieve the objective. Therefore, it is necessary to develop a method and system that allows solving this problem.allowing the movement of the structure to be altered quickly and adaptable to external conditions. DESCRIPTION OF THE INVENTION The object of the invention is a method and system for controlling the inclination of an oscillating structure. The invention makes it possible to solve the problems described above using active control based on the use of moving masses, as well as, in some cases, predictive control based on a single linear model for the entire operating range, which allows it to be adapted to the dynamics of the oscillating structure, to the estimation of disturbances and to the practical restrictions of said oscillating structure. The invention also makes it possible to solve the aforementioned problems by adjusting the curvature of a guide and / or a transmission ratio as explained in the present disclosure. Therefore,The system of the invention is intended to be linked to an oscillating structure. An oscillating structure or oscillating installation is considered to be: - an installation for the extraction and / or production and distribution of energy products, such as an oil / gas platform, a floating platform for an offshore wind turbine (an English term that can be translated into Spanish as "located at sea and far from the coast"), an onshore wind turbine and an offshore turbine on the seabed, etc., - an installation in the fishing and maritime transport sector and, in general, an installation for economic activities developed based on the use of structures subject to the force of the sea, P231106ES - an installation in the construction sector to stabilize structures, such as bridges, buildings, etc., subject to disturbances, among other possible oscillating structures subject to disturbances, by way of example and not limitation. For its part,Any alteration or disturbance that affects one of these oscillating structures (i.e., those that can oscillate) is considered a disturbance. The disturbances can be both internal and external to the oscillating structure itself. For example, in the case of marine oscillating structures, waves and / or wind are external disturbances. The detachment of a load transported in the hold of a ship is considered an internal disturbance. In the case of structures in the construction sector, disturbances can be, in addition to wind, tectonic movements, among others. Furthermore, an oscillating structure is considered to be one that performs a back-and-forth movement between at least two positions. This movement can be barely perceptible or it can be a large displacement. A first aspect of the invention relates to a method for controlling the inclination of an oscillating structure, the method comprising adjusting a displacement of a mass (called a moving mass,in some passages of the present disclosure), the mass being mechanically coupled to an electric machine by means of a mechanical transmission, the mechanical transmission being such that an adjustment of the electromagnetic torque of the electric machine allows adjusting the displacement of the mass in the oscillations, the displacement being a displacement with respect to the oscillating structure; the mass being coupled to the oscillating structure with a mechanical coupling, the mechanical coupling of the mass with the oscillating structure allowing the displacement of the mass caused by a gravitational force and by a force applied by the electric machine to the mass in the oscillations through the mechanical transmission,by adjusting the electromagnetic torque of the electric machine; causing the oscillations to vary an angle of inclination of the oscillating structure with respect to the direction of the gravitational force; the displacement being adjusted by adjusting the force applied, by the electric machine, to the mass; the method comprising: i) providing a control with a model of the dynamics of the oscillating structure, of the mass, of the mechanical transmission, of the mechanical coupling and of the electric machine, ii) establishing as a first objective of the model-based predictive control a certain inclination of the oscillating structure, P231106ES iii) obtaining: o a parameter indicative of a position of the mass, and / or a parameter indicative of an angle of inclination of the oscillating structure,where r is the angle relative to a direction of the gravitational force; and providing the parameter indicative of a position of the mass and the parameter indicative of an angle of inclination to the control as control inputs, iv) executing the control, using the model, the first control objective, the parameter indicative of a position of the mass and the parameter indicative of an angle of inclination of the oscillating structure, to obtain an indicative parameter of adjustment of the force applied, by the electric machine, to the mass, through the adjustment of the electromagnetic torque, v) adjusting, based on the indicative parameter of adjustment of the force through the adjustment of the electromagnetic torque, the force applied, by the electric machine, to the mass, and vi) repeating iii) to v). The first aspect of the invention is based on applying the control to control the inclination of the oscillating structure. The control allows adjusting, at each instant,the movement of the mass to changes in the oscillation conditions of the structure (e.g., changes in the disturbances experienced by the structure). In some embodiments, the control is a model-based predictive control. Model-based predictive control allows for improved speed and flexibility of adjustment. In some embodiments, the model of the model-based predictive control is valid for the entire oscillation range of the oscillating structure. A model valid for the entire oscillation range of the oscillating structure allows for even improved speed and stability of adjustment, since the model used by the control does not need to be changed based on the operating range (i.e., oscillation range) of the oscillating structure. In some embodiments, the model-based predictive control is a predictive control based on a single linear model, i.e.,in a linear model valid for the entire oscillation range of the oscillating structure. If the model-based predictive control uses a single linear model for the entire operating range (LUMPC) of the invention, the stability of the controlled system can be guaranteed a priori and compliance with the restrictions of the assembly formed by the oscillating structure, the moving mass, the electric machine, the transmission and the coupling can be optimally managed. Such restrictions may be, for example, the limits of the displacement of the moving mass and / or the limits of the electromagnetic torque of the rotor of the electric machine used to manage the movement of said mass. When it is indicated that the mechanical transmission is such that an adjustment of the electromagnetic torque of the electric machine allows adjusting the displacement of the mass in the oscillations, it should be noted that the electric machine can generate or consume electrical power,depending on the adjustment to be made. Mechanical transmission is, for example, a mechanical transmission between the mass and a rotor of the electric machine. Thus, adjusting the torque exerted by the rotor makes it possible to adjust the displacement of the mass. At least i), ii), iii) and iv) are carried out using processing means. iii) may involve the use of one or more sensors adapted to obtain a measurement indicative of a position of the mass and a measurement indicative of an angle of inclination of the oscillating structure. v) may involve an actuator adapted to adjust the force applied by the electric machine to the moving mass. While the position of the mass indicated by the parameter indicative of a mass position may be absolute, it is necessary to know said position in relation to the oscillating structure, i.e.the relative position with respect to the oscillating structure. Model-based predictive control uses a model (commonly known as an "internal model") of an assembly consisting of the oscillating structure, the moving mass, the mechanical transmission, the mechanical coupling, and the electric machine to predict the future behavior (over a given time horizon) of said oscillating structure and of one or more variable(s) to be controlled (electromagnetic torque of the electric machine). Based on this future behavior, it can obtain one (or more) adjustment setpoint(s) that optimize(s) said variable(s) to be controlled over said time horizon. The internal model is implemented in processing means as mathematical relationships that represent the dynamics of the oscillating structure and the moving mass. For example, the model may relate to each other: the angle of inclination of the oscillating structure, the position of the moving mass, the torque on the rotor of the electric machine,the rotation speed of the rotor of the electric machine, one or more external moments applied to the oscillating structure and caused by one or more disturbances and a parameter of a control objective. Logically, these relations also include characteristics of the components necessary to define the dynamics such as, for example: characteristics of the oscillating structure (for example, righting arm and displacement of a floating platform), of the moving mass (for example, the total mass value -for example, in kg- of the mass), of the electric machine (for example, moment of inertia of the rotor), of the mechanical transmission (for example, the transmission ratio) and the curvature of guides for the mechanical coupling between the moving mass and the oscillating structure. In some embodiments,The adjustment of the force applied to the moving mass is performed by an actuator (electrical machine), and the model includes a model of the actuator (electrical machine). In this way, the dynamics are represented more accurately, allowing for improved control through model-based predictive control. In some embodiments, the model comprises a model of a mechanical coupling between the electric machine and the oscillating structure. In this way, model-based predictive control can be improved, since the control also considers the dynamic behavior of the coupling between the electric machine and the oscillating structure. In some embodiments, the internal model used by the MPC controller is a single linear model for the entire operating range of the invention, a variant known as LUMPC, for Linear Unique Model-based Predictive Control. Using a single linear model is advantageous because it allows the stability of the controlled system to be guaranteed in advance.which cannot be done when using either a non-linear internal model or multiple linear models obtained through different linearizations for the different operating points through which the installation passes during its performance. Furthermore, using a single linear model substantially reduces the computational load associated with the controller's performance, which facilitates its practical implementation. In some embodiments, in order to use a single linear internal model throughout the entire operating range, it is necessary to calculate, by means of processing blocks external to the controller, the highly non-linear variables that cannot be linearized in a unique way for the entire operating range and that have a significant impact on the system dynamics. Subsequently, said variables are introduced, as inputs declared as measured disturbances, into the controller, to allow a prediction adjusted to the reality of the system dynamics,over a certain time horizon. In some embodiments, the internal model used for such prediction comprises the relationships: where: P231106ES is the vector of the descriptive states of the system at each instant t; is the vector of the variables manipulated (MV) by the controller at each instant t; v ^ t ^ is the vector of the measured perturbations (MD) of the system at each instant t; d ^ t ^ is the vector of the unmeasured perturbations (UD) of the system at each instant t; y ^ t ^ is the vector of the outputs of the system at each instant t; A c , B c , B cp , B cd , C c , D c , D cp and D cd are matrices, invariant in time, whose elements determine the descriptive characteristics of the dynamics of the system in the degrees of freedom that are of interest for the objective of the invention. It has been observed that these linear relationships are suitable for modeling, in a sufficiently accurate manner in the context of the LUMPC control of the invention, even in embodiments where the dynamics of the oscillating structure contain important highly non-linear elements.In some embodiments, executing the model predictive control of iv) comprises using one or more constraints on at least one variable involved in the dynamics of the system formed by the oscillating structure, the moving mass, and the actuator for positioning said mass. An example of a constraint is a constraint on the displacement of the mass relative to the oscillating structure. This constraint can be formulated as: ^xm^ax^ x ' ^ x ' maxwhere x^ is a location of the mass with respect to the oscillating structure and'max is an extreme location of the mass with respect to the structure. Other examples of constraints are: - A constraint on the electromagnetic torque that can be applied to the rotor of the electric machine. Said torque can be restricted to be between two extreme values ​​^T genmax and T genmax of the torque. - A constraint on the maximum angle of inclination (e.g., heeling) of the structure.The angle of inclination can be restricted to lie between two extreme values. -A maximum speed restriction of the mass. P231106ES In some embodiments, a parameter indicative of the position of the mass is obtained from the electric machine. Specifically, the electric machine comprises a stator and a rotor; the rotor being coupled to the mass by means of mechanical transmission, and the parameter indicative of the position of the mass may be a parameter indicative of the angular position of the rotor obtained directly by means of a sensor (for example, a rotary encoder) and / or may be calculated from measurements obtained by a sensor (for example, a tachometer). For its part, the parameter indicative of the inclination of the oscillating structure may be obtained directly by means of a sensor (for example, by means of an inclinometer) and / or may be calculated from measurements obtained by a sensor (for example, an accelerometer).In some embodiments, the parameter indicative of inclination of the oscillating structure is a parameter indicative of an instantaneous angle of inclination of the oscillating structure and, optionally, is obtained directly by a sensor (for example, by an inclinometer) and / or is calculated, with processing means, from measurements obtained by a sensor (for example, an accelerometer). The instantaneous angle is an angle that varies, due to the oscillations of the oscillating structure, with respect to the direction of the gravitational force applied to the mass. In some embodiments, the parameter indicative of the position of the mass may be a parameter indicative of the instantaneous position of the mass and, optionally, is obtained directly by a sensor (for example, a rotary encoder) and / or is calculated, with processing means, from measurements obtained by a sensor (for example, a tachometer).In some embodiments, the parameter indicative of mass position comprises a measure of the instantaneous velocity of displacement of the mass and, optionally, is obtained directly by a sensor (for example, a tachometer) and / or is calculated, with processing means, from measurements obtained by a sensor (for example, a rotary encoder). In some embodiments, the measured instantaneous angle of inclination is from the same instant as at least one of: instantaneous position of the mass and instantaneous velocity of displacement of the mass measured. The use of measurements from a same instant by the control facilitates predictions and estimates of the model-based predictive control in those embodiments in which the control model uses variables from a same instant. In some embodiments, the parameter indicative of adjustment of the force applied, by the electric machine, to the mass is an output of the model-based predictive control.P231106ES In this way, the model-based predictive control itself determines the force adjustment setpoint, and no further processing of an output from said model-based predictive control is required. In other embodiments, the parameter indicative of adjusting the force applied by the electric machine to the mass is a result of processing an output from the model-based predictive control. In some embodiments, the parameter indicative of adjusting the force applied by the electric machine to the moving mass is a parameter indicative of adjusting the electromagnetic torque applied by the stator of the electric machine to its rotor, which in turn is coupled to the moving mass by means of a mechanical transmission. For example, it is a signal received by an actuator of said torque, the actuator being adapted to adjust said torque based on the received control signal.In some embodiments, the calculation of the control action is based on the minimization of a cost function that includes three additive elements. First, an element consisting of the deviations that the variables of interest in the system dynamics present with respect to their desired values ​​during the prediction time horizon, which quantifies the error that the controller will have in pursuing the control objectives. Second, an element that accumulates the increases that, during that same time period, are predicted for the variables manipulated by the controller, and which quantifies the control effort that will be necessary to achieve said control objectives. Finally, a third element, called the terminal cost, represents the cost function of the system from the end of the prediction horizon used to infinity.This last element serves to formally and in advance guarantee the stability of the controller, provided that the internal model used is unique and linear for the entire operating range (LUMPC). In some embodiments, the relative importance assigned to achieving each of the control objectives included in the first element, as well as the relative penalties imposed on the use of the different control variables manipulated by the controller to achieve said objectives, and included in the second element of the cost function to be minimized, can be assigned through the use of specific numerical weights. In this way, during the performance of the invention, several control objectives with varying degrees of relative importance in their achievement can be combined, as well as specifically limiting the use of the various manipulated variables necessary for the control action.In some embodiments, the first control objective sets the inclination of the oscillating structure to a desired value at each instant. P231106EN In some embodiments, the second control objective is to adapt the movement of the moving mass so that it is in favor of gravity at all times of the oscillations, and, the control considering the instantaneous inclination of the oscillating structure, comprising iv) using the second control objective in the execution of the control. In this way, it is possible to maximize the extraction of electrical power from the movement of said mass. In some embodiments, the method comprises establishing a second objective of the model-based predictive control, the second control objective being dedicated to the monitoring, by the output D of the system, defined by: from a D* instruction, where: where b is a damping coefficient of the oscillating structure, m is a mass value of the mass, x' is the position of the mass, ^ is the instantaneous angle of inclination of the oscillating structure and x'max is the maximum displacement that the mass can have in its confined movement. The second proposed control objective seeks to extract the maximum possible energy from the environment of the oscillating structure, while respecting the restrictions on the bounded movement of the mass, regardless of the value that the derivative of the inclination of the structure takes with respect to time at any given time.In some embodiments, the method comprises assigning a first weight to the first control objective and a second weight to the second control objective, the first weight being relative to the second weight; the use of the first control objective and the second control objective comprising in iv) a use of a combination of the first weight with the first control objective and a combination of the second weight with the second control objective. Both control objectives may be physically compatible in some circumstances, since, by extracting electrical energy from the movement of the oscillating structure due to external disturbances, it is logical that said movement is attenuated. However, this depends on the type of disturbance causing the movement, as well as the inclination that is desired to set for the oscillating structure, that is, the performance sought for the inclination control of the oscillating structure at any given time.In some embodiments, the oscillations of the structure comprise rotations of the structure around an imaginary axis of rotation, the mechanical coupling of the movable mass to the oscillating structure comprising a guide with a curvature (for example, a constant curvature, i.e., a curvature defined by a constant radius of curvature; in other words, the guide has the shape of an arc of a circle), the guide defining a direction of movement of the contained mass in a plane perpendicular to the imaginary axis of rotation of the oscillating structure, and the guide being a guide for the movement of the mass in its oscillations. For example, the guide may be in the shape of an inverted arc of a circle, i.e., with the concave part of the arc of a circle facing upwards. In this way, the mass moves along the guide, and consequently along a curved path and, simultaneously, in a plane perpendicular to the axis of rotation of the oscillating structure.The fact that the guide defines a direction of travel perpendicular to the axis does not necessarily mean that the direction of mass displacement is perpendicular to the axis of rotation. That is, the direction of travel can be the direction of a vector resulting from the addition of a first non-zero vector in the direction perpendicular to the axis of rotation and a second non-zero vector in a direction perpendicular to the direction of the first vector. The curvature makes it possible to favor a specific frequency (undamped natural frequency) of oscillation of the mass as it travels along the guide, such that it favors the desired control of the structure's inclination. Specifically, the curvature makes it possible to establish a default displacement of the mass along the guide (this displacement of the mass can be considered as an oscillation of the mass) at the expected oscillation frequency(ies) for the oscillating structure.At this point, we recall that the undamped natural frequency of a dynamic system, described with a single degree of freedom, is the frequency of the applied excitation force at which said system presents the highest amplitude oscillatory response, if we neglect the damping of the system. The undamped natural frequency of the mass oscillation depends on the curvature of the guide. The curvature of the guide can have a specific radius of curvature so that the undamped natural frequency of the mass oscillation is close to (or coincident with) an oscillation frequency of the oscillating structure. P231106EN In some embodiments, the guide is perpendicular to the axis of rotation of the oscillating structure. In these embodiments, the displacement of the mass along the guide is exclusively perpendicular to said axis.That is, the mass moves simultaneously along a curved path and exclusively perpendicular to the structure's axis of rotation. A guide perpendicular to the structure's axis of rotation simplifies the control of the oscillating structure's rotations and, thus, the control of the oscillating structure's tilt. The simplification of the control of the oscillating structure's rotations is due to the fact that, as explained below, the frequency of the mass's displacement in the direction perpendicular to the axis of rotation has a relatively large impact on the tilt control. In some embodiments, the oscillating structure is floating in water, and the oscillations of the oscillating structure are caused by water waves. The oscillating structure floating in water may be, for example, a ship.In some embodiments, the method comprises measuring a wave height before (a distance away from) the wave reaching the oscillating structure; providing the wave height measurement (preview) to the control in advance (i.e., before the wave reaches the oscillating structure); the provided wave height measurement being an input to the control; and comprising iv) using the provided wave height measurement in optimizing the control action generated by the model-based predictive control.In this way, the control does not have to use a state observer to estimate the disturbance caused by the incident wave, but can use the measured preview of the wave height to anticipate the effect of that disturbance and thus aid in the control of the structure's tilt in the face of future disturbances, for example, by allowing compensation for delays in the mass motion actuators. In some embodiments, the wave height is obtained by measuring the height of a buoy some distance from the oscillating structure. In some embodiments, the wave height is obtained using a wave radar installed on the oscillating structure.In some embodiments, the method comprises predicting, at each instant and based on estimates of the disturbance caused by the incident waves made up to that moment by the state observer, the future disturbance - preview - due to the incident waves that the oscillating structure will suffer during the prediction horizon used by the proposed controller. In some embodiments, said prediction can be made following, for example, one of the methods described in: F. Fusco and J. V. Ringwood, "Short-Term Wave Forecasting for Real-Time Control of Wave Energy Converters," in IEEE P231106ES Transactions on Sustainable Energy, vol. 1, no. 2, pp. 99-106, July 2010. In these cases, the predicted preview of the effect of the wave disturbance can be used to assist in the control of the tilt of the structure in the face of future disturbances, for example, by allowing compensation for the delays presented by the mass movement actuators.In some embodiments, the method comprises adjusting a torque transmission ratio of the mechanical transmission connecting the movable mass to the oscillating structure; the displacement of the mass comprising an oscillation of the mass; the natural frequency of the oscillation of the mass being adjusted by adjusting the torque transmission ratio, the method comprising at least one of a) and b), where: a) - obtaining a parameter indicative of a frequency of the disturbance ^d that causes movement of the oscillating structure; and - adjusting the torque transmission ratio based on the parameter indicative of the frequency of the disturbance ^. dwhich causes the oscillating structure to move, so that the undamped natural frequency ^m of the moving mass coincides with the frequency of the disturbance, such that ^m =^dy b) -obtain a parameter indicative of the undamped natural frequency of the oscillating structure ^s; and -adjust the torque transmission ratio to adjust the undamped natural frequency of the moving mass ^m, so that: where ms and m are the masses of the oscillating structure and the moving mass, respectively. These embodiments of the first aspect of the invention have similar advantages to those of the third aspect of the invention. As can be inferred from the above, the torque transmission ratio can be adjusted as a function of the changing operating circumstances of the invention, for example, the frequency components that appear in the movement of the oscillating structure, which in turn depends on external disturbances. However, the changes produced in said operating circumstances occur much more slowly than the dynamics of the complete system, formed by mass and structure,so that P231106ES the transmission ratio can be considered invariant during the operation of the invention with regard to the internal prediction of the LUMPC controller. The torque transmission ratio of the mechanical transmission is a relationship between the rotation speeds of two or more elements of this, coupled to each other. For example, in the case of using a rack and pinion transmission and an electric machine to join the mass with the oscillating structure, the stator of the electric machine would be attached to the mass and the rotor shaft of said machine attached to the pinion geared in the rack, the rack being supported on the oscillating structure. Then, if a multiplier is installed between the rotor and the pinion, the rotation speed of the pinion and the rotation speed of the rotor of the electric machine coupled to the mass maintain a certain speed and torque transmission ratio,which in some cases can be variable and set by the controller. Adjusting the torque transmission ratio makes it possible to adjust the undamped natural frequency of the oscillations of the moving mass (that is, of the oscillations of the moving mass in the displacement of the moving mass caused by the oscillations of the structure and by the control action). For example, if the moving mass moves on a mechanical guide (for example, on the guide comprised by the means for coupling the mass to the structure), the mass completes an oscillation by passing from one end of its displacement along the guide (at zero speed) to said end of the guide at zero speed. The aforementioned adjustment of the oscillation frequency of the mass, although optional, makes it possible to facilitate the control of the inclination of the oscillating structure, improving several practical aspects of the performance of the invention. For example, as can be seen from the present disclosure,Correct adjustment of the torque transmission ratio makes it possible to reduce the maximum electromagnetic torque required by the electric machine during operation in active mode, reducing the size required for the electric machine used, as well as that of the power electronics associated with it. Furthermore, correct adjustment of the transmission ratio of the moving mass improves the performance to be achieved by the invention when operating in passive mode, that is, without using any control action. In some embodiments, the method comprises adjusting a curvature of the guide of the mechanical coupling of the mass with the structure; the displacement of the mass comprising an oscillation of the mass along the curvature of the guide of the mechanical coupling; the natural frequency of the oscillation of the mass being adjusted by adjusting the curvature of the guide of the mechanical coupling; the method comprising at least one of a) and b),where: P231106ES a) - obtaining a parameter indicative of a frequency of the disturbance ^d that causes the oscillating structure to move; and - adjusting the curvature of the mechanical coupling guide based on the parameter indicative of the frequency of the disturbance ^d that causes the oscillating structure to move, so that the undamped natural frequency ^m of the moving mass coincides with the frequency of the disturbance, such that ^m = ^d; and b) - obtaining a parameter indicative of the undamped natural frequency of the oscillating structure ^s; and - adjusting the curvature of the mechanical coupling guide to adjust the undamped natural frequency of the moving mass ^, m , so that: where ms and m are the masses of the oscillating structure and the movable mass, respectively. These embodiments of the first aspect of the invention have similar advantages to those of the fourth aspect of the invention. Adjusting the curvature of the mechanical coupling guide (i.e., adjusting the curvature of the path of displacement of the mass relative to the oscillating structure) is another way of adjusting the undamped natural frequency of the oscillations of the movable mass. In many applications, adjusting the curvature is less desirable than adjusting the transmission ratio, because it usually requires a more complex and expensive adjustment system. The aforementioned adjustment of the oscillation frequency of the mass, although optional, makes it possible to facilitate the control of the inclination of the oscillating structure, improving several practical aspects of the performance of the invention.For example, as can be seen from the present disclosure, correct adjustment of the curvature of the guide of the mechanical coupling of the moving mass to the oscillating structure makes it possible to reduce the maximum electromagnetic torque required by the electric machine during operation in active mode, reducing the size required for the electric machine used, as well as that of the power electronics associated with it. Furthermore, correct adjustment of the curvature of the guide of the moving mass improves the performance to be achieved by the invention when operating in passive mode, that is, without using any control action. P231106ES The adjustments in a), both in the case of the curvature adjustment and in the adjustment of the transmission ratio, use the estimate of a frequency of the disturbance that affects the oscillating structure at any given time.For this estimation, the dynamic model of the complete system and the measurements taken on it (e.g., inclination of the oscillating structure and position of the moving mass at any given time) are used. However, the estimation of the unmeasured input disturbance is usually performed by the MPC controller during normal operation, so it can be used to obtain the frequency used in the adjustment in a), for example, if the device is operating in active mode using an MPC controller. The estimation could be implemented using processing external to that of the MPC controller. On the other hand, the adjustments in b) do not have this estimate of the disturbance frequency, for example, during operation of the device in passive mode, with the MPC controller and its state estimator disabled.In this case, the undamped natural frequency of the moving mass is adjusted using the frequency response of the entire system, that is, the frequency response of the structure with the moving mass device coupled to it, within a range of disturbance frequencies that sufficiently covers the operating conditions that the installation may encounter at its location. Adjustments a) are based on antiresonance theory, which indicates that adjusting the undamped natural frequency of the moving mass so that it is close to the disturbance frequency at all times minimizes the oscillations of the oscillating structure caused by said disturbance. Adjustments b) can, in principle, be carried out in numerous ways (see, for example, Michele Zilletti, Stephen J.Elliott, Emiliano Rustighi, “Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximise internal power dissipation”Journal of Sound and Vibration, Volume 331, Issue 18, 2012, pp. 4093-4100., which is a summary of the different methods that exist to adjust the natural frequency and the damping of a dynamic vibration absorption device). However, although there are several methods, those that seek to maximise the stability of the structure and minimise its displacements all propose the same optimal adjustment for the undamped natural frequency of the moving mass coupled to it, that is, the adjustment described in option b).On the other hand, it is true that these methods propose different ways of adjusting the values ​​for optimal mass damping, but since it may be interesting to keep the damping in the passive mode as low as possible, so as not to harm the active mode, adjustment b) can be considered as the lowest common multiple of all of them with respect to the undamped natural frequency of the moving mass. Observing the recommended adjustment b), it can be seen that the natural frequency of the moving mass ^m is closer to the natural frequency of the oscillating structure ^s, the smaller the moving mass m is with respect to the total mass of the structure ms (including the total mass of the structure, the mass of the structure and all the components supported by the structure, including the moving mass).Specifically, for example, in the case where the moving mass is 10% of the mass of the oscillating structure, the recommended natural frequency for said mass is already very close to the natural frequency of the structure (^m=0.91 ^s). In some embodiments of the invention, the moving mass used is very small relative to the mass of the oscillating structure. Specifically, for example, moving mass devices typically installed on floating structures rarely exceed 5% of the mass of the structure to which they are coupled (thus, ^m=0.95 ^s) and are typically around 2% (thus, ^m=0.98 ^s). In such cases, the error margin for the frequency calculation ^s is close. Therefore, the natural frequency of the moving mass ^m can, in many cases, be adjusted to be close to (e.g., coincident with) the natural frequency of the first vibration mode of the structure to which it is coupled.Once determined, by at least one of a) and b), the desired undamped natural frequency for the moving mass ^. m, the transmission ratio and / or the curvature of the guide can be adjusted to fix said undamped natural frequency in the moving mass. A second aspect of the invention relates to a system for controlling an inclination of an oscillating structure (i.e. capable of oscillating), the system comprising an oscillating structure, a moving mass, processing means, a mechanical coupling of the mass to the oscillating structure, and a mechanical transmission coupling a rotor of an electrical machine to the moving mass, the mechanical transmission being such that displacement of the mass relative to the oscillating structure causes a variation in the angular velocity of the rotor of the electrical machine (and vice versa, a variation in the angular velocity of the rotor of the electrical machine causes a displacement of the mass relative to the oscillating structure);allowing mechanical coupling of a displacement of the mass relative to the oscillating structure caused by a gravitational force and by a force applied by the electric machine to the mass in the oscillations through the mechanical transmission, by adjusting the electromagnetic torque of the electric machine; the system being configured to adjust the displacement of the mass by adjusting a force applied by the electric machine to the mass;the processing means being configured to: i) provide a control with a model of the dynamics of the oscillating structure, of the mass, of the mechanical transmission, of the mechanical coupling and of the electrical machine, ii) establish as a first objective of the model-based predictive control a certain inclination of the oscillating structure, iii) obtain: o a parameter indicative of a position of the mass, and / or a parameter indicative of an angle of inclination of the oscillating structure, the angle being relative to a direction of the gravitational force;and providing the parameter indicative of a position of the mass and the parameter indicative of an angle of inclination to the control as inputs of the control, iv) executing the control, using the model, the first control objective, the parameter indicative of a position of the mass and the parameter indicative of an angle of inclination of the oscillating structure, to obtain an indicative adjustment parameter of the force applied, by the electric machine, to the mass, through the electromagnetic torque adjustment; v) adjusting, based on the indicative adjustment parameter of the force through the electromagnetic torque adjustment, the force applied, by the electric machine, to the mass;and vi) repeating steps of iii) to v). A third aspect of the invention relates to a method of controlling the tilt of an oscillating structure, the method comprising adjusting a torque transmission ratio of a mechanical transmission between a mass and a rotor of an electric machine, the mechanical transmission being such that an adjustment of the electromagnetic torque of the electric machine allows adjusting the displacement of the mass in oscillations, the displacement being a displacement with respect to the oscillating structure; the mass being coupled to the oscillating structure by a mechanical coupling, the mechanical coupling of the mass to the oscillating structure allowing the displacement of the mass caused by a gravitational force and by a force applied by the electric machine to the mass in oscillations through the mechanical transmission, by adjusting its electromagnetic torque;causing the oscillations to vary in an angle of inclination of the oscillating structure with respect to the direction of the gravitational force; P231106ES the displacement of the mass comprising an oscillation of the mass; the natural frequency of the oscillation of the mass being adjusted by adjusting the torque transmission ratio; the method comprising at least one of a) and b), where: a) - obtaining a parameter indicative of a frequency of the disturbance ^d that causes the oscillating structure to move; and - adjusting the torque transmission ratio based on the parameter indicative of the frequency of the disturbance ^; dwhich causes the oscillating structure to move, so that the undamped natural frequency ^m of the moving mass coincides with the frequency of the disturbance, such that ^m =^d; and b) -obtain a parameter indicative of the undamped natural frequency of the oscillating structure ^s; and -adjust the torque transmission ratio to adjust the undamped natural frequency of the moving mass ^ m , so that: where ms and m are the masses of the oscillating structure and the moving mass, respectively. As can be inferred from the above, the torque transmission ratio can be adjusted based on the changing operating circumstances of the invention, for example, the frequency components that appear in the movement of the oscillating structure, which in turn depends on external disturbances. However, the changes produced in said operating circumstances occur much more slowly than the dynamics of the complete system, formed by mass and structure, such that the transmission ratio can be considered invariant during the operation of the invention with regard to the internal prediction of the LUMPC controller. The torque transmission ratio of the mechanical transmission is a relationship between the rotational speeds of two or more elements of the same, coupled to each other.For example, in the case of using a rack and pinion transmission (in English, rack and pinion) and an electric machine to connect the mass with the oscillating structure, the stator of the electric machine would be connected to the mass and the rotor shaft of said machine connected to the pinion meshed in the rack, with the rack resting on the oscillating structure. Then, if a multiplier is installed between the rotor and the pinion, the P231106ES rotational speed of the pinion and the rotational speed of the rotor of the electric machine coupled to the mass maintain a certain speed and torque transmission ratio, which in some cases can be variable and fixed by the controller.Adjusting the torque transmission ratio makes it possible to adjust the undamped natural frequency of the oscillations of the movable mass (i.e., of the oscillations of the movable mass in the displacement of the movable mass caused by the oscillations of the structure and by the control action). For example, if the movable mass moves along a mechanical guide (e.g., along the guide comprised by the means for coupling the mass to the structure), the mass completes an oscillation by passing from one end of its displacement along the guide (at zero speed) to said end of the guide at zero speed. The aforementioned adjustment of the undamped natural frequency of the oscillation of the mass, although optional, makes it possible to facilitate the control of the inclination of the oscillating structure, improving several practical aspects of the performance of the invention.For example, as can be seen from the present disclosure, the correct adjustment of the torque transmission ratio makes it possible to reduce the maximum electromagnetic torque required by the electric machine during operation in active mode, reducing the size required for the electric machine used, as well as that of the power electronics associated with it. Furthermore, the correct adjustment of the transmission ratio of the moving mass improves the performance achieved by the invention when operating in passive mode, that is, without using any control action. The adjustments in a), in the case of the transmission ratio, use the estimate of a frequency of the disturbance that affects the oscillating structure at any given time. For said estimate, the dynamic model of the complete system and the measurements taken on it (for example, inclination of the oscillating structure and position of the moving mass at any given time) are used.However, the estimation of the unmeasured input disturbance is usually performed by the MPC controller during its normal operation, so it can be used to obtain the frequency used in the adjustment in a), for example, if the device is operating in its active mode by means of an MPC controller. The estimation could be implemented using processing external to that of the MPC controller. On the other hand, the adjustments in b) do not have such an estimate of the disturbance frequency, for example, during operation of the device in passive mode, with the MPC controller and its state estimator disabled.In this case, the undamped natural frequency of the moving mass is adjusted using the frequency response of the entire system, that is, the frequency response of the structure with the moving mass device coupled to it, within a range of disturbance frequencies that sufficiently covers the operating conditions that the installation may encounter at its location. Adjustments a) are based on antiresonance theory, which indicates that adjusting the undamped natural frequency of the moving mass so that it is close to the disturbance frequency at all times minimizes the oscillations of the oscillating structure caused by said disturbance. Adjustments b) can, in principle, be carried out in numerous ways (see, for example, Michele Zilletti, Stephen J.Elliott, Emiliano Rustighi, “Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximise internal power dissipation”Journal of Sound and Vibration, Volume 331, Issue 18, 2012, pp. 4093-4100., which is a summary of the different methods that exist to adjust the natural frequency and the damping of a dynamic vibration absorption device). However, although there are several methods, those that seek to maximize the stability of the structure and minimize its displacements all propose the same optimal adjustment for the undamped natural frequency of the moving mass coupled to it, that is, the adjustment described in option b).On the other hand, it is true that these methods propose different ways of adjusting the values ​​for optimal mass damping, but since it may be interesting to keep the damping in the passive mode as low as possible, so as not to harm the active mode, adjustment b) can be considered as the lowest common multiple of all, with respect to the undamped natural frequency of the moving mass. Observing the recommended adjustment b), it can be seen that the natural frequency of the moving mass ^m is closer to the natural frequency of the oscillating structure ^s, the smaller the moving mass m is with respect to the total mass of the structure ms (including the total mass of the structure, the mass of the structure and all the components supported by the structure, including the moving mass).Specifically, for example, in the case where the moving mass is 10% of the mass of the oscillating structure, the recommended natural frequency for said mass is already very close to the natural frequency of the structure (^m=0.91 ^s). In some embodiments of the invention, the moving mass used is very small relative to the mass of the oscillating structure. Specifically, for example, the moving mass devices that are typically installed on floating structures rarely exceed 5% of the mass of the structure to which they are coupled (then, ^m=0.95 ^s) and are normally around 2% (then, ^m=0.98 ^s). In these cases, the margin of error in calculating the frequency ^s is close. Therefore, the natural frequency of the moving mass ^. mcan be adjusted, in many cases, to be close to (e.g., coincident with) the natural frequency of the first mode of vibration of the structure to which it is coupled. Once determined, by at least one of a) and b), the desired undamped natural frequency for the moving mass ^ m, the transmission ratio can be adjusted to set said undamped natural frequency in the moving mass. In some embodiments, the method comprises adjusting the torque transmission ratio to adjust the undamped natural frequency of the movement of the moving mass, after modifying the mass of the oscillating structure (for example, when loading / unloading a vessel), since the undamped natural frequency of the oscillating structure depends on its mass. Therefore, in some cases it may be advantageous to make said adjustment to adapt to the change in the natural frequency of the structure. This adjustment can be made, for example, based on pre-established relationships between the mass of the structure and the transmission ratio. In some embodiments, the mechanical transmission only supports a finite number of transmission ratios, and the value of the transmission ratio for which the natural frequency of the oscillations of the mass are equal,either to the main frequency of the external disturbances - setting a) - (for those embodiments in which the disturbance frequency is estimated), or to the frequency given by setting b) (for example, for those embodiments in which the estimate of the disturbance frequency is not available), is not included in said finite number of transmission ratios. Then, the method comprises adjusting the transmission ratio to the available transmission ratio closest to the transmission ratio for which the natural frequency of the mass oscillations is equal to either the main frequency of the external disturbances (for example, for the active mode of the proposed system), or to the frequency proposed by setting b) (for example, for the passive mode of the proposed system). In some embodiments, the mechanical transmission is a continuously variable transmission - in English,Continuously Variable Transmission (CVT) -. Using a continuously variable transmission makes it possible to obtain in practice values ​​for torque transmission ratios closer to or even equal to the optimal transmission ratios desirable for controlling the inclination of the structure mentioned above. The third aspect of the invention has advantages similar to those of the first aspect of the invention when the first aspect of the invention comprises adjusting the torque transmission ratio of the mechanical transmission used to connect the electrical machine to the moving mass. P231106ES In some embodiments, the oscillations of the structure comprise rotations of the structure around an imaginary axis of rotation, the mechanical coupling of the moving mass to the oscillating structure comprising a guide with a curvature (e.g., a constant curvature, i.e., a curvature defined by a constant radius of curvature; in other words,the guide is shaped like an arc of a circle), the guide defining a direction of movement of the mass contained in a plane perpendicular to the imaginary axis of rotation of the oscillating structure, and the guide being a guide for the movement of the mass in its oscillations. For example, the guide may be shaped like an inverted arc of a circle, that is, with the concave part of the arc of a circle facing upwards. In this way, the mass moves along the guide, and consequently along a curved path and, simultaneously, in a plane perpendicular to the axis of rotation of the oscillating structure. The fact that the guide defines a direction of movement perpendicular to the axis does not necessarily mean that the direction of movement of the mass is perpendicular to the axis of rotation. That is,the direction of travel may be the direction of a vector resulting from adding a first non-zero vector in the direction perpendicular to the axis of rotation and a second non-zero vector in a direction perpendicular to the direction of the first vector. A fourth aspect of the invention relates to a method of tilt control of an oscillating structure, the method comprising adjusting a curvature of a guide of a mechanical coupling of a movable mass with the oscillating structure, said mechanical coupling allowing the displacement, with respect to the oscillating structure, of the mass caused by a gravitational force and by a force applied by an electric machine to the mass in the oscillations through the mechanical transmission,by adjusting the electromagnetic torque of the electric machine; the oscillations of the mass causing variations in an angle of inclination of the oscillating structure with respect to the direction of the gravitational force; the displacement of the mass comprising an oscillation of the mass; the natural frequency of the oscillation of the mass being adjusted by adjusting a curvature of a guide of the mechanical coupling; the method comprising at least one of a) and b), where: a) - obtaining a parameter indicative of a frequency of the disturbance ^d causing movement of the oscillating structure; and - adjusting the curvature of the guide of the mechanical coupling based on the parameter P231106ES indicative of the frequency of the disturbance ^d causing movement of the oscillating structure, so that the undamped natural frequency ^m of the moving mass coincides with the frequency of the disturbance,such that ^m =^d; and b) -obtain a parameter indicative of the undamped natural frequency of the oscillating structure ^s; and -adjust the curvature of the mechanical coupling guide to adjust the undamped natural frequency of the moving mass ^, m , so that: where ms and m are the masses of the oscillating structure and the moving mass, respectively. As can be inferred from the above, the curvature of the mechanical coupling guide can be adjusted—using actuators adapted for this purpose—based on the changing operating circumstances of the invention, for example, the frequency components that appear in the movement of the oscillating structure, which in turn depends on external disturbances. However, the changes produced in said operating circumstances occur much more slowly than the dynamics of the complete system, formed by mass and structure, such that the curvature of the mechanical coupling guide can be considered invariant during the operation of the invention with regard to the internal prediction of the LUMPC controller.Adjusting the curvature of the mechanical coupling guide makes it possible to adjust the undamped natural frequency of the oscillations of the movable mass (i.e., of the oscillations of the movable mass in the displacement of the movable mass caused by the oscillations of the structure and by the control action). For example, if the movable mass moves along a mechanical guide (e.g., along the guide comprised by the means for coupling the mass to the structure), the mass completes an oscillation by passing from one end of its displacement along the guide (at zero speed) to said end of the guide at zero speed. The aforementioned adjustment of the undamped natural frequency of the oscillation of the mass, although optional, makes it possible to facilitate the control of the inclination of the oscillating structure, improving several practical aspects of the performance of the invention.For example, as can be seen from the present disclosure, correct adjustment of the curvature of the mechanical coupling guide makes it possible to reduce the maximum electromagnetic torque required by the electric machine during operation in active mode, P231106ES by reducing the size required for the electric machine used, as well as that of the power electronics associated with it. Furthermore, correct adjustment of the curvature of the mechanical coupling guide of the moving mass improves the performance to be achieved by the invention when operating in passive mode, that is, without using any control action. The adjustments in a), in the case of the curvature of the mechanical coupling guide, use the estimate of a frequency of the disturbance that affects the oscillating structure at any given time.For this estimation, the dynamic model of the complete system and the measurements taken on it (e.g., inclination of the oscillating structure and position of the moving mass at any given time) are used. However, the estimation of the unmeasured input disturbance is usually performed by the MPC controller during normal operation, so it can be used to obtain the frequency used in the adjustment in a), for example, if the device is operating in active mode using an MPC controller. The estimation could be implemented using processing external to that of the MPC controller. On the other hand, the adjustments in b) do not have this estimate of the disturbance frequency, for example, during operation of the device in passive mode, with the MPC controller and its state estimator disabled.In this case, the undamped natural frequency of the moving mass is adjusted using the frequency response of the entire system, that is, the frequency response of the structure with the moving mass device coupled to it, within a range of disturbance frequencies that sufficiently covers the operating conditions that the installation may encounter at its location. Adjustments a) are based on antiresonance theory, which indicates that adjusting the undamped natural frequency of the moving mass so that it is close to the disturbance frequency at all times minimizes the oscillations of the oscillating structure caused by said disturbance. Adjustments b) can, in principle, be carried out in numerous ways (see, for example, Michele Zilletti, Stephen J.Elliott, Emiliano Rustighi, “Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximise internal power dissipation”Journal of Sound and Vibration, Volume 331, Issue 18, 2012, pp. 4093-4100., which is a summary of the different methods available for adjusting the natural frequency and damping of a dynamic vibration absorption device). However, although there are several methods, those that seek to maximise the stability of the structure and minimise its displacements all propose the same optimal setting for the undamped natural frequency of the moving mass coupled to it, that is, the P231106ES setting described in option b).On the other hand, it is true that these methods propose different ways of adjusting the values ​​for optimal mass damping, but since it may be interesting to keep the damping in the passive mode as low as possible, so as not to harm the active mode, setting b) can be considered as the lowest common multiple of all of them with respect to the undamped natural frequency of the moving mass. Observing the recommended setting b), it can be seen that the natural frequency of the moving mass ^. m is closer to the natural frequency of the oscillating structure ^ sthe smaller the moving mass m is relative to the total mass of the structure ms (including the total mass of the structure, the mass of the structure and all the components supported by the structure, including the moving mass). Specifically, for example, for the case in which the moving mass is 10% of the mass of the oscillating structure, the recommended natural frequency for said mass is already very close to the natural frequency of the structure (^ m =0.91·^ s ). In some embodiments of the invention, it is the case that the moving mass used is very small with respect to the mass of the oscillating structure. Specifically, for example, the moving mass devices that are usually installed on floating structures rarely exceed 5% of the mass of the structure to which they are coupled (then, ^ m =0.95·^ s ) and are usually around 2% (so, ^ m =0.98·^ s). In these cases, the error margin for calculating the frequency ^s is close to ). Therefore, the natural frequency of the moving mass ^m can be adjusted, in many cases, to be close to (e.g., coincident with) the natural frequency of the first vibration mode of the structure to which it is coupled. Once the desired undamped natural frequency for the moving mass ^m has been determined, by means of at least one of a) and b), the guide curvature can be adjusted to set said undamped natural frequency in the moving mass. In some embodiments, the method comprises adjusting the guide curvature of the mechanical coupling to adjust the undamped natural frequency of the movement of the moving mass, after the mass of the oscillating structure has been modified (e.g., when loading / unloading a vessel), since the undamped natural frequency of the oscillating structure depends on its mass.Therefore, it may sometimes be advantageous to perform such an adjustment to adapt to the change in the natural frequency of the structure. This adjustment may be performed, for example, based on pre-established relationships between the mass of the structure and the curvature of the guide of the mechanical coupling. The fourth aspect of the invention has similar advantages to those of the first aspect of the invention when the first aspect of the invention comprises adjusting the curvature of the guide of the mechanical coupling. A fifth aspect of the invention is a method comprising a method according to the first aspect of the invention and a method according to the third aspect of the invention. A sixth aspect of the invention is a method comprising a method according to the first aspect of the invention and a method according to the fourth aspect of the invention.A seventh aspect of the invention is a system comprising an oscillating body, an electrical machine, a movable mass, a mechanical transmission, processing means, and a mechanical coupling configured to perform the method of the first aspect of the invention. An eighth aspect of the invention is a system comprising an oscillating body, an electrical machine, a movable mass, a mechanical transmission, processing means, a mechanical coupling, and an actuator configured to perform the method of either the third or fourth aspect of the invention.BRIEF DESCRIPTION OF THE DRAWINGS To complement the description and in order to aid in a better understanding of the features of the invention, in accordance with some practical embodiments of the invention, a set of figures is attached as an integral part of the description, in which, for illustrative and non-limiting purposes, the following is represented: Figure 1 schematically shows a movable mass that can be displaced along the imaginary axis X' and mechanically coupled to an oscillating structure according to the present invention. Figure 2 shows a diagram of a controlled oscillating structure according to the present invention. Figure 3 shows a possible mechanical coupling between a movable mass and an oscillating structure according to the invention. Figure 4 shows a movable mass that can be displaced along a variable curvature guide; the mass being mechanically coupled to an oscillating structure.Figure 5A shows a time course of a heel angle of an oscillating structure according to the present invention, the structure being subjected to regular waves. Figure 5B shows a time course of a heel angle of an oscillating structure according to the present invention, the structure being subjected to irregular waves. Figure 6A shows a time course of energy consumed / generated in oscillations of a structure according to the present invention, the structure being subjected to regular waves. Figure 6B shows a time course of energy consumed / generated in oscillations of a structure according to the present invention, the structure being subjected to irregular waves.Figure 7A shows a time evolution of an angular velocity and a torque of a rotor of an electric machine coupled to a moving mass coupled to an oscillating structure according to the present invention, the oscillating structure being subjected to regular swells. Figure 7B shows a time evolution of an angular velocity and a torque of a rotor of an electric machine coupled to a moving mass coupled to an oscillating structure according to the present invention, the oscillating structure being subjected to irregular swells. Figure 8A shows a time evolution of an instantaneous electrical power consumed / generated by an electric machine in oscillations of an oscillating structure according to the present invention, the structure being subjected to regular swells.Figure 8B shows a time course of an instantaneous electrical power consumed / generated by an electrical machine during oscillations of an oscillating structure according to the present invention, the structure being subjected to irregular waves. Figure 9A shows a time course of a heeling of an oscillating structure using two partial control objectives according to the present invention, the structure being subjected to regular waves. Figure 9B shows a time course of a heeling of an oscillating structure using two partial control objectives according to the present invention, the structure being subjected to irregular waves. Figure 10A shows a time course of a consumed / generated energy during oscillations of a structure using two partial control objectives according to the present invention, the structure being subjected to regular waves.Figure 10B shows a time evolution of an energy consumed / generated in oscillations of a structure using two partial control objectives according to the present invention, the structure being subjected to irregular waves. Figure 11A shows a time evolution of a displacement of a moving mass coupled to an oscillating structure according to the present invention, the structure being subjected to regular waves. Figure 11B shows a time evolution of a displacement of a moving mass coupled to an oscillating structure according to the present invention, the structure being subjected to irregular waves. Figure 12A shows a comparison of a time evolution of a moment applied to an oscillating structure according to the present invention by regular waves to which the structure is subjected with a time evolution of an estimate of said moment made by a state observer.Figure 12B shows a comparison of a time evolution of a moment applied to an oscillating structure according to the present invention by irregular waves to which the structure is subjected with a time evolution of an estimate of said moment made by a state observer. Figure 13A shows a time evolution of an angular velocity and a torque of a rotor of an electric machine coupled to a moving mass coupled to an oscillating structure using an adjustable hybrid mass damper according to the present invention, the structure being subjected to regular waves. Figure 13B shows a time evolution of an angular velocity and a torque of a rotor of an electric machine coupled to a moving mass coupled to an oscillating structure using an adjustable hybrid mass damper according to the present invention, the structure being subjected to irregular waves.Figure 14A shows a time evolution of an instantaneous electrical power consumed / generated by an electrical machine coupled to a moving mass coupled to a structure using an adjustable hybrid mass damper according to the present invention, the structure being subjected to regular waves. Figure 14B shows a time evolution of an instantaneous electrical power consumed / generated by an electrical machine coupled to a moving mass coupled to a structure using an adjustable hybrid mass damper according to the present invention, the structure being subjected to irregular waves. DESCRIPTION OF EMBODIMENTS OF THE INVENTION In the description of the possible embodiments of the invention, it is necessary to give numerous details in order to favor a better understanding of the invention. Even so, it will be apparent to the person skilled in the art that the invention can be implemented without these specific details.On the other hand, well-known features have not been described in detail in order to avoid unnecessarily complicating the description. In the equations of the description of embodiments of the invention, the definition of parameters and variables, of said equations, represented with identical signs is the same. Figure 1 schematically illustrates an example of a mass 1 mechanically coupled to an oscillating structure. Figure 1 shows a fixed reference system defined by the imaginary axes X and Y, and shows a mobile reference system defined by the imaginary axes X' and Y'. The imaginary axes X' and Y' rotate in the same way as the oscillating structure in the oscillations of the structure. The oscillating structure has an instantaneous angle of inclination. with respect to a direction perpendicular to the direction of the force of gravity. The instantaneous angle of inclination varies with the oscillations of the structure (for example, in those cases where the structure is floating in water, the angle Φ may be an angle of heel of the structure). Figure 1 shows a mechanical coupling between oscillating structure and mass 1 that allows mass 1 to move, with respect to the oscillating structure, along the imaginary axis X'. Although it can be deduced from Figure 1 that the displacement of mass 1 with respect to the oscillating structure is rectilinear, in other embodiments (for example, the one illustrated in Figure 4) said displacement may be curved. Continuing with Figure 1, mass 1 is subjected to a gravitational force Fg. The gravitational force Fg can be broken down into a first component Fgx' parallel to the direction of displacement of mass 1 and into a second component Fgy' perpendicular to the direction of displacement of mass 1.As explained later in the description, the present invention makes it possible to influence the angle of inclination of the structure during its oscillations by controlling, at least, the position of the mass 1 coupled to the structure. Moreover, in some embodiments, the tilt control operation can be made easier and more cost-effective by adjusting: - a transmission ratio Ngear of a transmission between the mass 1 and a rotor of an electric machine mechanically coupled, via the transmission, to the mass 1 to control the position of the mass 1; and / or - a curvature R2 of a mechanical coupling between the mass 1 and the oscillating structure. Specifically, in the present application example, we will consider the optional use of a continuously variable transmission (CVT) and assume that the constructive curvature of the guide of the mechanical coupling of the movable mass can be selected. Of course, in other implementations any other combination may occur.While in the following examples the oscillating structure is a floating structure in water and the angle of inclination. is a heeling angle of the floating structure, the person skilled in the art will understand that these examples can be adapted to other types of structures and oscillations. Figure 2 shows a diagram illustrating the control in combination with the controlled system. Specifically, a first portion 2 of the diagram represents the different dynamic components of the system whose behaviors can be described in sufficient detail by means of the linear expressions (1.2)-(1.6). A second portion 3 of the diagram refers to calculations performed by the processing means of the system to control the inclination of the structure. Specifically, portion 3 is used, on the one hand, to optimize the manipulated variable (MV) which, in this case, is the setpoint of the electromagnetic torque T* gof the electrical machine coupled to the moving mass. On the other hand, it is used to adjust in the best possible way the configuration of the natural frequency of the moving mass when it moves along guides with curvature R2, by manipulating the Ngear ratio of a transmission between mass 1 and a rotor of a mechanically coupled electrical machine. Portion 3 is used to numerically calculate at all times the variables of interest in the dynamics of the system that present a highly non-linear behavior -see expressions (1.8) and that, therefore, cannot be included in the internal model of the LUMPC controller, so they are declared as measured disturbances (MD) of said controller. The first portion 2 of the diagram comprises a first block 1, described by expression (1.3), which refers to the dynamics of the moving mass 1, a second block 4, described by (1.2) and (1.6), which refers to the motion of the oscillating structure and a third block 5, modeled by (1.4) and (1.5), which refers to the actuator of mass 1 (specifically, to a rotating electrical machine) and to the mechanical transmission between the rotor of the electrical machine and the moving mass 1. The second portion of the diagram comprises a fourth block 6 for the numerical calculation at each instant of the system variables that present a highly non-linear behavior -see expressions (1.8)-, which forces them to be formally considered as measured disturbances (MD) and to obtain their value externally to the controller, in order to maintain its internal strictly unique and linear prediction model (LUMPC), a fifth block 7 for processing a linear unique model predictive control (LUMPC), a sixth block 8 for processing the possible objectives of the model-based predictive control and a seventh block 9 for calculating the transmission ratio Ngear between the rotor and mass 1.Note that, in this application example, the controller is considered a LUMPC control, although another type of control could be used, obtaining similar results. Continuing with Figure 2, the actuator for mass 1 applies a force +FL to mass 1, the oscillating structure defining an instantaneous tilt angle. of mass 1 (since mass 1 is mechanically coupled to said structure), and mass 1 is subjected to a disturbance MD2. The relative instantaneous position x' of mass 1 with respect to the oscillating structure influences the oscillation of the oscillating structure. A parameter indicative of the relative instantaneous position x' of mass 1 is an input to the model-based predictive control. The parameter indicative of the relative instantaneous position x' of mass 1 is an input to the third block 5. In block 5, the dynamic behavior of the force F is calculated Ldepending on the mass movement, the torque setpoint of the electric machine, the transmission torque ratio, and the machine and transmission construction parameters. Continuing with Figure 2, structure 4 is subjected to a force -FL as a result of the force +F Lapplied to mass 1 and the principle of action and reaction (this is because the mechanical transmission -the rack, specifically- is supportedby the oscillating structure). The structure is also subjected to a measured perturbationMD1, to a force due to the relative instantaneous position x' of mass 1 (and to the weightof mass 1) and to an unmeasured perturbation UD. In the illustrated example, the unmeasured perturbation UD causes a moment Mω, applied to the oscillating structure by the waves.Continuing with figure 2, the third block 5 receives, as outputs from the second portion 3 of the diagram, a parameter indicative of the adjustment of the electromagnetic torque setpoint T*g to be applied, by the rotor of the electric machine, to mass 1 and a parameter indicative of the configuration of the moving mass through the adjustment of the transmission ratio Ngear.In this way, by obtaining adequate values ​​of the manipulated variable (MV) T*g at different times, the heel angle of the oscillating structure can be controlled, having optionally set the ratio Ngear to a favorable value that facilitates the control action in some sense. The fourth block 6 numerically determines the disturbances MD1 and MD2 based on parameters indicative of the position of the mass 1 and the angle of inclination of the oscillating structure at each moment, using expressions (1.8). Continuing with the description of figure 2, the outputs of the model-based predictive control are the indicative parameter for adjusting the manipulated variable T*g P231106ES and the estimate of the unmeasured disturbance Mω.Model predictive control has as inputs the parameter indicative of the relative instantaneous position x' of mass 1, the instantaneous heel angle Φ, the indicative parameter of the transmission ratio adjustment Ngear and the control objective dependent parameter OC. In the illustrated example, the indicative parameter of the control objective (OC) can be a desired heel angle (or its derivative with respect to time) and / or a parameter D that is used to optimize the motion of mass 1, in order to extract electrical power –see (1.1)-.Operational approach 1: Straight guides (infinite curvature R2): A first operational approach is described below for the example in which the coupling between mass 1 and the oscillating structure has infinite curvature.Therefore, the coupling between the mass 1 and the oscillating structure includes a guide on which the mass 1 moves, which defines a rectilinear direction of travel of the mass 1 with respect to the oscillating structure. Furthermore, the coupling between the mass 1 and the oscillating structure includes a mechanical transmission which, in this example, comprises a toothed wheel 10 that meshes with a rack 11 forming a rack-pinion connection, as can be seen described in Figure 3. The rack 11 is supported by the portion 12 of the oscillating structure and is fixed with respect to the portion 12 of the oscillating structure, such that the rack 11 tilts in the same manner as the structure when the structure oscillates. In this way, when the portion 12 of the body oscillates, the rack 11 also oscillates.In addition to the rack 11, the mechanical coupling of the mass 1 to the portion 12 of the structure may comprise fixed guides (not shown) with respect to the structure, the mass 1 being coupled to the guides such that the guides guide the movement of the mass 1 as the mass moves relative to the structure during oscillations. The guides are also supported by the portion 12 of the structure and are fixed with respect to the portion 12 of the structure, such that the guides incline in the same way as the structure during oscillations. The transmission between the rotor of the electric machine and the gearwheel 10 optionally comprises a gearbox between the gearwheel 10 and the rotor of the electric machine. As will be appreciated later, this gearbox, in combination with an adjustment of the torque transmission ratio Ngear of said gearbox, is advantageous in certain circumstances. The guides are parallel to the imaginary axis X'.Thus, when portion 12 of the structure oscillates, the guides also oscillate. The guides comprise, for example, P231106ES rails; and the mass 1 comprises, for example, wheels mechanically coupled to the guide rails. Model-based predictive control uses a model of the system to be controlled, that is, the assembly formed by the oscillating structure, the mass, the electrical machine, and the couplings between them, which, in the case of the present example, include the coupling between the mass and the oscillating structure, the transmission between the rotor and the mass 1, the behavior of the electrical machine, and a mechanical coupling between the electrical machine and the oscillating structure. LUMPC uses this model to predict the future behavior of the system and estimate unmeasured states of the system. LUMPC optimizes some future variables of the system over a finite time horizon while respecting the system constraints.The internal model used by the LUMPC control to obtain the expected dynamic behavior over the prediction horizon is now proposed, allowing for optimization of the control action based on the management of the manipulated variable (T*g) while respecting the system restrictions. Furthermore, using this model, the state observer that forms part of the LUMPC control is used to estimate the perturbations that act on said structure at any given time, based on the measurable effects on the structure. The design of this model generally complies with the functional scheme of the system described in Figure 2 and is made up of the dynamic model of the oscillating structure itself, that of the moving mass 1, and the positioning system made up of the actuator (electrical machine) and the mechanical transmission.In this example, to avoid the previously mentioned control implementation drawbacks associated with the use of a non-linear internal model, an approximate, linear internal model is used, described by the following expressions: P231106ES where: equation (1.2) is a dynamic model of the tilt of the oscillating structure; equation (1.3) is a dynamic model of the mass 1; equation (1.4) is a dynamic model of the force FL applied to the mass by the electric machine and the mechanical transmission from the rotor; equation (1.5) describes the dynamics of the electromagnetic torque of the electric machine; equation (1.7) describes a reactive force applied to the structure; I0 is a moment of inertia of the floating structure (this moment of inertia being relevant for the dynamics of the structure in oscillations); ^ is the instantaneous angle of heel; b is a damping coefficient of the hull of the floating structure; GMT is a righting arm of the structure; ^ is a displacement of the structure (the righting moment can be calculated as the product of the displacement of the structure and the righting arm); g is the acceleration due to gravity; mes a total mass value (e.g., in kg) of mass 1; x' is the instantaneous relative position of the moving mass with respect to the center of the guides; B is a coefficient of viscous friction between the guides and mass 1; FL is the force applied, by the transmission and from the electric machine, to mass 1; F. His a reactive force applied to the structure; Ngear is the gear ratio of the multiplier (i.e. the gear ratio between the rotor and the mass 1), R is a radius of the gear wheel 10, R2 is a radius of curvature of the mechanical coupling between mass and oscillating structure, considered constant (and infinite in the present operational approach, which cancels some terms of expressions (1.3) and (1.6) in this case); T gen is an electromagnetic torque applied by the rotor of the electric machine; T*gen is the parameter indicative of the desired setting for the electromagnetic torque applied by the rotor of the electric machine; T lagis a time constant of the electromagnetic torque dynamics of the rotor of the electric machine; P231106ES Dgen is an angular damping of the rotor; Jgen is a moment of inertia of the rotor calculated with respect to the rotation axis where the gear wheel 10 is installed (low speed axis); y'0 is a height of the mechanical coupling of the mass 1, with respect to the center of gravity of the oscillating structure; µ is a dynamic friction coefficient of the guides of the mass 1 with the mass 1; UD is a moment created by disturbances to which the structure is subjected and which is defined as an unmeasured disturbance and is estimated; and MD1 and MD2 are highly nonlinear disturbances of the internal model that are defined as measured disturbances that can be calculated externally to the model-based predictive control according to the following equations (1.8), and which allow the internal model to be maintained as single and linear, without harming the accuracy of the prediction or the estimation of external disturbances:. The objective of model-based predictive control is set, which in this example is a zero heel angle, i.e., ^ ^ 0 . Alternatively, the control objective could be set to maintain a constant heel angle, i.e., ^ 0.Initially, the oscillating structure is considered to be subjected to regular waves. If, initially, the floating structure is subjected to harmonic (regular) waves with a frequency close to the natural frequency of the structure (to cause a significant list in the structure), the results presented below are obtained. In these numerical simulations, the proposed LUMPC control system, described in greater detail below, acts on the complete model of the system, which includes the most important nonlinearities from a physical point of view (in this example, the righting arm of the structure and the moment created by mass 1, as well as the nonlinearities described by expressions (1.8)). A wave height, typical in the Cantabrian Sea, of 1.25 meters and a wave peak period of 5 and a half seconds are assumed.Figure 5A (“Device in active mode”) shows that the heel is almost completely eliminated, while the electric machine consumes a certain amount of energy (in joules) – see Figure 6A (“Device in active mode”). Complete elimination is not possible due to the inevitable delay in estimating the wave disturbance. In theory, if a preview of this disturbance were available, either by using a system that measures sea level at a certain distance from the structure or by predicting future disturbance based on previous estimates, the structure could be completely stabilized. Recall that, in this case, mass 1 is considered to move on straight guides (infinite radius of curvature R2).In addition to the above, Figure 7A shows the rotation speed of the electric machine's rotor and the electromagnetic torque applied by it during control, the latter multiplied by 1e-4 to make both signals of similar magnitude and to be able to observe the phase shift between them. The phase shift is close to 90º, which causes the electric machine to spend part of the cycle accelerating and another part braking the moving mass, the former being somewhat greater, which causes energy consumption. This can also be observed in Figure 8A, where the instantaneous power consumed (+ sign) and generated (- sign) by the electric machine is shown in watts. At this point, the flexibility provided by the LUMPC is used to choose partial control objectives. In particular, for this application example, a second control objective is defined, which consists of achieving tracking by output D described by the expression (1.9), of a setpoint D*, generated by processing block 8 in figure 2. Fulfillment of this control objective allows maximizing the electrical energy generated by the electric machine from the displacement of mass 1 from the oscillations of the structure to which it is coupled. Specifically, the output D of the system is:. where a' is a parameter that can be set from certain known parameters of the oscillating structure and the moving mass 1. The setpoint D* to be followed by D can be calculated – in block 8 of Figure 2 – from the instantaneous measurement of the oscillation of the structure (from which its derivative with respect to time is obtained numerically) and the movement restrictions (limits of the confined path of the mass 1, maximum speed, relative to the structure, of the mass 1, maximum torque applicable by the electric machine, ...). For example, in some embodiments, to extract the maximum electrical power from the invention, while respecting the maximum displacement allowed for the mass 1 x'max, the following can be used: P231106EN where b is a damping coefficient of the oscillating structure, m is a total mass value (e.g. in kg) of mass 1 and ^ is the instantaneous angle of inclination of said structure. Expression (1.10) seeks to extract the maximum possible energy from the environment of the oscillating structure, provided that the restrictions on the bounded motion of mass 1 are respected, when the time derivative of the heel takes on very high values. The idea in introducing a second control objective is to enable, during operation of the device, balancing between the elimination of the heel and the consumption / generation of electrical energy in order to allow a midpoint to be found between both control objectives, which can be chosen at will, depending on the operating circumstances of the invention. By partially distributing the weight of both control objectives in a cost function – specifically in the weight matrix Q, see expression (1.46) - to be optimized by the LUMPC and using (1.9) and (1.10), the results that can be seen in figures 9A and 10A are obtained. It is observed that it is possible to reduce the heel by up to 75%, while still generating some electrical energy during the oscillations of the structure. Obviously, the distribution of the mentioned weights can be adjusted to obtain greater amounts of energy at the expense of reducing the elimination of the heel, and vice versa. If the weight assigned to the first control objective (optimization of the inclination) is totally eliminated, increasing to the maximum the second control objective (optimization of the energy generation) - using only the control objective described by (1.9) - (1.10), the heel is still reduced by approximately 45%.Figure 11A shows the displacement of the moving mass during operation, to verify that in this case it does not exceed the established limits. Figure 12A checks the MPC state observer's estimate of the moment causing the swell on the structure. It can be seen that there is an inevitable delay in estimating the moment of the swell, which in turn implies a delay in the control action, meaning that the heeling cannot be completely eliminated. To achieve this, a preview of the disturbance would need to be incorporated into the system (through an advance measurement of the incident swell or through a prediction made from the estimates made up to that point).Advance measurements can be made with relative ease using, for example, a microwave radar-based wave height sensor (for vessels on voyage), or by installing a wave height measuring buoy at a certain distance from the floating structure, if said structure is anchored (oil platforms, floating wind turbines, etc.). The prediction can be made, for example, by following any of the methods described in: F. Fusco and J.V. Ringwood, "Short-Term Wave Forecasting for Real-Time Control of Wave Energy Converters," in IEEE Transactions on Sustainable Energy, vol. 1, no. 2, pp. 99-106, July 2010. Having described in detail the operation of the invention under regular waves, a more realistic operating case is now considered. In reality, waves in the open sea are composed of a superposition of harmonic components of diverse amplitudes and frequencies that also affect the structure with a random phase.It is, however, possible to statistically process the histogram for each swell situation and extract a statistical representation (spectrum). Various types of representations exist that may be better adapted to different geographical areas and climatic conditions. For these tests, an irregular swell is represented by a Pierson-Moskowitz (PM) spectrum, which assumes an equilibrium relationship between the sea surface and the prevailing wind at that time. This spectrum was developed for the North Atlantic and is recommended when the sea situation is stable with respect to the wind. For changing sea (wind) conditions, an evolution of this spectrum called the JONSWAP spectrum is recommended. For this example, it is also assumed that the significant wave height and the mean apparent period coincide with the wave height of 1.25 meters and the peak period of 5.5 seconds, previously considered for regular swells.By repeating the previous tests, the version implemented in the previous section, shown in version B of the previous figures, is obtained for irregular waves. Observing these results, it can be concluded that the invention maintains its main operating characteristics (performance) described for regular waves. However, it is true that, in some cases, performance is more difficult to observe. For example, in the case of using partial objectives with the intention of continuing to reduce the heel while generating energy. Figure 9B clearly shows that the heel is reduced in a proportion similar to that of regular waves. However, Figure 8B makes it difficult to conclude that energy is indeed generated in a sustained manner. In fact, it is necessary to wait several minutes to observe how the average value of the generated energy grows steadily (-4.86e-4 Joules generated at 800 seconds of operation / oscillation of the structure).P231106EN Operational approach 2: Guides with finite curvature R2 and Ngear adjustment: A possible embodiment example is described below that takes into account the design and / or adjustment of the installation of the moving mass in the oscillating structure using guides with a finite radius of curvature R2 (an example of the radius of curvature R2 is shown in figure 4). In this case, equations (1.2)-(1.8) can be set out to describe the dynamics of the complete system with two degrees of freedom (2DOFs), such as that of a primary structure to which a dynamic vibration absorber (DVA) is coupled, consisting of mass 1 and the rotor of the electric machine coupled to mass 1 through a mechanical transmission. Said dynamic vibration absorber can be designed to have a certain natural frequency that is convenient for its use in passive and / or active mode.In passive mode, model predictive control is not executed. In active mode, model predictive control (or another controller) is executed, and the electric machine can consume and generate electrical power. In this sense, the correct adjustment of the natural frequency of the moving mass depends on several factors (among others, incident disturbance, state of the structure and control objective(s)), and therefore it is advisable for the DVA to offer flexibility in this regard. It is known, for example, that according to the theory of the antiresonance phenomenon that appears between coupled harmonic oscillators, considering two degrees of freedom - the basis of tuned mass dampers (TMDs), the optimal adjustment consists of matching - within a certain margin - the natural frequency of the TMD with the frequency of the disturbance suffered by the oscillating structure at any given time, assuming the latter is unique and constant (or slowly varying).This causes the oscillation of the DVA to exert a reactive force on the oscillating structure in counterphase with the exciting force. In fact, if the damping of the DVA is sufficiently small (and its displacement, which is greater the smaller the moving mass is relative to the main mass, is not restricted), the disturbing force can be completely nullified ("neutralized"), thus completely eliminating the oscillation of the structure. This can be achieved provided that the natural frequency of the DVA coincides with the disturbing frequency, regardless of the natural frequency of the structure. There are many practical cases in which the disturbance acting on the structure has a constant (or slowly varying) frequency, for example, when constant-speed rotating machines are involved.In these cases, the content of the previous paragraph is fully applicable, both for passive systems and active vibration neutralization systems. However, there are many other cases in which the significant frequency of the disturbance may be heterogeneous and changing, and furthermore, there is no practical possibility of making an efficient calculation of said frequency. In these cases, we must concern ourselves with a certain range of disturbance frequencies, and since the incorporation of the DVA into the main structure causes the resulting system to present two resonant frequencies on either side of the structure's initial natural frequency (where the aforementioned attenuation occurs), the DVA's characteristics must be adjusted differently. Specifically, the DVA's damping must be carefully adjusted—in the case of vibration neutralizers, it is advisable to reduce it as much as possible.This is because said damping, along with the natural frequency of the DVA, are the parameters that affect the frequency response of the entire system. Specifically, the frequency and damping can be adjusted to achieve a frequency response of the entire system that is optimal in some sense (maximum stabilization, greater power extraction, etc.). In the present case, the "passive" adjustment of the natural frequency of the moving mass is particularly important, since it is desirable for the device to operate correctly in a passive mode and, in turn, improve the operating conditions in active mode. It should be noted that a preferred operation of the invention, as described in this example, is in active mode. Otherwise, the use of the electric machine would not be justified, since, in passive mode, the same could be done with a simple flywheel.It will be seen later how the correct adjustment of the natural frequency of the moving mass also improves the performance of the invention during use in active mode. However, it is clear that it is desirable to keep the damping of the mass (in passive mode) as low as possible so as not to impair the performance of active mode, in terms of energy consumption. Focusing then on the adjustment of the undamped natural frequency of the DVA, several ways of setting this parameter are known –see, for example, a good summary of these methods in: Zilletti M., Elliott S., Rustighi E., Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximise internal power dissipation, Journal of Sound and Vibration, Volume 331, Issue 18, 2012, Pages 4093-4100, ISSN 0022- 460X, https: / / doi.org / 10.1016 / j.jsv.2012.04.023–.However, all these ways of adjusting the undamped natural frequency of the moving mass, for the passive case, coincide in the adjustment method b) of the general description of the third and fourth aspects of this invention, if what we are looking for is to maximize the stability of the oscillating structure and / or minimize its displacement. -Furthermore, the natural frequency for the mass 1 proposed by said P231106ES method is relatively close to the natural frequency of the oscillating structure, when the mass 1 is relatively small with respect to the mass of said structure...This invention is intended to preferably use moving masses 1 that represent less than 10% (normally, between 2% and 5%) of the mass of the oscillating structure.Therefore, one possibility, when continuous monitoring of the characteristics of the disturbance is not possible (the state estimator is out of operation, for example), consists of adjusting the parameters of the moving mass 1 so that it presents a natural frequency close to the natural frequency of the oscillating structure, using adjustment method b) of the general description of the third and fourth aspects of this invention, which seeks to optimize the frequency response of the entire system to disturbances with a certain bandwidth, in the sense of reducing the movement of the oscillating structure. This is what is proposed in this case for operation in passive mode, when the LUMPC controller - and, therefore, the disturbance estimation - is not operating, as explained later.However, since the LUMPC has a built-in state observer – for example, a Kalman filter – which, in this example, continuously estimates the characteristics of the disturbance due to the effect of the waves on the vessel M. w-generically, the UD signal in equation (1.1)- from the measured effects of said disturbance on the structure, for this application example, in active mode (with the LUMPC controller running), the adjustment of the natural frequency of the moving mass is proposed based on the frequency characteristics of the estimate of said disturbance. Specifically, in the proposed case (vessel at sea) the wave period is considered (if the waves are regular) or the average value of the apparent period (if the waves are irregular). It should be noted that, in the passive mode of this application example, only the transmission ratio Ngear between the rotor and mass 1 is manipulated (possibly from tables that relate the load level of the structure with its natural frequency) and no control action would be applied by the electric machine, so that the electric machine does not consume electrical energy.This adjustment of the natural frequency of mass 1 can guarantee good performance - it would not be optimal, since, as we have said before, the damping is not adjusted to its optimal value, but is left as low as possible to reduce the power consumption of the active mode - in passive mode, something that is also important in order to maintain the guarantees of use in case of suspension of the active mode (energy saving, technical problems, maintenance, ...), and simplifies the necessary machinery (dimensions of the electrical machine, mechanical transmission and P231106ES power electronics) for use in active mode, as can be seen later in the results of the numerical simulations. On the other hand, it must be taken into account that the dynamic behavior (mainly, the natural frequency) of the oscillating structure can also change (in the case of a boat, for example, due to changes in the load on the structure).Therefore, for active mode as well, it is highly recommended to include mechanisms that allow for these changes to be introduced into the internal model used by the LUMPC. This way, the accuracy of both the disturbance estimation and the control action itself is maintained. These mechanisms can be very varied and with varying degrees of sophistication. For example, from the aforementioned use of tables of internal parameters tabulated for different load levels, to the programming of online identification algorithms for these parameters, based on the measured input and output signals to the system. At this point, it should be noted that, although the mass of the structure (the displacement of the vessel, in this example) changes and, therefore, some parameters of the internal model change (the displacement itself, the moment of inertia, changes in N. gearto conveniently readjust the movement of the moving mass, etc., ...), said changes take place slowly, with respect to the dynamics of the system (flooding), or, punctually and with the device out of operation (loading / unloading of vehicles on a ferry, for example), so that the internal model can continue to be considered formally invariable during the operation of the invention. The curvature adjustment and the transmission ratio adjustment are described in greater detail below, each of which is applicable in active mode and in passive mode. It is known that a forced harmonic oscillator can be described according to the generic equation (1.11): m ^^ d2x ^^ k ^ ^ dxdt 2 ^ x ^ b ^ ^ Fdt exc (1.11)where each of the parameters and variables of the equation takes the values ​​indicated below. If (1.11) is compared with (1.3) it can be deduced that, by manipulating the torque of the electric machine in a manner proportional to the position and / or speed of mass 1, the stiffness or damping of the forced harmonic oscillator can be altered at will, consisting of said mass 1 moving along the curvature guides R2 due to the oscillation of the structure to which it is coupled. On the other hand, if we do not consider, for the moment, the use of the electromagnetic torque Tgen of the rotor of the electric machine (passive mode P231106ES) and, therefore, the exciting force F exc depends only on the inclination of the structure (listing), we have, operating in equations (1.3)-(1.4), that the dynamics of the moving mass can be described as (1.11), if we do: As previously mentioned, the natural frequency of the mass can be set by adjusting the radius of curvature R2 of the guides and the transmission ratio N gear to achieve good performance in passive / active mode. As is well known, the undamped natural frequency of the mass is: If we want the motion of the mass to have a certain natural period Tm, we can substitute (1.12) in (1.13) and solve for the curvature R2: It is clear that the natural frequency of the moving mass can be set to the desired value by fixing a radius of curvature R2 of the guides in (1.14). It is now assumed that an oscillatory motion of period T1 has been set for mass 1, using a guide with a constant curvature given by (1.14) making Tm = T1. In the event that the period T1 changes to T2, the natural frequency of the mass could be adapted by altering the radius of curvature R2 of the guides according to (1.14), for example, using a hydraulic system, as represented in figure 4. For this purpose, a flexible guide 13 with a maximum initial curvature is used (for example, the curvature that makes the movement of the moving mass 1 stable in passive mode: a radius of curvature R2 = 47 meters, for this example). This guide is supported on several pistons 14 that, initially, have a reduced length, so that the guide has a first radius of curvature R21.By means of a controlled increase in the length of the pistons 14 (for example, hydraulic pistons), the radius of curvature R2 of the flexible guide 13 can be reduced in order to adapt the oscillation to the mass 1. For example, the guide can be curved up to a second radius of curvature R22. Figure 4 shows a mass 1 that can move along the guide 13. To do this, the mass 1 is coupled to a toothed wheel 18 and the toothed wheel 18 is coupled to a rack 15. The rack 15 is curved in the same way as the guide 13. At the ends of the guide 13 and / or the rack 15, stops 16 are provided, which limit the movement of the mass 1. The pistons are coupled to a base 17 that is fixed with respect to the oscillating structure and supported by the oscillating structure. However, since the moving mass can be several tons in weight, a variable radius adjustment system R2 can be expensive to install and complex to operate and maintain.Therefore, it may be more practical to adjust the oscillation frequency of mass 1 in another way. Observing expressions (1.12) and (1.13) and remembering that, when a mechanical multiplier is installed on the rotating shaft that joins the gear wheel of radius R coupled to mass 1 and the rotor of the electric machine, it is possible to relate the construction data of an electric machine measured from the low speed shaft (Dgen and Jgen) with those same parameters, but measured from the high speed shaft, on the other side of the multiplier (Dgen_HSS and Jgen_HSS), using the expression:. And, if we substitute this in (1.12), we have: Now (1.16) can be substituted into (1.13) to calculate the Ngear that sets the desired oscillation period in the mass, without needing to modify the radius of curvature R2: where the Ngear values ​​calculated by (1.17) are real whenever: At this point, we return to the assumption that we initially set an undamped natural period Tm=T1 for the passive oscillation of the moving mass. To do so, in this case, we used an inverted arc-shaped guide, constructed with a certain curvature R2c and a gear ratio Ngear_m in the gearbox. The curvature R2c can be easily calculated from (1.14) and (1.16): If we then change the value of the undamped natural period that we want to set for the moving mass to Tm=T2, we can do so by manipulating Ngear according to (1.17), where we set R2c =R2c. Now, if we want to obtain a valid (real) value for Ngear, we have to fulfill the condition (1.18) that remains: where Ngear_m is the transmission ratio between the rotor and the mass 1 initially implanted in the gearbox. So, for the new Ngear to be real: T2>T1, Jgen_HSS>0 and R>0. Taking the above into account, what can be done, for example, is to consider the highest frequency that may be of interest (Nyquist frequency of the structure, that is, the highest to which it responds, under any operating circumstance) and, with the period T1 associated with said frequency (which will be the smallest that we are interested in imposing on the moving mass), the “constructive” radius of curvature R2c of the guide is calculated, with (1.14) and (1.16)), assuming that the Ngear_m used in that case is the smallest that can implement the mechanical transmission (N gear_m =0.1 in the specific case of this example). Then, decreasing frequencies (increasing T2) of interest are assumed, for which N can be set gearcorresponding, also increasing, by (1.17). Taking into account the above, for the present example, the maximum frequency at which the oscillating structure can oscillate noticeably is analyzed, assuming that it is a low-pass system (like all dynamic systems with mass). In this case, it could be the maximum frequency with which the vessel has a notable list, being completely empty. Then, using (1.14) and (1.16) the constructive curvature radius R2c of the guide is calculated, which is the one that sets a natural period for the moving mass 1, coinciding with the minimum period that a notable oscillation of the vessel T1 can take, whose data appear in Table 1. In the case of the example, we have Tm`=T1`=5 s, and we calculate a constructive curvature R2c=6.2019 m, for a minimum torque transmission ratio Ngear_m=0.1.Then, setting this value for the radius of curvature R2, if we increase the oscillation period and enter this in (1.17), the values ​​of the transmission ratio Ngear are cleared, which make the oscillatory movement of the moving mass 1 on the curvature guides R2c=6.2019 m acquire the desired natural frequencies. Thus, a series of adjustments are obtained (T2`=5.4 s, R2=6.2019 m, Ngear=1; T2`=6 s, R2=6.2019 m, Ngear=1.60; T2`=7 s, R2=6.2019 m, Ngear=2.37; T2`=8 s, R2=6.2019 m, Ngear=3.02; T2`=9s, R2=6.2019 m. R2=6.2019 m, Ngear=9.37), which They cover the entire bandwidth of the operation of the system of the invention.It follows from the above that, for this example, it is desirable to be able to impose mechanical multiplier gear ratios between 1:0.1 and 1:10 that can be continuously varied in order to tune the moving mass 1, depending on the operational circumstances. Therefore, the use of a continuously variable transmission (CVT) device with a range of gear ratios that includes, in the case of this application example, the range from 1:0.1 to 1:10 is proposed. This device makes it possible to improve the versatility of the invention, since it can be "tuned" simply by manipulating the gear ratio of the CVT. This adjustment method is valid for both passive use (without Tgen) and active use.In the active case, it is convenient to retune the internal model of the LUMPC to the gear ratio setting each time the CVT gear ratio is adjusted (or to tune it to the curvature radius R2 setting, each time the curvature radius is adjusted, if a curvature radius setting system such as the one in Figure 4 is used), by adjusting the value of the gear ratio N. gear (or the value of the radius of curvature R2) in the internal model (1.34), once the expression (1.15) is applied to Jgen and Dgen. However, the changes in N geartake place very slowly - changes in the frequency of the disturbance (swell), in this example - with respect to the dynamics of the system, so the internal linear model of the LUMPC controller - which includes Ngear - can be considered invariant (unique) during the operation of the invention. For operation in passive mode, with the LUMPC controller out of operation, an undamped natural frequency is set for the moving mass 1, using method b) of the general description of the third aspect of the invention. Then, an Ngear is set in the CVT transmission, to match the undamped natural frequency ^m of the device including the moving mass 1 with the frequency ( ) m s m ^ ^ s , described in the third aspect of the invention. Said transmission ratio should be adapted in the event that the parameters of the oscillating structure (m s and / or ^ s). The latter may occur either circumstantially (e.g. a ferry loading / unloading vehicles) or deliberately (e.g. by using ballast to “tune” the floating structure to the waves and thus achieve greater heeling intensity, in the case of a power generation facility). P231106EN The results, based on numerical simulation, obtained for this application example in operational approach 2 (with finite radius of curvature R2 and Ngear ratio adjustment) for passive mode - can also be seen in graphs 5A, 5B, 11A and 11B. It can be seen that a substantial reduction in heeling is achieved without any energy consumption.In fact, a very similar performance to that observed in active mode (see Figures 9A, 9B, 10A, and 10B) is achieved when partial objectives are set to balance the optimization of heel reduction and the minimization of electrical energy consumption / maximization of electrical energy generation. From a physical point of view, this is fully consistent with the conservation principle, since in both cases there is hardly any energy consumption / generation, and therefore, similar degrees of structural stabilization must occur. However, heel reduction in passive mode cannot be compared with that obtained in active mode, especially in the realistic case of irregular waves (see Figure 5B).Specifically, it is observed that, with irregular waves, the passive mode (that is, without the LUMPC control and without the electric machine consuming electrical power) does not work as well as with regular waves, so the active mode (that is, with the LUMPC control in operation) must be used if we want to obtain heeling reductions that exceed 50%. The results of tests carried out by activating the LUMPC control (active mode of the invention) with the new value of the radius of curvature R2 for the same application case and adjusting the undamped natural frequency of the moving mass based on the frequency characteristics of the estimate that the LUMPChace of the moment Mw due to the incident waves are shown below.If the disturbance that affects the structure has a given period T1 (or, statistically, said period is relevant), the movement of the mass can be synchronized with the moment that creates said disturbance in the structure, using a guide with a constant curvature given by (1.14) making Tm = T1 or manipulating the transmission ratio of the CVT transmission device, as explained above. It is observed – in figures 5A, 5B, 6A, 6B, 11A and 11B that the effects on the list, the associated energy consumption and the displacement of the moving mass 1 are the same now (with guides of curvature R2 = 6.2019 m) as those obtained in the example referred to in figure 1 (that is, for the case of rectilinear displacement of mass 1 or, in other words, infinite radius of curvature R2), both in the case of receiving a regular or irregular disturbance. These results can be explained by the principle of conservation of energy.P231106EN However, it is observed, on the other hand, -compare figures 7A and 13A- that the torque applied by the electric machine is synchronized with the movement of the moving mass 1, which allows the variable manipulated by the LUMPC control to reach much lower values ​​(around 80% reduction) than those achieved in the case of rectilinear displacement to achieve the same control objective. In the case of the infinite radius of curvature, the mass is not "tuned" to the disturbance introduced by the waves and this forces the mass to brake and accelerate. On the other hand, in operational approach 2, the LUMPC control only needs to slightly accelerate the moving mass 1 at the end of each cycle in order to, from a physical point of view, compensate for the damping of the system and ensure that the moving mass 1 functions as an ideal DVA configured as a vibration neutralizer.Finally, it can be observed that, when the displacement of mass 1 becomes large, the effects of some nonlinear behaviors of the system become noticeable in the manipulated variable, slightly deforming the electromagnetic torque and moving it away from strictly harmonic behavior. This demonstrates the LUMPC's ability to correctly manage nonlinear behaviors of the system, using a single internal linear model. Obviously, in the case of irregular waves (compare Figures 7B and 13B), it is impossible for the controller, due to the necessary limitations imposed on the control action, to fully achieve the effect described for the case of regular waves, but it is observed that it manages to greatly reduce (slightly more than 50%) the maximum values ​​reached by the generator torque in the case of rectilinear displacement of mass 1.These consequences can also be observed in the instantaneous power consumed –compare Figures 8A with Figures 14A-, where it can be seen that, in the case of regular waves, the instantaneous power is always in positive values ​​and that they reach a magnitude noticeably lower (80%) than in the operating case 1 (with rectilinear guides), which could imply the use of simpler power electronics. In the case of irregular waves –compare Figures 8B with Figures 14B- this occurs only to a certain extent, which finally forces the use of power electronics for the electric machine that allows its operation in the 4 quadrants, since negative powers also appear at some instants of the oscillation cycle of the moving mass 1.These effects discussed result in a reduction in the sizing of the electric machine and its associated power electronics, which implies a notable advantage of the use of curved guides, together with the possibility of using, in a very cost-effective manner, the passive mode of the adjustable hybrid mass damper. P231106ES It is worth commenting on the effect that the height y'0 has on the center of gravity of the oscillating structure, in which the device of the invention is installed. A dynamic analysis of the complete system concludes that a positive value (an installation of the device above the center of gravity of the oscillating structure) of the parameter y'0 always aids the control action, more so the higher up it is installed, making less energy necessary to achieve the reduction in heeling.However, it also follows that placing the device above the center of gravity in turn reduces the righting lever of the floating structure (in the case of this example, and reduces the stability margin of the movement of the oscillating structure in the general case) and, above all, makes the safety of the structure more dependent on the proper functioning of the LUMPC - even when the ratio between the mass of the oscillating structure and the moving mass 1 is small. Therefore, it is advisable to be cautious when deciding on the placement of the device of the invention and to take into account the circumstances of the structure (manned or unmanned, control objectives, etc.).In fact, it can also be deduced from the previous study on the dynamic behavior of the entire system that, when the control objective is focused on obtaining energy, it is advisable to place mass 1 at negative values ​​of y'0 since, in that case, a wide movement of the moving mass 1 of the adjustable hybrid mass damper is of interest, but one that does not reduce too much the inclination of the oscillating structure that causes the movement of the moving mass 1. Therefore, if the intention is to use the adjustable hybrid mass damper for both objectives, alternatively or simultaneously - partial objectives - depending on the circumstances, it is possible to either consider moving the height of the installation of the moving mass, or place said mass in a neutral position. Therefore, in the example we have used to describe the operation we have used a height y'0 = 0, right at the height of the center of gravity of the vessel.An example of a possible implementation of the proposed LUMPC control algorithm is described below, with reference to the fifth block 7 of Figure 2, which may be used in the invention, for example, in the embodiments of the invention discussed above. At each execution instant, the LUMPC controller optimizes the future dynamics of some system variables over a finite time horizon while respecting certain constraints. This optimization problem may be stated as the minimization of a cost function: ^k ^ (0,1,..., N ^ 1) (1.20). P231106ESwhere N is a prediction horizon and the system dynamics are described as a discrete-time model (1.21): The cost function (1.20) is composed of a stage cost J(y,u) and a terminal cost Vf(xN). The states xk, inputs uk and output yk can be bounded xk^ X ^Rn , uk ^ U ^ R v , yk ^ Y ^ R ^, with X, U and Y containing the origin within them. Finally, vk and dk are the measured and unmeasured disturbance input vectors, respectively. The solution to equation (1.20) gives an optimal input and state sequence, but only the first element of the optimal input sequence is applied, discarding the rest. At the next sampling time, the whole process is repeated, creating a recessionary horizon scheme. Moreover, since the initial state x(0) is usually not fully measured, a state observer is used to estimate it, obtaining xˆ ^ 0 ^ . The optimal input sequence, obtained by solving (1.20), has M different values ​​(control horizon), where 1≤M≤N. Thus, it is proposed, considering (1.20), that: where Q and R are weight matrices that penalize the deviation from the tracking made by the outputs and k of their respective slogans r k and the input increments, respectively. Some considerations are made about the stability of the MPC. In the case where the dynamical system is linear, the state-space model (1.21) can be written: To analyze the stability of LUMPC, it is necessary to study the behavior of the system over the infinite horizon, even if control is only defined over a finite horizon. This assumption leads to the well-known dual MPC, where a terminal control is assumed to start controlling the system once the predicted final state has been reached. The cost associated with such control is the terminal cost Vf(xN) presented in (1.20). The way in which the terminal regulator, cost, and constraint have to be set to guarantee stability depends on the type of system and the imposed constraints. If the system is linear, asymptotically stable, and only has control constraints, but not state constraints, the terminal control can be simply u(k)=0 for k>N (regulator problem). Now, the cost function (1.22) over an infinite horizon is exactly (1.20), if the terminal cost is: where the solution of the matrix Lyapunov equation: provides the terminal weight matrix Q , given A, C, and Q. Furthermore, it is widely known that Q^ 0 , if Q^ 0 and A has all its eigenvalues ​​inside the unit disk. Additionally, in this case, imposing a terminal constraint becomes unnecessary. Thus, by using a terminal cost given by (1.24)-(1.25) in expression (1.20) and a positive definite weight matrix Q in (1.22), the stability of the LUMPC can be guaranteed in advance. On the other hand, if one has a system (1.23) with some unstable mode, one cannot proceed in this way. In this case, one can decompose the system into its stable and unstable parts, by means of an eigenvalue-eigenvector decomposition (Jordan), such that: where Wu, Ws, Ju and Js are the similarity transforms and Jordan forms of the unstable and stable parts, respectively, of matrix A. Now, to guarantee obtaining a stable a priori LUMPC control, a terminal cost (1.24) is imposed, being thus: Q ^ W ^ W (1.27)where ^ is obtained by solving the Lyapunov matrix equation: ^^W Ts CT QCW s ^ J Ts ^ J s (1.28)In addition, the following terminal restriction is imposed, which guarantees the disappearance of the unstable modes of the system beyond the control horizon of the LUMPC: Wu ^ xk ^ k ^ M ^ ^ 0 (1.29)Restriction (1.29) is added to the quadratic formulation of the optimization of function (1.20), which eliminates from the optimization as many degrees of freedom as unstable modes exist in the system (1.23), thus reducing the number of decision variables during the optimization. Now we consider the internal model of the LUMPC, used for the prediction and estimation of state, linear and unique for the entire range of use (that is, for any type of movement of the oscillating structure). To do this, the general discrete-time model (1.21) becomes, based on what was discussed above, the linear discrete-time model: Let's see how we obtain model (1.30). First, let's propose, in continuous time, the state vector x(t), the input vectors su(t), v(t), d(t), and the output vectors y(t) of the aforementioned internal model. Taking into account the physical description we gave at the beginning of this section: where:u(t) is the input vector, whose only component is T*gen, the electromagnetic torque setpoint of the electric machine, which is the only manipulated variable (MV) by the LUMPC controller in this case.v(t) is the measured disturbance vector (MD) –which, in our case, are calculated externally using (1.8), since they are highly non-linear-.d(t) is the unmeasured disturbance vector (UD), whose only component, in this case, is Mw, moment due to waves, which will be estimated by the Kalman filter included in the LUMPC, based on the internal model and the effect of said disturbance on the measured variables –list and position of the moving mass 1-.y(t) is the output vector of the dynamic system. We have first proposed, as measured outputs (MO), the variables that we will have available in the instrumentation of our system, that is, the list y1=^ (MO1) of the boat and the angular velocity^gen (MO2) of the electric machine.We also consider, as a possible measured variable, the position of the moving mass x' (MO3) on the guides, at any given time. The monitoring of a heeling setpoint r1 -normally fixed at zero (r1=0)- for the output MO1 is the basis of the first control objective (OC1) of the invention. Finally, to enable the use of the second control objective (OC2), we define the output y4=D given by (1.9), to which we will impose a setpoint r4=D*, described by (1.10) and processed at any given time by block 8 in figure 2, in order to optimize the extraction of electrical power from the invention, while complying with the physical restrictions of the installation. 5Therefore, the state-space model that the LUMPC can use to predict the future behavior of the system and estimate states can be formulated, starting from the unique linear model described by expressions (1.2)- (1.6), as: A C 15 The LUMPC controller comprises a state observer (e.g., a Kalman filter) configured to estimate unmeasured states of the system in order to more accurately predict how changes in the manipulated variable will affect future system outputs. Considering that the variable Mw is not measured (it could even be measured in advance), it can be estimated by the state observer from the system model, measured variables such as, for example, the instantaneous heel angle of the oscillating structure and the instantaneous position of the moving mass. To do this, a model of the input disturbance is chosen to obtain said input disturbance. For example, the following model can be formulated: Being A id , C id and D id are state-space constant matrices, x id is a vector of the input perturbation model states (which are added to the system state vector), and w id is a vector of dimensionless white noise inputs with zero mean and variance equal to one. In this case, considering that there is a single unmeasured perturbation and that the one-integrator model (offset-free estimator) is used to estimate M w , we have: where w is a gain representing an estimated magnitude for the unmeasured disturbance, and w 1 is a dimensionless white noise input, with white noise having a mean of zero and a variance of one. Finally, models (1.34) and (1.38), with the parameter values ​​presented in Table 1 and the fits described below, can be discretized, for example, using a “zero-order hold” discretization method using a specific sampling period (e.g., a sampling period of 0.02 seconds). In this way, the matrices A , B , B v , B d , C , D , D v and D d of the discrete-time model (1.30) can be obtained. To do this, values ​​are assigned to the model parameters. For example, the values ​​shown in Table 1 can be assigned. Table 1. Parameters of the dynamical system. I ^ N 2^R^0.25(m)0^1.43^107 ^ m ^ s ^ ra ^ ^ d^ b^ 2, 95028271 ^ 106 ^ N ^ m ^ s ^^ Tlag ^ 0.1 (s) ^ rad ^ ^ P231106ES g^ 9.8 (m / s2) J ^ 5.341·102 N ^ m 2gen_ HSS ^ ^ s ^m ^ 50000 (kg) Dgen_ HSS ^ 6.605·102^ N ^ m ^ s ^^ ^ 707000 (kg) y 0 ^ 0 ( m )GMt ^ 3.34 (m) B ^ 0.008^N^s^ ^ ^ m ^ ^ The state observer also estimates output disturbance values ​​to estimate unmeasured states. To do this, the state observer can combine the system model with additional models of output disturbances and measurement noise. An example formulation of this combination is illustrated below: being: where:x ^ k ^ is the initial state vector of the system model,x is the state vector of the input disturbance model, the manipulated input to the system, v^k^ is the input to the measured disturbance model, wid^k^ is the white noise input to the input disturbance model, wod^k^ is the white noise input to the output disturbance model, and wn^k^ is the white noise input to the measurement noise model. All white noise inputs are independent of each other, each with zero mean and unit covariance. The terms x^k^, , wod ^ k ^ and wn ^ k ^ are defined in discrete time. To maintain state observability, in this case, the measurement noise and output disturbance models can be defined simply as static gains, with the formulation being as follows: P231106ES where A , B , B v , B d , C , D , D vy D d are obtained from the system model (1.30) as described above. A idk , B idk , C idk and D idk are discrete-time matrices obtained by discretizing (e.g., using the zero-order holdout method) the unmeasured input disturbance model (1.38) by using the expressions and D nk are the static gains used as models for the measurement noise and the output disturbance. Additional white noise signals wu ^ k ^ and wv ^ k ^ of zero mean and unit covariance are added to the inputs u ^ k ^ and v ^ k ^ . They are then assigned the value zero yav ^ k ^ and the effect of the stochastic inputs on the controller states xe ^ k ^ and the measured outputs of the system are obtained ^ k ^ , by means of: where: beingC me and the rows and columns of the observer parameters C e and D e from expression (1.42) that correspond to the measured system outputs and the measured disturbance inputs. Finally, the state observer gains are estimated. For example, if the state observer is a Kalman filter, the Kalman filter gain can be estimated based on the state observer matrices A e , C me from expressions (1.42)–(1.43) and the covariance matrices given by: Based on equations (1.20) and (1.22), the following weight matrices can be used for the stage cost function , thus penalizing the deviation of the outputs y1=^ and y4=D from their setpoints r1=0 (OC1) and r4=D* (OC2) –in the example presented here-, in order to follow the proposed control objectives (weight matrix Q ), and also penalizing (using the weight matrix R) the control effort, based on the increases in the manipulated variable that we have used T* g en : where diag(.) refers to a diagonal matrix. In this descriptive example, the only control objectives have been focused on heeling and electrical power production, affecting only the model outputs y1=^ and y4=D, so very small, non-zero values ​​are assigned to the rest of the weights to improve the numerical stability of the matrix calculations. All weights are divided by their respective scale factors. The weights we used to obtain the results presented here have been: q1=1, q4=10-14 (for the study on the stabilization of the structure) and q1=1, q4=2.5 (for the study on the use of partial control objectives). Then, if the system is unstable, the terminal weight matrix Q for the terminal cost function Vf(xN) -see equations (1.20), (1.24) and (1.27)- can be obtained once the Lyapunov equation (1.28) and the Jordan decomposition of the matrix A(1.26), using matrices A and C, obtained from equations (1.30), and matrix Q , from (1.46), as inputs. If the system is stable (the most common case), expressions (1.24) and (1.25) are used to obtain the terminal cost function and no terminal constraints are required. The adjustable gains involved in the measurement noise and disturbance models have been as follows: G 1^ 2 e 9, Dodk^1 and Dnk^0.01.Specifically, It is part of the input disturbance model defined in expressions (1.38)–(1.39). and D nk are static gains used in the output disturbance and measurement noise models in (1.40)–(1.42). The quadratic (QP) optimization KWIK algorithm can be used to solve (1.20) and obtain an optimal control action at each sampling time, taking into account the technical constraints of the system, which include the limits of the moving mass motion and the capacity limits of the electrical machine. These constraints may also include a maximum heel of the oscillating structure and / or a maximum acceleration of the moving mass. In case the system is unstable, the constraints may include the terminal constraint (1.29) to allow the stability of the LUMPC to be guaranteed in advance.

Claims

P231106ES CLAIMS 1.- A method for controlling the inclination of an oscillating structure, the method comprising adjusting a displacement of a mass (1), the mass being mechanically coupled to an electric machine by means of a mechanical transmission, the mechanical transmission being such that an adjustment of the electromagnetic torque of the electric machine allows adjusting the displacement of the mass (1) in the oscillations, the displacement being a displacement with respect to the oscillating structure; the mass (1) being coupled to the oscillating structure with a mechanical coupling, the mechanical coupling of the mass (1) with the oscillating structure allowing the displacement of the mass (1) caused by a gravitational force (Fg) and by a force applied by the electric machine to the mass (1) in the oscillations through the mechanical transmission, by adjusting the electromagnetic torque of the electric machine;causing the oscillations to be variations in an angle of inclination of the oscillating structure with respect to the direction of the gravitational force (Fg); the displacement being adjusted by adjusting the force applied, by the electric machine, to the mass (1); the method comprising: i) providing a control with a model of the dynamics of the oscillating structure, of the mass, of the mechanical transmission, of the mechanical coupling and of the electric machine, ii) establishing as a first objective of the model-based predictive control a certain inclination of the oscillating structure, iii) obtaining: o a parameter indicative of a position of the mass (1), and / or a parameter indicative of an angle of inclination of the oscillating structure, the angle being relative to a direction of the gravitational force (Fg);and provide the parameter indicative of a position of the mass (1) and the parameter indicative of an angle of inclination to the control as inputs of the control, iv) execute the control, using the model, the first objective of the control, the parameter indicative of a position of the mass (1) and the parameter indicative of an angle of inclination of the oscillating structure, to obtain an indicative parameter of adjustment of the force applied, by the electric machine, to the mass (1), through the adjustment of the electromagnetic torque; P231106ES v) adjusting, based on the indicative force adjustment parameter through electromagnetic torque adjustment, the force applied by the electric machine to the mass (1), and vi) repeating iii) to v).2.- The method of claim 1, wherein the control is a model-based predictive control; preferably, the model of the model-based predictive control is valid for all oscillation ranges of the oscillating structure; preferably, the model-based predictive control is a predictive control based on a single linear model.3.- The method of any one of the preceding claims, the method comprising establishing a second objective of the model-based predictive control, the second control objective being an adaptation of the movement of the movable mass to be in favor of gravity at all times of the oscillations and considering, the control, the instantaneous inclination of the oscillating structure; comprising iv) using the second control objective in the execution of the control.

4. - The method of claim 3, the method comprising assigning a first weight to the first control objective and a second weight to the second control objective, the first weight being relative to the second weight; comprising the use of the first control objective and the second control objective in iv) a use of a combination of the first weight with the first control objective and a combination of the second weight with the second control objective. 5.- The method of any one of the preceding claims, the oscillations of the structure comprising rotations of the structure around an imaginary axis of rotation, the mechanical coupling of the mass (1) to the oscillating structure comprising a guide with a curvature, the guide defining a direction of movement of the mass (1) contained in a plane perpendicular to the imaginary axis of rotation of the oscillating structure, and the guide being a guide for the movement of the mass (1) in the oscillations.

6. - The method of any one of the preceding claims, the oscillating structure being floating in water and the oscillations of the oscillating structure being caused by water waves. P231106ES7.- The method of claim 6, the method comprising measuring a wave height before the wave reaches the oscillating structure; providing the wave height measurement in advance to the model-based predictive control; the provided wave height measurement being an input to the control; and comprising iv) using the provided wave height measurement in optimizing the control action generated by the control. 8.The method of any one of the preceding claims, the method comprising adjusting a torque transmission ratio of the mechanical transmission connecting the movable mass (1) to the oscillating structure; the displacement of the mass (1) comprising an oscillation of the mass (1); the natural frequency of the oscillation of the mass (1) being adjusted by adjusting the torque transmission ratio, the method comprising at least one of a) and b), where: a) - obtaining a parameter indicative of a frequency of the disturbance ^d that causes movement of the oscillating structure; and - adjusting the torque transmission ratio based on the parameter indicative of the frequency of the disturbance ^. dwhich causes the oscillating structure to move, so that the undamped natural frequency ^m of the moving mass(1) coincides with the frequency of the disturbance, such that ^m =^d; and b) -obtain a parameter indicative of the undamped natural frequency of the oscillating structure ^s; and - adjust the torque transmission ratio to adjust the undamped natural frequency of the moving mass (1) ^m, so that: where ms and m are the masses of the oscillating structure and the movable mass (1), respectively.

9. The method of any one of the preceding claims, the method comprising adjusting a curvature of a guide of the mechanical coupling of the mass with the structure; the displacement of the mass (1) comprising an oscillation of the mass (1) along the curvature of the guide of the mechanical coupling; the natural frequency of the oscillation of the mass (1) being adjusted by adjusting the curvature of the P231106ES mechanical coupling guide; the method comprising at least one of a) and b), being: a) - obtaining a parameter indicative of a frequency of the disturbance ^d that causes the movement of the oscillating structure; and - adjusting the curvature of the mechanical coupling guide based on the parameter indicative of the frequency of the disturbance ^d that causes the movement of the oscillating structure, so that the undamped natural frequency ^m of the moving mass (1) coincides with the disturbance frequency, such that ^m =^d; and b) - obtaining a parameter indicative of the undamped natural frequency of the oscillating structure ^ s ; and -adjust the curvature of the mechanical coupling guide to adjust the undamped natural frequency of the moving mass (1) ^m, so that: where ms and m are the masses of the oscillating structure and the moving mass (1), respectively.10.- System for controlling an inclination of an oscillating structure, the system comprising an oscillating structure, a moving mass (1), processing means, a mechanical coupling of the mass (1) with the oscillating structure and a mechanical transmission that couples a rotor of an electric machine with the moving mass (1), the mechanical transmission being such that the displacement of the mass (1) with respect to the oscillating structure causes a variation in the angular velocity of the rotor of the electric machine; the mechanical coupling allowing a displacement of the mass (1) with respect to the oscillating structure caused by a gravitational force (Fg) and by a force applied by the electric machine to the mass (1) in the oscillations through the mechanical transmission, by means of adjusting the electromagnetic torque of the electric machine;the system being configured to adjust the displacement of the mass (1) by adjusting a force applied by the electric machine to the mass (1); the processing means being configured to: i) provide a control with a model of the dynamics of the oscillating structure, the mass (1), the mechanical transmission, the mechanical coupling and the electric machine; P231106EN ii) establishing as a first objective of the model-based predictive control a certain inclination of the oscillating structure, iii) obtaining: o a parameter indicative of a position of the mass (1), y a parameter indicative of an angle of inclination of the oscillating structuree, where the angle is relative to a direction of the gravitational force (Fg); and providing the parameter indicative of a position of the mass (1) and the parameter indicative of an angle of inclination to the control as inputs of the control, iv) executing the control, using the model, the first objective of the control, the parameter indicative of a position of the mass (1) and the parameter indicative of an angle of inclination of the oscillating structure, to obtain an indicative parameter of adjustment of the force applied, by the electric machine, to the mass (1), through the adjustment of the electromagnetic torque;(v) adjusting, based on the indicative force adjustment parameter through the adjustment of the electromagnetic torque, the force applied, by the electric machine, to the mass (1); and (vi) repeating steps of iii) to v). 11.- Method of controlling the inclination of an oscillating structure, the method comprising adjusting a torque transmission ratio of a mechanical transmission between a mass (1) and a rotor of an electric machine, the mechanical transmission being such that an adjustment of the electromagnetic torque of the electric machine allows adjusting the displacement of the mass (1) in the oscillations, the displacement being a displacement with respect to the oscillating structure;the mass (1) being coupled to the oscillating structure by a mechanical coupling, the mechanical coupling of the mass (1) with the oscillating structure allowing the displacement of the mass (1) caused by a gravitational force (Fg) and by a force applied by the electrical machine to the mass in the oscillations through the mechanical transmission, by adjusting its electromagnetic torque; causing the oscillations to be variations in an angle of inclination of the oscillating structure with respect to the direction of the gravitational force (Fg); the displacement of the mass (1) comprising an oscillation of the mass (1); the natural frequency of the oscillation of the mass (1) being adjusted by adjusting the torque transmission ratio; the method comprising at least one of a) and b), being: P231106EN a) -obtaining a parameter indicative of a disturbance frequency ^d that causes the oscillating structure to move; and -adjusting the torque transmission ratio based on the parameter indicative of the disturbance frequency ^d that causes the oscillating structure to move, so that the undamped natural frequency ^m of the moving mass (1) coincides with the disturbance frequency, such that ^m = ^d; and b) -obtaining a parameter indicative of the undamped natural frequency of the oscillating structure ^s; and- adjusting the torque transmission ratio to adjust the undamped natural frequency of the moving mass (1) ^m, so that: where ms and m are the masses of the oscillating structure and the moving mass (1), respectively.

12. The method of claim 11, the oscillations of the structure comprising rotations of the structure around an imaginary axis of rotation, the mechanical coupling of the mass (1) to the oscillating structure comprising a guide with a curvature, the guide defining a direction of movement of the mass (1) contained in a plane perpendicular to the imaginary axis of rotation of the oscillating structure, and the guide being a guide of the movement of the mass (1) in the oscillations 13. The method of claim 12, wherein adjusting the transmission ratio Ngear based on at least one of a) and b) of claim 11, comprises adjusting the transmission ratio Ngear to a value These values ​​being real if: 4^ 2 ^ 2 2 RT ^ ^ m2 g Jgen_HSS>0 R>0 P231106ESwhere m is the mass (1), R is a radius of the rack-and-pinion gearwheel, R2 is the radius of curvature of the guide, g is the acceleration of gravity, Tm2 is the oscillation period (Tm2=2^ / ^m, ^m being in radians / second) desired for the mass (1) according to the ^m obtained with at least one of a) and b) of claim 11 in its displacement along the guide and Jgen_HSS is a moment of inertia of the rotor of the electric machine.

14. - The method of any one of claims 11 to 13, the mechanical transmission being a continuously variable transmission.

15. - Method of tilt control of an oscillating structure, the method comprising adjusting a curvature of a guide of a mechanical coupling of a movable mass (1) with the oscillating structure, said mechanical coupling allowing the displacement, with respect to the oscillating structure,of the mass (1) caused by a gravitational force (Fg) and by a force applied by an electric machine to the mass (1) in oscillations through mechanical transmission, by adjusting the electromagnetic torque of the electric machine; causing the oscillations of the mass (1) variations of an angle of inclination of the oscillating structure with respect to the direction of the gravitational force (Fg); the displacement of the mass (1) comprising an oscillation of the mass (1); the natural frequency of the oscillation of the mass (1) being adjusted by adjusting a curvature of a guide of the mechanical coupling; the method comprising at least one of a) and b),where: a) - obtaining a parameter indicative of a frequency of the disturbance ^d that causes the oscillating structure to move; and - adjusting the curvature of the mechanical coupling guide based on the parameter indicative of the frequency of the disturbance ^d that causes the oscillating structure to move, so that the undamped natural frequency ^m of the moving mass (1) coincides with the frequency of the disturbance, such that ^m = ^d; and b) - obtaining a parameter indicative of the undamped natural frequency of the oscillating structure ^s; and - adjusting the curvature of the mechanical coupling guide to adjust the undamped natural frequency of the moving mass (1) ^m, so that: P231106ES where ms and m are the masses of the oscillating structure and the movable mass (1), respectively.

16. The method of claim 15, the oscillations of the structure comprising rotations of the structure around an imaginary axis of rotation, the mechanical coupling of the mass (1) to the oscillating structure comprising a guide with the curvature, the guide defining a direction of movement of the mass (1) contained in a plane perpendicular to the imaginary axis of rotation of the oscillating structure, the guide being a guide for the movement of the mass (1) in the oscillations; and the curvature of the guide being adjusted by the method.

17. The method of claim 16, wherein adjusting the curvature of the guide based on at least one of a) and b) of claim 15, comprises adjusting the curvature of the guide to a value given by: where R2 is the radius of curvature of the guide, m is the mass (1), g is the acceleration of gravity, Tm is the oscillation period (Tm=2^ / ^m, where ^m is in radians / second) desired for the mass (1) according to the ^ m obtained with at least one of a) and b) of claim 15 as it moves along the guide; and where Ngear is the transmission ratio between the rotor of the electric machine and the moving mass (1), R is a radius of the gear wheel of the rack-and-pinion transmission and Jgen_HSS is a moment of inertia of the rotor of the electric machine.18.- Method comprising the method according to any one of claims 1-7 and the method according to any one of claims 11-14.19.- Method comprising the method according to any one of claims 1-7 and the method according to any one of claims 15-17.20.- System comprising an oscillating body, an electric machine, a mass (1), P231106ES a mechanical transmission, processing means and a mechanical coupling configured to perform the method of any one of claims 1 to 7.21.- System comprising an oscillating body, an electric machine, a mass, a mechanical transmission, processing means, a mechanical coupling and an actuator configured to perform the method of any one of claims 8, 9, 11-17.

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