EP3649072B1 - Crane and method for controlling such a crane - Google Patents

Description

The present invention relates to a crane, in particular a tower crane, with a hoist cable that runs off a boom and carries a load-carrying device, drive devices for moving a plurality of crane elements and movement of the load-carrying device, a control device for controlling the drive devices in such a way that the load-carrying device moves along a travel path , as well as a pendulum damping device for damping pendulum movements of the load-carrying means, the said pendulum-damping device having a pendulum sensor system for detecting pendulum movements of the hoist rope and/or the load-carrying means and a controller module with a closed control circuit for influencing the activation of the drive devices as a function of pendulum signals generated by the pendulum sensors indicate detected pendulum movements and are fed back to the control loop. The invention also relates to a method for controlling a crane, in which the actuation of the drive devices is influenced by a sway damping device as a function of parameters relevant to swaying.

In order to be able to move the load hook of a crane along a travel path or between two target points, various drive devices are usually required operated and controlled. For example, in the case of a tower crane, in which the hoist rope runs off a trolley that can be moved on the jib of the crane, the slewing gear, by means of which the tower with the jib provided thereon or the jib relative to the tower are rotated about an upright axis of rotation, must usually as well as the trolley drive, by means of which the trolley can be moved along the jib, and the hoist, by means of which the hoist rope can be adjusted and the load hook raised and lowered, are each actuated and controlled. In cranes with a luffing telescopic boom, in addition to the slewing gear, which rotates the boom or the superstructure carrying the boom about an upright axis, and the hoist for adjusting the hoist rope, the luffing drive for luffing the boom up and down and the telescoping drive are also used - Actuates and extends the telescopic sections, possibly also a luffing jib drive if there is a luffing jib on the telescopic boom. In the case of mixed forms of such cranes and similar types of cranes, for example tower cranes with a luffing jib or derrick cranes with a luffing counter-jib, it is also possible to control further drive devices.

The drive devices mentioned are usually actuated and controlled by the crane operator using appropriate operating elements, for example in the form of joysticks, toggle switches, rotary knobs and sliders and the like, which experience has shown requires a lot of feeling and experience in order to approach the target points quickly and yet gently without major pendulum movements of the load hook. While the target points should be driven as quickly as possible in order to achieve a high work output, the target point should be stopped gently without the load hook swinging with the load attached to it.

Such a control of the drive devices of a crane is tiring in view of the required concentration for the crane driver, especially since recurring travel paths and monotonous tasks often have to be performed. In addition, if concentration decreases or if there is insufficient experience with the respective type of crane, there will be larger pendulum movements of the people being recorded Load and thus a corresponding risk potential if the crane driver does not operate the operating levers or elements of the crane sensitively enough. In practice, when the crane is controlled, even experienced crane operators sometimes quickly experience large pendulum swings in the load, which only subside very slowly.

In order to counteract the problem of undesired pendulum movements, it has already been proposed to provide the crane's control device with pendulum damping devices, which intervene in the control by means of control modules and influence the activation of the drive devices, for example excessive acceleration of a drive device by actuating the operating lever too quickly or too vigorously prevent or mitigate or limit certain travel speeds for larger loads or actively intervene in the travel movements in a similar way in order to prevent the load hook from swinging too much.

Such anti-sway devices for cranes are known in various designs, for example by controlling the slewing gear, luffing and trolley drives as a function of certain sensor signals, for example inclination and/or gyroscope signals. For example, the writings show DE 20 2008 018 260 U1 or DE 10 2009 032 270 A1 known load swing damping on cranes, to the extent of which, ie with regard to the basics of the swing damping device, is expressly referred to. In the DE 20 2008 018 206 U1 For example, a gyroscope unit is used to measure the cable angle relative to the vertical and its change in the form of the cable angular velocity in order to automatically intervene in the control when a limit value for the cable angular velocity relative to the vertical is exceeded.

Furthermore, the writings show EP16 28 902 B1 , DE 103 24 692 A1 , EP25 62 125 B1 , US 2013 01 61 279 A , DE100 64 182 A1 , or U.S. 55 26 946 B in each case concepts for the closed-loop control of cranes, the pendulum dynamics or the Consider pendulum and drive dynamics. However, the application of these known concepts to "soft", flexible cranes with elongated, exhausted structures, such as a tower crane with structural dynamics, usually leads very quickly to a dangerous, unstable swinging up of the excitable structural dynamics.

Such close-loop controls on cranes, taking pendulum dynamics into account, are already the subject of various scientific publications, cf. E. Arnold, O. Sawodny, J. Neupert and K. Schneider, "Anti-sway system for boom cranes based on a model predictive control approach", IEEE International Conference Mechatronics and Automation, 2005, Niagara Falls, Ont., Canada, 2005, pp. 1533-1538 Vol. 3 ., such as Arnold, E., Neupert, J., Sawodny, O., "Model predictive trajectory generation for flatness-based follow-up controls using the example of a mobile harbor crane", at - automation technology, 56(8/2008 ), or J. Neupert, E. Arnold, K. Schneider & O. Sawodny, "Tracking and anti-sway control for boom cranes", Control Engineering Practice, 18, pp. 31-44, 2010, doi: 10.1016/j.conengprac. 2009.08.003 .

Furthermore, a load swing damping system for maritime cranes is known from the Liebherr company under the name "Cycoptronic", which calculates load movements and influences such as wind in advance and, based on this precalculation, automatically initiates compensation movements in order to prevent the load from swinging. In concrete terms, this system also uses gyroscopes to record the cable angle relative to the vertical and its changes in order to intervene in the control depending on the gyroscope signals.

In the case of long, slender crane structures with an ambitious load capacity design, as is the case in particular with tower cranes, but can also be relevant with other cranes with booms that can be rotated about an upright axis, such as luffing telescopic boom cranes, it is sometimes difficult with conventional swing damping devices to intervene in the correct way in the control of the drives to achieve the desired, sway-damping to achieve effect. Dynamic effects and elastic deformation of the structural parts occur in the area of the structural parts, in particular the tower and jib, when a drive is accelerated or braked, so that interventions in the drive devices - for example braking or accelerating the trolley drive or the slewing gear - are not direct affect the pendulum movement of the load hook in the desired way.

On the one hand, time delays in the transmission to the hoist rope and the load hook can occur due to dynamic effects in the structural parts if drives are operated in a sway-dampening manner. On the other hand, the dynamic effects mentioned can also have excessive or even counterproductive effects on a load swing. If, for example, a load swings backwards towards the tower as a result of initially operating the trolley drive too quickly and the swing damping device counteracts this by decelerating the trolley drive, the jib can pitch, since the tower deforms accordingly, which impairs the desired swing-damping effect can be.

In particular with tower cranes, due to the lightweight construction, the problem also arises that, in contrast to certain other types of cranes, the vibrations of the steel structure are not negligible, but should be dealt with in a control (closed loop) for safety reasons, since otherwise there would usually be a dangerous unstable upswing of the steel structure.

The writings DE 10 2011 001 112 A1 , EP 25 74 819 A1 and DE 10 2010 038 218 A1 describe crane control systems which, in order to reduce vibrations in the structure of the crane during slewing movements, provide that system parameters in the form of the natural frequency and the damping rate of the crane system are automatically calculated during operation and the control signal as an active speed reference profile can be calculated in real time from an operator signal of the operator and the calculated natural frequency under damping rate of the crane system.

Proceeding from this, the object of the present invention is to provide an improved crane and an improved method for its control, which avoid the disadvantages of the prior art and develop the latter in an advantageous manner. The aim should preferably be to move the payload in accordance with the crane operator's setpoint values and to actively dampen undesired pendulum movements by means of a control system, while at the same time undesired movements of the structural dynamics are not stimulated but also dampened by the control system in order to increase safety, facilitate to achieve usability and automation. In particular, improved pendulum damping is to be achieved in tower cranes, which takes better account of the diverse influences of the crane structure.

According to the invention, the stated object is achieved by a crane according to claim 1 and a method according to claim 16. Preferred developments of the invention are the subject matter of the dependent claims.

It is therefore proposed that the pendulum-damping measures not only take into account the actual pendulum movement of the cable itself, but also the dynamics of the crane structure or the steel construction of the crane and its drive trains. The crane is no longer assumed to be an immobile rigid body that converts the drive movements of the drive devices directly and identically, ie 1:1, into movements of the suspension point of the hoist rope. Instead, the sway damping device considers the crane as a soft structure that shows elasticity and resilience during acceleration in its steel construction or structural parts such as the tower lattice and the boom, and in its drive trains, and takes these dynamics of the structural parts of the crane into account when influencing the sway damping Control of the drive devices.

Both the pendulum dynamics and the structural dynamics are actively dampened by means of a closed control loop. In particular, the entire system dynamics are actively controlled as a coupling of the pendulum, drive and structural dynamics of the tower crane in order to move the payload according to the target specifications. Sensors are used on the one hand to measure system variables of pendulum dynamics and on the other hand to measure system variables of structural dynamics, with non-measurable system variables being able to be estimated as system states in a model-based observer. The actuating signals for the drives are calculated using a model-based control system as a status feedback of the system statuses, which closes a control loop and results in changed system dynamics. The control is designed in such a way that the system dynamics of the closed control loop are stable and control errors are compensated for quickly.

According to the invention, a closed control circuit is provided on the crane, in particular a tower crane, with structural dynamics through the feedback of measurements not only of the pendulum dynamics but also of the structural dynamics. In addition to the pendulum sensor system for detecting movements of the hoist rope and/or load handling device, the sway control device also includes a structural dynamics sensor system for detecting dynamic deformations and movements of the crane structure or at least structural components thereof, with the controller module of the sway control device, which influences the activation of the drive device in a sway-damping manner , is designed to take into account both the pendulum movements detected by the pendulum sensor system and the dynamic deformations of the structural components of the crane detected by the structural dynamics sensor system when influencing the control of the drive devices. Both the pendulum sensor signals and the structural dynamics sensor signals are fed back to the closed control loop.

The anti-sway device therefore does not consider the crane or machine structure to be a rigid, infinitely stiff structure, so to speak, but is based on an elastically deformable and/or flexible and/or relatively soft structure which - in addition to the adjustment movement axes of the machine such as the boom luffing axis or the axis of rotation of the tower - allows movements and/or changes in position due to deformation of the structural components.

The consideration of the inherent mobility of the machine structure as a result of structural deformations under load or dynamic loads is particularly important in the case of elongated, slender structures that are consciously exhausted from the static and dynamic boundary conditions - taking into account the necessary safety - such as tower cranes or telescopic cranes, since there are noticeable movement components, for example for the boom and thus the load hook position, due to the deformation of the structural components. Around In order to be able to combat the causes of pendulum better, the pendulum damping takes into account such deformations and movements of the machine structure under dynamic loads.

Considerable advantages can be achieved in this way:
First of all, the vibration dynamics of the structural components are reduced by the control behavior of the control device. The vibration is actively dampened by the driving behavior or not even stimulated by the control behavior.

The steel construction is also protected and less stressed. In particular, shock loads are reduced by the control behavior.

Furthermore, the influence of the driving behavior can be defined by this method.

The knowledge of the structural dynamics and the control method can be used to reduce and dampen pitching oscillations in particular. As a result, the load behaves more smoothly and no longer fluctuates up and down later when it is at rest. Also, transverse pendulum motions in the circumferential direction about the upright jib axis of rotation can be better controlled by considering tower torsion and jib pivot bending deformations.

The above-mentioned elastic deformations and movements of the structural components and drive trains and the resulting movements of their own can basically be determined in different ways.

According to the invention, the structural dynamics sensor system provided for this purpose is designed to detect elastic deformations and movements of structural components under dynamic loads.

Such a structural dynamics sensor system can include, for example, deformation sensors such as strain gauges on the steel construction of the crane, for example the lattice framework of the tower and/or the boom.

Alternatively or additionally, yaw rate sensors, in particular in the form of gyroscopes, gyro sensors and/or gyrometers, and/or acceleration and/or speed sensors can be provided in order to detect certain movements of structural components such as pitching movements of the boom tip and/or rotational dynamic effects on the boom and/or To detect torsional and / or bending movements of the tower.

Furthermore, inclination sensors can be provided in order to detect inclinations of the jib and/or inclinations of the tower, in particular deflections of the jib from the horizontal and/or deflections of the tower from the vertical.

In principle, the structural dynamics sensor system can work with different sensor types, in particular also combine different sensor types with each other. Strain gauges and/or acceleration sensors and/or yaw rate sensors, in particular in the form of gyroscopes, gyro sensors and/or gyrometers, can advantageously be used to detect the deformations and/or dynamic internal movements of structural components of the crane, with the acceleration sensors and/or yaw rate sensors preferably being used are formed detecting three axes.

Such structural dynamics sensors can be provided on the jib and/or on the tower, in particular on its upper section on which the jib is mounted, in order to detect the dynamics of the tower. For example, jerky lifting movements lead to pitching movements of the jib, which are accompanied by bending movements of the tower, with post-vibration of the tower in turn leading to pitching vibrations of the jib, which is accompanied by corresponding load hook movements.

In particular, an angle sensor system can be provided for determining the differential angle of rotation between an upper tower end section and the jib, wherein, for example, an angle sensor can be attached to the upper turret end section and to the jib, the signals of which can indicate the stated differential angle of rotation when considering the difference. Furthermore, a yaw rate sensor for determining the rotational speed of the boom and/or the upper turret end section can advantageously also be provided in order to be able to determine the influence of the turret torsional movement in connection with the aforementioned differential rotational angle. From this, on the one hand, a more precise load position estimation, on the other hand, an active damping of the tower torsion during operation can be achieved.

In an advantageous development of the invention, two- or three-axis yaw rate sensors and/or acceleration sensors can be attached to the jib tip and/or to the jib in the area of the upright crane axis of rotation in order to be able to determine structural dynamic movements of the jib.

Alternatively or additionally, movement and/or acceleration sensors can also be assigned to the drive trains in order to be able to detect the dynamics of the drive trains. For example, encoders can be assigned to the deflection rollers of the trolley for the hoisting rope and/or deflection rollers for a guy rope of a luffing jib, in order to be able to detect the actual rope speed at the relevant point.

Advantageously, suitable movement and/or speed and/or acceleration sensors are also assigned to the drive devices themselves in order to record the drive movements of the drive devices accordingly and to correlate them with the estimated and/or recorded deformations of the structural components or the steel construction and flexibility in the drive trains to be able to

In particular, by comparing the signals from the motion and/or acceleration sensors directly assigned to the drive devices with the signals from the structural dynamics sensors and knowing the structural geometry, the motion and/or acceleration component of a structural part can be determined that indicates dynamic deformation or twisting of the crane structure and in addition to the actual crane movement as induced by the drive movement and which would also occur with a completely stiff, rigid crane. If, for example, the slewing gear of a tower crane is adjusted by 10°, but only a rotation of 9° is detected at the tip of the jib, conclusions can be drawn about torsion of the tower and/or bending deformation of the jib, which in turn can be detected at the same time, for example with the twisting signal of a Yaw rate sensor attached to the top of the tower can be adjusted in order to be able to differentiate between tower torsion and boom bending. If the load hook is lifted by the hoist by one meter, but at the same time a downward pitching movement of e.g. 1° is detected on the jib, the actual load hook movement can be deduced taking into account the radius of the trolley.

The structural dynamics sensor system can advantageously detect different directions of movement of the structural deformations. In particular, the structural dynamics sensor system can have at least one radial dynamics sensor for detecting dynamic movements of the crane structure in an upright plane parallel to the crane boom, and at least one pivoting dynamics sensor for detecting dynamic movements of the crane structure about an upright crane axis of rotation, in particular the tower axis. The controller module of the sway damping device can be designed to control the drive devices, in particular a trolley drive and slewing gear drive, depending on the detected dynamic movements of the crane structure in the upright plane parallel to the boom, in particular parallel to the longitudinal direction of the boom, and the detected dynamic movements of the crane structure around the to influence the vertical axis of rotation of the crane.

Furthermore, the structural dynamics sensor system can have at least one lifting dynamics sensor for detecting vertical dynamic deformations of the crane boom, and the controller module of the anti-sway device can be designed to influence the activation of the drive devices, in particular a hoist drive, depending on the detected vertical dynamic deformations of the crane boom.

The structural dynamics sensor system is advantageously designed to detect all natural modes of the dynamic torsion of the crane boom and/or the crane tower, the natural frequencies of which lie in a predetermined frequency range. For this purpose, the structural dynamics sensor system can have at least one, preferably several, tower sensor(s), which is/are arranged at a distance from a node of a natural tower vibration, for detecting tower torsion, as well as at least one, preferably several, boom sensor(s), which/are arranged at a distance from a node a boom natural vibration, for detecting boom twists.

In particular, several sensors for detecting a structural movement can be placed in such a way that it is possible to observe all natural modes whose natural frequencies are in the relevant frequency range. In principle, one sensor per pendulum movement direction can suffice for this purpose, but in practice the use of several sensors is recommended. For example, placing a single sensor in a node of a structure eigenmode measurand (e.g. trolley position at a rotation node of the first cantilever eigenmode) will result in loss of observability, which can be avoided by adding a sensor in a different position . In particular, the use of three-axis yaw rate sensors or acceleration sensors on the boom tip and on the boom near the slewing gear is recommended.

In principle, the structural dynamics sensor system can work with different types of sensors to detect the natural modes, in particular also different types of sensors combine with each other. Advantageously, the aforementioned strain gauges and/or acceleration sensors and/or rotation rate sensors, in particular in the form of gyroscopes, gyro sensors and/or gyrometers, can be used to detect the deformations and/or dynamic internal movements of structural components of the crane, with the acceleration sensors and/or or yaw rate sensors are preferably designed to detect three axes.

In particular, the structural dynamics sensor system can have at least one yaw rate and/or acceleration sensor and/or strain gauges for detecting dynamic tower deformations and at least one yaw rate and/or acceleration sensor and/or strain gauges for detecting dynamic boom deformations. Yaw rate and/or acceleration sensors can advantageously be provided on various tower sections, in particular at least on the top of the tower and at the articulation point of the boom and possibly in a middle section of the tower below the boom. Alternatively or additionally, rotation rate and/or acceleration sensors can be provided on various sections of the jib, in particular at least on the jib tip and/or the trolley and/or the jib foot to which the jib is articulated, and/or on a jib section in the hoist. The sensors mentioned are advantageously arranged on the respective structural component in such a way that they can detect the natural modes of its elastic torsion.

In a further development of the invention, the anti-sway device can also include an estimation device that calculates the deformations and movements of the machine structure under dynamic loads that vary as a function of the control commands entered at the control station and/or as a function of specific control actions of the drive devices and/or as a function of specific speed and /or result in acceleration profiles of the drive devices, taking into account the circumstances characterizing the crane structure. In particular, by means of such an estimation device System variables of the structural dynamics, if necessary also of the pendulum dynamics, are estimated, which cannot or only with difficulty be detected by sensors.

Such an estimation device can, for example, access a data model in which structural variables of the crane such as tower height, jib length, rigidity, area moments of inertia and the like are stored and/or linked to one another, in order to then use a specific load situation, i.e. weight of the load picked up on the load hook and the current radius , to estimate which dynamic effects, i.e. deformations in the steel construction and in the drive trains, result for a specific actuation of a drive device. Depending on a dynamic effect estimated in this way, the sway damping device can then intervene in the control of the drive devices and influence the manipulated variables of the drive controllers of the drive devices in order to avoid or reduce swaying movements of the load hook and the hoist cable.

In particular, the determination device for determining such structural deformations can have a calculation unit which calculates these structural deformations and the movements of structural parts resulting therefrom using a stored calculation model as a function of the control commands entered at the control station. Such a model can be constructed similarly to a finite element model or be a finite element model, but it is advantageous to use a model that is significantly simplified compared to a finite element model /or load conditions can be determined on the real crane or the real machine. Such a calculation model can work, for example, with tables in which specific control commands are assigned specific deformations, with intermediate values of the control commands being able to be converted into corresponding deformations by means of an interpolation device.

According to a further advantageous aspect of the invention, the controller module in the closed control loop can include a filter device or an observer which, on the one hand, monitors the structure-dynamic crane reactions and the hoisting cable or Observed load hook pendulum movements, as they are detected by the structural dynamics sensor and the pendulum sensor and set with certain manipulated variables of the drive controller, so that the observer or filter device, taking into account predetermined laws of a dynamic model of the crane, which can be fundamentally different and through analysis and simulation of the steel construction can be obtained, based on the observed crane structure and pendulum reactions, can influence the manipulated variables of the controller.

Such a filter or observer device can be designed in particular in the form of a so-called Kalman filter, to which, on the one hand, the manipulated variables of the drive controller of the crane and, on the other hand, both the pendulum signals of the pendulum sensor system and the structural dynamics signals fed back to the control loop, the deformations and/or dynamic intrinsic Specify movements of the structural components, are supplied and which, from these input variables using Kalman equations that model the dynamic system of the crane structure, in particular its steel components and drive trains, influences the manipulated variables of the drive controllers accordingly in order to achieve the desired sway-damping effect.

Detected and/or estimated and/or calculated and/or simulated functions that characterize the dynamics of the structural components of the crane are advantageously implemented in the Kalman filter.

In particular, dynamic boom deformations and tower deformations detected by means of the structural dynamics sensor system and the position of the load hook detected by means of the pendulum sensor system, in particular its diagonal pull relative to the vertical, i.e. the deflection of the hoist rope relative to the vertical, are fed to the Kalman filter. The detection device for detecting the position of the load hook can advantageously be an imaging Sensors, for example include a camera that looks from the suspension point of the hoist rope, such as the trolley, substantially vertically downwards. An image evaluation device can identify the crane hook in the image provided by the imaging sensors and determine its eccentricity or its displacement from the center of the image, which is a measure of the deflection of the crane hook relative to the vertical and thus characterizes the swinging load. Alternatively or in addition, a gyroscopic sensor can detect the hoist cable pull-off angle from the boom and/or from the vertical and feed it to the Kalman filter.

As an alternative or in addition to such a pendulum detection of the load hook by means of an imaging sensor system, the pendulum sensor system can also work with an inertial detection device that is attached to the load hook or the load handling attachments and provides acceleration and yaw rate signals that reflect translational accelerations and yaw rates of the load hook.

Such an inertial measuring device attached to the load handling device, which is sometimes also referred to as an IMU, can have acceleration and yaw rate sensor means for providing acceleration and yaw rate signals, which on the one hand indicate translational accelerations along different spatial axes and on the other hand yaw rates or gyroscopic signals with regard to different spatial axes. In this case, rotational speeds, but in principle also rotational accelerations or even both, can be provided as rotational rates.

Advantageously, the inertial measuring device can detect accelerations in three spatial axes and yaw rates about at least two spatial axes. The acceleration sensor means can work on three axes and the gyroscope sensor means can work on two axes.

The inertial measuring device attached to the load hook can advantageously transmit its acceleration and yaw rate signals and/or signals derived therefrom wirelessly transmit to a control and / or evaluation device, which can be attached to a structural part of the crane or arranged separately in the vicinity of the crane. In particular, the transmission can be made to a receiver that can be attached to the trolley and/or to the suspension from which the hoist cable runs. The transmission can advantageously take place via a WLAN connection, for example.

With such a wireless connection of an inertial measuring device, a pendulum damping system can also be retrofitted very easily to existing cranes, without complex retrofitting measures being required for this. Essentially only the inertial measuring device has to be attached to the load hook and the receiver communicating with it, which transmits the signals to the control or regulation device.

From the signals of the inertial measuring device, the deflection of the load hook or the hoist rope relative to the vertical can advantageously be determined in a two-stage process. First, the tilting of the load hook is determined, since this does not have to correspond to the deflection of the load hook in relation to the trolley or the suspension point and the deflection of the hoisting rope in relation to the vertical of the hoist rope relative to the vertical. Since the inertial measuring device is attached to the load hook, the acceleration and yaw rate signals are influenced both by the pendulum movements of the hoist rope and by the dynamics of the load hook tilting relative to the hoist rope.

1. i. Eine Bestimmung der Hakenkippung, z.B. durch ein Komplementärfilter, der hochfrequente Anteile aus den Gyroskopsignalen und niederfrequente Anteile aus Richtung des Gravitationsvektors bestimmen und einander ergänzend zur Ermittlung der HAkenkippung zusammenführen kann;
2. ii. Eine Rotation der Beschleunigungsmessung bzw. eine Transformation vom körperfesten ins inertiale Koordinatensystem;
3. iii. Schätzung des Lastpendelwinkels mittels eines erweiterten Kaiman-Filters und/oder mittels einer vereinfachten Relation des Pendelwinkel zum Quotienten aus Querbeschleunigungsmessung und Gravitationskonstante.

In particular, three calculation steps can be used to precisely estimate the load sway angle, which can then be used by a controller for active sway control. The three calculation steps can include the following steps in particular:

1. i. A determination of the hook tilt, eg by a complementary filter, the high-frequency components from the gyroscope signals and low-frequency components can be determined from the direction of the gravitational vector and combined to determine hook tilt;
2. ii. A rotation of the acceleration measurement or a transformation from the body-fixed to the inertial coordinate system;
3. iii. Estimation of the load sway angle using an extended Kalman filter and/or using a simplified relation of the sway angle to the quotient of the lateral acceleration measurement and the gravitational constant.

Advantageously, the tilting of the load hook is first determined from the signals from the inertial measuring device with the aid of a complementary filter, which makes use of the different characteristics of the translational acceleration signals and the gyroscopic signals of the inertial measuring device, with a Kalman filter also being used as an alternative or in addition to the determination the tilting of the load hook from the acceleration and yaw rate signals can be used.

From the determined tilting of the load handling device, the desired deflection of the load hook relative to the trolley or relative to the suspension point of the hoisting rope and/or the deflection of the hoisting rope relative to the vertical can then be determined using a Kalman filter and/or by means of static calculation from horizontal inertial acceleration and gravitational acceleration will.

In particular, the pendulum sensor system can have first determination means for determining and/or estimating a tilting of the load handling device from the acceleration and yaw rate signals of the inertial measuring device and second determining means for determining the deflection of the hoist rope and/or the load handling device relative to the vertical from the determined tilting of the load handling device and an inertial -Exhibit acceleration of the lifting device.

The first determination means mentioned can in particular be a complementary filter with a high-pass filter for the yaw rate signal of the inertial measuring device and have a low-pass filter for the acceleration signal of the inertial measuring device or a signal derived therefrom, wherein said complementary filter can be designed to estimate the tilting of the load handling device based on the high-pass filtered rotation rate signal, and an acceleration-based estimation of the tilting of the load handling device, which is based on the low-pass filtered acceleration signal, and to determine the sought-after tilting of the load-handling device from the linked estimates of the tilting of the load-handling device based on the rate of rotation and acceleration.

In this case, the rotation rate-based estimation of the tilting of the load handling device can include an integration of the high-pass filtered rotation rate signal.

gewonnen wird.The acceleration-based estimation of the tilting of the load handling device can be based on the quotient of a measured horizontal acceleration component and a measured vertical acceleration component, from which the acceleration-based estimation of the tilting is based on the relationship $$e_{\beta ,a}=\arctan \left(\frac{{}_{K}a_x}{{}_{K}a_{\mathrm{e.g}}}\right).$$

is won.

The second determination means for determining the deflection of the load hook or the hoisting rope relative to the vertical based on the determined tilting of the load hook can have a filter and/or observer device which takes into account the determined tilting of the load lifting device as an input variable and calculates the deflection of the load lifting device from an inertial acceleration on the load lifting device Hoist rope and / or the lifting device determined relative to the vertical.

Said filter and/or observer device can in particular include a Kalman filter, in particular an extended Kalman filter.

As an alternative or in addition to such a Kalman filter, the second determination means can also have a calculation device for calculating the deflection of the hoisting rope and/or the load handling device relative to the vertical from a static relationship of the accelerations, in particular from the quotient of a horizontal inertial acceleration and the acceleration due to gravity.

According to a further advantageous aspect of the invention, a two-degree-of-freedom control structure is used for the sway control, through which the state feedback described above is supplemented by a feedforward control. The status feedback serves to ensure stability and to quickly compensate for control errors, while the pre-control, on the other hand, ensures good control behavior through which, ideally, no control errors occur at all.

In this case, the pilot control can advantageously be determined using the method of differential flatness, which is known per se. With regard to the mentioned method of differential flatness, reference is made to the dissertation " Application of the flatness-based analysis and control of nonlinear multivariable systems", by Ralf Rothfuss, VDI-Verlag, 1997 , referenced, which is made the subject matter of the present disclosure to this extent, ie with regard to the method of differential flatness mentioned.

Since the deflections of the structural movements are only small in contrast to the driven crane movements and the pendulum movements, the structural dynamics can be neglected to determine the pre-control, which means that the crane, especially the tower crane, can be represented as a flat system with the load coordinates as flat outputs.

Advantageously, the pilot control and the calculation of the reference states of the two-degree-of-freedom structure are calculated in contrast to the feedback control of the closed control loop, neglecting the structural dynamics, ie the crane is considered to be rigid or so-to-speak for the purposes of the pilot control assumed infinitely stiff structure. Due to the small deflections of the elastic structure, which are very small compared to the crane movements to be carried out by the drives, this only leads to very small and therefore negligible deviations in the pilot control. However, the description of the tower crane, which is assumed to be rigid for the purposes of the pilot control, in particular the tower crane, is made possible as a flat system which can be easily inverted. The coordinates of the load position are flat exits of the system. From the flat outputs and their time derivatives, the required course of the manipulated variables and the system states can be calculated exactly algebraically (inverse system) - without simulation or optimization. This allows the load to be brought to a target position without overshooting.

The load position required for the flatness-based pilot control and its derivatives can advantageously be calculated by a trajectory planning module and/or by setpoint filtering. If a target curve for the load position and its first four time derivatives is now determined via trajectory planning or setpoint filtering, the exact curve of the necessary control signals for controlling the drives, as well as the exact curve of the corresponding system states, can be calculated from this in the pre-control using algebraic equations.

In order not to excite any structural movements through the pre-control, notch filters can advantageously be switched between trajectory planning and pre-control in order to eliminate the excitable natural frequencies of the structural dynamics from the planned trajectory signal.

The model on which the control is based can fundamentally be of different types. Advantageously, a compact representation of the entire system dynamics as coupled pendulum, drive and structural dynamics is used, which is suitable as a basis for the observer and the controller. In an advantageous development of the invention, the crane control model is determined by a modeling method in which the overall crane dynamics are divided into largely independent Parts is separated, advantageously for a tower crane in a part of all movements that are essentially excited by a slewing gear drive (slewing dynamics), a part of all movements that are essentially excited by a trolley drive (radial dynamics) and the Dynamics in the direction of the hoist rope, which is stimulated by a winch drive.

The independent consideration of these parts, neglecting the couplings, allows the system dynamics to be calculated in real time and, in particular, simplifies the compact representation of the swivel dynamics as a distributed parametric system (described by a linear partial differential equation), which describes the structural dynamics of the boom exactly and can be easily expanded using known methods the required number of eigenmodes can be reduced.

The drive dynamics are advantageously modeled as a first-order delay element or as a static amplification factor, it being possible for a torque, a rotational speed, a force or a speed to be specified for the drives as the manipulated variable. This manipulated variable is regulated by the subordinate control in the frequency converter of the respective drive.

The pendulum dynamics can be modeled as an idealized single/double string pendulum with one/two point load masses and one/two simple ropes, which are assumed to be either massless or massed with modal order reduction to the most important rope eigenmodes.

The structural dynamics can be derived by approximating the steel structure in the form of continuous beams as a distributed parametric model, which can be discretized and reduced in system order by known methods, thereby adopting a compact form, can be computed quickly, and simplifies observer and control design.

When the crane is operated manually, the above-mentioned anti-sway device can monitor the input commands of the crane operator by actuating corresponding operating elements such as joysticks and the like and override them if necessary, in particular in the sense that accelerations specified by the crane operator are reduced, for example, or counter-movements are also automatically initiated if a crane movement specified by the crane driver has caused or would cause the load hook to swing. Advantageously, the controller module tries to stay as close as possible to the movements and movement profiles desired by the crane driver in order to give the crane driver a feeling of control, and only overrides the manually entered control signals to the extent necessary to keep the desired crane movement as oscillating as possible. and to carry it out without vibration.

Alternatively or additionally, the sway damping device can also be used for automated operation of the crane, in which the control device of the crane automatically moves the load handling device of the crane between at least two target points along a travel path in the sense of an autopilot. In such automatic operation, in which a travel path determination module of the control device determines a desired travel path, for example in the sense of a path control, and an automatic travel control module of the control device controls the drive controller or drive devices in such a way that the load hook is moved along the specific travel path, the anti-sway device in intervene in the activation of the drive controller by the above-mentioned travel control module in order to move the crane hook without swaying or to dampen swaying movements.

Fig. 1:

eine schematische Darstellung eines Turmdrehkrans, bei dem die Lasthakenposition und ein Seilwinkel gegenüber der Vertikalen durch eine bildgebende Sensorik erfasst wird, und bei dem eine Pendeldämpfungseinrichtung die Ansteuerung der Antriebseinrichtungen beeinflusst, um Pendelbewegungen des Lasthakens und dessen Hubseils zu verhindern,

Fig. 2:

eine schematische Darstellung einer Zwei-Freiheitsgrade-Regelstruktur der Pendeldämpfungseinrichtung und die von dieser vorgenommene Beeinflussung der Stellgrößen der Antriebsregler,

Fig. 3:

eine schematische Darstellung von Verformungen und Schwingungsformen eines Turmdrehkrans unter Last und deren Dämpfung bzw. Vermeidung durch eine Schrägzugregelung, wobei die Teilansicht a.) eine Nickverformung des Turmdehkrans unter Last und einen damit verknüpften Schrägzug des Hubseils zeigt, die Teilansichten b.) und c.) eine Querverformung des Turmdrehkrans in perspektivischer Darstellung sowie in Draufsicht von oben zeigen, und die Teilansichten d.) und e.) einen mit solchen Querverformungen verknüpften Schrägzug des Hubseils zeigen,

Fig. 4:

eine schematische Darstellung eines elastischen Auslegers in einem mit der Drehrate rotierenden Referenzsystem,

Fig. 5:

eine schematische Darstellung eines Auslegers als kontinuierlicher Balken mit Einspannung in den Turm unter Berücksichtigung von Turmbiegung und Turmtorsion,

Fig. 6:

eine schematische Darstellung eines elastischen Turms und eines Feder-Masse-Ersatzmodells der Turmbiegung quer zum Ausleger,

Fig. 7:

eine schematische Darstellung der Pendeldynamik in Schwenkrichtung des Krans mit konzentrierter Lastmasse und masselosem Seil,

Fig. 8:

eine schematische Darstellung der drei wichtigsten Eigenmoden eines Turmdrehkrans,

Fig. 9:

eine schematische Darstellung der Pendeldynamik in Radialrichtung des Krans und dessen Modellierung mittels mehrerer verkoppelter Starrkörper,

Fig. 10:

eine schaematische Darstellung eines pendelnden Hubseils mit Lasthaken, an dem eine Inertialmesseinrichtung befestigt ist, die ihre Messignale drahtlos an einen Empfänger an der Laufkatze übermittelt, von der das Hubseil abläuft,

Fig. 11:

eine schematische Darstellung verschiedener Lasthaken zur Verdeutlichung der möglichen Verkippung des Lasthakens gegenüber dem Hubseil,

Fig. 12:

ein schematisches zweidimensionales Modell der Pendeldynanamik der Lasthakenaufhängung aus den beiden vorhergehenden Figuren,

Fig. 13:

eine Darstellung der Verkippung bzw. des Kippwinkels des Lasthakens, der die Rotation zwischen Inertial- und Lasthakenkoordinaten beschreibt,

Fig. 14:

ein Blockdiagramm eines Komplementär-Filters mit Hochpass- und Tiefpass-Filter zum Bestimmen der Verkippung des Lasthakens aus den Beschleunigungs- und Drehratensignalen der Inertialmesseinrichtung,

Fig. 15:

eine vergleichsweise Darstellung der mittels erweitertem Kaman-Filter und mittels statischer Abschätzung bestimmten Pendelwinkel-Verläufe im Vergleich zu dem an einem Kardangelenk gemessenen Pendelwinkelverlauf, und

Fig. 16:

eine schematische Darstellung einer Steuerungs- bzw. RegelungsStruktur mit zwei Freiheitsgraden zur automatischen Beeinflussung der Antriebe, um Pendelschwingungen zu vermeiden.

The invention is explained in more detail below using a preferred exemplary embodiment and associated drawings. In the drawings show:

Figure 1:

a schematic representation of a tower crane, in which the load hook position and a rope angle relative to the vertical is detected by an imaging sensor system, and in which a pendulum damping device influences the control of the drive devices in order to prevent pendulum movements of the load hook and its hoist rope,

Figure 2:

a schematic representation of a two-degree-of-freedom control structure of the anti-sway device and the way it influences the manipulated variables of the drive controllers,

Figure 3:

a schematic representation of deformations and modes of vibration of a tower crane under load and their damping or avoidance by a diagonal pull control, wherein the partial view a.) shows a pitch deformation of the tower crane under load and an associated diagonal pull of the hoist rope, the partial views b.) and c. ) show a transverse deformation of the tower crane in a perspective view and in a plan view from above, and the partial views d.) and e.) show a diagonal pull of the hoist cable associated with such transverse deformations,

Figure 4:

a schematic representation of an elastic cantilever in a reference system rotating at the rate of rotation,

Figure 5:

a schematic representation of a cantilever as a continuous beam clamped in the tower, taking tower bending and tower torsion into account,

Figure 6:

a schematic representation of an elastic tower and a spring-mass equivalent model of the tower bending transverse to the boom,

Figure 7:

a schematic representation of the pendulum dynamics in the slewing direction of the crane with concentrated load mass and massless rope,

Figure 8:

a schematic representation of the three most important eigenmodes of a tower crane,

Figure 9:

a schematic representation of the pendulum dynamics in the radial direction of the crane and its modeling using several coupled rigid bodies,

Figure 10:

a schematic representation of a swinging hoist rope with a load hook, to which an inertial measuring device is attached, which transmits its measurement signals wirelessly to a receiver on the trolley from which the hoist rope runs off,

Figure 11:

a schematic representation of different load hooks to illustrate the possible tilting of the load hook in relation to the hoist rope,

Figure 12:

a schematic two-dimensional model of the pendulum dynamics of the load hook suspension from the two previous figures,

Figure 13:

a representation of the tilting or tilting angle of the load hook, which describes the rotation between inertial and load hook coordinates,

Figure 14:

a block diagram of a complementary filter with high-pass and low-pass filters for determining the tilting of the load hook from the acceleration and yaw rate signals of the inertial measuring device,

Figure 15:

a comparative representation of the pendulum angle curves determined by means of an extended Kaman filter and by means of static estimation in comparison to the pendulum angle curve measured on a cardan joint, and

Figure 16:

a schematic representation of a control or regulation structure with two degrees of freedom for automatically influencing the drives in order to avoid pendulum oscillations.

As 1 shows, the crane can be designed as a tower crane. the inside 1 The tower crane shown can have, for example, in a manner known per se, a tower 201 which carries a boom 202 which is balanced by a counter-jib 203 on which a counterweight 204 is provided. Said jib 202 can be rotated together with the counter jib 203 about an upright axis of rotation 205, which can be coaxial to the axis of the tower, by means of a slewing gear. A trolley 206 can be moved on the boom 202 by a trolley drive, with a hoist cable 207 running off the trolley 206, to which a load hook 208 is attached.

As 1 also shows, the crane 2 can have an electronic control device 3, which can include, for example, a control computer arranged on the crane itself. Said control device 3 can in this case control various actuators, hydraulic circuits, electric motors, drive devices and other working units on the respective construction machine. This can, for example, in the crane shown, the hoist, the slewing gear, the trolley drive, which -if necessary. existing - cantilever luffing drive or the like.

Said electronic control device 3 can communicate with a terminal device 4, which can be arranged on the control station or in the driver's cab and can, for example, be in the form of a tablet with a touchscreen and/or joysticks, rotary knobs, slide switches and similar control elements, so that on the one hand different Information from the control computer 3 can be displayed on the terminal 4 and, conversely, control commands can be entered into the control device 3 via the terminal 4 .

Said control device 3 of crane 1 can in particular be designed to control said drive devices of the hoist, trolley and slewing gear even when a sway damping device 340 detects movement parameters relevant to swaying.

For this purpose, the crane 1 can have a pendulum sensor system or detection device 60 that detects a diagonal pull of the hoist rope 207 and/or deflections of the load hook 208 relative to a vertical line 61 that passes through the suspension point of the load hook 208, ie the trolley 206. In particular, the cable pull angle φ can be detected against the line of action of gravity, ie the vertical 62, cf. 1 .

The determination means 62 of the pendulum sensor system 60 provided for this purpose can, for example, work optically in order to determine the said deflection. In particular, a camera 63 or another imaging sensor system can be attached to the trolley 206, which looks vertically downwards from the trolley 206, so that when the load hook 208 is undeflected, its image reproduction is in the center of the image provided by the camera 63. However, if the load hook 208 is deflected relative to the vertical 61, for example as a result of the trolley 206 starting up abruptly or the slewing gear braking abruptly, the image reproduction of the load hook 208 migrates from the center of the camera image, which can be determined by an image evaluation device 64.

As an alternative or in addition to such optical detection, the diagonal pull of the hoist rope or the deflection of the load hook relative to the vertical can also be carried out using an inertial measuring device IMU, which is attached to the load hook 208 and can transmit its measurement signals, preferably wirelessly, to a receiver on the trolley 206. see. 10 . The inertial measuring device IMU and the evaluation of its acceleration and yaw rate signals will be explained in more detail later.

Depending on the detected deflection relative to the vertical 61, in particular taking into account the direction and size of the deflection, the control device 3 can control the slewing gear drive and the trolley drive with the aid of the sway damping device 340 in order to bring the trolley 206 back more or less exactly over the load hook 208 and compensate for or reduce pendulum movements or prevent them from occurring in the first place.

For this purpose, sway damping device 340 comprises a structural dynamics sensor system 344 for determining dynamic deformations of structural components, controller module 341 of sway damping device 340, which influences the activation of the drive device in a sway-damping manner, being designed to determine the dynamic deformations of the structural components when influencing the activation of the drive devices of the crane must be taken into account.

An estimation device 343 can also be provided, which calculates the deformations and movements of the machine structure under dynamic loads, which change as a function of control commands entered at the control station and/or as a function of specific control actions of the drive devices and/or as a function of specific speed and/or Acceleration profiles of the drive devices result, taking into account the circumstances characterizing the crane structure. In particular, a calculation unit 348 can calculate the structural deformations and resulting structural part movements using a stored calculation model as a function of the control commands entered at the control station.

The pendulum damping device 340 advantageously detects such elastic deformations and movements of structural components under dynamic loads by means of the structural dynamics sensor system 344 . Such a sensor system 344 can include, for example, deformation sensors such as strain gauges on the steel construction of the crane, for example the lattice framework of the tower 201 or the jib 202 . Alternatively or additionally, acceleration and/or speed sensors and/or yaw rate sensors can be provided in order to detect specific movements of structural components such as, for example, pitching movements of the jib tip or rotary dynamic effects on jib 202 . Alternatively or additionally, such structural dynamics sensors can also be provided on the tower 201, in particular on its upper section, on which the boom is mounted, in order to detect the dynamics of the tower 201. Alternatively or additionally, movement and/or acceleration sensors can also be attached to the drive trains be assigned in order to be able to record the dynamics of the drive trains. For example, encoders can be assigned to the deflection pulleys of the trolley 206 for the hoist rope and/or deflection pulleys for a guy rope of a luffing jib, in order to be able to detect the actual rope speed at the relevant point.

As 2 clarified, the signals y(t) from the structural dynamics sensors 344 and the pendulum sensor system 60 are fed back to the controller module 341, so that a closed control circuit is implemented. Said controller module 341 influences the control signals u(t) for controlling the crane drives, in particular the slewing gear, the hoisting gear and the trolley drive, depending on the structural dynamics and pendulum sensor signals fed back.

As 2 shows, the controller structure also has a filter device or an observer 345, which observes the fed-back sensor signals or the crane reactions that occur with certain manipulated variables of the drive controller and taking into account predetermined laws of a dynamic model of the crane, which can fundamentally have different properties and Analysis and simulation of the steel construction can be obtained, based on the observed crane reactions, the manipulated variables of the controller are influenced.

Such a filter or observer device 345b can be embodied in particular in the form of a so-called Kalman filter 346, to which the manipulated variables u(t) of the drive controller 347 of the crane and the returned sensor signals y(t), i.e. the detected crane movements, in particular the cable pull angle, are input variables ϕ relative to the vertical 62 and/or its change over time or the angular velocity of said diagonal pull, as well as the structural dynamic torsion of boom 202 and tower 201 and from these input variables using Kalman equations that determine the dynamic system of the crane structure, in particular model its steel components and drive trains, which influences the manipulated variables of the drive controllers 347 accordingly in order to achieve the desired sway-damping effect.

With the help of such a closed-loop control, deformations and vibration patterns of the tower crane under load can be dampened or avoided from the start, as described in 3 are shown as examples, where the partial view a.) first shows schematically a pitching deformation of the tower crane under load as a result of bending of the tower 201 with the associated lowering of the boom 202 and an associated diagonal pull of the hoist cable.

Also show the partial views b.) and c.) of 3 example, in a schematic manner, a transverse deformation of the tower crane in a perspective view and in a plan view from above with the deformations of the tower 201 and the jib 202 that occur as a result.

Finally shows the 3 in their partial views d.) and e.) associated with such transverse deformations of the hoist rope.

As 2 also shows, the controller structure is designed in the form of a two-degree-of-freedom control and, in addition to the mentioned "closed-loop" control with feedback of the pendulum sensor technology and structural dynamics sensor signals, includes a pre-control or feed-forward control stage 350, which is controlled by a the best possible leadership behavior tries to ideally not allow any rule errors to occur at all.

Said pilot control 350 is advantageously designed based on flatness and is determined according to the so-called differential flatness method, as already mentioned at the outset.

Since the deflections of the structural movements and also the oscillating movements are very small compared to the driven crane movements, which represent the target travel path, the structural dynamics signals and oscillating movements signals are neglected for the determination of the pre-control signals u _d (t) and x _d (t), that is, the signals y(t) of the pendulum and structural dynamics sensors 60 and 344 are not fed back to the pilot control module 350 .

As 2 shows, the pre-control module 350 is fed setpoint values for the load handling device 208, wherein these setpoint values can be position information and/or speed information and/or path parameters for the named load handling device 208 and define the desired movement.

In particular, the target values for the desired load position and its time derivatives can advantageously be fed to a trajectory planning module 351 and/or a target value filter 352, by means of which a target curve for the load position and its first four time derivatives can be determined, from which in the Pre-control module 350 can be calculated using algebraic equations to calculate the exact course of the required control signals u _d (t) for controlling the drives and the exact course u _d (t) of the corresponding system states.

To ensure that no structural movements are stimulated by the precontrol, a notch filter device 353 can advantageously be connected upstream of the precontrol module 350 in order to filter the input variables supplied to the precontrol module 350 accordingly, with such a notch filter device 353 in particular between the named trajectory planning module 351 or the setpoint filter module 352 on the one hand and the pilot control module 350 on the other hand can be provided. Said notch filter device 353 can in particular be designed to eliminate the excited natural frequencies of the structural dynamics from the setpoint value signals supplied to the pilot control.

In order to reduce vibration dynamics or prevent them from occurring in the first place, the pendulum damping device 340 can be designed to correct the slewing gear and the trolley and possibly also the hoist so that the cable is always perpendicular to the load, if possible when the crane tilts more and more forward due to the increasing load moment.

For example, when lifting a load from the ground, the pitching movement of the crane as a result of its deformation under the load can be taken into account and the trolley can be tracked taking into account the recorded load position or positioned with anticipatory estimation of the pitching deformation in such a way that the hoist rope is in the vertical position during the resulting crane deformation Lot is above the load. The greatest static deflection occurs at the point where the load leaves the ground. Correspondingly, alternatively or additionally, the slewing gear can also be tracked, taking into account the detected load position, and/or positioned with anticipatory estimation of a transverse deformation in such a way that the hoist cable is perpendicular to the load during the resulting crane deformation.

The model on which the anti-sway control is based can fundamentally be of different types.

For the control-oriented mechanical modeling of elastic slewing cranes, the decoupled consideration of the dynamics in the slewing direction and within the tower-jib plane is useful. The slewing dynamics are stimulated and controlled by the slewing gear drive, while the dynamics in the tower-boom plane are stimulated and controlled by the trolley and hoist drives. The load swings in two directions - on the one hand transversely to the jib (pivoting direction), on the other hand in the longitudinal direction of the jib (radial). Due to the low elasticity of the hoist rope, the vertical movement of the load largely corresponds to the vertical movement of the boom, which in tower cranes is small compared to the deflection of the load due to the pendulum movement.

In order to stabilize the swinging load movement, the parts of the system dynamics that are excited by the slewing gear and the trolley must be taken into account in particular. These are referred to as swivel and radial dynamics. As long as the pendulum angles are not zero, both swivel and radial dynamics can also be influenced by the hoist. For one However, this is negligible in the control design, especially for the swing dynamics.

The slewing dynamics include, in particular, steel structure movements such as tower torsion, transverse bending of the boom around the vertical axis and bending of the tower transverse to the longitudinal direction of the boom, as well as pendulum dynamics transverse to the boom and the slewing gear drive dynamics. The radial dynamics include the tower bending in the direction of the boom, the pendulum dynamics in the direction of the boom and, depending on the perspective, also the bending of the boom in the vertical direction. In addition, the radial dynamics are also attributed to the drive dynamics of the trolley and, if applicable, the hoist.

A linear design method based on the linearization of the non-linear mechanical model equations around a rest position is advantageously sought for the regulation. With such a linearization, all couplings between pivoting and radial dynamics are eliminated. This also means that no couplings are taken into account when designing a linear control system, even if the model was first derived in a coupled manner. Both directions of can be regarded as decoupled from the outset, as this significantly simplifies the mechanical modeling. In addition, a clear model in compact form is achieved for the swing dynamics, which can be evaluated quickly, which saves computing power on the one hand and accelerates the development process of the control design on the other.

In order to derive the swivel dynamics as a compact, clear and accurate dynamic system model, the cantilever can be viewed as an Euler-Bernoulli beam and thus initially as a system with distributed mass (distributed parametric system). Furthermore, the repercussions of the lifting dynamics on the pivoting dynamics can also be neglected, which is a justified assumption for small pendulum angles due to the vanishing horizontal force component. If large pendulum angles occur, the effect of the winch on the slewing dynamics can also be taken into account as a disturbance variable.

The cantilever is modeled as a beam in a moving reference system, which rotates with the yaw rate γ̇ due to the slewing gear drive, as in 4 shown.

innerhalb des Referenzsystems die Scheinbeschleunigung a' zu $$a\prime =\underset{\mathrm{Coriolis}}{\underbrace{2\omega \times v}}\prime \underset{\mathrm{Euler}}{\underbrace{-\dot{\omega }\times r}}\prime \underset{\mathrm{Zentrifugal}}{\underbrace{-\omega \times \left(\omega \times r\prime \right)}},$$

wobei x das Kreuzprodukt darstellt, $$\omega ={\left[\begin{array}{ccc}0& 0& \dot{\gamma }\end{array}\right]}^T$$

den Rotationsvektor und v' den Geschwindigkeitsvektor des Punktes relativ zum rotierenden Referenzsystem.Thus three apparent accelerations act within the reference system, which are known as Coriolis, centrifugal and Euler acceleration. Since the reference system rotates around a fixed point, there is for each point $$\mathrm{right}\prime =\lfloor \begin{array}{ccc}{\mathrm{right}}_{x\prime }& {\mathrm{right}}_{y\prime }& {\mathrm{right}}_{\mathrm{e.g}\prime }\end{array}\rfloor$$

within the reference system the apparent acceleration a' increases $$a\prime =\underset{\mathrm{Coriolis}}{\underbrace{2\omega \times v}}\prime \underset{\mathrm{Euler}}{\underbrace{-\dot{\omega }\times \mathrm{right}}}\prime \underset{\mathrm{Centrifugal}}{\underbrace{-\omega \times \left(\omega \times \mathrm{right}\prime \right)}},$$

where x represents the cross product, $$\omega ={\left[\begin{array}{ccc}0& 0& \dot{g}\end{array}\right]}^T$$

the rotation vector and v' the velocity vector of the point relative to the rotating reference frame.

, weshalb die Coriolisbeschleunigung typischerweise kleine Werte annimmt im Vergleich zu den angetriebenen Beschleunigungen des Turmdrehkrans. Während der Stabilisierung der Lastpendelbewegung an einer festen Position ist die Drehrate sehr klein, während großer Führungsbewegungen kann die Coriolisbeschleunigung durch eine Vorsteuerung vorgeplant und explizit berücksichtigt werden. In beiden Fällen führt daher die Vernachlässigung der Coriolisbeschleunigung nur zu geringen Approximationsfehlern, weshalb sie im Folgenden vernachlässigt wird.Of the three apparent accelerations, only the Coriolis acceleration represents a bidirectional coupling between swivel and radial dynamics. This is proportional to the rotation speed of the reference system and to the relative speed. Typical maximum slewing rates of a tower crane are in the range of approx. $g_{\mathit{MAX}}\approx 0.1\frac{\mathit{wheel}}{\mathit{s}}$

, which is why the Coriolis acceleration typically assumes small values compared to the driven accelerations of the tower crane. During the stabilization of the load pendulum movement at a fixed position, the yaw rate is very small. During large guidance movements, the Coriolis acceleration can be pre-planned and explicitly taken into account by a pre-control. In both cases, neglecting the Coriolis acceleration only leads to small approximation errors, which is why it is neglected in the following.

Depending on the yaw rate, the centrifugal acceleration only affects the radial dynamics and can be taken into account as a disturbance variable for this. Due to the slow rotation rates, it hardly affects the panning dynamics and can therefore be neglected. What is important, however, is the linear Euler acceleration, which acts in the tangential direction and therefore plays a central role when considering the swing dynamics.

Due to the small cross-sectional area of the cantilever and small shear deformations, the cantilever can be viewed as an Euler-Bernoulli beam. The rotational kinetic energy of the beam rotation around the vertical axis is thus neglected. It is assumed that the mechanical parameters such as mass distributions and area moments of inertia of the Euler-Bernoulli approximation of the cantilever elements are known and can be used for the calculation.

für die Ausleger-Auslenkung w(x,t) an der Stelle x zur Zeit t angeben. Dabei ist µ(x) der Massebelag, I(x) das Flächenträgheitsmoment an der Stelle x, E der Elastizitätsmodul und q̃(x,t) die einwirkende verteilte Kraft auf den Ausleger. Der Nullpunkt der Ortskoordinate x liegt für diese Herleitung am Ende des Gegenauslegers. Die Schreibweise $\left(\cdot \right)\prime =\frac{\partial \left(\cdot \right)}{\partial x}$

beschreibt dabei die örtliche Differentiation. Dämpfungsparameter werden an späterer Stelle eingeführt.Bracing between the A-frame and the boom hardly affects the swing dynamics and is therefore not modeled. Deformations of the boom in the longitudinal direction are also so small that they can be neglected. This allows the undamped dynamics of the cantilever in the rotating reference system to be calculated using the well-known partial differential equation $$\mu \left(x\right)\ddot{w}\left(x,t\right)+\left(\mathit{EGG}\left(x\right)w"\left(x,t\right)\right)=\tilde{q}\left(x,t\right)$$

for the cantilever deflection w ( x,t ) at point x at time t . Here µ ( x ) is the mass covering, I ( x ) the area moment of inertia at the point x, E the modulus of elasticity and q̃ ( x,t ) the distributed force acting on the cantilever. For this derivation, the zero point of the spatial coordinate x is at the end of the counter-jib. The spelling $\left(\cdot \right)\prime =\frac{\partial \left(\cdot \right)}{\partial x}$

describes the local differentiation. Damping parameters will be introduced later.

führt. Dabei ist l cj die Länge des Gegenauslegers und q(x,t) die tatsächliche verteilte Kraft auf den Ausleger ohne die Eulerkraft. Beide Balkenenden sind frei und nicht eingespannt. Daher gelten die Randbedingungen $$\begin{array}{cc}w"\left(0,t\right)=0,& w"\left(L,t\right)=0\end{array}$$

$$\begin{array}{cc}w‴\left(0,t\right)=0& w‴\left(L,t\right)=0\end{array}$$

mit der Gesamtlänge L von Ausleger und Gegenausleger.In order to get a description of the cantilever dynamics in the inertial frame, the Euler force is separated from the distributed force, resulting in the partial differential equation $$\mu \left(x\right)\left(x-l_{\mathit{cj}}\right)\ddot{g}+\mu \left(x\right)\ddot{w}\left(x,t\right)+E\left(I\left(x\right)w"\left(x,t\right)\right)"=q\left(x,t\right)$$

leads. where l cj is the length of the counter jib and q(x,t) is the actual distributed force on the jib without the Euler force. Both beam ends are free and not clamped. Therefore the boundary conditions apply $$\begin{array}{cc}w"\left(0,t\right)=0,& w"\left(L,t\right)=0\end{array}$$

$$\begin{array}{cc}w‴\left(0,t\right)=0& w‴\left(L,t\right)=0\end{array}$$

with the total length L of the jib and counter-jib.

A sketch of the boom is in figure 5 shown. The spring stiffnesses c _t and c _b represent the torsional stiffness and flexural stiffness of the tower and are explained below.

Tower torsion and tower bending perpendicular to the boom direction are advantageously taken into account for modeling the pivoting dynamics. Due to its geometry, the tower can initially be assumed to be a homogeneous Euler-Bernoulli beam. For the sake of simpler modelling, the tower is represented here by a rigid body substitute model. Only one eigenmode for tower bending and one for tower torsion is considered. Since essentially only the movement at the top of the tower is relevant for the pivoting dynamics, the tower dynamics can be used as a substitute system for bending or torsion by means of a spring-mass system with a matching natural frequency. If the tower is more elastic, the spring-mass systems can be more easily supplemented with additional eigenmodes by adding a corresponding number of masses and springs, cf. 6 .

und der ersten Eigenfrequenz $${\omega }_1=\sqrt{\frac{12.362{\mathit{EI}}_T}{{\mu }_T{l_T}^4}}$$

eines homogenen Euler-Bernoulli Balkens analytisch zu $$\begin{array}{cc}{c}_b=\frac{F}{y_0}=\frac{3{\mathit{EI}}_T}{l_T^3},& m_T=\frac{c_b}{{\omega }_1^2}\end{array}=\frac{3{\mu }_T{l}_T}{12.362}.$$

berechnen.The parameters spring stiffness c _b and mass m _T are chosen in such a way that the deflection at the tip and the natural frequency correspond to that of the Euler-Bernoulli beam, which represents the tower dynamics. Are for the tower the constant area moment of inertia I _T , the tower height l _T and the If mass per unit area µ _T is known, the parameters can be calculated from the static deflection at the end of the beam $$y_{}$$$${}_0=\frac{{{\mathit{<figure-callout\; id="3"\; label="bottle\; T"\; filenames="imgf0001.png,imgf0014.png"\; state="\{\{state\}\}">bottle</figure-callout>}}_T}^3}{3{\mathit{EGG}}_T}$$

and the first natural frequency $${\omega }_{}$$$${}_1=\sqrt{\frac{\mathrm{12,362}{\mathit{EGG}}_T}{{\mu }_T{l_T}^4}}$$

of a homogeneous Euler-Bernoulli beam analytically $$\begin{array}{cc}{c}_b=\frac{\mathrm{<figure-callout\; id="0"\; label="f\; y"\; filenames="imgf0013.png"\; state="\{\{state\}\}">f</figure-callout>}}{y_{}}=\frac{3{\mathit{EGG}}_{\mathrm{<figure-callout\; id="3"\; label="T\; l\; T"\; filenames="imgf0001.png,imgf0014.png"\; state="\{\{state\}\}">T</figure-callout>}}}{l_T^{}},& m_T=\frac{{\mathrm{<figure-callout\; id="1"\; label="c\; b\; \omega "\; filenames="imgf0010.png"\; state="\{\{state\}\}">c</figure-callout>}}_b}{{\omega }_{}^{}}\end{array}=\frac{3{\mu }_T{l}_T}{\mathrm{12,362}}.$$

calculate.

For the tower torsion, a rigid body substitute model with the inertia J _T and the torsional spring stiffness c _t can be derived analogously as in Fig. 5 shown.

bestimmen, um eine übereinstimmende erste Eigenfrequenz zu erzielen.If the polar area moment of inertia I _p , the torsional moment of inertia J _T (which corresponds to the polar area moment of inertia for circular ring cross-sections), the mass density p and the shear modulus G are known for the tower, the parameters of the substitute model can be used $$\begin{array}{cc}{c}_t=\frac{{\mathit{GJ}}_T,T}{l_T},& J_T=0.405{\mathit{\rho I}}_p{l}_T\end{array}$$

determine to achieve a matching first natural frequency.

die Masse m_T und bezüglich seines Schwerpunkts die Trägheit J_T besitzt. D.h. der Massebelag des Auslegers µ(x) wird an der Stelle der Turmeinspannung über eine Länge von b um den konstanten Wert $\frac{{\mathit{m}}_T}{\mathit{b}}$

m_T erhöht.In order to consider both the equivalent mass m _T and the equivalent inertia J _T in the form of an additive mass distribution of the cantilever, the approximation of the inertia for slender objects can be used, from which it follows that a slender beam segment of length $$b=\sqrt{\frac{12J_T}{m_T}}$$

has the mass m _T and the inertia J _T with respect to its center of gravity. This means that the ground covering of the jib μ (x) is increased by the constant value over a length of b at the point where the tower is clamped $\frac{{\mathit{m}}_T}{\mathit{b}}$

m _T increased.

Since the dimensions and moments of inertia of a tower crane payload are usually unknown, the payload can still be modeled as a lumped mass point. The rope mass can be neglected. Unlike the cantilever, the payload is slightly more affected by Euler, Coriolis, and centrifugal forces. The centrifugal acceleration only acts in the direction of the jib, so it is not relevant at this point. The Coriolis acceleration results from the distance x _L of the load from the tower $$a_{\mathit{Coriolis},y}=2\dot{g}{\dot{x}}_L.$$

Due to the low boom rotation rates, the Coriolis acceleration on the load can be neglected, especially when the load is to be positioned. However, in order to be able to implement a feedforward control if necessary, it is carried along for a few more steps.

To derive the pendulum dynamics, this is projected onto a tangential plane that is orthogonal to the boom and intersects the position of the trolley.

The Euler acceleration results in: $$a_{\mathit{Euler},L}=\dot{g}{x}_L.$$

aus der die Approximation $$a_{\mathit{Euler},L}=a_{\mathit{Euler}}$$

folgt, dass die Euler-Beschleunigung aufgrund der Drehung des Referenzsystems in etwa gleiche Weise auf Last und Laufkatze wirkt.Due to the generally small pendulum angles, the approximation applies $$x_L/x_{\mathit{tr}}\approx 1$$

from which the approximation $$a_{\mathit{Euler},L}=a_{\mathit{Euler}}$$

it follows that the Euler acceleration due to the rotation of the reference system acts on the load and trolley in approximately the same way.

The acceleration on the load are in 7 shown.

die y-Position der Laufkatze in der Tangentialebene. Die Position der Laufkatze auf dem Ausleger x_tr wird aufgrund der Entkopplung von Radial- und Schwenkdynamik hier als konstanter Parameter approximiert.there is $$s\left(t\right)=x_{\mathit{tr}}g\left(t\right)+w\left(x_{\mathit{tr}},t\right).$$

the y position of the trolley in the tangent plane. The position of the trolley on the jib x _tr is approximated here as a constant parameter due to the decoupling of radial and slewing dynamics.

mit der Lastmasse m_L, der Erdbeschleunigung g und der Seillänge l(t) aufgestellt sowie die kinetische Energie $$T=\frac{1}{2}{m}_L{\dot{r}}^T\dot{r},$$

wobei $$r\left(t\right)=\left[\begin{array}{c}s\left(t\right)+l\left(t\right)\sin \left(\varphi \left(t\right)\right)\\ -l\left(t\right)\cos \left(\varphi \left(t\right)\right)\end{array}\right].$$

die y-Position der Last in der Tangentialebene. Mit der Lagrange Funktion $$L=T-U$$

und den Lagrange'schen Gleichungen der 2. Art $$\frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial \dot{\varphi }}-\frac{\partial L}{\partial \varphi }=Q$$

mit der nicht-konservativen Corioliskraft $$Q={\left[\begin{array}{c}{m}_{\mathrm{L}}{a}_{\mathit{Coriolis},y}\\ 0\end{array}\right]}^T\cdot \frac{\partial r}{\partial \varphi }=m_{\mathrm{L}}{\mathit{la}}_{\mathit{Coriolis},y}\cos \left(\varphi \right)$$

folgt die Pendeldynamik in Schwenkrichtung als $$2\dot{\varphi }\dot{l}+\left(\ddot{s}-a_{\mathit{Coriolis},y}\right)\cos \varphi +g\sin \varphi +\ddot{\varphi }l=0.$$

The pendulum dynamics can be easily derived using the Lagrange formalism. First of all, the potential energy $$u=-m_{L}l\left(t\right)G\cos \left(\varphi \left(t\right)\right)$$

with the load mass m _L , the acceleration due to gravity g and the rope length l(t) as well as the kinetic energy $$T=\frac{1}{2}{m}_L{\dot{\mathrm{right}}}^T\dot{\mathrm{right}},$$

whereby $$\mathrm{right}\left(t\right)=\left[\begin{array}{c}s\left(t\right)+l\left(t\right)\sin \left(\varphi \left(t\right)\right)\\ -l\left(t\right)\cos \left(\varphi \left(t\right)\right)\end{array}\right].$$

the y-position of the load in the tangent plane. With the Lagrange function $$L=T-u$$

and the Lagrangian equations of the 2nd kind $$\frac{\mathrm{i.e}}{\mathrm{i.e}t}\frac{\partial L}{\partial \dot{\varphi }}-\frac{\partial L}{\partial \varphi }=Q$$

with the non-conservative Coriolis force $$Q={\left[\begin{array}{c}{m}_{\mathrm{L}}{a}_{\mathit{Coriolis},y}\\ 0\end{array}\right]}^T\cdot \frac{\partial \mathrm{right}}{\partial \varphi }=m_{\mathrm{L}}{\mathit{la}}_{\mathit{Coriolis},y}\cos \left(\varphi \right)$$

follows the pendulum dynamics in the pivoting direction as $$2\dot{\varphi }\dot{l}+\left(\ddot{s}-a_{\mathit{Coriolis},y}\right)\cos \varphi +G\sin \varphi +\ddot{\varphi }l=0.$$

Linearized around φ = 0, φ = 0, neglecting the change in rope length i ≈0 and the Coriolis acceleration a _Coriolis,y ≈0, the simplified pendulum dynamics follows $$\ddot{\varphi }=\frac{-\ddot{s}-\mathit{g\varphi }}{l}=\frac{-x_{\mathit{tr}}\ddot{g}-\ddot{w}\left(x_{\mathit{tr}},t\right)-\mathit{g\varphi }}{l}.$$

approximiert. Ihr horizontaler Anteil in y -Richtung ergibt sich damit zu $$F_{R,h}=m_{L}g\cos \left(\varphi \right)\sin \left(\varphi \right),$$

bzw. linearisiert um φ= 0 zu $$F_{R,h}=m_L\mathit{g\varphi }.$$

In order to describe the repercussions of the pendulum dynamics on the structural dynamics of the jib and tower, the rope force F _R must be determined. The easiest way to do this is through its main part due to the gravitational acceleration $$f_{R,H}=m_{L}G\cos \left(\varphi \right)\sin \left(\varphi \right),$$

approximated. Their horizontal component in the y-direction thus results in: $$f_{R,H}=m_{L}G\cos \left(\varphi \right)\sin \left(\varphi \right),$$

or linearized around φ = 0 $$f_{R,H}=m_L\mathit{g\varphi }.$$

The distributed parametric model (5) of the cantilever dynamics describes an infinite number of eigenmodes of the cantilever and is not yet suitable for a control design in this form. Since only a few of the lowest-frequency eigenmodes are relevant for observers and controllers, a modal transformation with subsequent modal order reduction to these few eigenmodes is appropriate. However, an analytical modal transformation of equation (5) is rather difficult. Instead, it makes sense to first locally discretize equation (5) using finite differences or the finite element method and thus obtain an ordinary differential equation.

aufgeteilt. Die Balkenauslenkung an jeder dieser Positionen wird als $$w_i=w\left(x_i,t\right)$$

notiert. Die örtlichen Ableitungen werden mit dem zentralen Differenzenquotient $$w_i^{\prime }\approx \frac{-w_{i-1}+w_{i+1}}{2{\mathrm{\Delta }}_x}$$

$$w_i^{"}\approx \frac{w_{i-1}-2w_i+w_{i+1}}{{\mathrm{\Delta }}_x^2}$$

approximiert, wobei Δ _x = x _i+1 -x_i den Abstand der diskreten Massepunkte und $w_i^{\prime }$

die örtliche Ableitung w'(x_i ,t) beschreiben.With a discretization using the finite differences, the beam is distributed on N equidistant mass points at the cantilever positions $$x_i,i\in \left[1...N\right]$$

divided up. The beam deflection at each of these positions is given as $$w_i=w\left(x_i,t\right)$$

written down. The local derivatives are calculated using the central difference quotient $$w_i^{\prime }\approx \frac{-w_{i-1}+w_{i+1}}{2{\mathrm{\Delta }}_x}$$

$$w_i^{"}\approx \frac{w_{i-1}-2w_i+w_{i+1}}{{\mathrm{\Delta }}_x^2}$$

approximates, where Δ _x = x _{i+ 1} -x _i the distance of the discrete mass points and $w_i^{\prime }$

describe the local derivative w' ( x _i , t ).

$$\begin{array}{cc}-w_{i-2}+2w_{i-1}-2w_{i+1}+w_{i+2}=0,& i\in \left\{1,N\right\}\end{array}$$

nach w _-1,w _-2,w _N+1 und w _N+2 aufgelöst werden. Die Diskretisierung des Terms (I(x)w")" in Gleichung (5) ergibt sich zu $$\left(I\left(x\right)w"\right)"\approx \frac{{\eta }_{i-1}-2{\eta }_i+{\eta }_{i+1}}{{\mathrm{\Delta }}_x^2}$$

mit $${\eta }_i=I\left(x_i\right)w_i".$$

For the discretization of w"(x) the boundary conditions (6)-(7) $$\begin{array}{cc}{w}_{i-1}-2w_i+w_{i+1}=0,& i\in \left\{1,N\right\}\end{array}$$

$$\begin{array}{cc}-w_{i-2}+2w_{i-1}-2w_{i+1}+w_{i+2}=0,& i\in \left\{1,N\right\}\end{array}$$

can be solved for w _-1 , w _-2 , w _{N+ 1} and w _{N+ 2} . The discretization of the term ( I ( x ) w" ) " in equation (5) results in $$\left(I\left(x\right)w"\right)"\approx \frac{n_{i-1}-2n_i+n_{i+1}}{{\mathrm{\Delta }}_x^2}$$

With $$n_i=I\left(x_i\right)w_i".$$

Due to the choice of the central difference approximation, equation (35) depends on the edges of the values I _-1 , and I _{N+ 1} , which in practice can be replaced by the values I ₁ , and I _N .

bezeichnet, womit die Diskretisierung des Terms (I(x)w")" in Vektorschreibweise als $$K_0\overrightarrow{w}$$

mit der Steifigkeitsmatrix $$K_0=\left(\begin{array}{ccccc}{I}_1+I_2& -2I_1-2I_2& I_1+I_2& 0& 0\\ -2I_2& 4I_2+I_3& -2I_2-2I_3& I_3& 0\\ I_2& -2I_2-2I_3& I_2+4I_3+I_4& -2I_3-2I_4& I_4\\ & & \ddots & & \\ 0& I_{\mathrm{N}-2}& -2I_{\mathrm{N}-2}-2I_{\mathrm{N}-1}& I_{\mathrm{N}-2}+4I_{\mathrm{N}-1}& -2I_{\mathrm{N}-1}\\ 0& 0& I_{\mathrm{N}-1}+I_{\mathrm{N}}& -2I_{\mathrm{N}-1}-2I_{\mathrm{N}}& I_{\mathrm{N}-1}+I_{\mathrm{N}}\end{array}\right)$$

ausgedrückt werden kann.For the further procedure, a vector notation (bold) is recommended. The vector of the cantilever deflections is given as $$\overrightarrow{w}={\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="imgf0010.png"\; state="\{\{state\}\}">w</figure-callout>}}_1& ...& w_N\end{array}\right]}^T$$

denotes, whereby the discretization of the term (I ( x ) w")" in vector notation as $$K_0\overrightarrow{w}$$

with the stiffness matrix $$K_{}$$$${}_0=\left(\begin{array}{ccccc}{I}_1+I_2& -2I_1-2I_2& I_1+I_2& 0& 0\\ -2I_2& 4I_2+I_3& -2I_2-2I_3& I_3& 0\\ I_2& -2I_2-2I_3& I_2+4I_3+I_4& -2I_3-2I_4& I_4\\ & & \ddots & & \\ 0& I_{\mathrm{N}-2}& -2I_{\mathrm{N}-2}-2I_{\mathrm{N}-1}& I_{\mathrm{N}-2}+4I_{\mathrm{N}-1}& -2I_{\mathrm{N}-1}\\ 0& 0& I_{\mathrm{N}-1}+I_{\mathrm{N}}& -2I_{\mathrm{N}-1}-2I_{\mathrm{N}}& I_{\mathrm{N}-1}+I_{\mathrm{N}}\end{array}\right)$$

can be expressed.

definiert, mit dem Vektor $${\overrightarrow{x}}_T={\left[\begin{array}{ccc}\left(x_1-l_{\mathit{cj}}\right)& \dots & \left(x_N-l_{\mathit{cj}}\right)\end{array}\right]}^T$$

welcher für jeden Knoten den Abstand zum Turm beschreibt.Likewise, the mass matrix of the mass covering (unit kgm) as a diagonal matrix $$M_{}$$$${}_0=\mathrm{diag}\left(\left[\begin{array}{ccc}\mu \left(x_1\right)& ...& \mu \left(x_N\right)\end{array}\right]\right)$$

defined with the vector $${\overrightarrow{x}}_T={\left[\begin{array}{ccc}\left(x_1-l_{\mathit{cj}}\right)& ...& \left(x_N-l_{\mathit{cj}}\right)\end{array}\right]}^T$$

which describes the distance to the tower for each node.

mit den Einträgen q_i=q(x_i ) definiert, so dass die Diskretisierung der partiellen Balkendifferentialgleichung (5) in diskretisierter Form als $$M_0\ddot{\overrightarrow{w}}+\frac{E}{{\mathrm{\Delta }}_x^4}{K}_0=\overrightarrow{q}-M{\overrightarrow{x}}_T\ddot{\gamma }.$$

angegeben werden kann.For the distributed applied force, the vector $$\overrightarrow{q}=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="imgf0010.png"\; state="\{\{state\}\}">q</figure-callout>}}_1& ...& q_N\end{array}\right]$$

with the entries q _i =q ( x _i ), so that the discretization of the partial beam differential equation (5) in discretized form is given as $$M_0\ddot{\overrightarrow{w}}+\frac{E}{{\mathrm{\Delta }}_x^4}{\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="imgf0013.png"\; state="\{\{state\}\}">K</figure-callout>}}_0=\overrightarrow{q}-M{\overrightarrow{x}}_T\ddot{g}.$$

can be specified.

Now the dynamic interaction of steel structure movement and pendulum dynamics should be described.

hinzugefügt.For this purpose, the additional point masses on the boom, namely the counter-ballast mass m _c , , the equivalent mass for the tower m _T and the trolley mass m _tr of the distributed mass matrix, are first calculated $${\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0010.png"\; state="\{\{state\}\}">M</figure-callout>}}_1={\mathrm{<figure-callout\; id="0"\; label="M"\; filenames="imgf0013.png"\; state="\{\{state\}\}">M</figure-callout>}}_0+\mathit{diag}\left(\left[\begin{array}{cccccccc}\frac{m_{\mathit{cj}}}{{\mathrm{\Delta }}_x}& ...& \frac{m_T}{b}& ...& \frac{m_T}{b}& ...& \frac{m_{\mathit{tr}}}{{\mathrm{\Delta }}_x}& 0\end{array}\right]\right)$$

added.

mit q_T = q(l_cj ) gegeben. Für die Bestimmung des Moments durch die Turmtorsion wird zunächst die Verdrehung des Ausleger-Balkens an der Einspannungsstelle, $$\psi =w_T^{\prime }=\frac{-w_{T-1}+w_{T+1}}{2{\mathrm{\Delta }}_x}$$

benötigt, aus der sich dann das Torsionsmoment $$\tau =-c_T\frac{-w_T-1+w_T+1}{2{\mathrm{\Delta }}_x}$$

ergibt, das beispielsweise durch zwei gleich weit vom Turm entfernt angreifende (Hebelarm), gleichgroße Kräfte approximiert werden kann. Der Wert dieser beiden Kräfte ist $$F_{\tau }=\frac{\tau }{2{\mathrm{\Delta }}_x},$$

wenn Δx jeweils der Hebelarm ist. Dadurch kann das Moment durch den Vektor q der Kräfte auf den Ausleger beschrieben werden. Dazu müssen nur die beiden Einträge $$\begin{array}{cc}{q}_{T-1}{\mathrm{\Delta }}_x=-F_{\tau },& q_{T+1}{\mathrm{\Delta }}_x=F_{\tau },\end{array}$$

gesetzt werden.In addition, the forces and moments with which the tower and load act on the jib can be described. The force due to tower deflection is through through the replacement model $$q_T{\mathrm{\Delta }}_x=-c_{b}w\left(x_T\right).$$

with q _T = q ( l _cj ). To determine the moment caused by the tower torsion, the torsion of the cantilever beam at the clamping point is first $$\psi =w_T^{\prime }=\frac{-w_{T-1}+w_{T+1}}{2{\mathrm{\Delta }}_x}$$

required, from which then the torsional moment $$\tau =-c_T\frac{-w_T-1+w_T+1}{2{\mathrm{\Delta }}_x}$$

results, which can be approximated, for example, by two equally large forces acting at the same distance from the tower (lever arm). The value of these two forces is $$f_{\tau }=\frac{\mathrm{<figure-callout\; id="2"\; label="\tau "\; filenames="imgf0003.png"\; state="\{\{state\}\}">\tau </figure-callout>}}{2{\mathrm{\Delta }}_x},$$

if Δ x is the lever arm in each case. Thereby the moment can be given by the vector q of the forces on the cantilever can be described. To do this, only the two entries $$\begin{array}{cc}{q}_{T-1}{\mathrm{\Delta }}_x=-f_{\tau },& q_{T+1}{\mathrm{\Delta }}_x=f_{\tau },\end{array}$$

be set.

in q. The entry results from the horizontal cable force (28). $$q_{\mathit{tr}}{\Delta }_x=m_L\mathit{g\varphi }$$

in q .

mit $$K_1=\frac{1}{4{\Delta }_x^3}\left[\begin{array}{ccccc}\cdots & & & & \\ & c_T& 0& -c_T& \\ & 0& 4{\Delta }_x^2{c}_b& 0& \\ & -c_T& 0& c_T& \\ & & & & \cdots \end{array}\right],$$

$$F_{\mathit{tr}}=\frac{1}{{\Delta }_x}{\left[\begin{array}{ccccc}0& \dots & -m_{L}g& \dots & 0\end{array}\right]}^T$$

und $$x_{\mathit{tr}}={\left[\begin{array}{ccccc}0& \dots & 1& \dots & 0\end{array}\right]}^T\mathrm{sodass}\ddot{w}\left(x_{\mathit{tr}},t\right)={x_{\mathit{tr}}}^T\ddot{\overrightarrow{w}}.$$

Since all forces of φ or w depend, the coupling of structural and pendulum dynamics can be written in matrix notation as $$\underset{M}{\underbrace{\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="0"\; label="M"\; filenames="imgf0013.png"\; state="\{\{state\}\}">M</figure-callout>}}_0& 0\\ {x_{\mathit{tr}}}^T& l\end{array}\right]}}\underset{\ddot{\overrightarrow{x}}}{\underbrace{\left[\begin{array}{c}\ddot{\overrightarrow{w}}\\ \ddot{\varphi }\end{array}\right]}}+\underset{K}{\underbrace{\left[\begin{array}{cc}\left(\frac{E}{{\Delta }_x^4}{\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="imgf0013.png"\; state="\{\{state\}\}">K</figure-callout>}}_0+K_1\right)& f_{\mathit{tr}}\\ 0& G\end{array}\right]}}\underset{\overrightarrow{x}}{\underbrace{\left[\begin{array}{c}\overrightarrow{w}\\ \varphi \end{array}\right]}}=\underset{B}{\underbrace{\left[\begin{array}{c}-{\mathit{MX}}_T\\ -x_{\mathit{tr}}\end{array}\right]}}\ddot{g}$$

With $${\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="imgf0010.png"\; state="\{\{state\}\}">K</figure-callout>}}_1=\frac{1}{4{\Delta }_x^3}\left[\begin{array}{ccccc}\cdots & & & & \\ & {\mathrm{<figure-callout\; id="0"\; label="c\; T"\; filenames="imgf0013.png"\; state="\{\{state\}\}">c</figure-callout>}}_T& 0& -{\mathrm{<figure-callout\; id="0"\; label="c\; T"\; filenames="imgf0013.png"\; state="\{\{state\}\}">c</figure-callout>}}_T& \\ & 0& 4{\Delta }_x^2{\mathrm{<figure-callout\; id="0"\; label="c\; b"\; filenames="imgf0013.png"\; state="\{\{state\}\}">c</figure-callout>}}_b& 0& \\ & -c_T& 0& c_T& \\ & & & & \cdots \end{array}\right],$$

$$f_{\mathit{tr}}=\frac{1}{{\Delta }_x}{\left[\begin{array}{ccccc}0& ...& -m_{L}G& ...& 0\end{array}\right]}^T$$

and $$x_{\mathit{tr}}={\left[\begin{array}{ccccc}0& ...& 1& ...& 0\end{array}\right]}^T\mathrm{so\; that}\ddot{w}\left(x_{\mathit{tr}},t\right)={x_{\mathit{tr}}}^T\ddot{\overrightarrow{w}}.$$

At this point it should be noted that the three parameters position of the trolley on the jib x _tr' hoist cable length / and load mass m _L vary during operation. Therefore, (50) is a linear parameter-variant differential equation, the specific form of which can only be determined at runtime, especially online. This must be taken into account in later observer and control drafts.

The number of discretization points N should be chosen large enough to ensure an accurate description of the beam deformation and dynamics. Thus (50) becomes a large system of differential equations. However, a modal order reduction is suitable for the control in order to reduce the large number of system states to a lower number.

Modal order reduction is one of the most commonly used reduction methods. The basic idea is to first carry out a modal transformation, i.e. to specify the dynamics of the system on the basis of the eigenmodes (shapes) and the eigenfrequencies. subsequently become then only the relevant eigenmodes (usually the lowest-frequency ones) are selected and all higher-frequency modes are neglected. The number of eigenmodes taken into account is denoted by ξ in the following.

erfüllen. Diese Berechnung lässt sich über bekannte Standardverfahren leicht lösen. Die Eigenvektoren werden daraufhin mit steigender Eigenfrequenz sortiert in die Modalmatrix $$V=\left[\begin{array}{ccc}{\overrightarrow{\nu }}_1& {\overrightarrow{\nu }}_2& \dots \end{array}\right]$$

geschrieben. Die Modaltransformation lässt sich dann durchführen über die Berechnung $$\ddot{z}+\underset{K}{\underbrace{V^{-1}{M}^{-1}\mathit{KV}}}z=\underset{\widehat{B}}{\underbrace{V^{-1}{M}^{-1}B}}\ddot{\gamma }$$

wobei der neue Zustandsvektor z (t) = V ^-1 x (t) die Amplituden der Eigenmoden enthält. Da die modal transformierte Steifigkeitsmatrix K̂ eine Diagonalform aufweist, lässt sich das modal reduzierte System einfach durch Beschränkung auf die ersten ξ Spalten und Zeilen dieses Systems als $${\ddot{z}}_r+{\widehat{D}}_r{\dot{z}}_r+{\widehat{K}}_r{z}_r={\widehat{B}}_r\ddot{\gamma }.$$

erhalten, wobei der Zustandsvektor z _r nun nur noch die wenigen ξ Modalamplituden beschreibt. Durch experimentelle Identifikation lassen sich zudem die Einträge der diagonalen Dämpfungsmatrix D̂_r ermitteln.First, the eigenvectors v , with i ∈ [1, N +1] can be calculated, which together with the corresponding natural frequencies ω _i , the eigenvalue problem $$K{\overrightarrow{v}}_i={\omega }_i^{2}M{\overrightarrow{v}}_i$$

fulfill. This calculation can be easily solved using known standard methods. The eigenvectors are then sorted into the modal matrix with increasing eigenfrequency $$V=\left[\begin{array}{ccc}{\overrightarrow{v}}_1& {\overrightarrow{v}}_2& ...\end{array}\right]$$

written. The modal transformation can then be carried out via the calculation $$\ddot{\mathrm{e.g}}+\underset{K}{\underbrace{V^{-1}{M}^{-1}\mathit{KV}}}\mathrm{e.g}=\underset{\widehat{B}}{\underbrace{V^{-1}{M}^{-1}B}}\ddot{g}$$

where the new state vector e.g ( t ) = V ^-1 x ( t ) contains the amplitudes of the eigenmodes. Since the modally transformed stiffness matrix K̂ has a diagonal form, the modally reduced system can simply be written by restricting it to the first ξ columns and rows of this system as $${\ddot{\mathrm{e.g}}}_{\mathrm{right}}+{\widehat{D}}_{\mathrm{right}}{\dot{\mathrm{e.g}}}_{\mathrm{right}}+{\widehat{K}}_{\mathrm{right}}{\mathrm{e.g}}_{\mathrm{right}}={\widehat{B}}_{\mathrm{right}}\ddot{g}.$$

obtained, where the state vector e.g _r now only describes the few ξ modal amplitudes. The entries of the diagonal damping matrix D̂ _r can also be determined by experimental identification.

Three of the most important eigenmodes are in 8 shown. The top one describes the slowest natural mode, which is dominated by the pendulum movement of the load. The second eigenmode shown shows a clear tower bending, while in the third the boom bends clearly. All natural modes whose natural frequencies can be excited by the slewing gear drive should be taken into account.

mit der Zeitkonstanten Tγ aufweist. In Verbindung mit Gleichung (57) ergibt sich damit $$\dot{x}=\underset{A}{\underbrace{\left[\begin{array}{cccc}0& I& 0& 0\\ -{\widehat{K}}_r& -{\widehat{D}}_r& 0& \frac{-{\widehat{B}}_r}{T_{\gamma }}\\ 0& 0& 0& 1\\ 0& 0& 0& \frac{-1}{T_{\gamma }}\end{array}\right]}}x+\underset{B}{\underbrace{\left[\begin{array}{c}0\\ \frac{{\widehat{B}}_r}{T_{\gamma }}\\ 0\\ \frac{1}{T_{\gamma }}\end{array}\right]}}u$$

mit dem neuen Zustandsvektor x = [z_r ż_r γ γ̇] ^T und dem Stellsignal u der Sollgeschwindigkeit des Drehwerks.The dynamics of the slewing gear drive is advantageously approximated as a PT1 element that the dynamics $$\ddot{g}=\frac{\mathrm{and}-\dot{g}}{T_g}$$

with the time constant Tγ . In conjunction with Equation (57) this results in $$\dot{x}=\underset{A}{\underbrace{\left[\begin{array}{cccc}0& I& 0& 0\\ -{\widehat{K}}_{\mathrm{right}}& -{\widehat{D}}_{\mathrm{right}}& 0& \frac{-{\widehat{B}}_{\mathrm{<figure-callout\; id="0"\; label="right\; T\; g"\; filenames="imgf0013.png"\; state="\{\{state\}\}">right</figure-callout>}}}{T_g}\\ 0& 0& 0& 1\\ 0& 0& 0& \frac{-1}{T_g}\end{array}\right]}}x+\underset{B}{\underbrace{\left[\begin{array}{c}0\\ \frac{{\widehat{B}}_{\mathrm{<figure-callout\; id="0"\; label="right\; T\; g"\; filenames="imgf0013.png"\; state="\{\{state\}\}">right</figure-callout>}}}{T_g}\\ 0\\ \frac{1}{T_g}\end{array}\right]}}\mathrm{and}$$

with the new state vector x = [ z _r ż _r γ γ̇ ] ^T and the control signal u of the setpoint speed of the slewing gear.

$$\overrightarrow{y}=C\overrightarrow{x}$$

ergänzt werden, so dass das System beobachtbar ist, d.h. dass alle Zustände im Vektor x durch die Ausgänge y , sowie endlich viele Zeitableitungen der Ausgänge rekonstruierbar sind und damit zur Laufzeit geschätzt werden können.For the observer and the control of the pivoting dynamics, the system (59) can have an output vector y to $$\dot{\overrightarrow{x}}=A\overrightarrow{x}+\mathit{Bu}$$

$$\overrightarrow{y}=C\overrightarrow{x}$$

be supplemented so that the system is observable, ie that all states are in the vector x through the exits y , and finitely many time derivatives of the outputs can be reconstructed and thus estimated at runtime.

The output vector y precisely describes the yaw rates, strains or accelerations, which are measured by the sensors on the crane.

entwerfen, wobei der Wert P aus der algebraischen Riccati Gleichung $$0=PA+P{A}^T+Q-P{C}^T{R}^{-1}CP$$

folgen kann, die sich mit Standardverfahren leicht lösen lässt. Q und R stellen die Kovarianzmatrizen des Prozess- und Messrauschens dar und dienen als Auslegungs-Parameter des Kalmanfilters.On the basis of the model (61), for example, an observer 345, cf. 2 , in the form of the Kalman filter $$\dot{\widehat{\overrightarrow{x}}}=A\widehat{\overrightarrow{x}}+B\overrightarrow{\mathrm{and}}+\mathit{personal\; computer}{\mathrm{}}^T{R}^{-1}\left(\overrightarrow{y}-C\widehat{\overrightarrow{x}}\right)\widehat{\overrightarrow{x}}\left(0\right)={\widehat{\overrightarrow{x}}}_0$$

design, where the value P comes from the algebraic Riccati equation $$0=PA+P{A}^T+Q-P{C}^T{R}^{-1}CP$$

can follow, which can easily be solved with standard methods. Q and R represent the covariance matrices of the process and measurement noise and serve as design parameters of the Kalman filter.

Since equations (60) and (61) describe a parameter-variant system, the solution P of equation (63) is always only valid for the corresponding parameter set { x _tr ,l,m _L }. However, the standard methods for solving algebraic Riccati equations are quite computationally intensive. In order not to have to evaluate equation (63) at runtime, the solution P for a finely resolved map can be precalculated offline in the parameters x _tr ,l,m _L . At runtime (online), the value is then selected from the characteristics map whose parameter set { x _tr ,l,m _L } is closest to the current parameters.

realisieren. Dabei enthält der Vektor x̂ _ref die Sollzustände, die in der Ruhelage typischerweise alle null sind (bis auf den Drehwinkel γ). Während dem Abfahren einer Bahn können die Werte ungleich null sein, sollten aber nicht zu weit von der Ruhelage abweichen, um die das Modell linearisiert wurde.Because through the observer 345 all system states x̂ can be estimated, the control can be done in the form of a status feedback $$\mathrm{and}=K\left({\overrightarrow{x}}_{\mathrm{ref}}-\widehat{\overrightarrow{x}}\right)$$

realize. The vector contains x̂ _ref the target states, which are typically all zero in the rest position (except for the angle of rotation γ ). While traversing a path, the values can be non-zero, but should not deviate too far from the rest position around which the model was linearized.

optimiert wird. Für den linearen Regelungsentwurf ergibt sich die optimale Rückführungsverstärkung zu $$K=R^{-1}{B}^{T}P,$$

wobei sich P analog zum Kaimanfilter über die algebraische Riccati-Gleichung $$0=\mathit{PA}+A^{T}P-{\mathit{PBR}}^{-1}{B}^{T}P+Q$$

bestimmen lässt.A linear-quadratic approach is suitable for this, for example, in which the feedback gain K is selected in such a way that the quality functional $$J={\displaystyle {\int }_{t=0}^{\infty }{x}^T\mathit{Qx}+{\mathrm{and}}^{T}R\mathbf{and}\mathit{German}}$$

is optimized. For the linear control design, the optimum feedback gain is given by $$K=R^{-1}{B}^{T}P,$$

where P is analogous to the Kalman filter via the algebraic Riccati equation $$0=\mathit{PA}+A^{T}P-{\mathit{PBR}}^{-1}{B}^{T}P+Q$$

can be determined.

Since the gain K in Equation (66) is also dependent on the parameter set { x _tr ,l,m _L }, a characteristic map is generated for this analogously to the procedure for the observer. In the context of regulation, this approach is known under the term "gain scheduling".

To apply the control to a tower crane, the observer dynamics (62) can be simulated on a control unit at runtime. For this purpose, on the one hand, the control signals u of the drives and, on the other hand, the measuring signals y of the sensors are used. The control signals are in turn calculated from the feedback gain and the estimated state vector according to (62).

Since the radial dynamics can also be represented by a linear model of the form (60)-(61), the procedure for controlling the radial dynamics can be analogous to the pivoting dynamics. Both controls then act independently on the crane and stabilize the pendulum dynamics in the radial direction and transverse to the boom, each taking into account the drive and structural dynamics.

An approach to modeling the radial dynamics is described below. This differs from the previously described approach to modeling the slewing dynamics in that the crane is now described by an equivalent system made up of several coupled rigid bodies and not by continuous beams. The tower can be divided into two rigid bodies, with another rigid body representing the boom, cf. 9 .

Here, α _y and β _y describe the angles between the rigid bodies and φ _y the radial pendulum angle of the load. The positions of the centers of gravity are described with P, where the index _CJ for the counterjib, _J for the jib, _TR for the trolley and _T for the tower (in this case the upper one). rigid body of the tower). The positions depend at least partially on the variables x _TR and l provided by the drives. At the joints between the rigid bodies there are springs with the spring stiffness c̃ _{a x} ,c̃ _{β y} and dampers whose viscous friction is described by the parameters d _αy and d _ßy .

zusammengefasst. Mit diesen lassen sich die translatorischen kinetischen Energien $$T_{\mathrm{kin}}=\frac{1}{2}\left(m_{\mathrm{T}}{\Vert {\dot{P}}_{\mathrm{T}}\Vert }_2^2+m_{\mathrm{J}}{\Vert {\dot{P}}_{\mathrm{J}}\Vert }_2^2+m_{\mathrm{CJ}}{\Vert {\dot{P}}_{\mathrm{CJ}}\Vert }_2^2+m_{\mathrm{TR}}{\Vert {\dot{P}}_{\mathrm{TR}}\Vert }_2^2+m_{\mathrm{L}}{\Vert {\dot{P}}_{\mathrm{L}}\Vert }_2^2\right)$$

sowie die potentiellen Energien aufgrund Gravitation und Federsteifigkeiten $$T_{\mathrm{pot}}=g\left(m_{\mathrm{T}}{P}_{\mathrm{T},z}+m_{\mathrm{J}}{P}_{\mathrm{J},z}+m_{\mathrm{CJ}}{P}_{\mathrm{CJ},z}+m_{\mathrm{TR}}{P}_{\mathrm{TR},z}+m_{\mathrm{L}}{P}_{\mathrm{L},z}\right)+\frac{1}{2}\left({\tilde{c}}_{{\alpha }_y}{\alpha }_y^2+{\tilde{c}}_{{\beta }_y}{b}_y^2\right)$$

ausdrücken. Da die rotatorischen Energien im Vergleich zu den translatorischen vernachlässigbar klein sind, kann die Lagrange Funktion als $$L=T_{\mathrm{kin}}-T_{\mathrm{pot}}$$

formuliert werden. Daraus ergeben sich die Euler-Lagrange Gleichungen $$\frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial {\dot{q}}_i}-\frac{\partial L}{\partial q_i}=Q_i^{\ast }$$

mit den generalisierten Kräften $Q_i^{*}$

, welche die Einflüsse der nicht-konservativen Kräfte, beispielsweise der Dämpfungskräfte, beschreiben. Ausgeschrieben ergeben sich die drei Gleichungen $$\frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial {\dot{\alpha }}_y}-\frac{\partial L}{\partial {\alpha }_y}=-d_{\mathit{\alpha y}}{\dot{\alpha }}_y,$$

$$\frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial {\dot{\beta }}_y}-\frac{\partial L}{\partial {\beta }_y}=-d_{\mathit{\beta y}}{\dot{\beta }}_y,$$

$$\frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial {\dot{\varphi }}_y}-\frac{\partial L}{\partial {\varphi }_y}=0.$$

The dynamics can be derived from the well-known Lagrange formalism. The three degrees of freedom are in the vector $$\overrightarrow{\mathrm{q}}=\left(a_y,{\beta }_y,{\varphi }_y\right)$$

summarized. With these, the translatory kinetic energies can be calculated $$T_{\mathrm{children}}=\frac{1}{2}\left(m_{\mathrm{T}}{\Vert {\dot{P}}_{\mathrm{T}}\Vert }_2^2+m_{\mathrm{J}}{\Vert {\dot{P}}_{\mathrm{J}}\Vert }_2^2+m_{\mathrm{CJ}}{\Vert {\dot{P}}_{\mathrm{CJ}}\Vert }_2^2+m_{\mathrm{TR}}{\Vert {\dot{P}}_{\mathrm{TR}}\Vert }_2^2+m_{\mathrm{L}}{\Vert {\dot{P}}_{\mathrm{L}}\Vert }_2^2\right)$$

and the potential energies due to gravity and spring stiffness $$T_{\mathrm{pot}}=G\left(m_{\mathrm{T}}{P}_{\mathrm{T},\mathrm{e.g}}+m_{\mathrm{J}}{P}_{\mathrm{J},\mathrm{e.g}}+m_{\mathrm{CJ}}{P}_{\mathrm{CJ},\mathrm{e.g}}+m_{\mathrm{TR}}{P}_{\mathrm{TR},\mathrm{e.g}}+m_{\mathrm{L}}{P}_{\mathrm{L},\mathrm{e.g}}\right)+\frac{1}{2}\left({\tilde{c}}_{a_y}{a}_{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0003.png"\; state="\{\{state\}\}">y</figure-callout>}}^2+{\tilde{c}}_{{\beta }_y}{\mathrm{<figure-callout\; id="2"\; label="b\; y"\; filenames="imgf0003.png"\; state="\{\{state\}\}">b</figure-callout>}}_y^{}\right)$$

to express. Since the rotational energies are negligibly small compared to the translational ones, the Lagrange function can be used as $$L=T_{\mathrm{children}}-T_{\mathrm{pot}}$$

be formulated. This results in the Euler-Lagrange equations $$\frac{\mathrm{i.e}}{\mathrm{i.e}t}\frac{\partial L}{\partial {\dot{q}}_i}-\frac{\partial L}{\partial q_i}=Q_i^{\ast }$$

with the generalized forces $Q_i^{*}$

, which describe the influences of non-conservative forces, such as damping forces. Written out, the three equations result $$\frac{\mathrm{i.e}}{\mathrm{i.e}t}\frac{\partial L}{\partial {\dot{a}}_y}-\frac{\partial L}{\partial a_y}=-{\mathrm{i.e}}_{\mathit{\alpha y}}{\dot{a}}_y,$$

$$\frac{\mathrm{i.e}}{\mathrm{i.e}t}\frac{\partial L}{\partial {\dot{\beta }}_y}-\frac{\partial L}{\partial {\beta }_y}=-{\mathrm{i.e}}_{\mathit{\beta y}}{\dot{\beta }}_y,$$

$$\frac{\mathrm{i.e}}{\mathrm{i.e}t}\frac{\partial L}{\partial {\dot{\varphi }}_y}-\frac{\partial L}{\partial {\varphi }_y}=0.$$

By inserting L and calculating the corresponding derivatives, the terms in these equations are very large, so that an explicit representation does not make sense here.

$$\ddot{l}=\frac{1}{{\tau }_l}\left(u_l-\dot{l}\right).$$

The dynamics of the drives of the trolley and the hoist can usually be well approximated by the PT1 dynamics of the first order $${\ddot{x}}_{\mathrm{TR}}=\frac{1}{{\tau }_{\mathrm{TR}}}\left({\mathrm{and}}_x-{\dot{x}}_{\mathrm{TR}}\right),$$

$$\ddot{l}=\frac{1}{{\tau }_l}\left({\mathrm{and}}_l-\dot{l}\right).$$

In it, τ _i describe the corresponding time constants and u _i the setpoint speeds.

fest, so lässt sich die gekoppelte Radialdynamik aus Antriebs-, Pendel- und Strukturdynamik darstellen als $$\underset{\tilde{A}\left(\mathbf{X}\right)}{\underbrace{\left(\begin{array}{ccc}{a}_{11}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{12}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{13}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\\ a_{31}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{22}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{23}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\\ a_{31}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{32}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{33}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\end{array}\right)}}\ddot{q}=\underset{\tilde{B}\left(\mathbf{X}\right)}{\underbrace{\left(\begin{array}{c}{b}_1\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\\ b_2\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\\ b_3\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\end{array}\right)}}$$

oder durch Umstellen zur Laufzeit als die nichtlineare Dynamik in der Form $$\ddot{q}=\mathbf{f}\left(\dot{q},\mathbf{q},{\mathbf{x}}_a\right).$$

If you now keep all drive-related variables in the vector $$x_a=\left(x_{\mathrm{TR}},l,{\dot{x}}_{\mathrm{TR}},\dot{l},{\ddot{x}}_{\mathrm{TR}},\ddot{l}\right)$$

firmly, the coupled radial dynamics of drive, pendulum and structural dynamics can be represented as $$\underset{\tilde{A}\left(\mathbf{X}\right)}{\underbrace{\left(\begin{array}{ccc}{a}_{11}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{12}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{13}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\\ a_{31}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{22}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{23}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\\ a_{31}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{32}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)& a_{33}\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\end{array}\right)}}\ddot{q}=\underset{\tilde{B}\left(\mathbf{X}\right)}{\underbrace{\left(\begin{array}{c}{b}_1\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\\ b_2\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\\ b_3\left(\mathbf{q},\dot{q},{\mathbf{x}}_a\right)\end{array}\right)}}$$

or by rearranging at runtime as the nonlinear dynamics in the form $$\ddot{q}=\mathbf{f}\left(\dot{q},\mathbf{q},{\mathbf{x}}_a\right).$$

nicht möglich. Um aus (75) ein lineares Modell der Form (60) für die Regelung zu erhalten, kann daher zur Laufzeit eine numerische Linearisierung durchgeführt werden. Hierfür kann zunächst die Ruhelage (q̇₀,q̇₀) bestimmt werden, für die $$0=\mathbf{f}\left({\dot{q}}_0,{\mathbf{q}}_0,0\right)$$

erfüllt ist. Dann lässt sich das Modell über die Gleichungen $${\dot{x}}_{\mathrm{lin}}=\underset{A}{\underbrace{{\frac{\partial \mathbf{f}}{\partial \left[\dot{q},\mathbf{q}\right]}|}_{\left({\dot{q}}_0,{\mathbf{q}}_0\right)}}}{\mathbf{x}}_{\mathrm{lin}}+\underset{B}{\underbrace{{\frac{\partial \mathbf{f}}{\partial \mathbf{u}}|}_{\left({\dot{q}}_0,{\mathbf{q}}_0\right)}}}\mathbf{u}.$$

linearisieren und es ergibt sich ein lineares System wie in Gleichung (60). Durch die Wahl einer geeigneten Sensorik für Struktur- und Pendeldynamik, beispielsweise mit Hilfe von Gyroskopen, ergibt sich ein Messausgang wie in (61), durch den die Radialdynamik beobachtbar ist.Since the radial dynamics are thus present in minimal coordinates, an order reduction is not necessary. However, due to the complexity of the equations described by (75), an analytical offline pre-calculation of the Jacobi matrix is required $\frac{\partial \mathbf{f}}{\partial \left[\dot{q},\mathbf{q}\right]}$

not possible. In order to obtain a linear model of the form (60) for the control from (75), a numerical linearization can therefore be carried out at runtime. For this purpose, the rest position (q˜ ₀ ,q˜ ₀ ) can first be determined for which $$0=\mathbf{f}\left({\dot{q}}_0,{\mathbf{<figure-callout\; id="0"\; label="q"\; filenames="imgf0013.png"\; state="\{\{state\}\}">q</figure-callout>}}_0,0\right)$$

is satisfied. Then the model can be calculated using the equations $${\dot{x}}_{\mathrm{lin}}=\underset{A}{\underbrace{{\frac{\partial \mathbf{f}}{\partial \left[\dot{q},\mathbf{q}\right]}|}_{\left({\dot{q}}_0,{\mathbf{q}}_0\right)}}}{\mathbf{x}}_{\mathrm{lin}}+\underset{B}{\underbrace{{\frac{\partial \mathbf{f}}{\partial \mathbf{and}}|}_{\left({\dot{q}}_0,{\mathbf{q}}_0\right)}}}\mathbf{and}.$$

linearize and a linear system results as in equation (60). Choosing a suitable sensor system for structural and pendulum dynamics, for example with the help of gyroscopes, results in a measurement output as in (61), through which the radial dynamics can be observed.

The further procedure of the observer and control draft corresponds to that for the swing dynamics.

As already mentioned, the deflection of the hoist rope relative to the vertical 62 can be determined not only by an imaging sensor system on the trolley, but also by an inertial measuring device on the load hook.

Such an inertial measuring device IMU can in particular have acceleration and yaw rate sensors for providing acceleration and yaw rate signals that indicate translatory accelerations along different spatial axes on the one hand and yaw rates or gyroscopic signals with respect to different spatial axes on the other hand. In this case, rotational speeds, but in principle also rotational accelerations or even both, can be provided as rotational rates.

The inertial measuring device IMU can advantageously record accelerations in three spatial axes and rates of rotation about at least two spatial axes. The acceleration sensor means can work on three axes and the gyroscope sensor means can work on two axes.

The inertial measuring device IMU attached to the load hook can advantageously transmit its acceleration and yaw rate signals and/or signals derived therefrom wirelessly to the control and/or evaluation device 3 or its anti-sway device 340 transmit, which can be attached to a structural part of the crane or arranged separately near the crane. In particular, the transmission can be made to a receiver REC, which can be attached to the trolley 206 and/or to the suspension from which the hoist cable runs. The transmission can advantageously take place, for example, via a WLAN connection, cf. 10 .

As 13 shows, the load hook 208 can tilt in different directions and in different ways relative to the hoist rope 207, depending on the connection. The diagonal pull angle β of the hoist rope 207 does not have to be identical to the orientation of the load hook. The tilting angle ε _β describes the tilting or rotation of the load hook 207 in relation to the diagonal pull β of the hoist rope 2017 or the rotation between inertial coordinates and load hook coordinates.

To model the swaying behavior of a crane, the two swaying directions in the travel direction of the trolley, i.e. in the longitudinal direction of the jib on the one hand, and in the direction of rotation or arcing around the tower axis, i.e. in the direction transverse to the longitudinal direction of the jib, can be considered separately from one another, since these differ both pendulum movements hardly affect each other. Each pendulum direction can therefore be modeled two-dimensionally.

definiert werden, wobei die zeitliche Ableitung $$\dot{r}=\left(\begin{array}{c}{\dot{s}}_x-\dot{l}\sin \left(\beta \right)-l\dot{\beta }\cos \left(\beta \right)\\ l\dot{\beta }\sin \left(\beta \right)-\dot{l}\cos \left(\beta \right)\end{array}\right)$$

die Inertialgeschwindigkeit unter Verwendung von $\frac{\mathbf{d}\beta }{\mathbf{d}\mathit{t}}=\dot{\beta }$

beschreibt. Die Hakenbeschleunigung $$\ddot{r}=\left(\begin{array}{c}{\ddot{s}}_x-2\dot{\beta }\dot{l}\cos \beta -\ddot{l}\sin \beta +l{\dot{\beta }}^2\sin \beta -l\ddot{\beta }\cos \beta \\ 2\dot{l}\dot{\beta }\sin \beta -\ddot{l}\cos \beta +l{\dot{\beta }}^2\cos \beta +l\ddot{\beta }\sin \beta \end{array}\right)$$

wird für die Ableitung der Lastdynamik nicht benötigt, jedoch für die Gestaltung des Filters verwendet, wie noch erläutert.Looking at that in 12 In the model shown, the pendulum dynamics can be described using the Lagrange equations. The trolley position s _x ( t ), the cable length l ( t ) and the cable or pendulum angle β ( t ) are defined as a function of the time t, whereby in the following for the sake of simplicity and better readability the time dependence is no longer specifically defined by the term (t) is specified. First, the load hook position in inertial coordinates as $$\mathbf{right}=\left(\begin{array}{c}{s}_x-l\sin \left(\beta \right)\\ -l\cos \left(\beta \right)\end{array}\right)$$

be defined, taking the time derivative $$\dot{\mathrm{right}}=\left(\begin{array}{c}{\dot{s}}_x-\dot{l}\sin \left(\beta \right)-l\dot{\beta }\cos \left(\beta \right)\\ l\dot{\beta }\sin \left(\beta \right)-\dot{l}\cos \left(\beta \right)\end{array}\right)$$

the inertial velocity using $\frac{\mathbf{i.e}\beta }{\mathbf{i.e}\mathit{t}}=\dot{\beta }$

describes. The hook acceleration $$\ddot{\mathrm{right}}=\left(\begin{array}{c}{\ddot{s}}_x-2\dot{\beta }\dot{l}\cos \beta -\ddot{l}\sin \beta +l{\dot{\beta }}^2\sin \beta -l\ddot{\beta }\cos \beta \\ 2\dot{l}\dot{\beta }\sin \beta -\ddot{l}\cos \beta +l{\dot{\beta }}^2\cos \beta +l\ddot{\beta }\sin \beta \end{array}\right)$$

is not required for the derivation of the load dynamics, but is used for the design of the filter, as explained below.

wobei die Masse m des Lasthakens und der Last später eliminiert wird. Die potentielle Energie infolge der Schwerkraft entspricht $$\begin{array}{cc}V=-m{\mathbf{r}}^T\mathbf{g},& \mathbf{g}={\left(\begin{array}{cc}0& -g\end{array}\right)}^T\end{array},$$

The kinetic energy is determined by $$T=\frac{1}{2}m{\dot{\mathrm{right}}}^T\dot{\mathrm{right}}$$

where the mass m of the load hook and the load is later eliminated. The potential energy due to gravity equals $$\begin{array}{cc}V=-m{\mathbf{right}}^T\mathbf{G},& \mathbf{G}={\left(\begin{array}{cc}0& -G\end{array}\right)}^T\end{array},$$

With the gravitational acceleration g .

wobei der Vector q = [β β̇] ^T die generalisierten Koordinaten beschreibt. Dies ergibt die Pendeldynamik als nicht-lineare Differentialgleichung zweiter Ordnung bezüglich β, $$l\ddot{\beta }+2\dot{l}\dot{\beta }-{\ddot{s}}_x\cos \beta +g\sin \beta =0.$$

Since V does not depend on r, the Euler-Lagrange equation is $$\frac{\mathrm{i.e}}{\mathit{German}}\frac{\partial T}{\partial \dot{q}}-\frac{\partial T}{\partial \mathrm{q}}+\frac{\partial V}{\partial \mathbf{q}}=0$$

where the vector q = [ β β̇ ] ^T describes the generalized coordinates. This gives the pendulum dynamics as a non-linear second-order differential equation with respect to β , $$l\ddot{\beta }+2\dot{l}\dot{\beta }-{\ddot{s}}_x\cos \beta +G\sin \beta =0.$$

The dynamics in the y - z plane can be expressed analogously.

In the following, the acceleration s̈ _x of the trolley or a gantry crane runner is considered as a known system input variable. This can sometimes be measured directly or estimated on the basis of the measured trolley speed. Alternatively or additionally, the trolley acceleration can be measured with a separate the trolley accelerometer or estimated if the drive dynamics are known. The dynamic behavior of electric crane drives can be determined using the first-order load behavior $${\ddot{s}}_x=\frac{{\mathrm{and}}_x-\dot{x}}{T_x}$$

Estimated where the input signal u _x corresponds to the desired speed and T _x is the time constant. If the accuracy is sufficient, no further measurement of the acceleration is required.

The tilting direction of the load hook is described by the tilting angle ε _β , cf. 13 .

von der gemessenen Drehrate ω_β zum Kippwinkel.Since the yaw rate or roll rate is measured gyroscopically, the model on which the estimate of the roll is based corresponds to the simple integrator $${\dot{e}}_{\beta }={\omega }_{\beta }$$

from the measured yaw rate ω _β to the tilt angle.

The IMU measures all signals in the moving, rotating, body-fixed coordinate system of the load hook, which is denoted by the prefix K , while vectors in inertial coordinates are denoted by I or remain without a subscript. Once ε _β is estimated, the measured acceleration _K a = [ _K a _{x K} a _z ] ^T in hook coordinates can be transformed to _K a in inertial coordinates using $${}_I\mathbf{a}=\left[\begin{array}{cc}\cos \left(e_{\beta }\right)& \sin \left(e_{\beta }\right)\\ -\sin \left(e_{\beta }\right)& \cos \left(e_{\beta }\right)\end{array}\right]\cdot {}_K\mathbf{a}.$$

The inertial acceleration can then be used to estimate the sway angle based on (107) and (103).

Estimating the rope angle β requires an accurate estimate of the tilting of the load hook ε _β . In order to be able to estimate this angle on the basis of the simple model according to (109), an absolute reference value is required, since the gyroscope has limited accuracy and an initial value is unknown. In addition, the gyroscopic measurement is regularly superimposed by an approximately constant deviation that is inherent in the measurement principle. Furthermore, it cannot be assumed that ε _β generally oscillates around zero. Therefore, the acceleration sensor is used to to provide such reference value by evaluating the gravitational acceleration constant (which appears in the low frequency signal) and in inertial coordinates as $${}_l\mathbf{G}={\left[\begin{array}{cc}0& -G\end{array}\right]}^T.$$

transformierbar ist. Die gemessene Beschleunigung ergibt sich als Summe von (103) and (112) $${}_K\mathbf{a}={}_K\ddot{r}-{}_K\mathbf{g}.$$

Is known and in load hook coordinates $${}_K\mathbf{G}=-G{\left[\begin{array}{cc}-\sin \left(e_{\beta }\right)& \cos \left(e_{\beta }\right)\end{array}\right]}^T.$$

is transformable. The measured acceleration is the sum of (103) and (112) $${}_K\mathbf{a}={}_K\ddot{\mathrm{right}}-{}_K\mathbf{G}.$$

The negative sign of _K g results from the fact that the gravitational acceleration is measured as a fictitious upward acceleration due to the sensor principle.

Since all components of _K r̈ are generally significantly smaller than g and oscillate around zero, the use of a low-pass filter with a sufficiently low cut-off frequency allows the approximation $${}_K\mathbf{a}\approx -{}_K\mathbf{G}.$$

Dividing the x component by the z component gives the reference flip angle for low frequencies as $$e_{\beta ,a}=\arctan \left(\frac{{}_{K}a_x}{{}_{K}a_{\mathrm{e.g}}}\right).$$

The simple structure of the linear pendulum dynamics according to (109) allows the use of various filters to estimate the orientation. One option is a so-called time-continuous Kalman Bucy filter, which can be adjusted by varying the process parameters and noise measurement. In the following, however, a complementary filter as in 14 shown, used, which can be adjusted with regard to its frequency characteristics by selecting the high-pass and low-pass transfer functions.

Like the block diagram of the 14 shows, the complementary filter can be designed to estimate the direction of the load hook tilting ε _β . A high-pass filtering of the gyroscope signal ω _β with G _{hp 1} ( s ) results in the offset-free yaw rate ω̃ _β as well as after Integration a first tilt angle estimate ε _{β , ω} . The further estimate ε _{β , a} comes from the signal _K a of the acceleration sensor.

und sehr niedriger Ausblendfrrequenz ω₀ auf das Gyroscopesignal ω_β angewendet werden, um den konstanten Messversatz zu eliminieren. Integration ergibt die Gyroskopbasierte Kippwinkel-Schätzung ε _β,ω die für hohe Frequenzen relativgenau ist, jedoch für niedrige Frequenzen relativ ungenau ist. Die grundlegende Idee des Komplementärfilters ist es, ε _β,ω und ε _β,a aufzusummieren bzw. miteinander zu verknüpfen, wobei die hohen Frequenzen von ε _β,ω durch Verwendung des Hochpassfilters stärker gewichtet werden und die niedrigen Frequenzen von ε _β,a durch die Verwendung des Tiefpassfilters stärker gewichtet werden, da (115) eine gute Abschätzung für niedrige frequenzen darstellt. Die Transferfunktionen können als einfache Filter erster Ordnung gewählt werden, nämlich $$\begin{array}{cc}{G}_{\mathit{hp}2}\left(s\right)=\frac{s}{s+\omega },& G_{\mathit{lp}}\left(s\right)=\frac{\omega }{s+\omega }\end{array}$$

wobei die Ausblendfrequenz ω niedriger als die Pendelfrequenz gewählt wird. Da $$G_{\mathit{hp}2}\left(s\right)+G_{\mathit{lp}}\left(s\right)=1$$

für alle Frequenzen gilt, wir die Abschätzung von ε_β nicht falsch skaliert.In particular, first a simple high-pass filter using the transfer function $$G_{\mathit{hp}}$$$${\mathit{}1}_{}=\frac{s}{s+{\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="imgf0013.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_0}$$

and very low skip frequency ω ₀ can be applied to the gyroscope signal ω _β to eliminate the constant measurement offset. Integration gives the gyro-based tilt angle estimate ε _{β , ω ,} which is relatively accurate for high frequencies but relatively inaccurate for low frequencies. The basic idea of the complementary filter is to sum or combine ε _{β , ω} and ε _{β , a} , where the high frequencies of ε _{β , ω} are weighted more heavily by using the high-pass filter and the low frequencies of ε _{β , a} are weighted by the use of the low-pass filter should be given more weight, since (115) is a good estimate for low frequencies. The transfer functions can be chosen as simple first-order filters, viz $$\begin{array}{cc}{G}_{\mathit{hp}2}\left(s\right)=\frac{s}{s+\omega },& G_{\mathit{lp}}\left(s\right)=\frac{\omega }{s+\omega }\end{array}$$

where the skip frequency ω is chosen to be lower than the oscillation frequency. There $$G_{\mathit{hp}2}\left(s\right)+G_{\mathit{lp}}\left(s\right)=1$$

for all frequencies, the estimate of ε _β is not incorrectly scaled.

Based on the estimated hook orientation, the inertial acceleration _I a of the hook can be determined from the measurement of _K a using (110), allowing the design of an observer based on the pendulum dynamics (107) and the rotated acceleration measurement $${}_I\mathbf{a}=\ddot{\mathrm{right}}{-}_I\mathbf{G}.$$

Although both components of this equation can be used equally for estimating the sway angle, good results can also be obtained using only the x component, which is independent of g .

wobei der Statusvektor x = [β β̈] ^T ist. Zur Bestimmung der Zustände kann der kontinuierliche, zeitlich erweiterte Kalman Filter $$\begin{array}{l}\dot{\widehat{x}}=\mathbf{f}\left(\widehat{x},u\right)+K\left(y-h\left(\widehat{x},u\right)\right),\widehat{x}\left(0\right)={\widehat{x}}_0,\\ \dot{P}=\mathit{AP}+{\mathit{PA}}^T-{\mathit{PC}}^T{R}^{-1}\mathit{CP}+Q,P\left(0\right)=P_0,\\ K={\mathit{PC}}^T{R}^{-1},\\ {\begin{array}{cc}A={\frac{\partial \mathbf{f}}{\partial \mathbf{x}}|}_{\widehat{x},u},& C=\frac{\partial h}{\partial \mathbf{x}}|\end{array}}_{\widehat{x},u},\end{array}$$

verwendet werden.In the following it is assumed that the pendulum dynamics are superimposed by process-related background noise w : N (0, Q ) and measurement noise ν : N (0, R ) so that it can be expressed as a non-linear stochastic system, namely $$\begin{array}{l}\begin{array}{cc}\dot{x}=\mathbf{f}\left(\mathbf{x},\mathrm{and}\right)+\mathbf{w},& \mathbf{x}\left(0\right)={\mathbf{x}}_0\end{array}\\ y=H\left(\mathbf{x},\mathrm{and}\right)+v\end{array}$$

where the status vector x = [ β β̈ ] ^T. The continuous, time-expanded Kalman filter can be used to determine the states $$\begin{array}{l}\dot{\widehat{x}}=\mathbf{f}\left(\widehat{x},\mathrm{and}\right)+K\left(y-H\left(\widehat{x},\mathrm{and}\right)\right),\widehat{x}\left(0\right)={\widehat{x}}_0,\\ \dot{P}=\mathit{AP}+{\mathit{PA}}^T-{\mathit{personal\; computer}}^T{R}^{-1}\mathit{CP}+Q,\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="imgf0013.png"\; state="\{\{state\}\}">P</figure-callout>}\left(0\right)={\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="imgf0013.png"\; state="\{\{state\}\}">P</figure-callout>}}_0,\\ K={\mathit{personal\; computer}}^T{R}^{-1},\\ {\begin{array}{cc}A={\frac{\partial \mathbf{f}}{\partial \mathbf{x}}|}_{\widehat{x},\mathrm{and}},& C=\frac{\partial H}{\partial \mathbf{x}}|\end{array}}_{\widehat{x},\mathrm{and}},\end{array}$$

be used.

wobei die Katzbeschleunigung u = s̈_x als Eingangsgröße des Systems behandelt wird. Um einen Systemausgang zu definieren, kann die horizontale Komponente der Lasthakenbeschleunigung aus (119) in Abhaängigkeit der Systemzustände fomuliert werden, woraus sich ergibt: $$\begin{array}{l}{}_I{a}_x={\ddot{r}}_x-\underset{0}{\underbrace{{}_I{g}_x}}\\ ={\ddot{s}}_x-2\dot{\beta }\dot{l}\text{cos}\beta -\ddot{l}\text{sin}\beta +l{\dot{\beta }}^2\text{sin}\beta -l\ddot{\beta }\text{cos}\beta \\ \text{=}\left(1-\text{cos}{\left(\beta \right)}^2\right){\ddot{s}}_x+\text{sin}\beta \left(-\ddot{l}+g\text{cos}\beta +l{\dot{\beta }}^2\right)\end{array}$$

The spatial state representation of the pendulum dynamics according to (107) is $$\mathbf{f}\left(\mathbf{x},{\ddot{s}}_x\right)=\left[\begin{array}{c}\dot{\beta }\\ \frac{-1}{l}\left(2\dot{l}\dot{\beta }-{\ddot{s}}_x\cos \beta +G\sin \beta \right)\end{array}\right]$$

where the trolley acceleration u = s̈ _x is treated as the input variable of the system. In order to define a system output, the horizontal component of the load hook acceleration can be formulated from (119) as a function of the system states, which results in: $$\begin{array}{l}{}_I{a}_x={\ddot{\mathrm{right}}}_x-\underset{0}{\underbrace{{}_I{G}_x}}\\ ={\ddot{s}}_x-2\dot{\beta }\dot{l}\text{cos}\beta -\ddot{l}\text{sin}\beta +l{\dot{\beta }}^2\text{sin}\beta -l\ddot{\beta }\text{cos}\beta \\ \text{=}\left(1-\text{cos}{\left(\beta \right)}^2\right){\ddot{s}}_x+\text{sin}\beta \left(-\ddot{l}+G\text{cos}\beta +l{\dot{\beta }}^2\right)\end{array}$$

ergibt sich der Linearisierungsterm als $$A={\left[\begin{array}{cc}0& 1\\ \frac{\left(-g\cos \beta -{\ddot{s}}_x\sin \beta \right)}{l}& \frac{-2\dot{l}}{l}\end{array}\right]|}_{\widehat{x},{\ddot{s}}_x,}$$

$$C={{\left[\begin{array}{c}\cos \beta \left(2g\cos \beta -\ddot{l}+l{\dot{\beta }}^2+2{\ddot{s}}_x\sin \beta \right)-g\\ 2l\dot{\beta }\sin \beta \end{array}\right]}^T|}_{\widehat{x},{\ddot{s}}_x}.$$

The horizontal component _l g _x of the gravitational acceleration is naturally zero. In doing so, l̇ , l̈ can be reconstructed from the measurement of l , e.g. using the drive dynamics according to (108). When using (123) as a measurement function $$H\left(\mathbf{x}\right){=}_I{a}_x,$$

the linearization term results as $$A={\left[\begin{array}{cc}0& 1\\ \frac{\left(-G\cos \beta -{\ddot{s}}_x\sin \beta \right)}{l}& \frac{-2\dot{l}}{l}\end{array}\right]|}_{\widehat{x},{\ddot{s}}_x,}$$

$$C={{\left[\begin{array}{c}\cos \beta \left(2G\cos \beta -\ddot{l}+l{\dot{\beta }}^2+2{\ddot{s}}_x\sin \beta \right)-G\\ 2l\dot{\beta }\sin \beta \end{array}\right]}^T|}_{\widehat{x},{\ddot{s}}_x}.$$

The covariance matrix estimates of the process noise are Q = I _{2 × 2} , the measurement noise R = 1000 and the initial error covariance matrix P = 0 _{2 × 2} .

As figure 15 shows, the sway angle, which is estimated using an extended Kalman filter (EKF) or also determined using a simple static approach, corresponds quite well to a validation measurement of the sway angle on a gimbal using a rotation angle encoder on the trolley.

$$y=\left[\begin{array}{cc}g& 0\end{array}\right]\mathbf{x}$$

und _la_x dient als Referenzwert für den Ausgang. Unter Vernachlässigung der Dynamikeffekte gemäß (127) und Berücksichtigung von nur der statischen Ausgangsfunktion (128), kann der Pendelwinkel aus der einfachen statischen Beziehung $$\beta =\frac{{}_{I}a_x}{g}$$

gewonnen werden, der interessanteerweise unabhängig von l ist. Fig. 15 zeigt, dass die hierdurch gewonnen Ergebnisse ebenso genau sind wie die des Kalman Filters.It is interesting that the calculation using a relatively simple static approach delivers results that are comparable to those of the extended Kalman filter. Therefore, the pendulum dynamics according to (122) and the initial equation according to (123) can be linearized around the stable state β = β̇ = 0. If the rope length l is assumed to be constant so that l̇ = l̈ = 0, this results for the linearized system $$\dot{x}=\left[\begin{array}{cc}0& 1\\ \frac{-G}{l}& 0\end{array}\right]\mathbf{x}+\left[\begin{array}{c}0\\ \frac{1}{l}\end{array}\right]{\ddot{s}}_x,$$

$$y=\left[\begin{array}{cc}G& 0\end{array}\right]\mathbf{x}$$

and _l a _x serves as a reference value for the output. Neglecting the dynamic effects according to (127) and considering only the static output function (128), the pendulum angle can be calculated from the simple static relationship $$\beta =\frac{{}_{I}a_x}{G}$$

can be obtained, which interestingly is independent of l . 15 shows that the results obtained are as accurate as those of the Kalman filter.

Thus, using β and equation (101), an accurate estimate of the load position can be achieved.

sehr klein. Insofern können Dynamikeffekte der Antriebe vernachlässigt werden.When modeling the dynamics of the speed-based crane drives according to (108) together with a parameter determination, the resulting time constants according to $T_i<\frac{1}{50}$

tiny. In this respect, dynamic effects of the drives can be neglected.

In order to specify the pendulum dynamics with the drive speed ṡ _x instead of the drive acceleration s̈ _x as the system input variable, the linearized dynamic system can be "increased" by integration according to (127), which results in: $$\dot{\tilde{x}}=\left[\begin{array}{cc}0& 1\\ \frac{-\mathrm{<figure-callout\; id="0"\; label="G\; l"\; filenames="imgf0013.png"\; state="\{\{state\}\}">G</figure-callout>}}{l}& 0\end{array}\right]\underset{\tilde{x}}{\underbrace{{\displaystyle {\int }_0^t\mathbf{x}\left(\tau \right)\mathrm{i.e}\tau }}}+\left[\begin{array}{c}0\\ \frac{1}{l}\end{array}\right]{\dot{s}}_x$$

berechnet werden. Dies kann auch als statischer Vorfilter F im Frequenzbereich angesehen werden, der sicherstellt, dass $\underset{\mathbf{s}\to 0}{\lim }{\mathit{G}}_{\mathit{u},{\mathit{x}}_1}\left(\mathit{s}\right)=1\mathit{F}$

für die Transferfunktion vom Geschwindigkeitseingang zum ersten Zustand $$G_{u,x_1}\left(s\right)=\frac{1}{{\mathit{ls}}^2+g}.$$

ist. Die erste Komponente des neuen Statusvektors x̃ kann mithilfe einesKalman-Bucy Filters auf Basis von (130) geschätzt werden, mit der Systemausgangsgröße y = [0 1]x̃. Das Ergebnis ist ähnlich, wenn ein Regler auf Basis von (127) entworfen wird und der Motorregler durch das integrierte Eingangssignal $\mathit{u}={\displaystyle {\int }_{\mathbf{O}}^{\mathit{t}}{\ddot{s}}_{\mathit{x}}\left(\tau \right)\mathbf{d}\tau }$

gesteuert wird.The new status vector is x̃ = [∫ β β ] ^T . The dynamics obviously remain the same, while the physical meaning and approach change. In contrast to (127), β and β̇ should be stabilized at zero, but not the time integral ∫ β . Since the controller should be able to maintain a desired speed ṡ _x,d , the desired stable state should be permanently off x̃ as $${\tilde{x}}_{\mathrm{i.e}}={\left[\begin{array}{cc}\frac{{\dot{s}}_{x,\mathrm{i.e}}}{G}& 0\end{array}\right]}^T.$$

be calculated. This can also be thought of as a static pre-filter F in the frequency domain, ensuring that $\underset{\mathbf{s}\to 0}{\mathrm{limited}}{\mathit{G}}_{\mathit{and},{\mathit{x}}_1}\left(\mathit{s}\right)=1\mathit{f}$

for the transfer function from the velocity input to the first state $$G_{\mathrm{and},x_1}\left(s\right)=\frac{1}{{\mathit{<figure-callout\; id="2"\; label="ls"\; filenames="imgf0003.png"\; state="\{\{state\}\}">ls</figure-callout>}}^2+G}.$$

is. The first component of the new status vector x̃ can be estimated using a Kalman-Bucy filter based on (130), with the system output y = [0 1] x̃ . The result is similar when a controller is designed based on (127) and the motor controller is designed by the integrated input signal $\mathit{and}={\displaystyle {\int }_{\mathbf{O}}^{\mathit{t}}{\ddot{s}}_{\mathit{x}}\left(\tau \right)\mathbf{i.e}\tau }$

is controlled.

The feedback obtained can be defined as a linear-quadratic controller (LQR), which can represent a linear-quadratic Gaussian controller (LQG) structure together with the Kalman-Bucy filter. Both the feedback and the Kalman gain can be adjusted to the rope length l , e.g. using gain plans.

ergibt, wobei u = ṡ_x ist, so dass die flache Ausgangsgröße $$\begin{array}{l}z={\mathrm{\lambda }}^T\mathbf{x},{\mathrm{\lambda }}^T\left[\begin{array}{ccc}\tilde{B}& \tilde{A}\tilde{B}& {\tilde{A}}^2\tilde{B}\end{array}\right]=\left[\begin{array}{ccc}0& 0& \frac{g}{l}\end{array}\right]\left(134\right)\\ =\left[\begin{array}{ccc}0& -l& 1\end{array}\right]=s_x-\mathit{l\beta },\left(135\right)\end{array}$$

ist, was mit der Hakenposition der linearisierten Fallkonstellation korrespondiert. Zustand und Eingang können durch den flachen Ausgang und dessen Ableitungen algebraisch parametrisiert werden, und zwar mit z = [z ż z̈] ^T als $$\mathbf{x}={\mathrm{\Psi }}_x\left(\mathbf{z}\right)={\left[\begin{array}{ccc}\frac{-\dot{z}}{g}& \frac{-\ddot{z}}{g}& z+\frac{l\ddot{z}}{g}\end{array}\right]}^T,$$

$$u={\mathrm{\Psi }}_u\left(\mathbf{z},\stackrel{\left(3\right)}{z}\right)=\dot{z}+\frac{l\stackrel{⃛}{z}}{g}$$

was die algebraische Berechnung der Referenzzustände und des nominalen Eingangsstellsignals aus der geplanten Trajektorie für z ermöglicht. Ein Wechsel des Einstellpunkts zeigt dabei, dass der nominale Fehler nahe Null gehalten werden kann, so dass Feedback Signal u_fb des Reglers K signifikant kleiner als die nominale Eingangsstellgröße u_ff ist. In der Praxis kann die Eingangsstellgröße auf u_fb = 0 gesetzt werden, wenn das Signal der drahtlosen Intertialmesseinrichtung verloren wird.In order to steer the load hook close along trajectories, a structure with two degrees of freedom as in 16 shown can be used in conjunction with a trajectory planner that provides a C ³ differentiable reference trajectory for the hook position. The trolley position can be added to the dynamics system according to (130), resulting in the system $${\displaystyle \sum :}\dot{x}=\underset{\tilde{A}}{\underbrace{\left[\begin{array}{ccc}0& 1& 0\\ \frac{-\mathrm{<figure-callout\; id="0"\; label="G\; l"\; filenames="imgf0013.png"\; state="\{\{state\}\}">G</figure-callout>}}{l}& 0& 0\\ 0& 0& 0\end{array}\right]}}\mathbf{x}+\underset{\tilde{B}}{\underbrace{\left[\begin{array}{c}0\\ \frac{1}{l}\\ 1\end{array}\right]}}\mathrm{and}$$

yields, where u = ṡ _x , so that the flat output quantity $$\begin{array}{l}\mathrm{e.g}={\mathrm{\lambda }}^T\mathbf{x},{\mathrm{\lambda }}^T\left[\begin{array}{ccc}\tilde{B}& \tilde{A}\tilde{B}& {\tilde{A}}^2\tilde{B}\end{array}\right]=\left[\begin{array}{ccc}0& 0& \frac{G}{l}\end{array}\right]\left(134\right)\\ =\left[\begin{array}{ccc}0& -\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="imgf0010.png"\; state="\{\{state\}\}">l</figure-callout>}& 1\end{array}\right]=s_x-\mathit{l\beta },\left(135\right)\end{array}$$

is, which corresponds to the hook position of the linearized case constellation. State and input can be algebraically parameterized by the flat output and its derivatives, with z = [ z ż z̈ ] ^T as $$\mathbf{x}={\mathrm{\Psi }}_x\left(\mathbf{e.g}\right)={\left[\begin{array}{ccc}\frac{-\dot{\mathrm{e.g}}}{G}& \frac{-\ddot{\mathrm{e.g}}}{G}& \mathrm{e.g}+\frac{l\ddot{\mathrm{e.g}}}{G}\end{array}\right]}^T,$$

$$\mathrm{and}={\mathrm{\Psi }}_{\mathrm{and}}\left(\mathbf{e.g},\stackrel{\left(3\right)}{\mathrm{e.g}}\right)=\dot{\mathrm{e.g}}+\frac{l\stackrel{⃛}{\mathrm{e.g}}}{G}$$

which allows the algebraic calculation of the reference states and the nominal input drive signal from the planned trajectory for z . A change in the set point shows that the nominal error can be kept close to zero, so that the feedback signal u _fb of the controller K is significantly smaller than the nominal input manipulated variable u _ff . In practice, the input manipulated variable can be set to u _fb =0 if the signal from the wireless inertial measuring device is lost.

As figure 16 shows, the two-degree-of-freedom controller structure can have a trajectory planner TP that calculates a smooth trajectory z ∈ C ³ for the flat output with limited derivatives, the input variable Ψ _u and the parameterization of the state Ψ _x , and the controller K .

Claims (17)

1. A crane, in particular a revolving tower crane, having a hoist rope (207) that runs off from a crane boom (202) and carries a load suspension means (208); having drive devices for moving a plurality of crane elements and for traveling the load suspension means (208); having a control device (3) for controlling the drive devices such that the load suspension means (208) travels along a travel path; and having an oscillation damping device (340) for damping oscillating movements of the load suspension means (208) and/or of the hoist rope (207), wherein the oscillation damping device (340) has an oscillation sensor system (60) for detecting oscillating movements of the hoist rope (207) and/or of the load suspension means (208) and has a regulator module (341) having a closed feedback loop for influencing the control of the drive devices in dependence on a oscillation signal of the oscillation sensor system (60) fed back to the feedback loop, characterized in that the oscillation damping device (340) has a structural dynamics sensor system (342) for detecting deformations and/or dynamic movements in themselves of structural components of the crane; and in that the regulator module (341) of the oscillation damping device (340) is configured to take account of both the oscillation signal of the oscillation sensor system (60) and the structural dynamics signals fed back to the feedback loop that indicate deformations and/or dynamic movements in themselves of the structural components on the influencing of the control of the drive devices, with the structural dynamics sensor system (342) being configured to determine dynamic torsions of a crane tower (201) carrying the crane boom and/or of the crane boom (202); and with the regulator module (341) of the oscillation damping device (340) being configured to influence the control of the drive devices in dependence on the detected dynamic torsions of the crane boom (202) and/or of the crane tower (201).
2. A crane in accordance with the preceding claim, wherein the regulator module (341) has a regulation structure having two degrees of freedom and/or has a feedforward module (350), in addition to the closed feedback loop, to feed forward the control signals for the drive devices; wherein the feedforward module (350) is configured as a differential flatness model to carry out the feed forward without taking account of the oscillation signals of the oscillation sensor system (60) and of the structural dynamics signals of the structural dynamics sensor system (342).
3. A crane in accordance with the preceding claim, wherein the feed forward module (350) has a notch filter device (353) for filtering the input signals supplied to the feedforward that is configured to eliminate stimulable eigenfrequencies of the structural dynamics from said input signals and/or a desired value filter module (352) for determining a desired progression for the load suspension means position and its time derivatives from predetermined desired values for the load suspension means are associated with the feedforward module (350); and wherein the notch filter device (353) is provided between the trajectory planning module (351) and the desired value filter module (352), on the one hand, and the feedforward module (350), on the other hand.
4. A crane in accordance with one of the preceding claims, wherein the regulator module (341) has a regulation model that divides the structural dynamics of the crane into mutually independent portions that at least comprise a pivot dynamics portion that takes account of the structural dynamics with respect to the pivoting of the boom (202) about the upright crane pivot axis and a radial dynamics portion that takes account of structural dynamics movements in parallel with a vertical plane in parallel with a boom.
5. A crane in accordance with one of the preceding claims, wherein the structural dynamics sensor system (342) at least has

   - a radial dynamics sensor for detecting dynamic movements of the crane structure in an upright plane in parallel with the crane boom (202); and

   - a pivot dynamics sensor for detecting dynamic movements of the crane structure about an upright axis of rotation of the crane, in particular the tower axis (205),

   and the regulator module (341) of the oscillation damping device (340) is configured to influence the control of the drive devices, in particular of a trolley drive and a slewing gear drive, in dependence on the detected dynamic movements of the crane structure in the upright plane in parallel with the boom and on the detected dynamic movements of the crane structure about the upright axis of rotation of the crane.
6. A crane in accordance with one of the preceding claims, wherein the structural dynamics sensor system (342) further has

   - a hoist dynamics sensor for detecting vertical dynamic deformations of the crane boom (202); and wherein the regulator module (341) of the oscillation damping device (340) is configured to influence the control of the drive devices, in particular of a hoisting gear drive, in dependence on the detected vertical deformations of the crane boom (202).
7. A crane in accordance with the preceding claim, wherein the structural dynamics sensor system (342) is configured to detect all the eigenmodes of the dynamic torsions of the crane boom (202) and/or of the crane tower (201) whose eigenfrequencies lie in a predefined frequency range and has at least one tower sensor, preferably a plurality of tower sensors, that is/are arranged spaced apart from a node of a eigen-oscillation of a tower for detecting tower torsions and has at least one boom sensor, preferably a plurality of boom sensors, that is/are arranged spaced apart from a node of a eigen-oscillation of a boom for detecting boom torsions.
8. A crane in accordance with one of the preceding claims, wherein the structural dynamics sensor system (342) has strain gauges and/or accelerometers and/or rotational rate sensors, in particular in the form of gyroscopes, for the detection of deformations and/or dynamic movements of structural components of the crane in themselves and/or at least one rotational rate sensor and/or accelerometer and/or strain gauge for detecting dynamic tower deformations and at least one rotational rate sensor and/or accelerometer and/or strain gauge for detecting dynamic boom deformations.
9. A crane in accordance with one of the preceding claims, wherein the oscillation sensor system (60) has a detection device for detecting and/or estimating a deflection (ϕ; β) of the hoist rope (207) and/or of the load suspension means (208) with respect to a vertical (61); and wherein the regulator module (341) of the oscillation damping device (340) is configured to influence the control of the drive devices in dependence on the determined deflection (ϕ; β) of the hoist rope (207) and/or of the load suspension means (208) with respect to the vertical (61).
10. A crane in accordance with the preceding claim, wherein the detection device (60) has an imaging sensor system, in particular a camera (62) that looks substantially straight down in the region of a suspension point of the hoist rope (207), in particular of a trolley (206), and wherein an image evaluation device (64) is provided for evaluating an image provided by the imaging sensor system with respect to the position of the load suspension means (208) in the provided image and for determining the deflection (ϕ) of the load suspension means (208) and/or of the hoist rope (207) and/or the deflection speed with respect to the vertical (61);
11. A crane in accordance with one of the two preceding claims, wherein the detection apparatus (60) has an inertial measurement unit (IMU) attached to the load suspension means (208) having accelerometer means and rotational rate sensor means for providing acceleration signals and rotational rate signals; first determination means (401) for determining and/or estimating a tilt (ε_β) of the load suspension means (208) from the acceleration signals and rotational rate signals of the inertial measurement unit (IMU); and second determination means (410) for determining the deflection (β) of the hoist rope (207) and/or of the load suspension means (208) with respect to the vertical (61) from the determined tilt (ε_β) of the load suspension means (208) and an inertial acceleration (_Ia) of the load suspension means (208); wherein the first determination means (401) have a complementary filter (402) having a highpass filter (403) for the rotational rate signal of the inertial measurement unit (MU) and a lowpass filter (404) for the acceleration signal of the inertial measurement unit (IMU) or a signal derived therefrom, which complementary filter (402) is configured to link an estimate of the tilt (ε_β,ω) of the load suspension means (208) that is supported by the rotational rate and that is based on the highpass filtered rotational rate signal and an estimate of the tilt (ε_β,a) of the load suspension means (208) that is supported by acceleration and that is based on the lowpass filtered acceleration signal with one another and to determine the sought tilt (ε_β) of the load suspension means (208) from the linked estimates of the tilt (ε_β,w ; ε_β,a ) of the load suspension means (208) supported by the rotational rate and by the acceleration; and wherein the estimate of the tilt (ε_β,ω) of the load suspension means (208) supported by the rotational rate comprises an integration of the highpass filtered rotational rate signal; and/or wherein the estimate of the tilt (ε_β,a) of the load suspension means (208) supported by the acceleration is based on the quotient of a measured horizontal acceleration (_ka_x) and on a measured vertical acceleration (_ka_z) from which the estimate of the tilt (ε_β,a) supported by the acceleration is acquired using the relationship $${\epsilon }_{\beta ,a}=\arctan \left(\frac{{}_{K}a_x}{{}_{K}a_z}\right).$$

    
12. A crane in accordance with the preceding claim, wherein the second determination means (410) have a filter device and/or an observer device that comprises a Kalman filter (411), in particular an extended Kalman filter, and that takes account of the determined tilt (ε_β) of the load suspension means (208) as the input value and determines the deflection (ϕ; β) of the hoist rope (207) and/or of the load suspension means (208) with respect to the vertical (61) from an inertial acceleration (la) at the load suspension means (208) and/or have a calculation device for calculating the deflection (β) of the hoist rope (207) and/or of the load suspension means (208) with respect to the vertical (61) from the quotient of a horizontal inertial acceleration (_la_x) and of an acceleration due to gravity (g).
13. A crane in accordance with one of the preceding claims 11 and 12, wherein the inertial measurement unit (IMU) has a wireless communication module for the wireless transmission of measurement signals and/or of signals derived therefrom to a receiver, with the communication module and the receiver preferably being connectable to one another via a wireless LAN connection and with the receiver being arranged at the trolley from which the hoist rope runs off.
14. A crane in accordance with one of the preceding claims, wherein the regulator module (341) has a filter device and/or observer device (345) for influencing the control variables of drive regulators (347) for controlling the drive devices, with said filter device and/or observer device (345) being configured to obtain the control variables of the drive regulators (347), on the one hand, and both the oscillation signal of the oscillation sensor system (60) and the structural dynamics signals that are fed back to the feedback loop that give the deformations and/or dynamic movements of the structural components in themselves, on the other hand, as input values, and to influence the regulator control variables in dependence on the dynamically induced movements of crane elements and/or deformations of structural elements obtained for specific regulator control variables; wherein the filter device and/or observer device (345) is configured as a Kalman filter (346) in which detected and/or estimated and/or calculated and/or simulated functions that characterize the dynamics of the structural elements of the crane are implemented in the Kalman filter (346).
15. A crane in accordance with one of the preceding claims, wherein the regulator module (341) is configured to track and/or to adapt at least one characteristic regulation value, in particular regulation gains, in dependence on changes in at least one parameter from the parameter group load mass (m_L), hoist rope length (I), trolley position (x_tr), and radius.
16. A method of controlling a crane, in particular a revolving tower crane, whose load suspension means (208) attached to a hoist rope (207) is traveled by drive devices, which drive devices are controlled by a control apparatus (3) of the crane, wherein the control of the drive devices is influenced by an oscillation damping device (340) comprising a regulator module (341) having a closed feedback loop in dependence on parameters relevant to the oscillation, characterized in that both oscillation signals of an oscillation sensor system (60) by means of which oscillating movements of the hoist rope and/or of the load suspension means are detected and structural dynamics signals of a structural dynamics sensor system (342) by means of which deformations and/or dynamic movements of the structural components in themselves are detected, are fed back to the closed feedback loop, and control signals (u(t)) for controlling the drive devices are influenced by the regulator module (341) in dependence on both the fed back oscillation signals of the oscillation sensor system (60) and the fed back structural dynamics signals of the structural dynamics sensor system (342), with dynamic torsions of a crane tower (201) and/or of the crane boom (202) carrying the crane boom determined by the structural dynamics sensor system (342) and the control of the drive devices being influenced by the regulator module (341) in dependence on the detected dynamic torsions of the crane boom (202) and/or of the crane tower (201).
17. A method in accordance with the preceding claim, wherein the fed back oscillation signals of the oscillation sensor system (60) and the fed back structural dynamics signals of the structural dynamics sensor system (342) are supplied to a Kalman filter (346) to which the control variables of the drive regulators (347) for controlling the drive devices are furthermore supplied as input values, wherein the Kalman filter (346) carries out an influencing of the control variables of the drive regulators (347) in dependence on said oscillation signals of the oscillation sensor system (60), on the structural dynamics signals of the structural dynamics sensor system (342), and on the fed back control variables of the drive regulators (347); wherein the control signals for controlling the drive devices are fed forward by a feedforward module (350) connected upstream of the regulator module (341), with said feedforward module (350) being configured to carry out the feedforward without taking account of the oscillation signals of the oscillation sensor system (60) and of the structural dynamics signals of the structural dynamics sensor system (342).

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