CRANE AND METHOD FOR CONTROLLING SUCH A CRANE

Description

[0001] The present invention relates to a crane in the form of a tower crane, with a hoist rope running from a boom and carrying a load-handling device, drive devices for moving several crane elements and for moving the load-handling device, a control device for controlling the drive devices such that the load-handling device moves along a travel path, and a pendulum damping device for damping pendulum movements of the load-handling device, wherein said pendulum damping device comprises a pendulum sensor for detecting pendulum movements of the hoist rope and / or the load-handling device, and a controller module with a closed control loop for influencing the control of the drive devices depending on pendulum signals, which indicate pendulum movements detected by the pendulum sensor and are fed back to the control loop.The invention further relates to a method for controlling such a crane, in which the control of the drive devices is influenced by a pendulum damping device depending on pendulum-relevant parameters.

[0002] In order to move the load hook of a crane along a travel path or between two target points, various drive devices usually have to be operated and controlled.

[0003] In order to move the load hook of a crane along a travel path or between two target points, various drive devices usually have to be operated and controlled.

[0004] Operators of bridge cranes (or loading bridges) typically control the drives directly, requiring considerable practice and concentration to quickly move a load to the unloading point and safely set it down. In particular, controlling the crane can quickly cause large pendulum swings in the load, which, due to the low damping, subside only very slowly. Avoiding this manually is very difficult and even experienced crane operators rarely succeed.

[0005] With some crane types, the added complication is that they are inherently flexible and can oscillate, which, given the various axes of movement, is difficult for the crane operator to predict. For example, in a tower crane where the hoist cable runs from a trolley that travels along the crane's boom, the slewing mechanism (which rotates the tower with the boom attached to it, or the boom itself, relative to the tower around an upright axis), the trolley drive (which moves the trolley along the boom), and the hoist mechanism (which adjusts the hoist cable and thus raises and lowers the load hook) each typically require separate operation and control. Cranes with a luffing telescopic boom require additional components besides the slewing mechanism, which rotates the boom.The upper structure supporting the boom is rotated around a vertical axis, and the hoist mechanism is used to adjust the hoist cable. It also operates the luffing drive for raising and lowering the boom, as well as the telescoping drive for extending and retracting the telescopic sections, and possibly a luffing jib drive if the telescopic boom has a luffing jib. In hybrid cranes and similar crane types, such as tower cranes with a luffing jib or derrick cranes with a luffing counter jib, additional drive mechanisms may also need to be controlled.

[0006] The aforementioned drive systems are typically operated and controlled by the crane operator using appropriate controls, such as joysticks, toggle switches, rotary knobs, and sliders. Experience has shown that this requires considerable skill and experience to approach the target points quickly yet smoothly without significant swinging of the load hook. While the goal is to travel as quickly as possible between target points to achieve high productivity, the crane should come to a smooth stop at each target point without the load hook and attached load swinging.

[0007] Controlling a crane's drive systems in this way is tiring for the crane operator, given the required concentration, especially since repetitive travel paths and monotonous tasks often need to be performed. Furthermore, waning concentration or insufficient experience with the specific crane type can lead to significant pendulum movements of the load, creating a corresponding risk if the operator does not handle the crane's controls with sufficient precision. In practice, even experienced crane operators sometimes experience rapid and significant pendulum swings of the load when controlling the crane, which then subside only very slowly.

[0008] To address the problem of unwanted pendulum movements, it has already been proposed to equip the crane's control device with pendulum damping devices that intervene in the control system via control modules and influence the actuation of the drive devices, for example, preventing or mitigating excessive acceleration of a drive device caused by too rapid or excessive forceful operation of the control lever, limiting certain travel speeds for larger loads, or actively intervening in the travel movements in a similar manner to prevent excessive pendulum swing of the load hook.

[0009] Such pendulum damping devices for cranes are known in various designs, for example, by controlling the slewing, luffing, and trolley drives depending on specific sensor signals, such as tilt and / or gyroscope signals. For example, documents DE 20 2008 018 260 U1 and DE 10 2009 032 270 A1 disclose known load pendulum damping devices for cranes, to which explicit reference is made insofar as the subject matter, i.e., the fundamentals of the pendulum damping device, is concerned. Furthermore, document DE 10 2016 004350 A1 discloses a tower crane according to the preamble of claim 1. In DE 20 2008 018 206 U1, for example, a gyroscope unit measures the rope angle relative to the vertical and its change in the form of the rope angular velocity in order to automatically intervene in the control system when a limit value for the rope angular velocity relative to the vertical is exceeded.

[0010] Furthermore, the documents EP16 28 902 B1, DE 103 24 692 A1, EP25 62 125 B1, US 2013 01 61 279 A, ​​DE100 64 182 A1, and US 55 26 946 B each present concepts for closed-loop control of cranes that take into account pendulum dynamics or pendulum and drive dynamics. However, the application of these known concepts to "soft," compliant cranes with elongated, stressed structures, such as a tower crane with structural dynamics, generally leads quite quickly to a dangerous, unstable oscillation of the excitable structural dynamics.

[0011] Such close-loop control systems for cranes, taking pendulum dynamics into account, have already been the subject of various scientific publications; see, for example, 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; as well as Arnold, E., Neupert, J., Sawodny, O., "Model-predictive trajectory generation for flatness-based tracking control using the example of a mobile harbor crane", at - Automatisierungstechnik, 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.coneng-prac.2009.08.003.

[0012] Furthermore, Liebherr is known for a load sway damping system for maritime cranes called "Cycoptronic," which calculates load movements and influences such as wind in advance and automatically initiates compensatory movements based on this calculation to prevent load oscillation. Specifically, this system also uses gyroscopes to detect the rope angle relative to the vertical and its changes, in order to intervene in the control system depending on the gyroscope signals.

[0013] From EP 2 436 637 A1, a device for determining the position of a load hook of a telescopic crane is known, in which translational accelerations and the inclination of the load hook relative to the vertical are determined at the load hook, wherein the device operates with two coordinate systems and determines the tilt of the two coordinate systems relative to each other. Further devices for determining the position of a load hook are known from CN 207 418 145 U, DE 10 2016 004350 A1, JP H08 143273 A and JP 2016 222363 A.

[0014] With long, slender crane structures and ambitious load-bearing capacities, as is particularly the case with tower cranes, but also relevant for other cranes with booms that can rotate around a vertical axis, such as luffing telescopic boom cranes, it is sometimes difficult to intervene in the drive control in the correct way to achieve the desired pendulum-damping effect using conventional pendulum damping devices. In this case, dynamic effects and elastic deformation of the structural components, especially the tower and boom, occur when a drive is accelerated or decelerated, so that interventions in the drive systems—for example, decelerating or accelerating the trolley drive or the slewing mechanism—do not directly affect the pendulum movement of the load hook in the desired way.

[0015] Firstly, dynamic effects within the structural components can cause time delays in the transmission of the signal to the hoist rope and load hook when drives are operated with pendulum damping. Secondly, these dynamic effects can also have excessive or even counterproductive effects on a load's pendulum motion. For example, if a load swings backward towards the tower due to initially excessively rapid activation of the trolley drive, and the pendulum damping device counteracts this by slowing the trolley drive, the boom may pitch as the tower deforms, thus impairing the desired pendulum damping effect.

[0016] Particularly with tower cranes, the lightweight construction also presents the problem that, unlike certain other crane types, the vibrations of the steel structure are not negligible, but should be addressed in a closed-loop control system for safety reasons, as otherwise a dangerous, unstable oscillation of the steel structure can usually occur.

[0017] The fundamental goal is therefore to detect the pendulum movements and actively counteract them through a control system. Such a system can serve as an assistance system, allowing the crane operator to directly control the load movement via the operating devices (instead of the bridge or trolley movement). This support can increase occupational safety and productivity. Furthermore, vibration damping is an important prerequisite for the full automation of bridge cranes.

[0018] A particular problem is that active vibration damping systems have not been cost-effective to retrofit or universally applicable. Many devices and methods for such vibration damping can be found in scientific publications and industrial products. However, research shows that The devices are usually either not retrofittable or only with considerable effort and expense; the control methods used are not universally applicable, but only in special cases (e.g., only loading bridges for container cranes).

[0019] Further disadvantages arise from the fact that Known vibration damping methods based on pendulum angle measurements are currently quite expensive; solutions that use special constructions to measure the rope movement just below the trolley reduce the possible lifting heights / lowering depths of the crane and are therefore often undesirable in practice, especially since they are often difficult to retrofit and usually only inadequately consider possible tilting movements of the hook.

[0020] Based on this, the present invention aims to create an improved crane and an improved method for controlling it, avoiding the disadvantages of the prior art and advantageously developing the latter further. Preferably, the goal is to move the payload according to the crane operator's setpoints and to actively dampen undesired pendulum movements via a control system, while simultaneously preventing undesired movements of the structural dynamics from being stimulated and also dampening them by the control system, in order to increase safety, ease of operation, and automation. In particular, improved pendulum damping is to be achieved in tower cranes, which better accounts for the manifold influences of the crane structure.

[0021] According to the invention, the aforementioned problem is solved by a crane according to claim 1 and a method according to claim 13. Preferred embodiments of the invention are the subject of the dependent claims.

[0022] It is therefore proposed to perform pendulum detection on the load hook and to equip the pendulum sensor on the load hook with an inertial detection device that is attached to the load hook or the load-bearing devices and provides acceleration and rotation rate signals that represent translational accelerations and rotation rates of the load hook.

[0023] Such an inertial measurement unit (IMU) mounted on the load-handling device can include acceleration and gyroscopic sensors to provide acceleration and gyroscopic signals. These signals represent translational accelerations along various spatial axes and gyroscopic rates or signals with respect to different spatial axes. The gyroscopic rates can be rotational velocities, but also, in principle, rotational accelerations, or both.

[0024] Advantageously, the inertial measurement device can detect accelerations in three spatial axes and rotation rates about at least two spatial axes. The accelerometers can be configured to operate in three axes, and the gyroscopes can be configured to operate in two axes.

[0025] The inertial measurement device attached to the load hook can advantageously transmit its acceleration and rotation rate signals and / or derived signals wirelessly to a control and / or evaluation unit, which can be attached to a structural part of the crane or located separately near the crane. In particular, the transmission can be to a receiver that may be attached to the trolley and / or the suspension from which the hoist rope runs. Advantageously, the transmission can be carried out, for example, via a WLAN connection.

[0026] Such a wireless connection of an inertial measuring device allows for the simple retrofitting of pendulum damping to existing cranes, without the need for complex retrofitting measures. Essentially, only the inertial measuring device needs to be attached to the load hook, along with the receiver that communicates with it and transmits the signals to the control unit.

[0027] The deflection of the load hook or the hoist rope relative to the vertical can advantageously be determined from the signals of the inertial measuring device in a two-stage process. First, the tilt of the load hook is determined. Since this does not necessarily correspond to the deflection of the load hook relative to the trolley or the suspension point and the deflection of the hoist rope relative to the vertical, the desired deflection of the load hook or the hoist rope relative to the vertical is then determined from the tilt of the load hook and its acceleration. Because the inertial measuring device is attached to the load hook, the acceleration and rotation 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.

[0028] In particular, three calculation steps can be used to accurately estimate the load oscillation angle, which can then be used by the controller for active oscillation damping. These three calculation steps can include, in particular, the following: i. Determining the hook tilt, e.g., using a complementary filter that can determine high-frequency components from the gyroscope signals and low-frequency components from the direction of the gravitational vector and combine them to determine the hook tilt; ii. Rotating the acceleration measurement or transforming it from a body-fixed to an inertial coordinate system; iii. Estimating the load pendulum angle using an extended Kalman filter and / or a simplified relationship between the pendulum angle and the quotient of the lateral acceleration measurement and the gravitational constant.

[0029] A model-based control system calculates a stabilizing feedback of this pendulum angle estimate to the control signals of the bridge or tower crane.

[0030] The resulting highly accurate pendulum angle estimation is fundamentally applicable to universal hook types (which may be susceptible to certain pendulum oscillations) and requires only a very cost-effective, retrofittable sensor system. At the same time, considerable advantages arise, such as increased safety, improved operability, increased throughput, and automation potential. Furthermore, the pendulum sensor system can be retrofitted cost-effectively.

[0031] Advantageously, the tilt of the load hook is first determined from the signals of the inertial measuring device using a complementary filter, which takes advantage of the different characteristics of the translational acceleration signals and the gyroscopic signals of the inertial measuring device, whereby alternatively or additionally a Kalman filter can also be used to determine the tilt of the load hook from the acceleration and rotation rate signals.

[0032] From the determined tilt of the load-bearing device, the desired deflection of the load hook relative to the trolley or relative to the suspension point of the hoist rope and / or the deflection of the hoist 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.

[0033] In particular, the pendulum sensor system can have first means of determining and / or estimating a tilting of the load-handling device from the acceleration and rotation rate signals of the inertial measuring device and second means of determining the deflection of the lifting rope and / or the load-handling device relative to the vertical from the determined tilting of the load-handling device and an inertial acceleration of the load-handling device.

[0034] The aforementioned first determination means can in particular comprise a complementary filter with a high-pass filter for the rotation rate signal of the inertial measuring device and a low-pass filter for the acceleration signal of the inertial measuring device or a signal derived therefrom, wherein the aforementioned complementary filter can be configured to combine a rotation rate-based estimate of the tilt of the load-handling device, which is based on the high-pass filtered rotation rate signal, and an acceleration-based estimate of the tilt of the load-handling device, which is based on the low-pass filtered acceleration signal, and to determine the desired tilt of the load-handling device from the combined rotation rate- and acceleration-based estimates of the tilt of the load-handling device.

[0035] The rotation rate-based estimation of the tilting of the load-bearing device can include an integration of the high-pass filtered rotation rate signal.

[0036] The acceleration-based estimation of the tilting of the load-bearing 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 tilt can be derived using the relationship ε β , a = arctan a x <none / > <mprescripts / > K <none / > a z <none / > <mprescripts / > K <none / > . is won.

[0037] The second means of determining the deflection of the load hook or the lifting rope relative to the vertical based on the determined tilt of the load hook can include a filter and / or observer device which takes the determined tilt of the load-handling device as its input variable and determines the deflection of the lifting rope and / or the load-handling device relative to the vertical from an inertial acceleration at the load-handling device.

[0038] The aforementioned filter and / or observer device may in particular include a Kalman filter, especially an extended Kalman filter.

[0039] Alternatively or in addition to such a Kalman filter, the second determining means can also include a calculation device for calculating the deflection of the lifting cable and / or the load-bearing 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.

[0040] The detection device for position sensing the load hook can advantageously also include an imaging sensor, for example, a camera, that looks essentially vertically downwards from the suspension point of the hoist rope, for example, the trolley. An image processing device can identify the crane hook in the image provided by the imaging sensor and determine its eccentricity, or its displacement from the image center, which is a measure of the crane hook's deflection relative to the vertical and thus characterizes the load swing. Alternatively or additionally, a gyroscopic sensor can detect the hoist rope's angle of deflection from the boom and / or relative to the vertical and feed this information to the Kalman filter.

[0041] To achieve improved pendulum damping, pendulum damping measures can consider not only the actual pendulum motion of the cable itself, but also the dynamics of the crane structure, specifically the steel construction and its drive trains. The crane is no longer treated as an immobile rigid body that directly and identically translates the drive movements of the drive units into movements of the hoist cable's suspension point (1:1). Instead, the pendulum damping system views the crane as a flexible structure whose steel components, such as the tower lattice and boom, and its drive trains exhibit elasticity and compliance under acceleration. This dynamic behavior of the crane's structural components is then taken into account when influencing the control of the drive units to reduce pendulum damping.

[0042] A closed-loop control system actively dampens both the pendulum dynamics and the structural dynamics. Specifically, the entire system dynamics, including the coupling of the pendulum, drive, and structural dynamics of the tower crane, are actively controlled to move the payload according to the target specifications. Sensors are used to measure system parameters related to the pendulum dynamics as well as those related to the structural dynamics. Non-measurable system parameters can be estimated as system states by a model-based observer. The control signals for the drives are calculated by a model-based control system as feedback of the system states, thus closing the control loop and resulting in a modified system dynamics. The control system is designed to ensure stable system dynamics within the closed loop and to quickly compensate for control errors.

[0043] Advantageously, a closed control loop is provided on the crane, particularly a tower or bridge crane, with structural dynamics through the feedback of measurements not only of the pendulum dynamics but also of the structural dynamics. In addition to pendulum sensors for detecting hoist rope and / or load-handling device movements, the pendulum damping device also includes structural dynamics sensors for detecting dynamic deformations and movements of the crane structure or at least structural components thereof. The controller module of the pendulum damping device, which influences the control of the drive unit in a pendulum-damping manner, is designed to take into account both the pendulum movements detected by the pendulum sensors and the dynamic deformations of the crane's structural components detected by the structural dynamics sensors when influencing the control of the drive units.Both the pendulum sensor signals and the structural dynamics sensor signals are fed back into the closed control loop.

[0044] The pendulum damping device therefore does not consider the crane or machine structure as a rigid, so to speak infinitely stiff structure, but assumes an elastically deformable and / or compliant and / or relatively soft structure which - in addition to the positioning axes of the machine such as the outrigger rib axis or the tower rotation axis - allows movements and / or changes in position through deformations of the structural components.

[0045] Considering the internal movement of the machine structure due to structural deformations under load or dynamic stresses is particularly important for elongated, slender structures, such as tower cranes or telescopic cranes, where static and dynamic boundary conditions are deliberately pushed to their limits – while taking necessary safety margins into account. This is because noticeable movement, for example of the boom and thus the load hook position, results from the deformations of the structural components. To better combat the causes of pendulum motion, pendulum damping takes such deformations and movements of the machine structure under dynamic loads into account.

[0046] This can achieve considerable advantages: First, the vibration dynamics of the structural components are reduced by the control behavior of the control unit. The driving behavior actively dampens the vibration, or the control behavior prevents it from being excited in the first place.

[0047] The steel structure is also protected and subjected to less stress. In particular, impact loads are reduced by the control behavior.

[0048] Furthermore, this method can be used to define the influence of driving behavior.

[0049] Knowledge of structural dynamics and the control method allows for the reduction and damping of pitching oscillations. This results in smoother load behavior, preventing oscillations in the rest position. Lateral pendulum movements around the vertical boom axis can also be better controlled by considering tower torsion and boom flexure deformations.

[0050] The aforementioned elastic deformations and movements of the structural components and drive trains, and the resulting intrinsic movements, can fundamentally be determined in various ways.

[0051] In particular, the structural dynamics sensors provided for this purpose can be designed to detect elastic deformations and movements of structural components under dynamic loads.

[0052] Such structural dynamics sensors can include, for example, deformation sensors such as strain gauges on the steel structure of the crane, for example the lattice trusses of the tower and / or the boom.

[0053] Alternatively or additionally, rotation rate sensors, in particular in the form of gyroscopes, gyrosensors and / or gyrometers, and / or acceleration and / or velocity sensors may be provided 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 torsional and / or bending movements of the tower.

[0054] Furthermore, tilt sensors may be provided to detect inclinations of the boom and / or inclinations of the tower, in particular deflections of the boom from the horizontal and / or deflections of the tower from the vertical.

[0055] In principle, structural dynamics sensors can operate with various sensor types, and in particular, they can combine different sensor types. Advantageously, strain gauges and / or acceleration sensors and / or angular rate sensors, especially in the form of gyroscopes, gyrosensors 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 angular rate sensors preferably being designed to detect three axes.

[0056] Such structural dynamic sensors can be provided on the boom and / or on the tower, particularly on its upper section where the boom is mounted, to detect the tower's dynamics. For example, jerky lifting movements cause pitching movements of the boom, which are accompanied by bending movements of the tower, with subsequent tower oscillations in turn leading to pitching oscillations of the boom, which are accompanied by corresponding load hook movements.

[0057] In particular, angle sensors can be provided to determine the differential rotation angle between an upper tower section and the boom. For example, an angle sensor can be mounted on both the upper tower section and the boom, and their signals, when compared, can indicate the aforementioned differential rotation angle. Furthermore, a rotation rate sensor can advantageously be provided to determine the rotational speed of the boom and / or the upper tower section in order to determine the influence of tower torsion in conjunction with the aforementioned differential rotation angle. This allows for both a more accurate estimate of the load position and active damping of tower torsion during operation.

[0058] In an advantageous further development of the invention, two- or three-axis gyroscopes and / or accelerometers can be attached to the boom tip and / or to the boom in the area of ​​the upright crane axis of rotation in order to determine structural dynamic movements of the boom.

[0059] Alternatively or additionally, motion and / or acceleration sensors can be assigned to the drive trains to capture their dynamics. For example, rotary encoders can be assigned to the trolley's pulleys for the hoist rope and / or pulleys for a guy rope of a luffing jib to capture the actual rope speed at the relevant point.

[0060] Advantageously, suitable motion 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 be able to relate them to the estimated and / or recorded deformations of the structural components or the steel structure and compliances in the drive trains.

[0061] In particular, by comparing the signals from the motion and / or acceleration sensors directly assigned to the drive units 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. This component is attributable to a dynamic deformation or twisting of the crane structure and is in addition to the actual crane movement induced by the drive movement, which would also occur in a completely rigid crane. For example, if the slewing mechanism of a tower crane is adjusted by 10°, but only a rotation of 9° is detected at the jib tip, a torsion of the tower and / or a bending deformation of the jib can be inferred. This can then be compared with, for example, the rotation signal of a gyroscope mounted at the tower tip to differentiate between tower torsion and jib bending.If the load hook is lifted by one meter by the hoist, but at the same time a downward pitching movement of, for example, 1° is detected on the boom, the actual load hook movement can be deduced by taking into account the reach of the trolley.

[0062] Advantageously, the structural dynamics sensor system can detect various directions of structural deformation. In particular, the structural dynamics sensor system can include 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 slewing dynamics sensor for detecting dynamic movements of the crane structure around an upright crane axis of rotation, especially the tower axis. The control module of the pendulum damping device can be configured to influence the control of the drive devices, especially a trolley drive and slewing drive, depending on the detected dynamic movements of the crane structure in the upright, boom-parallel plane, especially parallel to the boom's longitudinal direction, and the detected dynamic movements of the crane structure around the upright crane axis of rotation.

[0063] Furthermore, the structural dynamics sensor system can include at least one lifting dynamics sensor for detecting vertical dynamic deformations of the crane boom, and the control module of the pendulum damping device can be designed to influence the control of the drive devices, in particular a hoist drive, depending on the detected vertical dynamic deformations of the crane boom.

[0064] Advantageously, the structural dynamics sensor system is designed to detect all natural modes of the dynamic twists of the crane boom and / or the crane tower whose natural frequencies lie within a predetermined frequency range. For this purpose, the structural dynamics sensor system can comprise at least one, preferably several, tower sensor(s) spaced apart from a node of a tower natural frequency for detecting tower twists, as well as at least one, preferably several, boom sensor(s) spaced apart from a node of a boom natural frequency for detecting boom twists.

[0065] In particular, multiple sensors for detecting structural movement can be positioned to ensure the observation of all eigenmodes whose natural frequencies lie within the relevant frequency range. While one sensor per pendulum motion direction may suffice in principle, the use of multiple sensors is recommended in practice. For example, placing a single sensor at a node of the measured variable of a structural eigenmode (e.g., the trolley's position at a rotation node of the first boom eigenmode) leads to a loss of observability, which can be avoided by adding a sensor at a different position. The use of three-axis gyroscopes or accelerometers at the boom tip and on the boom near the slewing mechanism is particularly recommended.

[0066] Structural dynamics sensors can, in principle, operate with various sensor types to detect eigenmodes, and in particular, they can also combine different sensor types. Advantageously, the aforementioned strain gauges and / or acceleration sensors and / or gyroscopes, especially in the form of gyroscopes, gyrosensors and / or gyrometers, can be used to detect the deformations and / or dynamic internal movements of structural components of the crane, wherein the acceleration sensors and / or gyroscopes are preferably designed to detect in three axes.

[0067] In particular, the structural dynamics sensor system can include at least one angular rate and / or acceleration sensor and / or strain gauge for detecting dynamic tower deformations and at least one angular rate and / or acceleration sensor and / or strain gauge for detecting dynamic boom deformations. Advantageously, angular rate and / or acceleration sensors can be provided on various tower sections, in particular at least at the tower top and at the boom pivot point, and optionally in a tower midsection below the boom. Alternatively or additionally, angular rate and / or acceleration sensors can be provided on various sections of the boom, in particular at least at the boom tip and / or the trolley and / or the boom base where the boom is pivoted, and / or on a boom section at the hoist.Advantageously, the sensors mentioned are arranged on the respective structural component in such a way that they can detect the eigenmodes of its elastic twisting.

[0068] In a further development of the invention, the pendulum damping device can also include an estimating device that estimates deformations and movements of the machine structure under dynamic loads, which result from control commands input at the control station and / or from specific actuation actions of the drive devices and / or from specific speed and / or acceleration profiles of the drive devices, taking into account conditions characterizing the crane structure. In particular, such an estimating device can be used to estimate system parameters of the structural dynamics, and optionally also of the pendulum dynamics, which cannot be detected or can only be detected with difficulty by sensors.

[0069] Such an estimating device can, for example, access a data model in which structural parameters of the crane, such as tower height, boom length, stiffnesses, area moments of inertia, and similar data, are stored and / or linked together. Based on a specific load situation—that is, the weight of the load on the hook and the current reach—it can then estimate the dynamic effects, i.e., deformations in the steel structure and drive trains, that will result from a particular actuation of a drive unit. Depending on this estimated dynamic effect, the pendulum damping device can then intervene in the control of the drive units and influence the actuators of the drive units to prevent or reduce pendulum movements of the load hook and the hoist rope.

[0070] In particular, the device for determining such structural deformations can include a calculation unit that calculates these structural deformations and the resulting structural component movements based on a stored calculation model, depending on the control commands entered at the control station. Such a model can be structured similarly to a finite element model or be a finite element model itself, but advantageously a significantly simplified model compared to a finite element model is used, which can be determined empirically, for example, by recording structural deformations under specific control commands and / or load conditions on the actual crane or machine.Such a calculation model can, for example, work with tables in which specific deformations are assigned to specific control commands, whereby intermediate values ​​of the control commands can be converted into corresponding deformations using an interpolation device.

[0071] According to a further advantageous aspect of the invention, the controller module in the closed control loop can comprise a filter device or an observer which, on the one hand, observes the structural dynamic crane reactions and the lifting rope or load hook pendulum movements as they are detected by the structural dynamic sensors and the pendulum sensors and which adjust to certain control 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 can be obtained through analysis and simulation of the steel structure, can influence the control variables of the controller based on the observed crane structural and pendulum reactions.

[0072] Such a filter or observer device can be designed in particular in the form of a so-called Kalman filter, to which, as input variables, on the one hand, the control variables of the crane's drive controllers and, on the other hand, both the pendulum signals of the pendulum sensors and the structural dynamic signals fed back to the control loop, which indicate deformations and / or dynamic inward movements of the structural components, and which, based on Kalman equations that model the dynamic system of the crane structure, in particular its steel components and drive trains, influences the control variables of the drive controllers accordingly in order to achieve the desired pendulum damping effect.

[0073] The Kalman filter advantageously implements captured and / or estimated and / or calculated and / or simulated functions that characterize the dynamics of the crane's structural components.

[0074] In particular, dynamic boom and tower deformations detected by means of the structural dynamics sensors, as well as the position of the load hook detected by means of the pendulum sensors, especially its oblique pull relative to the vertical, i.e. the deflection of the hoist rope relative to the vertical, are fed to the aforementioned Kalman filter.

[0075] According to a further advantageous aspect of the invention, a two-degrees-of-freedom control structure is used in the pendulum damping, which supplements the state feedback described above with a feedforward control. The state feedback serves to ensure stability and to quickly compensate for control errors, while the feedforward control ensures good control behavior, ideally preventing any control errors altogether.

[0076] The feedforward control can advantageously be determined using the known method of differential flatness. Regarding the aforementioned method of differential flatness, reference is made to the dissertation "Application of flatness-based analysis and control of nonlinear multivariable systems" by Ralf Rothfuß, VDI-Verlag, 1997, which, insofar as it relates to the aforementioned method of differential flatness, is incorporated into the present disclosure.

[0077] Since the deflections of the structural movements are small in contrast to the driven crane movements and the pendulum movements, the structural dynamics can be neglected to determine the feedforward control, which means that the crane, especially a tower crane, can be represented as a flat system with the load coordinates as flat outputs.

[0078] Advantageously, the feedforward control and the calculation of the reference states of the two-degrees-of-freedom structure are calculated, in contrast to the feedback control of the closed-loop system, neglecting the structural dynamics. This means that for feedforward control purposes, the crane is assumed to be a rigid, or virtually infinitely stiff, structure. Due to the small deflections of the elastic structure, which are very small compared to the crane movements to be executed by the drives, this results in only very small and therefore negligible deviations in the feedforward control. However, this allows the tower crane—assumed to be rigid for feedforward control purposes—to be described as a flat system that is easily invertible. The coordinates of the load position are flat outputs of the system.From the flat outputs and their time derivatives, the required target response 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 moved to a target position without overshoot.

[0079] The load position and its derivatives required for flatness-based feedforward control can advantageously be calculated by a trajectory planning module and / or by setpoint filtering. If a target profile for the load position and its first four time derivatives is determined via trajectory planning or setpoint filtering, the exact profile of the necessary control signals for driving the actuators, as well as the exact profile of the corresponding system states, can be calculated in the feedforward control using algebraic equations.

[0080] To avoid exciting structural movements through feedforward control, notch filters can advantageously be placed between trajectory planning and feedforward control to eliminate the excitable natural frequencies of the structural dynamics from the planned trajectory signal.

[0081] The underlying control model can be fundamentally different. Advantageously, a compact representation of the entire system dynamics is used as coupled pendulum, drive, and structural dynamics, which is suitable as a basis for the observer and the control system. In an advantageous further development of the invention, the crane control model is determined by a modeling method in which the entire crane dynamics are separated into largely independent parts, advantageously for a tower crane into a part of all movements that are essentially excited by a slewing 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 are excited by a winch drive.

[0082] The independent consideration of these parts, neglecting the couplings, allows for a calculation of the system dynamics in real time and, in particular, simplifies the compact representation of the swivel dynamics as a distributed parameter system (described by a linear partial differential equation) that accurately describes the structural dynamics of the boom and can be easily reduced to the required number of eigenmodes using known methods.

[0083] The drive dynamics are advantageously modeled as a first-order delay element or as a static gain factor, whereby a torque, rotational speed, force, or velocity can be specified as the control variable for the drives. This control variable is regulated by the underlying control system in the frequency converter of the respective drive.

[0084] The pendulum dynamics can be modeled as an idealized simple / double pendulum with one / two point mass loads and one / two simple ropes, which are either assumed to be massless or massed with modal order reduction to the most important rope eigenmodes.

[0085] The structural dynamics can be derived by approximating the steel structure in the form of continuous beams as a distributed-parameter model, which can be discretized and reduced in system order using known methods, thus taking on a compact form, allowing it to be calculated quickly and simplifying observer and control design.

[0086] The aforementioned pendulum damping device can monitor the crane operator's input commands when the crane is operated manually via appropriate controls such as joysticks and the like, and override them if necessary. This is particularly important in that it reduces excessively high accelerations set by the crane operator or automatically initiates counter-movements if a crane movement initiated by the operator has caused, or would cause, the load hook to oscillate. The control module advantageously attempts to remain as close as possible to the movements and motion profiles desired by the crane operator, thus providing the operator with a sense of control. It overrides the manually entered control signals only to the extent necessary to execute the desired crane movement with minimal pendulum and vibration.

[0087] Alternatively or additionally, the pendulum damping device can also be used in automated crane operation, where the crane's control system, acting as an autopilot, automatically moves the crane's load-handling device between at least two target points along a travel path. In such automated operation, where a travel path determination module of the control system defines a desired travel path, for example, in the sense of path control, and an automatic travel control module of the control system controls the drive controllers or drive units so that the load hook is moved along the defined travel path, the pendulum damping device can intervene in the control of the drive controllers by the aforementioned travel control module to move the crane hook without pendulum motion or to dampen pendulum movements.

[0088] The invention is explained in more detail below with reference to a preferred embodiment and the accompanying drawings. The drawings show: Fig. 1: A schematic representation of a tower crane in which the load hook position and a rope angle relative to the vertical are detected by an imaging sensor, and in which a pendulum damping device influences the control of the drive devices to prevent pendulum movements of the load hook and its hoist rope. Fig. 2: A schematic representation of a two-degrees-of-freedom control structure of the pendulum damping device and its influence on the control variables of the drive controllers. Fig. 3: A schematic representation of deformations and vibration modes of a tower crane under load and their damping or prevention by a skew control, wherein partial view a.) shows a pitching deformation of the tower crane under load and an associated skew of the hoist rope, partial views b.) and c.) show...) a transverse deformation of the tower crane in perspective view and in top view, and partial views d.) and e.) show an oblique pull of the hoist rope associated with such transverse deformations, Fig. 4: a schematic representation of an elastic boom in a reference system rotating with the rotation rate, Fig. 5: a schematic representation of a boom as a continuous beam with clamping in the tower taking into account tower bending and tower torsion, Fig. 6: a schematic representation of an elastic tower and a spring-mass equivalent model of the tower bending transverse to the boom, Fig. 7: a schematic representation of the pendulum dynamics in the slewing direction of the crane with concentrated load mass and massless rope, Fig. 8: a schematic representation of the three main modes of motion of a tower crane, Fig.Fig. 9: A schematic representation of the pendulum dynamics in the radial direction of the crane and its modeling using several coupled rigid bodies; Fig. 10: A schematic representation of a pendulum hoist rope with a load hook to which an inertial measuring device is attached, which wirelessly transmits its measurement signals to a receiver on the trolley from which the hoist rope runs; Fig. 11: A schematic representation of various load hooks to illustrate the possible tilting of the load hook relative to the hoist rope; Fig. 12: A schematic two-dimensional model of the pendulum dynamics of the load hook suspension from the two preceding figures; Fig. 13: A representation of the tilting or tilt angle of the load hook, which describes the rotation between inertial and load hook coordinates.Fig. 14: a block diagram of a complementary filter with high-pass and low-pass filters for determining the tilt of the load hook from the acceleration and rotation rate signals of the inertial measuring device; Fig. 15: a comparative representation of the pendulum angle profiles determined by means of an extended Kaman filter and by means of static estimation in comparison to the pendulum angle profile measured at a cardan joint; and Fig. 16: a schematic representation of a control structure with two degrees of freedom for automatically influencing the drives in order to prevent pendulum oscillations.

[0089] How Fig. 1 As shown, the crane can be designed as a tower crane. The one in Fig. 1 The tower crane shown can, for example, have a tower 201 in a manner known per se, which supports a jib 202 balanced by a counter jib 203 on which a counterweight 204 is provided. The jib 202, together with the counter jib 203, can be rotated about an upright pivot axis 205, which may be coaxial with the tower axis, by means of a slewing mechanism. A trolley 206 can be moved along the jib 202 by means of a trolley drive, with a hoist rope 207 extending from the trolley 206, to which a load hook 208 is attached.

[0090] How Fig. 10 Furthermore, it shows that the crane can also be designed as a bridge crane.

[0091] How Fig. 1 As also shown, the crane 2 – naturally also when configured as a bridge crane or other type of crane – can have an electronic control device 3, which may, for example, include a control computer located on the crane itself. This control device 3 can control various actuators, hydraulic circuits, electric motors, drive devices, and other working units on the respective construction machine. These could include, for example, the hoist, slewing mechanism, trolley drive, and – if present – ​​boom luffing drive of the crane shown, or similar components.

[0092] The aforementioned electronic control device 3 can communicate with an end device 4, which can be located at the control station or in the driver's cab and can, for example, take the form of a tablet with touchscreen and / or joysticks, rotary knobs, slide switches and similar operating elements, so that on the one hand various information from the control computer 3 can be displayed on the end device 4 and, conversely, control commands can be entered into the control device 3 via the end device 4.

[0093] The aforementioned control device 3 of the crane 1 can in particular be designed to control the aforementioned drive devices of the hoist, trolley and slewing mechanism even when a pendulum damping device 340 detects pendulum-relevant motion parameters.

[0094] For this purpose, the crane 1 can have a pendulum sensor or detection device 60 that detects an oblique pull of the hoist rope 207 and / or deflections of the load hook 208 relative to a vertical 61 passing through the suspension point of the load hook 208, i.e., the trolley 206. In particular, the rope pull angle φ relative to the line of action of gravity, i.e., the vertical 62, can be detected, cf. Fig. 1 .

[0095] For this purpose, the pendulum sensor 60 can be equipped with a camera 63 or other imaging sensor on the trolley 206, which looks vertically downwards from the trolley 206, so that when the load hook 208 is not deflected, its image is located 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 by a jerky start of the trolley 206 or abrupt braking of the slewing mechanism, the image of the load hook 208 moves out of the center of the camera image, which can be determined by an image evaluation device 64.

[0096] On the other hand, the inclined pull of the lifting rope or the deflection of the load hook relative to the vertical is also achieved using an inertial measuring device (IMU) which is attached to the load hook 208 and can preferably transmit its measurement signals wirelessly to a receiver on the trolley 206, cf. Fig. 10 The inertial measurement unit (IMU) and the evaluation of its acceleration and rotation rate signals will be explained in more detail later.

[0097] Depending on the detected deflection relative to the vertical 61, in particular taking into account the direction and magnitude of the deflection, the control device 3 can use the pendulum damping device 340 to control the slewing drive and the trolley drive in order to bring the trolley 206 more or less exactly over the load hook 208 again and to compensate for pendulum movements, or to reduce them or prevent them from occurring in the first place.

[0098] For this purpose, the pendulum damping device 340 includes a structural dynamics sensor 344 for determining dynamic deformations of structural components, wherein the controller module 341 of the pendulum damping device 340, which influences the control of the drive device in a pendulum damping manner, is designed to take into account the determined dynamic deformations of the structural components of the crane when influencing the control of the drive devices.

[0099] This may also include an estimation device 343, which estimates the deformations and movements of the machine structure under dynamic loads that result from control commands entered at the control station and / or from specific control actions of the drive devices and / or from specific speed and / or acceleration profiles of the drive devices, taking into account the characteristics of the crane structure. In particular, a calculation unit 348 can calculate the structural deformations and the resulting structural component movements based on a stored calculation model, depending on the control commands entered at the control station.

[0100] Advantageously, the pendulum damping device 340 uses structural dynamics sensors 344 to detect such elastic deformations and movements of structural components under dynamic loads. Such sensors 344 can, for example, include deformation sensors such as strain gauges on the steel structure of the crane, such as the lattice trusses of the tower 201 or the boom 202. Alternatively or additionally, acceleration and / or velocity sensors and / or yaw rate sensors can be provided to detect certain movements of structural components, such as pitching movements of the boom tip or rotational dynamic effects on the boom 202. Alternatively or additionally, such structural dynamics sensors can also be provided on the tower 201, in particular on its upper section where the boom is mounted, to detect the dynamics of the tower 201.Alternatively or additionally, motion and / or acceleration sensors can be assigned to the drive trains to capture their dynamics. For example, rotary encoders can be assigned to the pulleys of trolley 206 for the hoist rope and / or pulleys for a guy rope of a luffing jib to capture the actual rope speed at the relevant point.

[0101] How Fig. 2 To clarify, the signals y(t) from the structural dynamics sensors 344 and the pendulum sensors 60 are fed back to the controller module 341, thus realizing a closed control loop. The controller module 341 influences the control signals u(t) for controlling the crane drives, in particular the slewing mechanism, the hoist, and the trolley drive, depending on the fed-back structural dynamics and pendulum sensor signals.

[0102] How Fig. 2 As shown, the controller structure also has a filter device or an observer 345, which observes the feedback sensor signals or the crane reactions that occur at certain control variables of the drive controller and, taking into account predetermined laws of a dynamic model of the crane, which can be fundamentally different and can be obtained through analysis and simulation of the steel structure, influences the control variables of the controller based on the observed crane reactions.

[0103] Such a filter or observer device 345b can in particular be designed in the form of a so-called Kalman filter 346, to which as input variables the manipulated variables u (t) of the drive controllers 347 of the crane and the feedback sensor signals y (t), i.e. the detected crane movements, in particular the rope pull angle φ relative to the vertical 62 and / or its change over time or the angular velocity of the said inclined pull, as well as the structural dynamic twists of the boom 202 and the tower 201, are supplied and which, based on these input variables and on the basis of 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 347 accordingly in order to achieve the desired pendulum damping effect.

[0104] With the help of such a closed-loop control system, deformations and vibration patterns of the tower crane under load can be dampened or avoided from the outset, as are found in Fig. 3 are shown as examples, where the partial view a.) initially schematically shows a pitching deformation of the tower crane under load as a result of a bending of the tower 201 with the associated lowering of the boom 202 and a related diagonal pull of the hoist rope.

[0105] Furthermore, partial views b.) and c.) show the Fig. 3 An exemplary schematic representation shows a transverse deformation of the tower crane in perspective and in top view, showing the resulting deformations of the tower 201 and the boom 202.

[0106] Finally, the Fig. 3 in their partial views d.) and e.) a skewed pull of the lifting cable associated with such transverse deformations.

[0107] How Fig. 2 Furthermore, the controller structure is designed in the form of a two-degrees-of-freedom control and includes, in addition to the aforementioned "closed-loop" control with feedback of the pendulum sensor and structural dynamics sensor signals, a feed-forward control stage 350, which, through the best possible guidance behavior, tries to prevent any control errors from occurring in the first place.

[0108] The aforementioned feedforward control 350 is advantageously designed to be flatness-based and determined according to the so-called differential flatness method, as already mentioned at the beginning.

[0109] Since the deflections of the structural movements and also the pendulum movements are very small compared to the driven crane movements, which represent the target travel distance, the structural dynamics signals and pendulum movement signals are neglected for the determination of the feedforward signals ud (t) and xd (t), i.e. the signals y (t) of the pendulum and structural dynamics sensors 60 and 344 respectively are not fed back to the feedforward module 350.

[0110] How Fig. 2 As shown, the pre-control module 350 setpoint values ​​for the load handling device 208 are supplied, whereby these setpoint values ​​can be position information and / or speed information and / or path parameters for the aforementioned load handling device 208 and define the desired travel movement.

[0111] In particular, the setpoints for the desired load position and their time derivatives can advantageously be supplied to a trajectory planning module 351 and / or a setpoint filter 352, by means of which a target profile for the load position and its first four time derivatives can be determined, from which the exact profile of the necessary control signals ud (t) for controlling the drives as well as the exact profile ud (t) of the corresponding system states can be calculated in the feedforward control module 350 using algebraic equations.

[0112] To prevent the feedforward control from exciting structural movements, a notch filter device 353 can advantageously be connected upstream of the feedforward module 350 to filter the input variables supplied to the feedforward module 350 accordingly. Such a notch filter device 353 can be provided, in particular, between the aforementioned trajectory planning module 351 or the setpoint filter module 352 on the one hand and the feedforward module 350 on the other. The aforementioned notch filter device 353 can be configured, in particular, to eliminate the excited natural frequencies of the structural dynamics from the setpoint signals supplied to the feedforward control.

[0113] In order to reduce vibration dynamics or prevent them from arising in the first place, the pendulum damping device 340 can be designed to correct the slewing mechanism and the trolley drive and, if necessary, also the hoisting mechanism so that the rope is always perpendicular to the load, even if the crane tilts forward more and more due to the increasing load moment.

[0114] For example, when lifting a load from the ground, the crane's pitching motion due to its deformation under the load can be taken into account. The trolley can then be moved along the track, taking into account the detected load position, or positioned by anticipating the pitching deformation, so that the hoist cable remains vertically above the load during the resulting crane deformation. The greatest static deformation occurs at the point where the load leaves the ground. Similarly, or alternatively, the slewing mechanism can also be moved along the track, taking into account the detected load position, and / or positioned by anticipating lateral deformation, so that the hoist cable remains vertically above the load during the resulting crane deformation.

[0115] The model underlying the pendulum damping control can fundamentally be of a different nature.

[0116] For the control-oriented mechanical modeling of elastic slewing cranes, a decoupled consideration of the dynamics in the slewing direction and within the tower-jib plane is useful. The slewing dynamics are excited and controlled by the slewing drive, while the dynamics in the tower-jib plane are excited and controlled by the trolley and hoist drives. The load oscillates in two directions – firstly, perpendicular to the jib (slewing direction), and secondly, longitudinally along the jib (radially). Due to the low elasticity of the hoist rope, the vertical load movement largely corresponds to the vertical jib movement, which is small in tower cranes compared to the load deflections caused by the oscillation.

[0117] To stabilize the load's pendulum motion, the system dynamics generated by the slewing mechanism and the trolley must be considered. These are referred to as slewing and radial dynamics, respectively. As long as the pendulum angles are not zero, both slewing and radial dynamics can be additionally influenced by the hoist. However, this is negligible for control system design, especially for the slewing dynamics.

[0118] The slewing dynamics encompass, in particular, steel structure movements such as tower torsion, boom lateral bending around the vertical axis, and tower bending perpendicular to the boom's longitudinal direction, as well as pendulum dynamics perpendicular to the boom and the slewing drive dynamics. Radial dynamics include tower bending in the boom direction, pendulum dynamics in the boom direction, and, depending on the perspective, also boom bending in the vertical direction. Furthermore, the drive dynamics of the trolley and, if applicable, the hoist are also considered part of the radial dynamics.

[0119] For the control system, a linear design method is advantageously pursued, based on the linearization of the nonlinear mechanical model equations around a rest position. Such linearization eliminates all couplings between yaw and radial dynamics. This also means that no couplings need to be considered in the design of a linear control system, even if the model was initially derived in a coupled manner. Both directions can be considered decoupled from the outset, as this significantly simplifies the mechanical modeling. Furthermore, this approach yields a clear and compact model for the yaw dynamics, which can be evaluated quickly, thus saving computing power and accelerating the development process of the control system design.

[0120] To derive the slewing dynamics as a compact, clear, and accurate dynamic system model, the boom can be considered as an Euler-Bernoulli beam and thus initially as a system with distributed mass (distributed-parameter system). Furthermore, the feedback effect of the lifting dynamics on the slewing dynamics can be neglected, which is a justified assumption for small pendulum angles due to the negligible horizontal force component. When large pendulum angles occur, the effect of the winch on the slewing dynamics can be included as a disturbance variable.

[0121] The boom is modeled as a beam in a moving reference system, which is rotated at a rate determined by the slewing drive. γ̇ rotates, as in Fig. 4 shown.

[0122] This results in three apparent accelerations within the reference frame, known as Coriolis, centrifugal, and Euler accelerations. Since the reference frame rotates around a fixed point, the following results for each point: r ′ = r x ′ r y ′ r z ′ within the reference system, the apparent acceleration a' to a ′ = 2 ω × ν ′ ︸ Coriolis − ω ˙ × r ′ ︸ Euler − ω × ω × r ′ ︸ Zentrifugal , where × represents the cross product, ω = 0 0 γ ˙ T the rotation vector and v' the velocity vector of the point relative to the rotating reference system.

[0123] Of the three apparent accelerations, only the Coriolis acceleration represents a bidirectional coupling between slewing and radial dynamics. This is proportional to the rotational speed of the reference system as well as to the relative speed. Typical maximum rotational rates of a tower crane are in the range of approximately... γ MAX ≈ 0.1 rad s This is why the Coriolis acceleration typically assumes small values ​​compared to the driven accelerations of the tower crane. During stabilization of the load's pendulum motion at a fixed position, the rotation rate is very small; during large guiding movements, the Coriolis acceleration can be pre-planned and explicitly taken into account using feedforward control. In both cases, neglecting the Coriolis acceleration therefore leads only to minor approximation errors, which is why it is neglected in the following.

[0124] Centrifugal acceleration, depending on the rotation rate, only affects radial dynamics and can be considered as a disturbance variable for this purpose. Due to the slow rotation rates, it has little effect on swivel dynamics and can therefore be neglected. However, the linear Euler acceleration, which acts in the tangential direction, is important and therefore plays a central role in the analysis of swivel dynamics.

[0125] Due to the small cross-sectional area of ​​the cantilever and the small shear deformations, the cantilever can be considered an Euler-Bernoulli beam. This neglects the rotational kinetic energy of the beam's rotation about the vertical axis. 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.

[0126] The guy wires between the A-frame and the boom have virtually no effect on the slewing dynamics and are therefore not modeled. Longitudinal deformations of the boom are also so small that they can be neglected. Thus, the undamped dynamics of the boom in the rotating reference frame can be described using the well-known partial differential equation. μ x w ¨ x t + EI x w " x t = q ˜ x t for the boom deflection w(x,t) at that point x currently t specify. This includes µ ( x ) the mass coating, I ( x ) the area moment of inertia at that point x, E the modulus of elasticity and q̃ ( x,t ) the distributed force acting on the boom. The zero point of the position coordinate. x This derivation is based on the end of the counter-argument. The notation ⋅ ′ = ∂ ⋅ ∂ x This describes the local differentiation. Damping parameters will be introduced later.

[0127] To obtain a description of the cantilever dynamics in the inertial frame of reference, the Euler force is isolated from the distributed force, which leads to the partial differential equation μ x x − l cj γ ¨ + μ x w ¨ x t + E I x w " x t " = q x t leads to this. l cj the length of the counter boom and q ( x, t ) the actual distributed force on the cantilever without the Euler force. Both beam ends are free and not clamped. Therefore, the boundary conditions apply. w " 0 t = 0 , w " L t = 0 w ‴ 0 t = 0 w ‴ L t = 0 with the total length L of boom and counter boom.

[0128] A sketch of the boom is in Fig. 5 The spring stiffnesses are shown. c t and c b represent the torsional stiffness or bending stiffness of the tower and are explained below.

[0129] For modeling the slewing dynamics, it is advantageous to consider tower torsion and tower bending perpendicular to the boom direction. Due to its geometry, the tower can initially be assumed to be a homogeneous Euler-Bernoulli beam. For the sake of simpler modeling, the tower is represented at this point by a rigid body substitute model. Only one eigenmode for tower bending and one for tower torsion are considered. Since essentially only the movement at the tower top is relevant for the slewing dynamics, the tower dynamics can be represented by a spring-mass system with a matching natural frequency as a substitute system for bending and torsion, respectively. In the case of higher tower elasticity, the spring-mass systems can be more easily extended to include further eigenmodes at this point by adding a corresponding number of masses and springs (see [reference]). Fig. 6 .

[0130] The parameters spring stiffness cb and mass m T are chosen such that the deflection at the top and the natural frequency coincide with that of the Euler-Bernoulli beam, which represents the tower dynamics. The constant area moment of inertia for the tower is... I T , the tower height l T and the mass coating µ T If the parameters are known, they can be determined from the static deflection at the beam end. y 0 = Fl T 3 3 EI T and the first natural frequency ω 1 = 12.362 EI T μ T l T 4 analytically to a homogeneous Euler-Bernoulli beam c b = F y 0 = 3 EI T l T 3 , m T = c b ω 1 2 = 3 μ T l T 12.362 . calculate.

[0131] For tower torsion, an analogous rigid body substitute model can be used with inertia. J T and the torsional spring stiffness c t derive as in Abb. 5 shown.

[0132] Are the polar area moment of inertia for the tower I p , moment of inertia J T (which corresponds to the polar area moment of inertia for circular ring cross-sections), the mass density ρ and the thrust module G If the parameters of the replacement model are known, they can be determined. c t = GJ T , T l T , J T = 0.405 ρI p l T to determine in order to achieve a matching first natural frequency.

[0133] To both the replacement mass m T as well as the replacement inertia J T To account for the additive mass of the cantilever, the approximation of inertia for slender objects can be used, from which it follows that a slender beam segment of length b = 12 J T m T the mass m T and with regard to its center of gravity, inertia J T possesses. That is, the mass covering of the boom. µ ( x ) is applied at the point of the tower clamping over a length of b to the constant value m T b increased.

[0134] Since the dimensions and moments of inertia of the payloads of a tower crane are generally unknown, the payload can still be modeled as a concentrated mass point. The mass of the cable can be neglected. In contrast to the boom, the payload is somewhat more strongly influenced by Euler, Coriolis, and centrifugal forces. The centrifugal acceleration acts only in the boom direction and is therefore not relevant at this point; the Coriolis acceleration results from the distance x L the load to the tower a Coriolis , y = 2 γ ˙ x ˙ L .

[0135] Due to the low jib rotation rates, the Coriolis acceleration on the load can be neglected, especially when positioning the load. However, it is still carried along for a few steps to allow for disturbance feedforward if needed.

[0136] To derive the pendulum dynamics, it is projected onto a tangential plane that is oriented orthogonally to the boom and intersects the position of the trolley.

[0137] The Euler acceleration is given by a Euler , L = γ ˙ x L .

[0138] Due to the generally small pendulum angles, the following approximation applies: x L / x tr ≈ 1 from which the approximation a Euler , L = a Euler It follows that the Euler acceleration, due to the rotation of the reference system, acts on the load and the trolley in approximately the same way.

[0139] The acceleration on the load is in Fig. 7 depicted.

[0140] This is s t = x tr γ t + w x tr t . The y-position of the trolley in the tangent plane. The position of the trolley on the boom. x tr Due to the decoupling of radial and swivel dynamics, it is approximated here as a constant parameter.

[0141] The dynamics of a pendulum can be easily derived using the Lagrange formalism. This requires first determining the potential energy. U = − m L l t g cos ϕ t with the load mass m L , lt as well as the kinetic energy T = 1 2 m L r ˙ T r ˙ , where r t = s t + l t sin ϕ t − l t cos ϕ t . The y-position of the load in the tangent plane. Using the Lagrange function. L = T − U and the Lagrange equations of the second kind d d t ∂ L ∂ ϕ ˙ − ∂ L ∂ ϕ = Q with the non-conservative Coriolis force Q = m L a Coriolis , y 0 T ⋅ ∂ r ∂ ϕ = m L la Coriolis , y cos ϕ The pendulum dynamics in the direction of rotation follow as 2 ϕ ˙ l ˙ + s ¨ − a Coriolis , y cos ϕ + g sin ϕ + ϕ ¨ l = 0 .

[0142] Linearized by ϕ = 0, ϕ̇ = 0 follows from this, neglecting the change in rope length i ≈ 0 and the Coriolis acceleration a Coriolis,y ≈ 0 the simplified pendulum dynamics ϕ ¨ = − s ¨ − gϕ l = − x tr γ ¨ − w ¨ x tr t − gϕ l .

[0143] To describe the feedback effect of the pendulum dynamics on the structural dynamics of the boom and tower, the cable force must be considered. F R can be determined. This is most easily done by considering its main contribution due to gravity. F R , h = m L g cos ϕ sin ϕ , approximates. Its horizontal component in y The direction thus results in F R , h = m L g cos ϕ sin ϕ , or linearized by ϕ = 0 to F R , h = m L gϕ .

[0144] The distributed-parameter model (5) of the boom dynamics describes infinitely many eigenmodes of the boom and is not yet suitable for a control design in its current form. Since only a few of the lowest-frequency eigenmodes are relevant for the observer and the control system, a modal transformation followed by modal order reduction to these few eigenmodes is a viable option. However, an analytical modal transformation of equation (5) is rather difficult. Instead, it is advisable to first discretize equation (5) spatially using finite differences or the finite element method, thus obtaining an ordinary differential equation.

[0145] When discretizing using finite differences, the bar is reduced to NEquidistantly distributed mass points at the boom positions x i , i ∈ 1 … N The beam deflection at each of these positions is divided. w i = w x i t The local derivatives are calculated using the central difference quotient. w i ′ ≈ − w i − 1 + w i + 1 2 Δ x w i " ≈ w i − 1 − 2 w i + w i + 1 Δ x 2 approximates, where Δ x = x i+ 1 - x i the distance between the discrete mass points and w' i the local derivation w' ( x i , t ) describe.

[0146] For the discretization of w"(x), the boundary conditions (6)-(7) must be satisfied. w i − 1 − 2 w i + w i + 1 = 0 , i ∈ 1 N − w i − 2 + 2 w i − 1 − 2 w i + 1 + w i + 2 = 0 , i ∈ 1 N after w -1 ,w -2 , w N+ 1 and w N +2 can be solved. The discretization of the term (I(x)w")" in equation (5) is given by I x w " " ≈ η i − 1 − 2 η i + η i + 1 Δ x 2 with η i = I x i w i " .

[0147] By choosing the central difference approximation, equation (35) depends on the values ​​at the boundaries. I -1 and IN+ 1 from, which in practice are represented by the values I 1 and I N can be replaced.

[0148] For the further procedure, a vector notation (in bold) is recommended. The vector of the boom deflections is represented as w → = w 1 … w N T denoting, which denotes the discretization of the term ( I ( x ) w" )" in vector notation as K 0 w → with the stiffness matrix K 0 = I 1 + I 2 − 2 I 1 − 2 I 2 I 1 + I 2 0 0 − 2 I 2 4 I 2 + I 3 − 2 I 2 − 2 I 3 I 3 0 I 2 − 2 I 2 − 2 I 3 I 2 + 4 I 3 + I 4 − 2 I 3 − 2 I 4 I 4 ⋱ 0 I N − 2 − 2 I N − 2 − 2 I N − 1 I N − 2 + 4 I N − 1 − 2 I N − 1 0 0 I N − 1 + I N − 2 I N − 1 − 2 I N I N − 1 + I N can be expressed.

[0149] Similarly, the mass matrix of the mass covering (unit kgm) is given as a diagonal matrix. M 0 = diag μ x 1 … μ x N defined with the vector x → T = x 1 − l cj … x N − l cj T which describes the distance to the tower for each node.

[0150] The vector is used for the distributed acting force. q → = q 1 … q N with the entries q i = q ( x i ) defined, so that the discretization of the partial beam differential equation (5) in discretized form is as M 0 w → ¨ + E Δ x 4 K 0 = q → − M x → T γ ¨ . can be specified.

[0151] Now, the dynamic interaction of steel structure movement and pendulum dynamics will be described.

[0152] For this purpose, the additional point masses on the boom, namely the counterweight mass, are first added. m cj , m T as well as the cat mass m tr the distributed mass matrix M 1 = M 0 + diag m cj Δ x … m T b … m T b … m tr Δ x 0 added.

[0153] Furthermore, the forces and moments with which the tower and load act on the boom can be described. The force due to tower bending is determined via the substitute model by q T Δ x = − c b w x T . with q T = q ( l cj ) given. To determine the moment due to tower torsion, the rotation of the cantilever beam at the clamping point is first measured. ψ = w T ′ = − w T − 1 + w T + 1 2 Δ x required, from which the torsional moment can then be derived τ = − c T − w T − 1 + w T + 1 2 Δ x This results in the approximation being that, for example, two equal forces acting at the same distance from the tower (lever arm) can be applied. The value of these two forces is F τ = τ 2 Δ x , if Δ x The lever arm is in each case. This allows the moment to be determined by the vector. →q The forces acting on the boom are described. Only the two entries are needed for this. q T − 1 Δ x = − F τ , q T + 1 Δ x = F τ , be set.

[0154] The horizontal rope force (28) results in the entry q tr Δ x = m L gϕ in →q.

[0155] Since all forces of ϕ or →w The coupling of structural and pendulum dynamics can be written in matrix notation as... M 0 0 x tr T l ︸ M w → ¨ ϕ ¨ ︸ x → ¨ + E Δ x 4 K 0 + K 1 F tr 0 g ︸ K w → ϕ ︸ x → = − MX T − x tr ︸ B γ ¨ with K 1 = 1 4 Δ x 3 ⋯ c T 0 − c T 0 4 Δ x 2 c b 0 − c T 0 c T ⋯ , F tr = 1 Δ x 0 … − m L g … 0 T and x tr = 0 … 1 … 0 T sodass w ¨ x tr t = x tr T w → ¨ .

[0156] It should be noted at this point that the three parameters are the position of the trolley on the boom. x tr , l m L The parameters vary during operation. Therefore, equation (50) is a linear parameter-variant differential equation whose specific form can only be determined at runtime, particularly online. This must be taken into account in the subsequent observer and control design.

[0157] The number of discretization points N should be chosen large enough to ensure a precise description of the beam deformation and dynamics. This makes (50) a large system of differential equations. However, for control purposes, modal order reduction is suitable to reduce the number of system states to a smaller number.

[0158] Modal order reduction is one of the most frequently used reduction methods. The basic idea is to first perform a modal transformation, i.e., to describe the dynamics of the system based on its eigenmodes (shapes) and eigenfrequencies. Subsequently, only the relevant eigenmodes (usually the lowest frequencies) are selected, and all higher-frequency modes are neglected. The number of eigenmodes considered is denoted below by ξ designated.

[0159] First, the eigenvectors must be determined. →v i with i ∈ [1,N + 1] are calculated, which together with the corresponding natural frequencies ω i the eigenvalue problem K ν → i = ω i 2 M ν → i This calculation can be easily solved using well-known standard methods. The eigenvectors are then sorted into the modal matrix according to increasing eigenfrequency. V = ν → 1 ν → 2 … written. The modal transformation can then be performed via the calculation. z ¨ + V − 1 M − 1 KV ︸ K z = V − 1 M − 1 B ︸ B ^ γ ¨ where the new state vector →Z ( t ) = V -1< →x ( t ) contains the amplitudes of the eigenmodes. Since the modally transformed stiffness matrix K̂ If the system has a diagonal shape, the modally reduced system can be easily defined by restricting it to the first few parts. ξ Columns and rows of this system as z ¨ r + D ^ r z ˙ r + K ^ r z r = B ^ r γ ¨ . obtained, where the state vector →z r now only the few ξ Modal amplitudes are described. Furthermore, the entries of the diagonal damping matrix can be determined through experimental identification. D̂ r determine.

[0160] Three of the most important in-house trends are in Fig. 8 The uppermost mode represents the slowest natural mode, dominated by the pendulum motion of the load. The second mode shows a pronounced tower deflection, while the third shows a significant bending of the boom. All natural modes whose natural frequencies can be excited by the slewing drive should be taken into account.

[0161] The dynamics of the rotary drive are advantageously approximated as a PT1 element, which represents the dynamics γ ¨ = u − γ ˙ T γ with the time constant T γ exhibits. In conjunction with equation (57), this results in x ˙ = 0 I 0 0 − K ^ r − D ^ r 0 − B ^ r T γ 0 0 0 1 0 0 0 − 1 T γ ︸ A x + 0 B ^ r T γ 0 1 T γ ︸ B u with the new state vector →x = [ z r ż r γ γ̂ T< and the control signal u the target speed of the rotary mechanism.

[0162] For the observer and the control of the swivel dynamics, the system (59) can be configured around an output vector →y to x → ˙ = A x → + Bu y → = C x → to be supplemented so that the system is observable, i.e., that all states in the vector →x through the exits →y , as well as finitely many time derivatives of the outputs can be reconstructed and thus estimated at runtime.

[0163] The initial vector →y This describes precisely the rotation rates, strains, or accelerations that are measured by the sensors on the crane.

[0164] Based on model (61), for example, an observer 345 can be identified, cf. Fig. 2 , in the form of the Kalman filter x → ^ ˙ = A x → ^ + B u → + P C T R − 1 y → − C x → ^ x → ^ 0 = x → ^ 0 design, where the value P is from the algebraic Riccati equation 0 = P A + P A T + Q − P C T R − 1 C P This can follow, which can be easily solved using standard procedures. Q R and represent the covariance matrices of the process and measurement noise and serve as design parameters for the Kalman filter.

[0165] Since equations (60) and (61) describe a parameter-variant system, the solution P of equation (63) is always only valid for the corresponding set of parameters { x tr ,l,m L } valid. However, the standard methods for solving algebraic Riccati equations are quite computationally intensive. In order to avoid having to evaluate equation (63) at runtime, the solution can be P for a finely resolved characteristic map in the parameters x tr,l, m L The calculations are performed offline. At runtime (online), the value whose parameter set { x tr , l, m L } is closest to the current parameters.

[0166] Since the observer 345 can see all system states x → ^ The regulation can be estimated in the form of a state feedback mechanism. u = K x → ref − x → ^ realize this. The vector contains →x ref the target states, which are typically all zero in the rest position (except for the rotation angle). γ ). While following a path, the values ​​can be non-zero, but should not deviate too far from the equilibrium position around which the model was linearized.

[0167] For this purpose, a linear-quadratic approach is suitable, for example, in which the feedback gain K is chosen such that the quality functional J = ∫ t = 0 ∞ x T Q x + u T R u dt is optimized. For the linear control design, the optimal feedback gain is calculated as follows: K = R − 1 B T P , where P can be determined analogously to the Kalman filter via the algebraic Riccati equation 0 = PA + A T P − PBR − 1 B T P + Q can be determined.

[0168] Since the reinforcement K in equation (66) depending on the parameter set { x tr , l, m L If the value is zero, a characteristic map is generated for it analogously to the procedure for the observer. In the context of control systems, this approach is known as "gain scheduling".

[0169] To apply the control system to a tower crane, the observer dynamics (62) can be simulated on a control unit during operation. For this purpose, the control signals can be used. u the drives, and on the other hand the measurement signals y the sensors are used. The control signals are in turn calculated from the feedback gain and the estimated state vector according to (62).

[0170] Since the radial dynamics can also be represented by a linear model of the form (60)-(61), the control of the radial dynamics can proceed analogously to the slewing dynamics. Both control systems then act independently of each other on the crane and stabilize the pendulum dynamics in the radial direction as well as perpendicular to the boom, taking into account the drive and structural dynamics in each case.

[0171] The following describes an approach to modeling radial dynamics. This differs from the previously described approach to modeling slewing dynamics in that the crane is now described by a substitute system of several coupled rigid bodies, rather than by continuous beams. The tower can be divided into two rigid bodies, with another rigid body representing the boom (see figure). Fig. 9 .

[0172] This describes α y and β y the angles between the rigid bodies and ϕ y the radial pendulum angle of the load. With P The positions of the focal points are described, with the index CJ for the counter-extension, J for the boom, TR for the trolley and T This refers to the tower (in this case, the upper rigid body of the tower). The positions depend, at least in part, on the parameters set by the drives. x TR and l ab. At the joints between the rigid bodies are springs with spring stiffnesses c̃. αx , c̃ βy as well as dampers, whose viscous friction is determined by the parameters d αy and d βy is described.

[0173] The dynamics can be derived using the well-known Lagrange formalism. The three degrees of freedom in the vector are... q → = α y β y ϕ y In summary, these can be used to determine the translational kinetic energies. T kin = 1 2 m T P ˙ T 2 2 + m J P ˙ J 2 2 + m CJ P ˙ CJ 2 2 + m TR P ˙ TR 2 2 + m L P ˙ L 2 2 as well as the potential energies due to gravity and spring stiffnesses T pot = g m T P T , z + m J P J , z + m CJ P CJ , z + m TR P TR , z + m L P L , z + 1 2 c ˜ α y α y 2 + c ˜ β y β y 2 express. Since the rotational energies are negligibly small compared to the translational energies, the Lagrangian can be expressed as L = T kin − T pot These equations can be formulated. From this, the Euler-Lagrange equations result. d d t ∂ L ∂ q ˙ i − ∂ L ∂ q i = Q i ∗ with the generalized forces Q i ∗ , which describe the influences of non-conservative forces, such as damping forces. Written out, these result in the three equations. d d t ∂ L ∂ α ˙ y − ∂ L ∂ α y = − d αy α ˙ y , d d t ∂ L ∂ β ˙ y − ∂ L ∂ β y = − d βy β ˙ y , d d t ∂ L ∂ ϕ ˙ y − ∂ L ∂ ϕ y = 0 .

[0174] By inserting L When calculating the corresponding derivatives, these equations result in very large terms, so an explicit representation is not meaningful here.

[0175] The dynamics of the drives of the trolley mechanism and the hoist can generally be approximated well by the first-order PT1 dynamics. x ¨ TR 1 τ TR u x − x ˙ TR , l ¨ = 1 τ l u l − l ˙ .

[0176] In it they describe τ i the corresponding time constants and u i the target speeds.

[0177] If one now holds all drive-related variables in the vector x a = x TR l x ˙ TR l ˙ x ¨ TR l ¨ fixed, the coupled radial dynamics can be represented as drive, pendulum and structural dynamics. a 11 q q ˙ x a a 12 q q ˙ x a a 13 q q ˙ x a a 31 q q ˙ x a a 22 q q ˙ x a a 23 q q ˙ x a a 31 q q ˙ x a a 32 q q ˙ x a a 33 q q ˙ x a ︸ A ˜ X q ¨ = b 1 q q ˙ x a b 2 q q ˙ x a b 3 q q ˙ x a ︸ B ˜ X or by rearranging at runtime as the nonlinear dynamics in the form q ¨ = f q ˙ q x a .

[0178] Since the radial dynamics are thus given in minimal coordinates, order reduction is not necessary. However, due to the complexity of the equations described by (75), an analytical offline precomputation of the Jacobian matrix is ​​required. ∂ f ∂ q ˙ q not possible. To obtain a linear model of the form (60) for the control from (75), a numerical linearization can therefore be performed at runtime. For this purpose, the equilibrium position ( q̇ 0 , q 0) are determined for which 0 = f q ˙ 0 q 0 0 is satisfied. Then the model can be described using the equations x lin = ∂ f ∂ q ˙ q q ˙ 0 q 0 ︸ A x lin + ∂ f ∂ u q ˙ 0 q 0 ︸ B u . Linearizing the system results in a linear system as in equation (60). By selecting suitable sensors for structural and pendulum dynamics, for example using gyroscopes, a measurement output as in (61) is obtained, through which the radial dynamics can be observed.

[0179] The further procedure of the observer and control design corresponds to that for the swivel dynamics.

[0180] As already mentioned, the deflection of the lifting rope relative to the vertical 62 can be determined not only by an imaging sensor on the trolley, but also by an inertial measuring device on the load hook.

[0181] Such an inertial measurement unit (IMU) can, in particular, include acceleration and gyroscopic sensors for providing acceleration and gyroscopic signals that, on the one hand, indicate translational accelerations along various spatial axes and, on the other hand, gyroscopic signals with respect to various spatial axes. The gyroscopic rates can be rotational velocities, but also, in principle, rotational accelerations, or both.

[0182] Advantageously, the inertial measurement unit (IMU) can detect accelerations in three spatial axes and rotation rates about at least two spatial axes. The accelerometers can operate in three axes, and the gyroscopes can operate in two axes.

[0183] The inertial measurement unit (IMU) attached to the load hook can advantageously transmit its acceleration and rotation rate signals and / or signals derived therefrom wirelessly to the control and / or evaluation unit 3 or its pendulum damping unit 340, which can be attached to a structural part of the crane or arranged separately near the crane. In particular, the transmission can be to a receiver (REC) that can be attached to the trolley 206 and / or to the suspension from which the hoist rope runs. Advantageously, the transmission can be carried out, for example, via a WLAN connection (see Figure 1). Fig. 10 .

[0184] How Fig. 13 As shown, the load hook 208 can tilt relative to the lifting rope 207 in different directions and in different ways, depending on the connection. The inclined pull angle β of the lifting rope 207 does not have to be identical to the orientation of the load hook. The tilt angle ε β describes the tilting or rotation of the load hook 207 relative to the inclined pull β of the lifting rope 207, or the rotation between inertial coordinates and load hook coordinates.

[0185] For modeling the pendulum behavior of a crane, the two pendulum directions – in the direction of travel of the trolley, i.e., in the longitudinal direction of the boom, on the one hand, and in the direction of rotation or arcing around the tower axis, i.e., in the direction perpendicular to the longitudinal direction of the boom, on the other – can be considered separately, since these two pendulum movements hardly influence each other. Each pendulum direction can therefore be modeled two-dimensionally.

[0186] If one considers this in Fig. 12 The model shown demonstrates that the pendulum dynamics can be described using the Lagrange equations. The trolley position is then... s x ( t ) , the rope length l ( t ) and the rope or pendulum angle β ( t ) as a function of time t, whereby, for the sake of simplicity and readability, the time dependence will no longer be explicitly indicated by the term (t) in the following. First, the load hook position can be defined in inertial coordinates as r = s x − l sin β − l cos β be defined, where the time derivative r ˙ = s ˙ x − l ˙ sin β − l β ˙ cos β l β ˙ sin β − l ˙ cos β the inertial velocity using d β d t = β ˙ describes. The hook acceleration. r ¨ = s ¨ x − 2 β ˙ l ˙ cos β − l ¨ sin β + l β ˙ 2 sin β − l β ¨ cos β 2 l ˙ β ˙ sin β − l ¨ cos β + l β ˙ 2 cos β + l β ¨ sin β It is not needed for deriving the load dynamics, but is used for designing the filter, as explained below.

[0187] Kinetic energy is determined by T = 1 2 m r ˙ T r ˙ where the mass mthe load hook and the load are subsequently eliminated. The potential energy due to gravity corresponds to V = − m r T g , g = 0 − g T ,

[0188] With the acceleration due to gravity g .

[0189] There V not from ṙ The Euler-Lagrange equation depends on the specific circumstances. d dt ∂ T ∂ q ˙ − ∂ T ∂ q + ∂ V ∂ q = 0 where the vector q = [ β β̇ ] T< describes the generalized coordinates. This results in the pendulum dynamics as a non-linear second-order differential equation with respect to β , l β ¨ + 2 l ˙ β ˙ − s ¨ x cos β + g sin β = 0 .

[0190] The dynamics in y - z The level can be expressed analogously.

[0191] The acceleration will be discussed below. s̈ x The trolley or gantry crane runner is considered a known system input variable. This can sometimes be measured directly or estimated based on the measured trolley speed. Alternatively or additionally, the trolley acceleration can be measured with a separate trolley accelerometer or estimated if the drive dynamics are known. The dynamic behavior of electric crane drives can be determined based on the first-order load behavior. s ¨ x = u x − x ˙ T x can be estimated, whereby the input signal u x corresponds to the desired speed and T x The time constant is given. With sufficient accuracy, no further measurement of the acceleration is required.

[0192] The tilting direction of the load hook is determined by the tilting angle. ε β described, see below. Fig. 13 .

[0193] Since the rotation rate or tilting velocity is measured gyroscopically, the model underlying the estimation of the tilt corresponds to the simple integrator. ε ˙ β = ω β from the measured rotation rate ω β to the tilt angle.

[0194] The IMU measures all signals in the moving, rotating, body-fixed coordinate system of the load hook, which is indicated by the preceding index K is characterized, while vectors in inertial coordinates with I can be marked or remain completely unindexed. As soon as ε β The estimated acceleration can be determined by the measured acceleration. K a = [ K a x K a z ] T< in load hook coordinates K a are transformed into inertial coordinates using a <mprescripts / > I <none / > = cos ε β sin ε β − sin ε β cos ε β ⋅ a <mprescripts / > K <none / > .

[0195] Die inertiale Acceleration can then be used to estimate the pendulum angle based on (107) and (103).

[0196] Estimating the rope angle β requires an accurate assessment of the tilting of the load hook. ε β . To be able to do this, an absolute reference value is needed, since the gyroscope has limited accuracy and a baseline value is unknown. Furthermore, the gyroscopic measurement is regularly superimposed by an approximately constant deviation inherent in the measurement principle. Moreover, it cannot be assumed that ε β generally oscillates around zero. Therefore, the accelerometer is used to provide such a reference value by evaluating the gravitational acceleration constant (which appears in the low-frequency signal) and expressing it in inertial coordinates as g <mprescripts / > I <none / > = 0 − g T .

[0197] is known and in load hook coordinates g <mprescripts / > K <none / > = − g − sin ε β cos ε β T . is transformable. The measured acceleration is the sum of (103) and (112) a <mprescripts / > K <none / > = r ¨ <mprescripts / > K <none / > − g <mprescripts / > K <none / > .

[0198] The negative sign of K gThis results from the fact that, due to the sensor principle, the acceleration due to gravity is measured as a fictitious upward acceleration.

[0199] Since all components of K r̈ generally significantly smaller than g Since the values ​​are and oscillate around zero, the application of a low-pass filter with a sufficiently low cutoff frequency allows for the approximation. a <mprescripts / > K <none / > ≈ − g <mprescripts / > K <none / > .

[0200] If you divide the x component through the z Component, the reference tilt angle for low frequencies is obtained as ε β , α = arctan a <mprescripts / > K <none / > <mprescripts / > x <none / > a <mprescripts / > K <none / > <mprescripts / > z <none / > .

[0201] 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 continuous-time Kalman Bucy filter, which can be tuned by varying the procedure parameters and measuring noise. In the following, however, a complementary filter as in Fig. 14 shown, used, which can be adjusted with regard to its frequency characteristics by selecting the high-pass and low-pass transfer functions.

[0202] How the block diagram of Fig. 14 As shown, the complementary filter can be designed to determine the direction of the load hook tilt. ε β to estimate. A high-pass filter of the gyroscope signal. ω β with G hp 1 ( s ) yields the offset-free rotation rate ω̃ β as well as, after integration, an initial estimate of the tilt angle ε β,ω . ε β,a originates from the signal K a of the accelerometer.

[0203] In particular, a simple high-pass filter can first be created using the transfer function. G hp 1 = s s + ω o and very low fade-out frequency ω o on the gyroscope signal ω β This can be applied to eliminate the constant measurement offset. Integration yields the gyroscope-based tilt angle estimation. 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 ε β,ω and ε β,a to sum up or link together, whereby the high frequencies of ε β,ω by using the high-pass filter, the low frequencies are weighted more heavily. ε β,a The low-pass filter gives greater weight to the transfer functions, since equation (115) provides a good estimate for low frequencies. The transfer functions can be chosen as simple first-order filters, namely G ph 2 s = s s + ω , G lp s = ω s + ω where the fade-out frequency ω The frequency chosen is lower than the oscillation frequency. Because G hp 2 s + G lp s = 1 For all frequencies, we estimate... ε β not incorrectly scaled.

[0204] Based on the estimated load hook orientation, the inertial acceleration can be I a of the load hook from the measurement of K a can be determined using (110), which allows the design of an observer based on pendulum dynamics (107) as well as the rotated acceleration measurement a <mprescripts / > I <none / > = r ¨ − g <mprescripts / > I <none / > .

[0205] Although both components of this equation can be used equally for estimating the pendulum angle, good results can only be achieved using the x -component will be obtained, which is independent of g is.

[0206] It is subsequently assumed that the pendulum dynamics are affected by process-related background noise. w : N(0, Q ) and measurement noise v : N(0, R ) is superimposed, so that it can be expressed as a non-linear stochastic system, namely x ˙ = f x u + w , x 0 = x 0 y = h x u + ν where the status vector x = [ β β̇ ] T< The continuous, time-extended Kalman filter can be used to determine the states. x ^ ˙ = f x ^ u + K y − h x ^ u , x ^ 0 = x ^ 0 , P ˙ = AP + PA T − PC T R − 1 CP + Q , P 0 = P 0 , K = PC T R − 1 , A = ∂ f ∂ x x ^ , u , C = ∂ h ∂ x x ^ , u , be used.

[0207] The spatial representation of the state of the pendulum dynamics according to (107) is as follows: f x s ¨ x = β ˙ − 1 l 2 l ˙ β ˙ − s ¨ x cos β + g sin β where the cat acceleration u = s̈ x is treated as an input variable of the system. To define a system output, the horizontal component of the load hook acceleration from (119) can be formulated as a function of the system states, from which the following results: a x <none / > <mprescripts / > I <none / > = r ¨ x − g x <none / > <mprescripts / > I <none / > ︸ 0 = s ¨ x − 2 β ˙ l ˙ cos β − l ¨ sin β + l β ˙ 2 sin β − l β ¨ cos β = 1 − cos β 2 s ¨ x + sin β − l ¨ + g cos β + l β ˙ 2

[0208] The horizontal component I g x The acceleration due to gravity is naturally zero. Therefore, l̇, l̈ from the measurement of l can be reconstructed, e.g., using the drive dynamics according to (108). When using (123) as a measurement function h x = a x <none / > <mprescripts / > I <none / > , The linearization term is obtained as A = 0 1 − g cos β − s ¨ x sin β l − 2 l ˙ l x ^ , s ¨ x , C = cos β 2 g cos β − l ¨ + l β ˙ 2 + 2 s ¨ x sin β − g 2 l β ˙ sin β T x ^ , s ¨ x .

[0209] The covariance matrix estimates of the process noise are used here. Q = I 2×2 , of the measurement noise R= 1000 and the initial error covariance matrix P = 0 2x2 .

[0210] How Figur 15 As shown, the pendulum angle, which is estimated using an extended Kalman filter (EKF) or determined using a simple static approach, corresponds quite well to a validation measurement of the pendulum angle at a gimbal joint using a rotary angle encoder on the trolley.

[0211] Interestingly, the calculation using a relatively simple static approach yields comparably good results to the extended Kalman filter. Therefore, the pendulum dynamics according to (122) and the initial equation according to (123) can be modified around the stable state. β = β̇ = 0 can be linearized. If the line length continues l is assumed to be constant so that l̇ = l̈ = 0 , results for the linearized system x ˙ = 0 1 − g l 0 x + 0 1 l s ¨ x , y = g 0 x and I a x This 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 determined from the simple static relationship. β = a x <none / > <mprescripts / > I <none / > g to be won, which interestingly is independent of l is. Fig. 15 This shows that the results obtained are just as accurate as those of the Kalman filter.

[0212] Using β and equation (101), an accurate estimate of the load position can thus be achieved.

[0213] When modeling the dynamics of the speed-based crane drives according to (108) accompanied by parameter determination, the resulting time constants are determined according to T i < 1 50 very small. Therefore, dynamic effects of the drives can be neglected.

[0214] To compare the pendulum dynamics with the drive speed ṡ x instead of the drive acceleration s̈ x To specify as a system input variable, the linearized dynamic system g can be "increased" by integration according to (127), resulting in: x ˜ ˙ = 0 1 − g l 0 ∫ 0 t x τ d τ ︸ x ˜ + 0 1 l s ˙ x

[0215] The new status vector is x̃ = [∫ β β ] T< The dynamics remain evidently the same, whereas the physical meaning and the input change. In contrast to (127) β and β̇ They are stabilized at zero, but not the time integral ∫ β Since the controller sets a desired speed ṡ x , d The desired stable state should be able to be maintained permanently. x ˜ ˙ = 0 as x ˜ d = s ˙ x , d g 0 T . can be calculated. This can also be used as a static pre-filter. F in the frequency range, which ensures that lim s → 0 G u , x 1 s = 1 F for the transfer function from speed input to the first state G u , x 1 s = 1 ls 2 + g . is. The first component of the new state vector x̃ can be estimated using a Kalman-Bucy filter based on (130), with the system output size y = [0 1] x̃ The result is similar when a controller is designed based on (127) and the motor controller is controlled by the integrated input signal. u = ∫ 0 t s ¨ x τ d τ is controlled.

[0216] The feedback obtained can be determined as a linear-quadratic controller (LQR), which can represent a linear-quadratic Gaussian controller structure (LQG) together with the Kalman-Bucy filter. Both the feedback and the Kalman control factor can be adjusted according to the rope length. l can be adjusted, for example using adjustment factor plans.

[0217] To control the load hook closely along trajectories, a structure with two degrees of freedom, as described above, can be used – similar to what was explained previously. Fig. 16 shown together with a trajectory planner that provides a C3< differentiable reference trajectory for the load hook position. The trolley position can be added to the dynamic system according to (130), from which the system Σ : x ˙ = 0 1 0 − g l 0 0 0 0 0 ︸ A ˜ x + 0 1 l 1 ︸ B ˜ u results, where u = ṡ x is, so that the flat initial size z = λ T x , λ T B ˜ A ˜ B ˜ A ˜ 2 B ˜ = 0 0 g l = 0 − l 1 = s x − lβ , This corresponds to the hook position of the linearized case scenario. State and input can be algebraically parameterized by the flat output and its derivatives, specifically with z = [z ż z̈ ] T< as x = Ψ x z = − z ˙ g − z ¨ g z + l z ¨ g T , u = Ψ u z z 3 = z ˙ + l z ⃛ g This enables the algebraic calculation of the reference states and the nominal input control signal from the planned trajectory for z. A change in the setpoint shows that the nominal error can be kept close to zero, so that the feedback signal u fb of the controller Ksignificantly smaller than the nominal input control variable u ff is . In practice, the input control variable can be set to u fb = This will happen if the signal from the wireless inertial measurement device is lost.

[0218] How Figur 16 As shown, the two-degrees-of-freedom controller structure can have a trajectory planner TP that provides a smooth trajectory. z ∈ C 3< for the flat output with limited derivatives, the input quantity Ψ u and the parameterization of the state Ψ x , as well as the controller K .

Claims

1. Revolving tower crane, comprising a hoisting rope (207), which runs off from a trolley (206) that is movable along a crane jib (202) and carries a load-handling means (208), drive devices for moving a plurality of crane elements and for moving the load-handling means (208), a control device (3) for controlling the drive devices such that the load-handling means (208) travels along a travel path, and a sway damping device (340) for damping sway movements of the load-handling means (208) and / or of the hoisting rope (207), wherein the sway damping device (340) comprises a sway sensor system comprising a detection device for detecting and / or estimating a deflection (φ; β) of the hoisting rope (207) and / or of the load-handling means (208) relative to a vertical (61), and a controller module (341) comprising a closed control loop for influencing the actuation of the drive devices as a function of the determined deflection (φ; β), characterized in that the detection device (60) comprises an inertial measuring device (IMU), mounted on the load-handling means (208), with acceleration and angular-rate sensor means for providing acceleration and angular-rate signals, first determination means (401) for determining and / or estimating a tilting (εβ) of the load-handling means (208) from the acceleration and angular-rate signals of the inertial measuring device (IMU), and second determination means (410) for determining the deflection (β) of the hoisting rope (207) and / or of the load-handling means (208) relative to the vertical from the determined tilting (εβ) of the load-handling means (208) and an inertial acceleration (la) of the load-handling means (208), wherein the controller module (341) is configured to update and adapt control gains as a function of changes in at least the hoisting-rope length (I) and the trolley position (Xtr).

2. Revolving tower crane according to the preceding claim, wherein the first determination means (401) have a complementary filter (402) with a high-pass filter (403) for the angular-rate signal of the inertial measuring device (IMU) and a low-pass filter (404) for the acceleration signal of the inertial measuring device (IMU) or a signal derived therefrom, which complementary filter (402) is configured to link an angular-rate-based estimate of the tilting (εβ,ω) of the load-handling means (208), which is based on the high-pass-filtered angular-rate signal, and an acceleration-based estimate of the tilting (εβ,a) of the load-handling means (208), which is based on the low-pass-filtered acceleration signal, to one another and to determine, from the linked angular-rate-based and acceleration-based estimates of the tilting (εβ,ω; εβ,a) of the load-handling means (208), the sought tilting (εβ) of the load-handling means (208), wherein the angular-rate-based estimate of the tilting (εβ,ω) of the load-handling means (208) preferably comprises an integration of the high-pass-filtered angular-rate signal and / or the acceleration-based estimate of the tilting (εβ,a) of the load-handling means (208) is based on the quotient of a measured horizontal acceleration (Kax) and a measured vertical acceleration (Kaz), from which the acceleration-based estimate of the tilting (εβ,a) is obtained according to the relationship ε β , a = arctan K a x K a z .

3. Revolving tower crane according to one of the preceding claims, wherein the second determination means (410) have a.) a filter and / or observer device, in particular in the form of a Kalman filter (411) or an extended Kalman filter, which takes into account, as an input variable, the determined tilting (εβ) of the load-handling means (208) and determines, from an inertial acceleration (la) at the load-handling means (208), the deflection (φ ; β) of the hoisting rope (207) and / or of the load-handling means (208) relative to the vertical (61), and / or b.) a calculation device for calculating the deflection (β) of the hoisting rope (207) and / or of the load-handling means (208) relative to the vertical (61) from the quotient of a horizontal inertial acceleration (Iax) and the gravitational acceleration (g).

4. Revolving tower crane according to one of the preceding claims, wherein the inertial measuring device (IMU) has a wireless communication module for wirelessly transmitting measurement signals and / or signals derived therefrom to a receiver, wherein the communication module and the receiver are preferably connectable to one another via a WLAN connection and the receiver is arranged on the trolley from which the hoisting rope runs off, and / or at least one deflection pulley for the hoisting rope (207) is provided on the load-handling means (208), to which deflection pulley a generator for generating electrical energy is coupled, which energy can be fed into a storage device that supplies the inertial measuring device (IMU) with electrical energy.

5. Revolving tower crane according to the preceding claim, wherein the detection device (60) further has an imaging sensor system, in particular a camera (62), which looks substantially vertically downward in the region of a suspension point of the hoisting rope (207), in particular of a trolley (206), wherein an image evaluation device (64) is provided for evaluating an image provided by the imaging sensor system with regard to the position of the load-handling means (208) in the provided image and for determining the deflection (φ ; β) of the load-handling means (208) and / or of the hoisting rope and / or the deflection velocity relative to the vertical (61).

6. Revolving tower crane according to one of the preceding claims, wherein the sway damping device (340) has a structural-dynamics sensor system (342) for detecting deformations and / or dynamic internal movements of structural components of the crane, and the controller module (341) of the sway damping device (340) is configured, when influencing the actuation of the drive devices, to take into account both the sway signal of the sway sensor system (60) and the structural-dynamics signals fed back to the control loop, which indicate deformations and / or dynamic internal movements of the structural components, wherein the controller module (341) preferably has a two-degree-of-freedom control structure and / or, in addition to the closed control loop, has a feedforward module (350), which is preferably configured as a differential flatness model, for feedforward control of the control signals for the drive devices, wherein the feedforward module (350) is in particular configured to carry out the feedforward control without taking into account the sway signals of the sway sensor system (60) and the structural-dynamics signals of the structural-dynamics sensor system (342).

7. Revolving tower crane according to the preceding claim, wherein the feedforward module (350) is assigned - a notch filter device (353), preferably provided between the trajectory planning module (351) and the setpoint filter module (352), on the one hand, and the feedforward module (350), on the other hand, for filtering the input signals supplied to the feedforward control, which notch filter device is configured to eliminate natural frequencies of the structural dynamics that can be excited from said input signals, and / or - a trajectory planning module (351), and / or - a setpoint filter module (352) for determining a desired profile for the load-handling-means position and the time derivatives thereof from predetermined setpoint values for the load-handling means.

8. Revolving tower crane according to one of preceding claims 6 to 7, wherein the controller module (341) has a control model that divides the structural dynamics of the crane into mutually independent parts, which comprise at least one slewing-dynamics part, which takes into account the structural dynamics with respect to slewing of the jib (202) about the upright crane slewing axis, and a radial-dynamics part, which takes into account structural-dynamics movements parallel to a vertical plane parallel to the jib.

9. Revolving tower crane according to one of preceding claims 6 to 8, wherein the structural-dynamics sensor system (342) has at least - a radial-dynamics sensor for detecting dynamic movements of the crane structure in an upright plane parallel to the crane jib (202), and - a slewing-dynamics sensor for detecting dynamic movements of the crane structure about an upright crane rotation axis, in particular tower axis (205), and the controller module (341) of the sway damping device is configured to influence the actuation of the drive devices, in particular of a trolley drive and slewing-gear drive, as a function of the detected dynamic movements of the crane structure in the upright, jib-parallel plane and of the detected dynamic movements of the crane structure about the upright crane rotation axis.

10. Revolving tower crane according to one of preceding claims 6 to 9, wherein the structural-dynamics sensor system (342) further - has a hoisting-dynamics sensor for detecting vertical dynamic deformations of the crane jib (202), and the controller module (341) of the sway damping device (340) is configured to influence the actuation of the drive devices, in particular of a hoist drive, as a function of the detected vertical dynamic deformations of the crane jib (202), and / or - is configured to determine dynamic torsions of a crane tower (201) carrying the crane jib and / or of the crane jib (202), and the controller module (341) of the sway damping device (340) is configured to influence the actuation of the drive devices as a function of the detected dynamic torsions of the crane jib (202) and / or of the crane tower (201), and / or - is configured to detect all natural modes of the dynamic torsions of the crane jib (202) and / or of the crane tower (201), the natural frequencies of which lie in a predetermined frequency range, wherein the structural-dynamics sensor system (342) has at least one, preferably a plurality of, tower sensor(s), which is / are arranged at a distance from a node point of a natural tower vibration, for detecting tower torsions, and at least one, preferably a plurality of, jib sensor(s), which is / are arranged at a distance from a node point of a natural jib vibration, for detecting jib torsions.

11. Revolving tower crane according to one of preceding claims 6 to 10, wherein the structural-dynamics sensor system (342) has strain gauges and / or acceleration sensors and / or angular-rate sensors, in particular in the form of gyroscopes, for detecting the deformations and / or dynamic internal movements of structural components of the crane, wherein the acceleration sensors and / or angular-rate sensors are preferably configured for three-axis detection, wherein the structural-dynamics sensor system (344) preferably has at least one angular-rate and / or acceleration sensor and / or strain gauge for detecting dynamic tower deformations, and at least one angular-rate and / or acceleration sensor and / or strain gauge for detecting dynamic jib deformations.

12. Revolving tower crane according to one of the preceding claims, wherein the controller module (341) has a filter and / or observer device (345), in particular in the form of a Kalman filter (346), in which detected and / or estimated and / or calculated and / or simulated functions that characterize the dynamics of the structural components of the crane are implemented, for influencing the manipulated variables of drive controllers (347) for actuating the drive devices, wherein said filter and / or observer device (345) is configured to receive, as input variables, on the one hand the manipulated variables of the drive controllers (347) and, on the other hand, the sway signal of the sway sensor system (60) and / or the structural-dynamics signals fed back to the control loop, which indicate deformations and / or dynamic internal movements of the structural components, and to influence the controller manipulated variables as a function of the dynamically induced movements of crane elements and / or deformations of structural components obtained for specific controller manipulated variables.

13. Method for controlling a revolving tower crane that is configured according to one of claims 1 to 12 and the load-handling means (208) of which, attached to a hoisting rope (207), is moved by drive devices, which drive devices are actuated by a control device (3) of the crane, wherein the actuation of the drive devices is influenced by a sway damping device (340), comprising a controller module (341) with a closed control loop, as a function of sway-relevant parameters, characterized in that acceleration and angular-rate signals, which indicate the angular rates and translational accelerations at the load hook, are provided at the load hook by an inertial measuring device (IMU), mounted there, with acceleration and angular-rate sensors and are transmitted wirelessly to the controller module, wherein a tilting (εβ) of the load-handling means (208) is determined from the acceleration and angular-rate signals of the inertial measuring device (IMU), then the deflection (β) of the hoisting rope (207) and / or of the load-handling means (208) relative to the vertical (61) is determined from the determined tilting (εβ) of the load-handling means (208) and an inertial acceleration (Ia) of the load-handling means (208) and is supplied to the closed control loop, wherein control gains are updated and adapted by the controller module (341) as a function of changes in at least the hoisting-rope length (I) and the trolley position (Xtr).

14. Method according to the preceding claim, wherein the acceleration signals, which indicate the translational accelerations at the load hook, are determined with respect to three spatial axes and the angular-rate signals, which represent the angular rates at the load hook, are detected with respect to at least two spatial axes, wherein the acceleration and angular-rate signals are supplied to a complementary filter (402) with a high-pass filter (403) for the angular-rate signal of the inertial measuring device (IMU) and a low-pass filter (404) for the acceleration signal of the inertial measuring device (IMU) or a signal derived therefrom, wherein the complementary filter (402) makes and links to one another an angular-rate-based estimate of the tilting (εβ,ω) of the load-handling means (208), which is based on the high-pass-filtered angular-rate signal, and an acceleration-based estimate of the tilting (εβ,a) of the load-handling means (208), which is based on the low-pass-filtered acceleration signal, and determines, from the linked angular-rate-based and acceleration-based estimates of the tilting (εβ,ω ; εβ,a) of the load-handling means (208), the sought tilting (εβ) of the load-handling means (208), and / or wherein the deflection (φ ; β) of the hoisting rope (207) and / or of the load-handling means (208) relative to the vertical (61) is determined from an inertial acceleration (la) at the load-handling means by a filter and / or observer device to which the determined tilting (εβ) of the load-handling means (208) is supplied as an input variable.