EP2636635A1 - Crane controls with rope force mode - Google Patents

Abstract

The crane controller has a lifting mechanism (5) for lifting a load suspended on a rope (4), which is operated in cable power mode in which lifting is controlled, so that a target value of the rope force is adjusted. The speed and/or position of winch are controlled, so that the desired value of the cable force is established. The actual value of cable force is determined by comparing actual value and setpoint of cable force. Independent claims are included for the following: (1) a crane control system; (2) a method for controlling a crane; and (3) a software code for controlling a crane.

Description

The present invention relates to a crane control for a crane having a hoist for lifting a load suspended on a rope.

In known crane controls, a control or regulation is usually used, in which the desired position or speed of the load is used as a setpoint. For example, the crane operator uses a hand lever to specify a desired speed of the load, which then serves as input for the crane control.

The inventors of the present invention have recognized that such control of the hoist may be disadvantageous in certain constellations.

Object of the present invention is therefore to provide an improved crane control available.

This object is achieved by claim 1.

The present invention shows a crane control for a crane, which has a hoist for lifting a hanging on a rope load. According to the invention, the crane control has a cable force mode in which the crane control activates the lifting mechanism so that a desired value of the cable force is established. Such control of the hoist on the basis of the desired force acting in the cable, it may have advantages over a crane control for certain lifting situations, which operates on the basis of a desired position or target speed of the load. In particular, the emergence of slack rope when placing the load can be prevented by the cable force mode of the crane control according to the invention. Advantageously, the control takes place automatically.

Preferably, the speed and / or position of the winch is controlled. In particular, the speed and / or position of the winch, taking into account the elasticity of the system, can be controlled such that the desired value of the cable force is set.

Advantageously, the cable force in the cable force mode can be kept at a constant setpoint. Advantageously, the crane control controls the hoist in the cable force mode so that the cable force is automatically set to a predetermined setpoint.

In this case, a cable force determination unit can be provided, which determines an actual value of the cable force. Advantageously, the control then takes place on the basis of a comparison of the actual value and the nominal value of the cable force.

According to the invention, the cable force in the cable force mode can be regulated by returning at least one measured value. Advantageously, the cable force determination unit determines the actual value of the cable force on the basis of a measurement signal of a cable force sensor.

According to the invention, the cable force sensor can be arranged on the hoist, in particular on a fastening of the hoist winch and / or a fastening of a pulley. For example, the rope force sensor can be arranged in a tab which secures the hoist winch to a hoist winch platform, or which holds a pulley over which the hoist rope is guided.

Furthermore, the cable force determination unit determines the actual value of the cable force via a filtering of measured values or a model-based estimation. In particular, an observer can be provided, which determines the cable force on the basis of measured values and a physical model of the dynamics of the cable.

Furthermore, the crane control according to the invention can have a setpoint determination unit which determines the setpoint value of the cable force on the basis of measured values and / or control signals and / or inputs of a user.

For example, the setpoint determination unit can determine the static force acting on the cable during a stroke. In particular, it is possible to determine the static force acting on the cable during a lifting operation preceding the cable power mode. The static force corresponds in particular to the weight of the lifted load. The dynamic portion of the forces acting in the rope can be removed, for example by filtering.

Furthermore, according to the invention, the rope length can be included in the setpoint determination unit. Especially with strokes with a large rope length while the load acting on the rope suspension point also depends on the length of the unwound rope or its weight. Advantageously, the setpoint determination unit therefore takes into account the weight of the unwound cable.

In particular, the weight of the lifted load can thereby be determined by subtracting the weight of the unwound cable from a static portion of a measured force in the case of a free-hanging load. advantageously, the setpoint determination unit then takes into account the weight of the lifted load determined in this way and the weight of the cable currently being unwound in the cable power mode.

A nominal value determination unit, which takes into account the rope length, is particularly advantageous if the cable force is measured via a sensor which is not arranged on the load hook but, for example, on the hoist.

Furthermore, a crane control according to the invention may comprise an input element, via which the crane operator can change the desired value of the cable force. This allows the crane operator to adjust which tension should be maintained during the cable force mode in the rope.

Advantageously, for this purpose, a factor can be entered, which determines the ratio between the desired value of the cable force and the static force during a stroke. For example, the crane operator may pretend that at least a portion of the cable force during the cable power mode should be in some relation to the weight force of the load previously acting on the cable.

Advantageously, the desired value of the cable force is determined so that it is always above the weight force generated by the unwound load rope. This ensures that no slack rope can arise in the cable force mode. Advantageously, as described above, the rope length is taken into account and determines the weight of the unwound rope. In particular, the desired value of the cable force can consist of the sum of the weight force generated by the unwound load cable and a force which is in a certain ratio to the weight force of the load previously acting on the cable.

According to the invention, the crane control in the cable force mode can comprise a pre-control part, which takes into account the dynamics of the cable, and a return part, via which the cable force determined by the cable force determination unit is returned becomes. For example, the pilot control part can be based on the inversion of a model describing the vibration dynamics of the cable. Advantageously, the weight of the unwound rope is taken into account in this. The control is then stabilized via the feedback part.

Furthermore, the crane control according to the invention can have a state detection, wherein the crane control automatically changes based on the state detection in and / or from the cable power mode. Advantageously, the condition detection can detect settling and / or picking up the load. As a result, the crane control can automatically switch into or out of the cable power mode when it detects a drop or picking up the load.

Alternatively, the change in one or both directions can also be done manually by the crane operator.

Advantageously, the state detection can display the current state.

Advantageously, the condition detection monitors the cable force in order to detect the condition of the crane and in particular to detect a settling and / or receiving the load. Advantageously, a discontinuation of the load is detected when a negative load change is present and / or when the derivative of the cable force is below a certain threshold, while the crane operator prescribes a lowering of the load via an input device. Conversely, a pick-up of the load can be detected if there is a positive load change and / or if the derivative of the cable force is above a certain threshold, while the crane operator predetermines a lifting of the load via an input device.

The crane control according to the invention can furthermore comprise a lifting mode in which the lifting mechanism is actuated on the basis of a desired value of the load position and / or the load speed, and / or a desired value of the cable position and / or cable speed. In this case, a scheme may be provided, which in the lifting mode an actual value of the load position and / or load speed and / or rope position and / or rope speed leads back.

Advantageously, the crane control changes from the lifting mode in the cable force mode when it detects a discontinuation of the load.

Furthermore, the crane control or the crane operator can change from the cable force mode to the lift mode when the crane control detects a picking up of the load and possibly displays it.

The crane control according to the present invention can be used particularly preferably in strokes in which either the cable suspension point or the load settling moves, as is the case, for example, in cranes mounted on a ship or loads to be deposited on a ship due to the sea.

Due to the cable force mode according to the invention, the emergence of slack rope can be prevented despite a movement of the cable suspension point or the load release point, since a constant tension in the rope is maintained via the cable force mode. As a result, the sometimes enormous loads on the rope and on the crane, which can occur in slack rope situations, avoided.

The crane control according to the invention can have an active sea state compensation, which compensates for the movement of the cable suspension point and / or a Lastabsetzpunktes due to the sea state at least partially by a control of the hoist. In this way, a further improved control of the crane can be achieved at sea.

Advantageously, the active sea state compensation takes place on the basis of a prediction, which the future movement of the cable suspension point or of the Lastabsetzpunktes due to the sea state predicts and at least partially compensated by a corresponding control of the hoist.

The active sea state compensation can be used in the lifting mode and / or in the cable force mode of the crane control according to the invention.

The present invention further comprises a crane with a crane control as described above.

In particular, the crane according to the invention may be a ship crane. In a ship crane is a crane, which is arranged on a float. In such cranes, therefore, the rope suspension point can move due to the sea.

Alternatively, the crane according to the invention may, for example, also be a harbor crane or offshore crane or a crawler crane, in particular a mobile harbor crane. A harbor crane is used to load or unload loads from a ship. A crane according to the present invention can therefore also be installed on a drilling platform. In such cranes, which are used for loading or unloading a ship, the Lastabsetzpunkt can move due to the sea state.

The present invention further comprises the use of a crane control according to the invention in lifting situations in which the cable suspension point and / or the load suspension point moves due to external influences such as due to the sea. As external influences but also wind loads come into question, which move the rope suspension point.

Here, the cable force mode according to the invention can prevent slack rope from arising due to this external movement. The cable suspension point may in particular be the crane tip, from which the hoist cable is led to the load. If this is moved, for example due to the sea, transmits This movement affects the rope and thus the load. The load dumping point can be, for example, the loading area of a floating body, in particular of a ship. If this moves, either slack rope can arise or the load can be lifted when the load is lowered.

The present invention further includes the use of a crane control according to the invention with the load applied. In particular, the cable force mode according to the invention automatically ensures that a desired desired value of the cable force is maintained. Advantageously, this is done according to the invention by regulating the cable force.

The present invention further includes a method of driving a crane having a hoist for lifting a load suspended on a rope. According to the invention, the hoist is controlled based on a setpoint of the cable force. This also gives rise to the advantages which have already been described in more detail above with regard to the crane control and its use.

Advantageously, the method is carried out as described above with regard to the crane control according to the invention or its use.

In particular, the method according to the invention can be carried out with a crane control as described above.

Advantageously, the crane control according to the invention automatically switches to the cable force mode upon detection of a settling process. Advantageously, a ramp-shaped transition from the force currently measured during the detection of the settling process to the actual desired force takes place in order to avoid setpoint jumps in the reference variable.

Furthermore, in order to lift the load, the setpoint force can first be raised so far that the load is lifted. Further advantageously, then a change from Sollkraft- to the lifting mode is carried out at free-hanging load.

Advantageously, the crane operator can manually change from the cable power mode to a lift mode. Alternatively, this is done automatically by the crane control

Furthermore advantageously, during the cable power mode, the input device via which the crane operator predefines the movement of the load in the lifting mode is also automatically deactivated.

The present invention further includes software with code for performing a method as described above. The software can be stored in particular on a machine-readable data memory. Advantageously, by the inventive software, when it is loaded onto a crane control, a crane control according to the invention can be implemented.

The crane control according to the invention and in particular the cable force mode is advantageously realized by an electronic control. In particular, a control computer can be provided, which is in communication with input elements and / or sensors and generates control signals for driving the hoist. The control computer can continue to be in communication with a display device, which visually displays information about the state of the crane control to the crane operator. Advantageously, it is indicated according to the invention, whether the crane control is in the cable force mode and / or in the lifting mode. Furthermore, the setpoint can be visualized according to the invention. Advantageously, the control computer is connected to an input element via which the desired cable force can be set. Further advantageously, the control computer is in communication with a rope force sensor. The present invention will now be described in more detail with reference to an embodiment and drawings.

Figur 0:

einen auf einem Schwimmkörper angeordneten Kran gemäß der vorliegenden Erfindung,

Figur 1:

die Struktur einer getrennten Trajektorienplanung für die Seegangskompensation und die Bedienersteuerung,

Figur 2:

eine Integratorkette vierter Ordnung zur Planung von Trajektorien mit stetigem Ruck,

Figur 3:

eine nicht äquidistante Diskretisierung für die Trajektorienplanung, welche gegen Ende des Zeithorizontes größere Abstände verwendet als zu Anfang des Zeithorizontes,

Figur 4:

die Berücksichtigung von sich ändernden Beschränkungen zunächst am Ende des Zeithorizontes am Beispiel der Geschwindigkeit,

Figur 5:

die für die Trajektorienplanung der Bedienersteuerung verwendete Integratorkette dritter Ordnung, welche anhand einer Ruckaufschaltung arbeitet,

Figur 6:

die Struktur der Bahnplanung der Bedienersteuerung, welche Beschränkungen des Antriebs berücksichtigt,

Figur 7:

ein beispielhafter Ruckverlauf mit zugehörigen Schaltzeiten, aus welchen anhand der Bahnplanung eine Trajektorie für die Position und/oder Geschwindigkeit und/oder Beschleunigung des Hubwerks berechnet wird,

Figur 8:

ein mit der Ruckaufschaltung generierter Verlauf einer Geschwindigkeits- und Beschleunigungstrajektorie,

Figur 9:

eine Übersicht über das Ansteuerungskonzept mit einer aktiven Seegangskompensation und einem Sollkraftmodus, hier als Konstantspannungsmodus bezeichnet,

Figur 10:

ein Blockschaltbild der Ansteuerung für die aktive Seegangskompensation und

Figur 11:

ein Blockschaltbild der Ansteuerung für den Sollkraftmodus.

Showing:

Figure 0:

a crane mounted on a float according to the present invention,

FIG. 1:

the structure of separate trajectory planning for sea state compensation and operator control,

FIG. 2:

a fourth-order integrator chain for planning trajectories with a continuous jerk,

FIG. 3:

a non-equidistant discretization for trajectory planning, which uses greater distances towards the end of the time horizon than at the beginning of the time horizon,

FIG. 4:

the consideration of changing constraints first at the end of the time horizon using the example of speed,

FIG. 5:

the third-order integrator chain used for trajectory planning of the operator control, which operates on the basis of a jerk-over,

FIG. 6:

the structure of the path planning of the operator control, which takes into account restrictions of the drive,

FIG. 7:

an exemplary jerk course with associated switching times, from which, based on the path planning, a trajectory for the position and / or speed and / or acceleration of the hoisting gear is calculated,

FIG. 8:

a course of a velocity and acceleration trajectory generated with the jerk-over,

FIG. 9:

an overview of the control concept with an active sea state compensation and a desired force mode, here referred to as constant voltage mode,

FIG. 10:

a block diagram of the control for the active sea state compensation and

FIG. 11:

a block diagram of the control for the desired force mode.

Figure 0 shows an embodiment of a crane 1 with a crane control according to the invention for controlling the hoist 5. The hoist 5 has a hoist winch, which moves the cable 4. The cable 4 is guided over a cable suspension point 2, in the exemplary embodiment a deflection roller at the end of the crane boom, on the crane. By moving the cable 4, a load hanging on the rope 3 can be raised or lowered.

In this case, at least one sensor may be provided which measures the position and / or speed of the hoist and transmits corresponding signals to the crane control.

Furthermore, at least one sensor can be provided which measures the cable force and transmits corresponding signals to the crane control. The sensor can be arranged in the region of the crane structure, in particular in a fastening of the winch 5 and / or in a fastening of the pulley 2.

The crane 1 is arranged in the embodiment on a float 6, here a ship. Like also in Figure 0 to recognize the float 6 moves due to the sea at its six degrees of freedom. This will also arranged on the float 6 crane 1 and the cable suspension point 2 moves.

The crane control according to the present invention may have an active sea state compensation, which at least partially compensates for a control of the hoist and the movement of the cable suspension point 2 due to the sea. In particular, the vertical movement of the cable suspension point due to the sea is at least partially compensated.

The sea state compensation may include a measuring device which determines a current sea state movement from sensor data. The measuring device may comprise sensors which are arranged on the crane foundation. In particular, these may be gyroscopes and / or inclination angle sensors. Particularly preferably, three gyroscopes and three inclination angle sensors are provided.

Furthermore, a prediction device can be provided which predicts a future movement of the cable suspension point 2 on the basis of the determined seaward movement and a model of the seaward movement. In particular, the forecasting device alone predicts the vertical movement of the cable suspension point. Sometimes. can be converted in the context of the measuring and / or the forecasting device, a movement of the ship at the point of the sensors of the measuring device in a movement of the cable suspension point.

The forecasting device and the measuring device are advantageously designed as shown in the DE 10 2008 024513 A1 is described in more detail.

Alternatively, the crane according to the invention could also be a crane which is used for lifting and / or lowering a load from or onto a load settling point arranged on a floating body, which therefore moves with the seaway. The forecasting device must in this case predict the future movement of the load take-off point. This can be analogous to the procedure described above, wherein the sensors of the measuring device are arranged on the float of Lastabsetzpunktes. The crane may be, for example, a harbor crane, an offshore crane or a crawler crane.

The hoist winch of the hoist 5 is hydraulically driven in the embodiment. In particular, a hydraulic circuit of hydraulic pump and hydraulic motor is provided, via which the hoist winch is driven. Preferably, a hydraulic accumulator can be provided, via which energy is stored when the load is lowered, so that this energy is available when lifting the load.

Alternatively, an electric drive could be used. This could also be connected to an energy storage.

An embodiment of the present invention, in which a variety of aspects of the present invention are implemented together, will now be shown. However, the individual aspects can also be used separately from one another for the further development of the embodiment of the present invention described in the general part of the present application.

1 Planning of reference trajectories

In order to implement the required predictive behavior of the active sea state compensation, a follow-up control consisting of a precontrol and a feedback in the form of a two-degree-of-freedom structure is used in the exemplary embodiment. The feedforward control is calculated by a differential parameterization and requires twice continuously differentiable reference trajectories.

und ${\dot{\tilde{z}}}_a^h,$

welche z.B. mit Hilfe des in der DE 10 2008 024 513 beschriebenen Algorithmus über einen festen Zeithorizont vorhergesagt werden. Zusätzlich wird bei der Trajektorienplanung noch das Handhebelsignal des Kranfahrers, über das er die Last im inertialen Koordinatensystem verfährt, miteinbezogen.Decisive in the planning is that the drive can follow the given trajectories. Thus, limitations of the hoist must be considered. The starting point for consideration is the vertical position and / or speed of the cable suspension point ${\tilde{z}}_a^H$

and ${\dot{\tilde{z}}}_a^H.$

which eg with the help of in the DE 10 2008 024 513 algorithm can be predicted over a fixed time horizon. In addition, in trajectory planning, the hand lever signal of the crane driver, via which he moves the load in the inertial coordinate system, is also included.

For safety reasons, it is necessary that the winch can still be moved via the hand lever signal even in the event of failure of the active sea state compensation. Therefore, in the trajectory planning concept used, there is a separation between the planning of the reference trajectories for the compensation movement and that due to a hand lever signal, as described in US Pat Fig. 1 is shown.

${\dot{y}}_a^{*}$

und ${\ddot{y}}_a^{*}$

die für die Kompensation geplante Position, Geschwindigkeit und Beschleunigung und $y_l^{*},{\dot{y}}_l^{*}$

und ${\ddot{y}}_l^{*}$

die auf Basis des Handhebelsignals geplante Position, Geschwindigkeit und Beschleunigung zum überlagerten Ab- oder Aufwickeln des Seils. Innerhalb des weiteren Verlaufs der Ausführung werden geplante Referenztrajektorien für die Bewegung der Hubwinde grundsätzlich mit y*, ẏ* bzw. ÿ* bezeichnet, da sie als Referenz für den Systemausgang der Antriebsdynamik dienen.In the picture designate $y_a^{*}.$

${\dot{y}}_a^{*}$

and ${\ddot{y}}_a^{*}$

the position, speed and acceleration planned for the compensation and $y_l^{*}.{\dot{y}}_l^{*}$

and ${\ddot{y}}_l^{*}$

the planned position, speed and acceleration based on the hand lever signal for superimposed winding or winding of the rope. Within the further course of the execution, planned reference trajectories for the movement of the hoisting winches are generally designated by y *, ẏ * or ÿ * , since they serve as a reference for the system output of the drive dynamics.

Due to the separate trajectory planning, it is possible to use the same trajectory planning and the following slave controller in manual operation with switched off sea state compensation or in a complete failure of the sea state compensation (eg due to failure of the IMU) for the hand lever control in manual operation and thus an identical driving behavior to generate with activated sea state compensation.

In order not to violate the given restrictions in speed v _max and acceleration a _max despite the completely independent planning, v _max and a _{max is divided} using a weighting factor 0 ≦ k _l ≦ 1 (cf. Fig. 1 ). This is specified by the crane driver and thus allows the individual distribution of power, which is available for the compensation or the method of the load. Thus follows for the maximum speed and acceleration of the compensation movement ( 1-k _l ) v _max and ( 1-k _l ) a _max and for the trajectories for superimposed winding and winding of the cable k _l v _max and k _l a _max .

A change of k _l can be carried out during operation. Since the maximum possible travel speed or acceleration depends on the total mass of rope and load, v _max and a _max can also change during operation. Therefore, the valid values are also transferred to the trajectory planning.

Although the power factor distribution may not be fully utilized by sharing the power, the crane operator can easily and intuitively adjust the influence of the active sea state compensation.

A weighting of k _l = 1 is equivalent to disabling the active sea state compensation, allowing a smooth transition between on and off compensation.

und ${\ddot{y}}_a^{*}$

zur Kompensation der Vertikalbewegung des Seilaufhängepunkts. Der wesentliche Aspekt hierbei ist, dass mit den geplanten Trajektorien die Vertikalbewegung so weit kompensiert wird, wie es aufgrund der gegebenen und durch k_l eingestellten Beschränkungen möglich ist.The first part of the chapter first explains the generation of reference trajectories $y_a^{*}.{\dot{y}}_a^{*}$

and ${\ddot{y}}_a^{*}$

for compensating the vertical movement of the cable suspension point. The essential aspect here is that with the planned trajectories the vertical movement is compensated as far as is possible on the basis of the given restrictions set by k _l .

ein Optimalsteuerungsproblem formuliert, welches zyklisch gelöst wird, wobei K_p die Anzahl der vorhergesagten Zeitschritte bezeichnet. Die zugehörige numerische Lösung und Implementierung werden im Anschluss diskutiert.Therefore, first the vertical positions and velocities of the cable suspension point are predicted over a complete time horizon ${\tilde{\mathbf{z}}}_a^H={\left[\begin{array}{ccc}{\tilde{z}}_a^H\left(t_k+T_{p.1}\right)& ...& {\tilde{z}}_a^H\left(t_k+T_{p.K_p}\right)\end{array}\right]}^T\mathrm{and}{\dot{\tilde{\mathbf{z}}}}_a^H={\left[\begin{array}{ccc}{\dot{\tilde{z}}}_a^H\left(t_k+T_{p.1}\right)& ...& {\dot{\tilde{z}}}_a^H\left(t_k+T_{p.K_p}\right)\end{array}\right]}^T$

formulated an optimal control problem which is solved cyclically, where K _{p is} the Number of predicted time steps. The associated numerical solution and implementation are discussed below.

und ${\ddot{y}}_l^{*}$

zum Verfahren der Last. Diese werden direkt aus dem Handhebelsignal des Kranfahrers w_hh generiert. Die Berechnung erfolgt durch eine Aufschaltung des maximal zulässigen Rucks.The second part of the chapter deals with the planning of trajectories $y_l^{*}.{\dot{y}}_l^{*}$

and ${\ddot{y}}_l^{*}$

for moving the load. These are generated directly from the hand lever signal of the crane driver w _hh . The calculation is done by adding the maximum allowable jerk.

1.1 Reference trajectories for compensation

In trajectory planning for the compensating movement of the hoisting winch, sufficiently smooth trajectories are to be generated from the predicted vertical positions and speeds of the rope suspending point, taking into account the valid drive restrictions. This task is considered below as a limited optimization problem, which is to be solved online in each time step. Therefore, the approach is similar to the design of a model-predictive control, but in the sense of a model-predictive trajectory generation.

welche mit der entsprechenden Prädiktionszeit, z.B. mit Hilfe des in der DE 10 2008 024 513 beschriebenen Algorithmus, berechnet werden.Serving as references or setpoints for the optimization are the vertical positions and velocities of the cable suspension point predicted at time t _k over a complete time horizon with K _{p time} steps ${\tilde{\mathbf{z}}}_a^H={\left[\begin{array}{ccc}{\tilde{z}}_a^H\left(t_k+T_{p.1}\right)& ...& {\tilde{z}}_a^H\left(t_k+T_{p.K_p}\right)\end{array}\right]}^T\mathrm{and}{\dot{\tilde{\mathbf{z}}}}_a^H={\left[\begin{array}{ccc}{\dot{\tilde{z}}}_a^H\left(t_k+T_{p.1}\right)& ...& {\dot{\tilde{z}}}_a^H\left(t_k+T_{p.K_p}\right)\end{array}\right]}^T.$

which with the corresponding prediction time, eg with the help of in the DE 10 2008 024 513 described algorithm.

Taking into account the restrictions that are valid due to k _l , v _max and a _max, an optimal time sequence for the compensation movement can then be determined.

However, analogously to the model predictive control, only the first value of the trajectory calculated thereby is used for the subsequent control. in the Next time step, the optimization is repeated with an updated and thereby more accurate prediction of the vertical position and speed of the cable suspension point.

The advantage of the model-predictive trajectory generation with downstream control compared to a classical model-predictive control on the one hand is that the control part and the associated stabilization can be calculated with a higher sampling time compared to the trajectory generation. Therefore, you can shift the computationally intensive optimization into a slower task.

On the other hand, an emergency function can be implemented in this concept, in case the optimization does not find a valid solution, independently of the regulation. It consists of a simplified trajectory planning, whereupon the regulation resorts to such an emergency situation and continues to control the winds.

1.1.1 System model for the planning of the compensation movement

als sprungfähig erachtet werden. Allerdings sind bei der Kompensationsbewegung im Hinblick auf die Windenlebensdauer Sprünge im Ruck zu vermeiden, wodurch erst die vierte Ableitung ${\stackrel{\left(4\right)}{y}}_a^{*}$

als sprungfähig betrachtet werden kann.In order to meet the requirements for the continuity of the reference trajectories for the compensation movement, the third derivation must be made at the earliest ${\stackrel{...}{y}}_a^{*}$

be considered as capable of jumping. However, in the compensation movement with regard to the life of the winch jumps in the jerk to avoid, making only the fourth derivative ${\stackrel{\left(4\right)}{y}}_a^{*}$

can be considered as capable of jumping.

mindestens stetig zu planen und die Trajektoriengenerierung für die Kompensationsbewegung erfolgt anhand der in Fig. 2 veranschaulichten Integratorkette vierter Ordnung. Diese dient bei der Optimierung als Systemmodell und lässt sich im Zustandsraum als $$\begin{array}{l}{\dot{\mathrm{x}}}_a=\underset{{\mathrm{A}}_a}{\underbrace{\left[\begin{array}{cccc}0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\\ 0& 0& 0& 0\end{array}\right]}}{\mathrm{x}}_a+\underset{{\mathrm{B}}_a}{\underbrace{\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]}}{u}_a,x_a\left(0\right)={\mathrm{x}}_{a,0},\\ {\mathrm{y}}_a={\mathrm{x}}_a\end{array}$$

ausdrücken. Hier beinhaltet der Ausgang ${\mathbf{y}}_a={\left[y_a^{*}{\stackrel{\mathrm{.}}{y}}_y^{*}{\ddot{y}}_a^{*}{\stackrel{\dots }{y}}_a^{*}\right]}^T$

die geplanten Trajektorien für die Kompensationsbewegung. Zur Formulierung des Optimalsteuerungsproblems und in Hinblick auf die spätere Implementierung wird dieses zeitkontinuierliche Modell zunächst auf dem Gitter $${\tau }_0<{\tau }_1<\dots <{\tau }_{K_p-1}<{\tau }_{K_p}$$

diskretisiert, wobei K_p die Anzahl der Prädiktionsschritte für die Vorhersage der Vertikalbewegung des Seilaufhängepunkts darstellt. Um die diskrete Zeitdarstellung bei der Trajektoriengenerierung von der diskreten Systemzeit t_k zu unterscheiden, wird sie mit τ_k = kΔτ bezeichnet, wobei k = 0,···,K_p und Δτ das für die Trajektoriengenerierung verwendete Diskretisierungsintervall des Horizonts K_p ist.Thus, the jerk ${\stackrel{...}{y}}_a^{*}$

plan at least steadily and the Trajektoriengenerierung for the compensation movement is based on the in Fig. 2 illustrated fourth order integrator chain. This serves as a system model in the optimization and can be used in the state space as $$\begin{array}{l}{\dot{\mathrm{x}}}_a=\underset{{\mathrm{A}}_a}{\underset{\}}{\left[\begin{array}{cccc}0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\\ 0& 0& 0& 0\end{array}\right]}}{\mathrm{x}}_a+\underset{{\mathrm{B}}_a}{\underset{\}}{\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]}}{u}_a.x_a\left(0\right)={\mathrm{x}}_{a.0}.\\ {\mathrm{y}}_a={\mathrm{x}}_a\end{array}$$

express. Here is the output ${\mathbf{y}}_a={\left[y_a^{*}{\stackrel{\mathrm{,}}{y}}_y^{*}{\ddot{y}}_a^{*}{\stackrel{...}{y}}_a^{*}\right]}^T$

the planned trajectories for the compensation movement. To formulate the optimal control problem and with respect to the later implementation, this time-continuous model first becomes on the grid $${\tau }_0<{\mathrm{<figure-callout\; id="1"\; label="\tau "\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">\tau </figure-callout>}}_1<...<{\tau }_{K_p-1}<{\tau }_{K_p}$$

where K _{p represents} the number of prediction steps for the prediction of the vertical movement of the cable suspension point. In order to distinguish the discrete time representation in the trajectory generation from the discrete system time t _k , it is denoted by τ _k = k Δτ, where k = 0, ··· , K _p and Δ τ the discretization interval of the horizon K _p used for the trajectory generation is.

Fig. 3 makes it clear that the selected grid is not equidistant, which reduces the number of necessary nodes on the horizon. This makes it possible to keep the dimension of the optimal control problem to be solved small. The influence of the grosser discretization towards the end of the horizon does not adversely affect the planned trajectory since the prediction of vertical position and velocity towards the end of the prediction horizon is less accurate.

exakt berechnen. Für die Integratorkette aus Fig. 2 folgt sie zu $$\begin{array}{ccc}\hfill {\mathrm{x}}_a\left({\tau }_{k+1}\right)& =\left[\begin{array}{cccc}1& \mathrm{\Delta }{\tau }_k& \frac{\mathrm{\Delta }{\tau }_k^2}{2}& \frac{\mathrm{\Delta }{\tau }_k^3}{6}\\ 0& 1& \mathrm{\Delta }{\tau }_k& \frac{\mathrm{\Delta }{\tau }_k^2}{2}\\ 0& 0& 1& \mathrm{\Delta }{\tau }_k\\ 0& 0& 0& 1\end{array}\right]+\left[\begin{array}{c}\frac{\mathrm{\Delta }{\tau }_k^1}{24}\\ \frac{\mathrm{\Delta }{\tau }_k^3}{6}\\ \frac{\mathrm{\Delta }{\tau }_k^2}{2}\\ \mathrm{\Delta }{\tau }_k\end{array}\right]u_a\left({\tau }_k\right),\hfill & \hfill {\mathrm{x}}_a\left(0\right)={\mathrm{x}}_{a,0},\\ \hfill {\mathrm{y}}_a\left({\tau }_k\right)& ={\mathrm{x}}_a\left({\tau }_k\right),\hfill & \hfill k=0,\dots ,K_p-1,\end{array}$$

wobei Δτ_k = τ _k+1 - τ_k die für den jeweiligen Zeitschritt gültige Diskretisierungsschrittweite beschreibt.The time-discrete system representation valid for this grid can be determined by the analytical solution $${\mathrm{x}}_a\left(t\right)={\mathrm{e}}^{{\mathrm{A}}_{a}t}{\mathrm{x}}_a\left(0\right)+\underset{0}{\overset{t}{\int }}{e}^{{\mathrm{A}}_a\left(t-\tau \right)}{\mathrm{B}}_a{u}_a\left(\tau \right)\mathit{d\tau }$$

calculate exactly. For the integrator chain off Fig. 2 she follows $$\begin{array}{ccc}\hfill {\mathrm{x}}_a\left({\tau }_{k+1}\right)& =\left[\begin{array}{cccc}1& \mathrm{\Delta }{\tau }_k& \frac{\mathrm{\Delta }{\tau }_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}{2}& \frac{\mathrm{\Delta }{\tau }_{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}}^3}{6}\\ 0& 1& \mathrm{\Delta }{\tau }_k& \frac{\mathrm{\Delta }{\tau }_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}{2}\\ 0& 0& 1& \mathrm{\Delta }{\tau }_k\\ 0& 0& 0& 1\end{array}\right]+\left[\begin{array}{c}\frac{\mathrm{\Delta }{\tau }_{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}}^1}{24}\\ \frac{\mathrm{\Delta }{\tau }_{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}}^3}{6}\\ \frac{\mathrm{\Delta }{\tau }_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}{2}\\ \mathrm{\Delta }{\tau }_k\end{array}\right]u_a\left({\tau }_k\right).\hfill & \hfill {\mathrm{x}}_a\left(0\right)={\mathrm{x}}_{a.0}.\\ \hfill {\mathrm{y}}_a\left({\tau }_k\right)& ={\mathrm{x}}_a\left({\tau }_k\right).\hfill & \hfill k=0.....K_p-1.\end{array}$$

where Δτ _k = τ _{k +1} -τ _{k describes} the valid for the respective time step discretization step size.

1.1.2 Formulation and solution of the optimal control problem

By solving the optimal control problem, a trajectory is to be planned which follows the predicted vertical movement of the cable suspension point as close as possible and at the same time satisfies the given restrictions.

wobei w_a (τ_k ) die zum jeweiligen Zeitschritt gültige Referenz bezeichnet. Da hierfür nur die vorhergesagte Position ${\tilde{z}}_a^h\left(t_k+T_{p,k}\right)$

und Geschwindigkeit ${\dot{\tilde{z}}}_a^h\left(t_k+T_{p,k}\right)$

des Seilaufhängepunkts zur Verfügung stehen, werden die zugehörige Beschleunigung und der Ruck zu Null gesetzt. Der Einfluss dieser inkonsistenten Vorgabe lässt sich allerdings durch eine entsprechende Gewichtung der Beschleunigungs- und Ruckabweichung klein halten. Somit gilt: $${\mathrm{w}}_a\left({\tau }_k\right)={\left[\begin{array}{cccc}{\tilde{z}}_a^h\left(t_k+T_{p,k}\right)& {\dot{\tilde{z}}}_a^h\left(t_k+T_{p,k}\right)& 0& 0\end{array}\right]}^T,k=1,\dots ,K_p\mathrm{.}$$

To meet this requirement, the merit function is as follows: $$J=\frac{1}{2}{\displaystyle \underset{k=1}{\overset{K_p}{\Sigma }}}\left\{{\left[{\mathrm{y}}_a\left({\tau }_k\right)-{\mathrm{w}}_a\left({\tau }_k\right)\right]}^T{\mathrm{Q}}_w\left({\tau }_k\right)\left[{\mathrm{y}}_a\left({\tau }_k\right)-{\mathrm{w}}_a\left({\tau }_k\right)\right]+u_a\left({\tau }_k-1\right)r_u{u}_a\left({\tau }_k-1\right)\right\}$$

where w _a ( τ _k ) designates the reference valid for the respective time step. Because only the predicted position ${\tilde{z}}_a^H\left(t_k+T_{p.k}\right)$

and speed ${\dot{\tilde{z}}}_a^H\left(t_k+T_{p.k}\right)$

of the rope suspension point, the associated acceleration and jerk are set to zero. However, the influence of this inconsistent specification can be kept small by a corresponding weighting of the acceleration and jerk deviation. Thus: $${\mathrm{w}}_a\left({\tau }_k\right)={\left[\begin{array}{cccc}{\tilde{z}}_a^H\left(t_k+T_{p.k}\right)& {\dot{\tilde{z}}}_a^H\left(t_k+T_{p.k}\right)& 0& 0\end{array}\right]}^T.k=1.....K_p\mathrm{,}$$

werden Abweichungen von der Referenz in der Gütefunktion gewichtet. Der skalare Faktor r_u bewertet den Stellaufwand. Während r_u, q_w,3 und q_w,4 über den gesamten Prädiktionshorizont konstant sind, werden q_w,1 und q_w,2 in Abhängigkeit vom Zeitschritt τ_k gewählt. Dadurch lassen sich Referenzwerte am Anfang des Prädiktionshorizonts stärker gewichten als diejenigen am Ende. Mithin kann man die mit steigender Prognosezeit nachlassende Genauigkeit der Vertikalbewegungsprognose in der Gütefunktion abbilden. Wegen des Nichtvorhandenseins der Referenzen für die Beschleunigung und den Ruck bestrafen die Gewichte q_w,3 und q_w,4 nur Abweichungen von Null, weshalb sie kleiner als die Gewichte für die Position q _w,1 (τ_k) und Geschwindigkeit q _w,2 (τ_k) gewählt werden.About the positive semidefinite diagonal matrix $${\mathrm{Q}}_w\left({\tau }_k\right)=\mathrm{diag}\left(q_{w.1}\left({\tau }_k\right).q_{w.2}\left({\tau }_k\right).q_{w.3}.q_{w.4}\right).k=1.....K_p$$

deviations from the reference in the quality function are weighted. The scalar factor r _u evaluates the actuating effort. While r _u , q _{w, 3} and q _{w, 4} are constant over the entire prediction horizon, q _{w, 1} and q _{w, 2 are} chosen as a function of the time step τ _k . This allows reference values at the beginning of the prediction horizon stronger weights than those at the end. Thus, one can map the decreasing accuracy of the vertical motion forecast in the quality function with increasing forecast time. Because of the absence of the acceleration and jerk references, the weights q _{w, 3} and q _{w, 4} only penalize deviations from zero, which is why they are less than the weights for the position q _{w, 1} (τ _k ) and velocity q _{w, 2} (τ _k ) can be selected.

und für den Eingang: $$-{\delta }_a\left({\tau }_k\right)\frac{d}{dt}{j}_{\max }\le u_a\left({\tau }_k\right)\le {\delta }_a\left({\tau }_k\right)\frac{d}{dt}{j}_{\max },k=0,\dots ,K_p-1.$$

The associated constraints on the optimal control problem follow from the available power of the drive and the currently selected weighting factor k _l (cf. Fig. 1 ). Accordingly, for the states of the system model from (1.4): $$\begin{array}{cc}-{\delta }_a\left({\tau }_k\right)\left(1-k_l\right)v_{\mathrm{Max}}\le x_{a.2}\left({\tau }_k\right)\le {\delta }_a\left({\tau }_k\right)\left(1-k_l\right)v_{\mathrm{Max}}.& \\ -{\delta }_a\left({\tau }_k\right)\left(1-k_l\right){\alpha }_{\mathrm{Max}}\le x_{a.3}\left({\tau }_k\right)\le {\delta }_a\left({\tau }_k\right)\left(1-k_l\right)a_{\mathrm{Max}}.& k=1.....K_p.\\ -{\delta }_a\left({\tau }_k\right)j_{\mathrm{Max}}\le x_{a.4}\left({\tau }_k\right)\le {\delta }_a\left({\tau }_k\right)j_{\mathrm{Max}}& \end{array}$$

and for the entrance: $$-{\delta }_a\left({\tau }_k\right)\frac{d}{dt}{j}_{\mathrm{Max}}\le u_a\left({\tau }_k\right)\le {\delta }_a\left({\tau }_k\right)\frac{d}{dt}{j}_{\mathrm{Max}}.k=0.....K_p-1.$$

Here δ _a (τ _k ) represents a reduction factor chosen so that the respective limit at the end of the horizon is 95% of that at the beginning of the horizon. For the intervening time steps, δ _a ( τ _k ) follows from linear interpolation. The reduction of the restrictions along the horizon increases the robustness of the method with respect to the existence of permissible solutions.

konstant. Um die Lebensdauer der Hubwinde und des gesamten Krans zu erhöhen, werden sie in Hinblick auf eine maximal zulässige Schockbelastung gewählt. Für den Positionszustand gelten keine Beschränkungen.While the speed and acceleration limits may change during operation, the jerk limitations are j _max and the derivative of the jerk $\frac{d}{dt}{j}_{\mathbf{Max}}$

constant. To increase the lifespan of the hoist winch and the entire crane, they are selected for maximum shock load. There are no restrictions on the position condition.

Since the maximum speed v _max and acceleration a _max and the weighting factor of the power k _{l are} externally determined during operation, the speed and acceleration limitations for the optimal control problem inevitably change as well. The presented time-variant constraints take into account the presented concept as follows: As soon as a constraint changes, the updated value is first only at the end of the prediction horizon for the time step τ _{κ ρ} included. Then, as time progresses, it pushes it to the beginning of the prediction horizon.

Fig. 4 clarifies this procedure based on the speed limit. When reducing a restriction, care must also be taken that it matches its maximum permissible derivative. This means that, for example, the speed limit (1-k _l ) v _max can be reduced as fast as the current acceleration limitation (1 k _l ) a _max permits. Because of the pushing through of the updated constraints, a constrained initial condition x _a ( τ ₀ ) always has a solution which in turn does not violate the updated constraints. However, it takes the complete prediction horizon until a changed restriction finally affects the planned trajectories at the beginning of the horizon.

Thus, the optimal control problem is fully met by the quadratic merit function (1.5) to be minimized, the system model (1.4) and the inequality constraints from (1.8) and (1.9) in the form of a linear quadratic programming problem (QP problem). When the optimization is carried out for the first time, the initial condition is chosen to be x _a (τ ₀ ) = [0,0,0,0] ^T. Subsequently, the value x _a (τ ₁ ) calculated in the last optimization step for the time step τ ₁ is used as the initial condition.

The actual solution to the QP problem is calculated in each time step using a numerical method known as the QP solver.

Due to the computational effort for the optimization, the sampling time for the trajectory planning of the compensatory motion is greater than the discretization time of all remaining components of the active sea state compensation; thus Δτ> Δ t . However, so that the reference trajectories are available for the control at a faster rate, the simulation of the integrator chain takes place Fig. 2 outside the optimization with the faster sampling time A t instead. As soon as new values from the optimization are available, the states x _a ( τ ₀ ) are used as an initial condition for the simulation, and the manipulated variable at the beginning of the prediction horizon u _a (τ ₀ ) is written to the integrator chain as a constant input.

1.2 Reference trajectories for the method of load

auch in Bezug auf die Lebensdauer der Winde als ausreichend herausgestellt. Somit lässt sich im Gegensatz zu den für die Kompensationsbewegung geplanten Referenztrajektorien schon die dritte Ableitung ${\stackrel{\dots }{y}}_l^{*},$

welche dem Ruck entspricht, als sprungfähig erachten.Analogous to the compensatory movement, twice-continuously differentiable reference trajectories are necessary for the superimposed lever control (cf. Fig. 1 ). Since these movements, which can be predetermined by the crane operator, normally do not lead to any rapid changes of direction for the winch, the minimum requirement is a constantly planned acceleration ${\ddot{y}}_l^{*}$

also in terms of the life of the winch proved sufficient. Thus, in contrast to the reference trajectories planned for the compensatory movement, the third derivative can already be used ${\stackrel{...}{y}}_l^{*}.$

which corresponds to the jerk, consider as jumpable.

As Fig. 5 shows, it also serves as the input of a third-order integrator chain. In addition to the requirements for continuity, the planned trajectories must also meet the currently valid speed and acceleration restrictions which result for the lever control in k _l v _max and k _l a _max .

The hand lever signal of the crane driver -100 ≤ w _hh ≤ 100 is interpreted as a relative speed specification in relation to the currently maximum permissible speed k _l v _max . Thus, the predetermined speed given by the hand lever results Fig. 6 to $${\upsilon }_{\mathrm{hh}}^{*}=k_l{\upsilon }_{\mathrm{Max}}\frac{w_{\mathrm{hh}}}{100}\mathrm{,}$$

As can be seen, the setpoint speed currently given by the hand lever depends on the hand lever position w _hh , the variable weighting factor k _l and the current maximum permissible winch speed v _max .

The task of trajectory planning for the hand lever control can now be specified as follows: From the setpoint speed given by the hand lever, a continuously differentiable speed profile is to be generated so that the acceleration has a steady course. As a method for this task offers a so-called jerk-on.

Its basic idea is that the maximum permissible jerk j _max in a first phase acts on the input of the integrator chain until the maximum permissible acceleration is reached. In the second phase, the speed is increased with constant acceleration; and in the last phase, the maximum permissible negative jerk is switched on so that the desired final speed is reached.

Therefore, only the switching times between the individual phases are to be determined in the jerk connection. Fig. 7 illustrates an exemplary course of the jerk for a speed change together with the switching times. Here T _{l, 0} denotes the time at which a rescheduling takes place. The times T _{l, 1} , T _{l, 2} and T _{l, 3} each refer to the calculated switching times between the individual phases. Their calculation is outlined in the following paragraph.

oder die aktuell gültige maximale Beschleunigung für die Handhebelsteuerung k_la_max ändert. Die Sollgeschwindigkeit kann sich aufgrund einer neuen Handhebelstellung w_hh oder durch eine neue Vorgabe von k_l bzw. v_max ändern (vgl. Fig. 6). Analog dazu ist eine Variation der maximal gültigen Beschleunigung durch k_l oder a_max möglich.As soon as a new situation arises for the hand lever control, a rescheduling of the generated trajectories takes place. A new situation occurs as soon as the setpoint speed $v_{\mathit{hh}}^{*}$

or the currently valid maximum acceleration for the hand lever control k _l a _max changes. The desired speed may change due to a new hand lever position w _hh or by a new specification of k _l or v _max (cf. Fig. 6 ). Analogously, a variation of the maximum valid acceleration by k _l or a _{max is} possible.

und der entsprechenden Beschleunigung ${\ddot{y}}_l^{*}\left(T_{l,0}\right)$

diejenige Geschwindigkeit berechnet, welche sich bei einer Reduzierung der Beschleunigung auf Null ergibt: $$\tilde{\upsilon }={\dot{y}}_l^{*}\left(T_{l,0}\right)+\mathrm{\Delta }{\tilde{T}}_1{\ddot{y}}_l^{*}\left(T_{l,0}\right)+\frac{1}{2}\mathrm{\Delta }{\tilde{T}}_1^2{\tilde{u}}_{l,1},$$

wobei die minimal notwendige Zeit durch $$\mathrm{\Delta }{\tilde{T}}_1=-\frac{{\ddot{y}}_l^{*}}{{\tilde{u}}_{l,1}},{\tilde{u}}_{l,1}\ne 0$$

gegeben ist und ũ _l.1 den Eingang der Integratorkette benennt, also den aufgeschalteten Ruck (vgl. Fig. 5). Er ergibt sich in Abhängigkeit von der aktuell geplanten Beschleunigung ${\ddot{y}}_l^{*}\left(T_{l,0}\right)$

zu $${\tilde{u}}_{l,1}=\{\begin{array}{ll}{j}_{\max },& \mathrm{für}{\ddot{y}}_l^{*}<0\\ -j_{\max },& \mathrm{für}{\ddot{y}}_l^{*}>0\\ 0,& \mathrm{für}{\ddot{y}}_l^{*}=0\end{array}\mathrm{.}$$

When repurposing the trajectories is initially from the currently planned speed ${\dot{y}}_l^{*}\left(T_{l.0}\right)$

and the corresponding acceleration ${\ddot{y}}_l^{*}\left(T_{l.0}\right)$

calculates the speed which results when the acceleration is reduced to zero: $$\tilde{\upsilon }={\dot{y}}_l^{*}\left(T_{l.0}\right)+\mathrm{\Delta }{\tilde{T}}_1{\ddot{y}}_l^{*}\left(T_{l.0}\right)+\frac{1}{2}\mathrm{\Delta }{\tilde{T}}_1^2{\tilde{u}}_{l.1}.$$

being the minimum necessary time through $$\mathrm{\Delta }{\tilde{T}}_1=-\frac{{\ddot{y}}_l^{*}}{{\tilde{u}}_{l.1}}.{\tilde{u}}_{l.1}\ne 0$$

is given and ũ _{l .1 designates} the input of the integrator chain, that is, the connected jerk (cf. Fig. 5 ). It depends on the currently planned acceleration ${\ddot{y}}_l^{*}\left(T_{l.0}\right)$

to $${\tilde{u}}_{l.1}=\{\begin{array}{ll}{j}_{\mathrm{Max}}.& \mathrm{For}{\ddot{y}}_l^{*}<0\\ -j_{\mathrm{Max}}.& \mathrm{For}{\ddot{y}}_l^{*}>0\\ 0.& \mathrm{For}{\ddot{y}}_l^{*}=0\end{array}\mathrm{,}$$

ist, erreicht ν̃ den gewünschten Wert $v_{\mathit{hh}}^{*}$

nicht und die Beschleunigung kann weiter erhöht werden. Falls jedoch $v_{\mathit{hh}}^{*}<\tilde{v}$

gilt, ist ν̃ zu schnell und die Beschleunigung ist sofort zu reduzieren.Depending on the theoretically calculated speed and the desired setpoint speed, the course of the input can now be specified. If $v_{\mathit{hh}}^{*}>\tilde{v}$

is, ν reaches the desired value $v_{\mathit{hh}}^{*}$

not and the acceleration can be further increased. If so $v_{\mathit{hh}}^{*}<\tilde{v}$

ν is too fast and the acceleration has to be reduced immediately.

mit ${\mathbf{u}}_l=\lfloor u_{l,1},u_{l,2},u_{l,3}\rfloor$

und dem in der jeweiligen Phase aufgeschalteten Eingangssignal u_l,i. Die Dauer einer Phase ergibt sich zu ΔT_i = T_l,i - T _l,i-1 mit i = 1,2,3. Demnach lauten die geplante Geschwindigkeit und Beschleunigung am Ende der ersten Phase: $${\dot{y}}_l^{*}\left(T_{l,1}\right)={\dot{y}}_l^{*}\left(T_{l,0}\right)+\mathrm{\Delta }{T}_1{\ddot{y}}_l^{*}\left(T_{l,0}\right)+\frac{1}{2}\mathrm{\Delta }{T}_1^2{u}_{l,1},$$

$${\ddot{y}}_l^{*}\left(T_{l,1}\right)={\ddot{y}}_l^{*}\left(T_{l,0}\right)+\mathrm{\Delta }{T}_1{u}_{l,1}$$

und nach der zweiten Phase: $$\begin{array}{l}{\dot{y}}_l^{*}\left(T_{l,2}\right)={\dot{y}}_l^{*}\left(T_{l,1}\right)+\mathrm{\Delta }{T}_2{\ddot{y}}_l^{*}\left(T_{l,1}\right),\\ {\ddot{y}}_l^{*}\left(T_{l,2}\right)={\ddot{y}}_l^{*}\left(T_{l,1}\right),\end{array}$$

$${\ddot{y}}_l^{*}\left(T_{l,2}\right)={\ddot{y}}_l^{*}\left(T_{l,1}\right),$$

wobei u_l,2 = 0 angenommen wurde. Nach der dritten Phase folgt schließlich: $${\dot{y}}_l^{*}\left(T_{l,3}\right)={\dot{y}}_l^{*}\left(T_{l,2}\right)+\mathrm{\Delta }{T}_3{\ddot{y}}_l^{*}\left(T_{l,2}\right)+\frac{1}{2}\mathrm{\Delta }{T}_3^2{u}_{l,3},$$

$${\ddot{y}}_l^{*}\left(T_{l,3}\right)={\ddot{y}}_l^{*}\left(T_{l,2}\right)+\mathrm{\Delta }{T}_3{u}_{l,3}\mathrm{.}$$

From these considerations, the following switching sequences of the jerk for the three phases can be derived $${\mathrm{u}}_l=\{\begin{array}{ll}\left[\begin{array}{ccc}{j}_{\mathrm{Max}}& 0& -j_{\mathrm{Max}}\end{array}\right].& \mathrm{For}\tilde{\upsilon }\le {\upsilon }_{\mathrm{hh}}^{*}\\ \left[\begin{array}{ccc}{-j}_{\mathrm{Max}}& 0& j_{\mathrm{Max}}\end{array}\right].& \mathrm{For}\tilde{\upsilon }>{\upsilon }_{\mathrm{hh}}^{*}\end{array}$$

With ${\mathbf{u}}_l=\lfloor u_{l.1}.u_{l.2}.u_{l.3}\rfloor$

and the input in the respective phase input signal u _{l, i} . The duration of one phase is given by Δ T _i = T _{l, i} - T _{l, i-1} with i = 1,2,3. Therefore are the planned speed and acceleration at the end of the first phase: $${\dot{y}}_l^{*}\left(T_{l.1}\right)={\dot{y}}_l^{*}\left(T_{l.0}\right)+\mathrm{<figure-callout\; id="1"\; label="\Delta \; \; T"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}{T}_{}{}_1{\ddot{y}}_l^{*}\left(T_{l.0}\right)+\frac{1}{2}\mathrm{\Delta }{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2{u}_{l.1}.$$

$${\ddot{y}}_l^{*}\left(T_{l.1}\right)={\ddot{y}}_l^{*}\left(T_{l.0}\right)+\mathrm{<figure-callout\; id="1"\; label="\Delta \; \; T"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}{T}_{}{}_1{u}_{l.1}$$

and after the second phase: $$\begin{array}{l}{\dot{y}}_l^{*}\left(T_{l.2}\right)={\dot{y}}_l^{*}\left(T_{l.1}\right)+\mathrm{<figure-callout\; id="2"\; label="\Delta \; \; T"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}{T}_{}{}_2{\ddot{y}}_l^{*}\left(T_{l.1}\right).\\ {\ddot{y}}_l^{*}\left(T_{l.2}\right)={\ddot{y}}_l^{*}\left(T_{l.1}\right).\end{array}$$

$${\ddot{y}}_l^{*}\left(T_{l.2}\right)={\ddot{y}}_l^{*}\left(T_{l.1}\right).$$

where u _{l, 2} = 0 was assumed. After the third phase finally follows: $${\dot{y}}_l^{*}\left(T_{l.3}\right)={\dot{y}}_l^{*}\left(T_{l.2}\right)+\mathrm{<figure-callout\; id="3"\; label="\Delta \; \; T"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}{T}_{}{}_3{\ddot{y}}_l^{*}\left(T_{l.2}\right)+\frac{1}{2}\mathrm{\Delta }{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">T</figure-callout>}}_3^2{u}_{l.3}.$$

$${\ddot{y}}_l^{*}\left(T_{l.3}\right)={\ddot{y}}_l^{*}\left(T_{l.2}\right)+\mathrm{<figure-callout\; id="3"\; label="\Delta \; \; T"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}{T}_{}{}_3{u}_{l.3}\mathrm{,}$$

$$\mathrm{\Delta }{T}_3=\frac{0-\tilde{a}}{u_{l,3}},$$

wobei ã für die maximal erreichte Beschleunigung steht. Durch Einsetzen von (1.21) und (1.22) in (1.15), (1.16) und (1.19) entsteht ein Gleichungssystem, das sich nach ã auflösen lässt. Unter Beachtung von ${\dot{y}}_l^{*}\left(T_{l,3}\right)=v_{\mathit{hh}}^{*}$

ergibt sich letztendlich: $$\tilde{a}=\pm \sqrt{\frac{u_{l,3}\left[2{\dot{y}}_l^{*}\left(T_{l,0}\right)u_{l,1}-{\ddot{y}}_l^{*}{\left(T_{l,0}\right)}^2-2{\upsilon }_{\mathrm{hh}}^{*}{u}_{l,1}\right]}{u_{l,1}-u_{l,3}}}\mathrm{.}$$

For exact calculation of the switching times T _{l, i} , the acceleration limitation is initially neglected, whereby ΔT ₂ = 0. Due to this simplification, the lengths of the two remaining time intervals can be specified as follows: $$\mathrm{<figure-callout\; id="1"\; label="\Delta \; \; T"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}{T}_{}{}_1=\frac{\tilde{a}-{\ddot{y}}_l^{*}\left(T_{l.0}\right)}{u_{l.1}}.$$

$$\mathrm{<figure-callout\; id="3"\; label="\Delta \; \; T"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}{T}_{}{}_3=\frac{0-\tilde{a}}{u_{l.3}}.$$

where ã stands for the maximum acceleration achieved. Substituting (1.21) and (1.22) into (1.15), (1.16), and (1.19) produces a system of equations that can be solved for ã. In consideration of ${\dot{y}}_l^{*}\left(T_{l.3}\right)=v_{\mathit{hh}}^{*}$

finally results: $$\tilde{a}=\pm \sqrt{\frac{u_{l.3}\left[2{\dot{y}}_l^{*}\left(T_{l.0}\right)u_{l.1}-{\ddot{y}}_l^{*}{\left(T_{l.0}\right)}^2-2{\upsilon }_{\mathrm{hh}}^{*}{u}_{l.1}\right]}{u_{l.1}-u_{l.3}}}\mathrm{,}$$

The sign of ã follows from the condition that Δ T ₁ and Δ T ₃ must be positive in (1.21) and (1.22), respectively.

In a second step , the actual maximum acceleration is determined from ã and the maximum permissible acceleration k _l a _max : $$\tilde{a}={\ddot{y}}_l^{*}\left(T_{l.1}\right)={\ddot{y}}_l^{*}\left(T_{l.2}\right)=\min \left\{k_l{a}_{\mathrm{Max}}.\mathrm{Max}\left\{-k_l{a}_{\mathrm{Max}}.\tilde{a}\right\}\right\}\mathrm{,}$$

wobei ${\dot{y}}_l^{*}\left(T_{l,1}\right)$

aus (1.15) folgt. Die Schaltzeitpunkte lassen sich direkt aus den Zeitintervallen ablesen: $$T_{l,i}=T_{l,i-1}+\mathrm{\Delta }{T}_i,i=1,2,3.$$

With it finally the time intervals actually occurring Δ T ₁ and T Δ can be calculated. ₃ They result from (1.21) and (1.22) with ã = a̅. The unknown time interval Δ T ₂ is now determined from (1.17) and (1.19) with Δ t ₁ and Δ t ₃ from (1.21) and (1.22) to $$\mathrm{\Delta }{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">T</figure-callout>}}_2=\frac{2{\upsilon }_{\mathrm{hh}}^{*}{u}_{l.3}+{\tilde{a}}^2-2{\dot{y}}_l^{*}\left(T_{l.1}\right)u_{l.3}}{2\tilde{a}{u}_{l.3}}.$$

in which ${\dot{y}}_l^{*}\left(T_{l.1}\right)$

from (1.15) follows. The switching times can be read directly from the time intervals: $$T_{l.i}=T_{l.i-1}+\mathrm{\Delta }{T}_i.i=1.2.\mathrm{Third}$$

und ${\ddot{y}}_l^{*}$

kann man mit den einzelnen Schaltzeitpunkten analytisch berechnen. Hierbei ist zu erwähnen, dass die durch die Schaltzeitpunkte geplanten Trajektorien häufig nicht vollständig abgefahren werden, da vor Erreichen des Schaltzeitpunkts T_l,3 eine neue Situation eintritt, dadurch ein Umplanen stattfindet und neue Schaltzeitpunkte berechnet werden. Wie bereits erwähnt tritt eine neue Situation durch eine Änderung von w_hh, v_max, a_max oder k_l ein.The speed and acceleration curves to be planned ${\dot{y}}_l^{*}$

and ${\ddot{y}}_l^{*}$

can be calculated analytically with the individual switching times. It should be mentioned here that the trajectories planned by the switching times are often not traversed completely, since a new situation occurs before reaching the switching time T _{l, 3} , as a result a rescheduling takes place and new switching times are calculated. As already mentioned, a new situation occurs by a change of w _hh , v _max , a _max or k _l .

Fig. 8 shows a trajectory exemplified by the method presented. The course of the trajectories includes both cases, which can occur on the basis of (1.24). In the first case, the maximum allowable acceleration reached at the time t = 1 s and it follows a phase with constant acceleration. The second case occurs at time t = 3.5s. Here, the maximum allowable acceleration due to the hand lever position is not fully achieved. The result is that the first and second switching time coincide and ΔT ₂ = 0 applies. The associated position history is calculated according to Fig. 5 by integrating the velocity profile, the position being initialized at startup by the rope length currently being handled by the hoist winch.

2 Control concept for the hoist winch

In principle, the control consists of two different modes of operation: the active sea state compensation for decoupling the vertical load movement from the ship movement with free-hanging load and the constant voltage control to avoid slack rope, as soon as the load is deposited on the seabed. During a deep-sea stroke, the sea state compensation is initially active. Based on a detection of the settling process is automatically switched to the constant voltage control. Fig. 9 illustrates the overall concept with the associated control and control variables.

However, each of the two different modes of operation could also be implemented without the other mode of operation. Furthermore, a constant voltage mode, as described below, can also be used independently of the use of the crane on a ship and independently of an active sea state compensation.

ausgleicht und der Kranfahrer die Last mit Hilfe des Handhebels im als inertial betrachteten h-Koordinatensystem verfährt. Damit die Ansteuerung das geforderte prädiktive Verhalten zur Minimierung des Kompensationsfehlers aufweist, wird sie durch einen Vorsteuerungs- und Stabilisierungsteil in Form einer Zwei-Freiheitsgrade-Struktur umgesetzt. Die Vorsteuerung berechnet sich aus einer differentiellen Parametrierung mit Hilfe des flachen Ausgangs der Windendynamik und ergibt sich aus den geplanten Trajektorien zum Verfahren der Last $y_l^{*},{\dot{y}}_l^{*}$

und ${\ddot{y}}_l^{*}$

sowie den negativen Trajektorien für die Kompensationsbewegung $-y_a^{*},-{\dot{y}}_a^{*}$

und $-{\ddot{y}}_a^{*}$

(vgl. Fig. 9). Die daraus resultierenden Solltrajektorien für den Systemausgang der Antriebsdynamik bzw. der Windendynamik werden mit $y_h^{*},{\dot{y}}_h^{*}$

und ${\ddot{y}}_h^{*}$

bezeichnet. Sie stellen die Sollposition, -geschwindigkeit und -beschleunigung für die Windenbewegung und dadurch für das Auf- und Abwickeln des Seils dar.Active hoist compensation is intended to control the hoist winch so that the winch movement controls the vertical movement of the rope suspension point $z_a^H$

compensates and the crane operator moves the load with the help of the hand lever in the considered as inertial h-coordinate system. In order for the driver to have the required predictive behavior to minimize the compensation error, it is provided by a pilot control and stabilization part in the form of a two-degree-of-freedom structure implemented. The feedforward control is calculated from a differential parameterization with the aid of the flat output of the wind dynamics and results from the planned trajectories for moving the load $y_l^{*}.{\dot{y}}_l^{*}$

and ${\ddot{y}}_l^{*}$

and the negative trajectories for the compensation movement $-y_a^{*}.-{\dot{y}}_a^{*}$

and $-{\ddot{y}}_a^{*}$

(see. Fig. 9 ). The resulting desired trajectories for the system output of the drive dynamics or the wind dynamics are with $y_H^{*}.{\dot{y}}_H^{*}$

and ${\ddot{y}}_H^{*}$

designated. They represent the target position, speed and acceleration for the winch movement and thus for the winding and unwinding of the rope.

During the constant voltage phase, the cable force at the load F _{sl should} be regulated to a constant amount in order to avoid slack rope. Therefore, in this mode of operation, the hand lever is deactivated and the trajectories planned from the hand lever signal are no longer applied. The control of the winch is again by a two-degree-of-freedom structure with pilot control and stabilization part.

The exact load position z _l and the cable force at the load F _sl are not available for the control as measured variables, since the crane hook is equipped with no sensors due to the long cable lengths and great depths. Furthermore, there is no information about the form and type of the attached load. Therefore, the individual load-specific parameters such as load mass m _l , coefficient of hydrodynamic mass increase C _a , resistance coefficient C _d and immersed volume ∇ _l , are generally not known, whereby a reliable estimation of the load position is practically impossible in practice.

Consequently, only the unwound cable length l _s and the associated speed i _s and the force at the cable suspension point F _c are available as measured variables for the control. The length l _s is obtained indirectly from the angle of rotation φ _h measured using an incremental encoder and the winding radius r _h (j _l ) dependent on the winding position j _l . The associated rope speed i _s can be numerical Calculate differentiation with suitable low-pass filtering. The cable force F _c acting on the cable suspension point is detected by means of a force measuring axis.

2.1 Control for the active sea state compensation

rein vorsteuernd; Seil- und Lastdynamik werden vernachlässigt. Zwar wird infolge einer nicht vollständigen Kompensation der Eingangsstörung oder einer Windenbewegung die Seileigendynamik angeregt, aber man kann in der Praxis davon ausgehen, dass die resultierende Lastbewegung im Wasser stark gedämpft ist und sehr schnell abklingt. Fig. 10 illustrates the control of the hoist winch for the active sea state compensation with a block diagram in the frequency domain. As can be seen therein, only the return of the rope length and speed y _h = l _s and ẏ _h = i _s from the subsystem of the drive G _h ( s ). As a result, the compensation of the vertical movement of the cable suspension point acting as an input disturbance on the cable system G _{s, z} ( s ) takes place $Z_a^H\left(s\right)$

purely pre-taxing; Rope and load dynamics are neglected. Although due to an incomplete compensation of the input disturbance or a winch movement, the rope's own dynamics are excited, but in practice it can be assumed that the resulting load movement in the water is strongly damped and decays very rapidly.

mit dem Windenradius r_h (j_l ). Da der Systemausgang Y_h (s) gleichzeitig einen flachen Ausgang darstellt, folgt die invertierende Vorsteuerung F(s) zu $$F\left(s\right)=\frac{U_{\mathrm{ff}}\left(s\right)}{Y_h^{*}\left(s\right)}=\frac{1}{G_h\left(s\right)}=\frac{T_h}{K_h{r}_h\left(j_l\right)}{s}^2+\frac{1}{K_h{r}_h\left(j_l\right)}s$$

und lässt sich im Zeitbereich in Form einer differentiellen Parametrierung als $$u_{\mathrm{ff}}\left(t\right)=\frac{T_h}{K_h{r}_h\left(j_l\right)}{\ddot{y}}_h^{*}\left(t\right)+\frac{1}{K_h{r}_h\left(j_l\right)}{\dot{y}}_h^{*}\left(t\right)$$

schreiben. (2.3) zeigt, dass die Referenztrajektorie für die Vorsteuerung mindestens zweimal stetig differenzierbar sein muss.The transfer function of the drive system of the manipulated variable u _h (s) on the unwound cable length Y _h (s) can be approximated as ₁ system lT and results to be $$G_H\left(s\right)=\frac{Y_H\left(s\right)}{U_H\left(s\right)}=\frac{K_H{r}_H\left(j_l\right)}{T_H{s}^2+s}$$

with the radius of curvature r _h ( j _l ). Since the system output Y _h ( s ) simultaneously represents a flat output, the inverting feedforward control F (s) follows $$F\left(s\right)=\frac{U_{\mathrm{ff}}\left(s\right)}{Y_H^{*}\left(s\right)}=\frac{1}{G_H\left(s\right)}=\frac{T_H}{K_H{r}_H\left(j_l\right)}{s}^2+\frac{1}{K_H{r}_H\left(j_l\right)}s$$

and can be in the time domain in the form of a differential parameterization as $$u_{\mathrm{ff}}\left(t\right)=\frac{T_H}{K_H{r}_H\left(j_l\right)}{\ddot{y}}_H^{*}\left(t\right)+\frac{1}{K_H{r}_H\left(j_l\right)}{\dot{y}}_H^{*}\left(t\right)$$

write. (2.3) shows that the reference trajectory for precontrol must be continuously differentiable at least twice.

ablesen. Unter Vernachlässigung der Kompensationsbewegung $Y_a^{*}\left(s\right)$

kann die Führungsgröße $Y_h^{*}\left(s\right)$

bei konstanter bzw. stationärer Handhebelauslenkung als rampenförmiges Signal angenähert werden, da in solch einem Fall eine konstante Sollgeschwindigkeit ${\mathit{v}}_{\mathit{hh}}^{*}$

vorliegt. Zur Vermeidung einer stationären Regelabweichung bei einer derartigen Führungsgröße muss die offene Kette K_a(s)G_h(s) deshalb l ₂-Verhalten besitzen [9]. Dies lässt sich beispielsweise durch einen PID-Regler mit $$K_a\left(s\right)=\frac{T_h}{K_h{r}_h\left(j_l\right)}\left(\frac{{\kappa }_{\mathrm{AHC},0}}{s}+{\kappa }_{\mathrm{AHC},1}+{\kappa }_{\mathrm{AHC},2}s\right),{\kappa }_{\mathrm{AHC},i}>0$$

erreichen. Demnach folgt für den geschlossenen Kreis: $$G_{\mathrm{AHC}}\left(s\right)=\frac{{\kappa }_{\mathrm{AHC},0}+{\kappa }_{\mathrm{AHC},1}s+{\kappa }_{\mathrm{AHC},2}{s}^2}{s^3+\left(\frac{1}{T_h}+{\kappa }_{\mathrm{AHC},2}\right)s^2+{\kappa }_{\mathrm{AHC},1}s+{\kappa }_{\mathrm{AHC},0}},$$

wobei die genauen Werte von κ_AHC.i in Abhängigkeit von der jeweiligen Zeitkonstante T_h gewählt werden.The transfer function of the closed loop, consisting of the stabilization K _a (s) and the winch system G _h (s), can be turned off Fig. 10 to $$G_{\mathrm{AHC}}\left(s\right)=\frac{K_a\left(s\right)G_H\left(s\right)}{1+K_a\left(s\right)G_H\left(s\right)}$$

read off. Neglecting the compensation movement $Y_a^{*}\left(s\right)$

can be the reference size $Y_H^{*}\left(s\right)$

be approximated at constant or stationary Handhebelauslenkung as a ramp-shaped signal, since in such a case, a constant target speed ${\mathit{v}}_{\mathit{hh}}^{*}$

is present. To avoid a steady-state deviation in such a reference variable, the open chain K _a (s) G _h (s) must therefore have l ₂ behavior [9]. This can be done, for example, with a PID controller $$K_a\left(s\right)=\frac{T_H}{K_H{r}_H\left(j_l\right)}\left(\frac{{\kappa }_{\mathrm{AHC}.0}}{s}+{\kappa }_{\mathrm{AHC}.1}+{\kappa }_{\mathrm{AHC}.2}s\right).{\kappa }_{\mathrm{AHC}.i}>0$$

to reach. Accordingly follows for the closed circle: $$G_{\mathrm{AHC}}\left(s\right)=\frac{{\kappa }_{\mathrm{AHC}.0}+{\kappa }_{\mathrm{AHC}.1}s+{\kappa }_{\mathrm{AHC}.2}{s}^2}{{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">s</figure-callout>}}^3+\left(\frac{1}{T_H}+{\kappa }_{\mathrm{AHC}.2}\right)s^2+{\kappa }_{\mathrm{AHC}.1}s+{\kappa }_{\mathrm{AHC}.0}}.$$

where the exact values of κ _{AHC.i are chosen} as a function of the respective time constant T _h .

2.2 Detection of the settling process

wobei k_c und Δl_c die zur Elastizität des Seils äquivalente Federkonstante und die Auslenkung der Feder bezeichnen. Für letztere gilt: $$\mathrm{\Delta }{l}_c=\underset{0}{\overset{1}{\int }}{\epsilon }_s\left(\bar{s}t\right)d\bar{s}={\bar{z}}_{s,\mathrm{stat}}\left(1\right)-{\bar{z}}_{s,\mathrm{stat}}\left(0\right)-l_s=\frac{g{l}_s}{E_s{A}_s}\left(m_e+\frac{1}{2}{\mu }_s{l}_s\right)\mathrm{.}$$

As soon as the load hits the seabed, it should switch from the active sea state compensation to the constant voltage control. For this purpose, a detection of the settling process is necessary (see. Fig. 9 ). For them and the subsequent constant voltage control, the rope is approximated as a simple spring-mass element. Thus, the force acting on the rope suspension point is calculated approximately to $$F_c=k_c\mathrm{\Delta }{l}_c.$$

where k _c and Δl _c denote the elasticity of the rope equivalent spring constant and the deflection of the spring. For the latter applies: $$\mathrm{\Delta }{l}_c=\underset{0}{\overset{1}{\int }}{\epsilon }_s\left(\tilde{s}t\right)d\tilde{s}={\tilde{z}}_{s.\mathrm{stat}}\left(1\right)-{\tilde{z}}_{s.\mathrm{stat}}\left(0\right)-l_s=\frac{G{l}_s}{e_s{A}_s}\left(m_e+\frac{1}{2}{\mu }_s{l}_s\right)\mathrm{,}$$

The equivalent spring constant k _c can be determined from the following stationary observation. For a spring loaded with the mass m _f , in the stationary case: $$k_c\mathrm{\Delta }{l}_c=m_{f}G\mathrm{,}$$

Transforming (2.8) yields $$\frac{e_s{A}_s}{l_s}\mathrm{\Delta }{l}_c=\left(m_e+\frac{1}{2}{\mu }_s{l}_s\right)G\mathrm{,}$$

ablesen. Außerdem ist in (2.9) zu erkennen, dass die Auslenkung der Feder Δl_c im stationären Fall von der effektiven Lastmasse m_e und der halben Seilmasse $\frac{1}{2}{\mu }_s{l}_s$

beeinflusst wird. Dies liegt daran, dass bei einer Feder die angehängte Masse m_f als in einem Punkt konzentriert angenommen wird. Die Seilmasse ist jedoch über die Seillänge gleichmäßig verteilt und belastet daher die Feder nicht in vollem Umfang. Trotzdem fließt in die Kraftmessung am Seilaufhängepunkt die volle Gewichtskraft des Seils µ_sl_sg ein.Using a coefficient comparison between (2.9) and (2.10), the equivalent spring constant can be calculated as $$k_c=\frac{e_s{A}_s}{l_s}$$

read off. In addition, it can be seen in (2.9) that the deflection of the spring Δl _c in the stationary case of the effective load mass m _e and half the rope mass $\frac{1}{2}{\mu }_s{l}_s$

being affected. This is because with a spring, the attached mass m _f is assumed to be concentrated in one point. However, the rope mass is distributed evenly over the rope length and therefore does not burden the spring in full. Nevertheless, the full weight of the rope μ _s l _s g flows into the force measurement at the cable suspension point.

mit $$\mathrm{\Delta }{F}_c=-k_c\mathrm{\Delta }{l}_s,$$

wobei Δl_s das nach dem Auftreffen auf dem Meeresboden abgewickelte Seil bezeichnet. Aus (2.13) folgt, dass Δl_s proportional zur Änderung der gemessenen Kraft ist, da die Lastposition nach dem Aufsetzen konstant ist. Anhand von (2.12) und (2.13) lassen sich nun folgende Bedingungen für eine Detektion ableiten, die gleichzeitig erfüllt sein müssen:

• ■ Die Abnahme der negativen Federkraft muss kleiner als ein Schwellwert sein: $$\mathrm{\Delta }{F}_c<\mathrm{\Delta }{\hat{F}}_c\mathrm{.}$$
  
• ■ Die zeitliche Ableitung der Federkraft muss kleiner als ein Schwellwert sein: $${\dot{F}}_c<{\dot{\hat{F}}}_c\mathrm{.}$$
  
• ■ Der Kranfahrer muss die Last absenken. Diese Bedingung wird anhand der mit dem Handhebelsignal geplanten Trajektorie überprüft: $${\dot{y}}_l^{*}\ge 0.$$
  
• ■ Zur Vermeidung einer Fehldetektion beim Eintauchen in das Wasser muss eine Mindestseillänge abgewickelt sein: $$l_s>l_{s,\min }\mathrm{.}$$
  

With this approximation of the cable system, conditions for the detection of the settling process on the seabed can be derived. At rest, the force acting on the cable suspension point is composed of the weight of the unwound cable μ _s l _s g and the effective weight of the load mass m _e g . Therefore The measured force F _c is approximately equal to a load on the seabed $$F_c=\left(m_e+{\mu }_s{l}_s\right)G+\mathrm{\Delta }{F}_c$$

With $$\mathrm{\Delta }{F}_c=-k_c\mathrm{\Delta }{l}_s.$$

where Δl _s refers to the unwound after impact on the seabed rope. From (2.13) it follows that Δl _{s is} proportional to the change in the measured force, since the load position is constant after touchdown. Based on (2.12) and (2.13), the following conditions for a detection can now be derived, which must be satisfied simultaneously:

• ■ The decrease of the negative spring force must be smaller than a threshold value: $$\mathrm{\Delta }{F}_c<\mathrm{\Delta }{\hat{F}}_c\mathrm{,}$$
  
• ■ The time derivative of the spring force must be less than a threshold value: $${\dot{F}}_c<{\dot{\hat{F}}}_c\mathrm{,}$$
  
• ■ The crane operator must lower the load. This condition is checked on the basis of the hand lever signal planned trajectory: $${\dot{y}}_l^{*}\ge \mathrm{0th}$$
  
• ■ To avoid misdetection when submerging in the water, a minimum pitch must be unwound: $$l_s>l_{s.\min }\mathrm{,}$$
  

The decrease in the negative spring force Δ F _{c is} calculated in each case with respect to the last high point F _c in the measured force signal F _c . For suppression of measurement noise and high-frequency interference, the force signal is preprocessed by a corresponding low-pass filter.

Since conditions (2.14) and (2.15) must be satisfied at the same time, misdetection due to a dynamic ripple vibration is eliminated: as a result of the dynamic ripple vibration, the force signal F _c oscillates , whereby the change of the spring force Δ F _c with respect to the last high point F _c and the time derivative of the spring force Ḟ _{c have} a shifted phase. Consequently, with a suitable choice of the threshold values ΔF _c and F _c in the case of a dynamic rope natural oscillation, both conditions can not be met simultaneously. For this purpose, the static portion of the cable force must drop, as happens when submerged in the water or when settling on the seabed. However, a misdetection on immersion in the water is prevented by condition (2.17).

wobei χ _l <1 und der Maximalwert ΔF̂_c,max experimentell bestimmt wurden. Der Schwellwert für die Ableitung des Kraftsignals F_c lässt sich aus der zeitlichen Ableitung von (2.7) und der maximal zulässigen Handhebelgeschwindigkeit k_lv_max zu $${\dot{\hat{F}}}_c=\min \left\{-{\chi }_2{k}_c{k}_l{\upsilon }_{\max },{\dot{\hat{F}}}_{c,\max }\right\}$$

abschätzen. Die beiden Parameter χ ₂ <1 und F̂_c,max wurden ebenfalls experimentell ermittelt.The threshold value for the change in the spring force is calculated as a function of the last high point in the measured force signal $$\mathrm{\Delta }{\hat{F}}_c=\min \left\{-{\mathrm{<figure-callout\; id="1"\; label="\chi "\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">\chi </figure-callout>}}_1{\tilde{F}}_c.\mathrm{\Delta }{\hat{F}}_{c.\mathrm{Max}}\right\}.$$

where χ _l <1 and the maximum value Δ F _{c, max were} determined experimentally. The threshold for the derivation of the force signal F _c can be from the time derivative of (2.7) and the maximum allowable hand lever speed k _l v _max to $${\dot{\hat{F}}}_c=\min \left\{-{\mathrm{<figure-callout\; id="2"\; label="\chi "\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">\chi </figure-callout>}}_2{k}_c{k}_l{\upsilon }_{\mathrm{Max}}.{\dot{\hat{F}}}_{c.\mathrm{Max}}\right\}$$

estimated. The two parameters χ ₂ <1 and F _{c, max} were also determined experimentally.

in Abhängigkeit von der Summe aller an der Last angreifenden statischen Kräfte F_l,stat vorgegeben. Dazu wird F_l,stat in der Phase der Seegangskompensation unter Beachtung der bekannten Seilmasse µ_sl_s berechnet: $$F_{l,\mathrm{stat}}=F_{c,\mathrm{stat}}-{\mu }_s{l}_{s}g\mathrm{.}$$

Since constant force control uses force control instead of position control, a reference force is used as the reference variable $F_c^{*}$

dependent on of the sum of all acting on the load static forces F _{l, stat} given. For this purpose, F _{l, stat is} calculated in the phase of the sea state compensation taking into account the known cable mass μ _s l _s : $$F_{l.\mathrm{stat}}=F_{c.\mathrm{stat}}-{\mu }_s{l}_{s}G\mathrm{,}$$

wobei mit 0 < p_s <1 die resultierende Spannung im Seil durch den Kranfahrer vorgegeben wird. Zur Vermeidung eines Sollwertsprungs in der Führungsgröße erfolgt nach einer Detektion des Absetzvorgangs ein rampenförmiger Übergang von der aktuell bei der Detektion gemessenen Kraft zur eigentlichen Sollkraft $F_c^{*}\mathrm{.}$

In this case, F _{c, stat} denotes the static force component of the measured force at the cable suspension point F _c . It comes from a corresponding low-pass filtering of the measured force signal. The group delay arising during filtering is not a problem since only the static force component is of interest and a time delay has no significant influence on this. From the sum of all static forces acting on the load, the setpoint force follows, taking into account the additional weight force of the rope acting on the cable suspension point $$F_c^{*}=p_s{F}_{l.\mathrm{stat}}+{\mu }_s{l}_{s}G.$$

where 0 < p _s <1, the resulting tension in the rope is specified by the crane operator. In order to avoid a desired value jump in the reference variable, after a detection of the settling process, a ramp-shaped transition takes place from the force currently measured during the detection to the actual desired force $F_c^{*}\mathrm{,}$

To release the load from the seabed, the crane operator manually maneuvers the change from the constant tension mode to the active sea state compensation with the load suspended.

2.3 Control for the constant voltage mode

Fig. 11 shows the converted control of the hoist winch in the constant voltage mode in a block diagram in the frequency domain. Unlike the in Fig. 10 1, the output of the cable system F _c ( s ), ie the force measured at the cable suspension point, is returned instead of the output of the winch system Y _h ( s ). The measured force F _c ( s ) decreases (2.12) from the force change Δ F _c ( s ) and the static weight force m _e g + μ _s l _s g, which is denoted by M (s) in the image area. For the actual control, the cable system is again approximated as a spring-mass system.

und $-{\ddot{y}}_a^{*}$

für die Kompensationsbewegung besteht. Der Vorsteuerungsanteil kompensiert zunächst wiederum die Vertikalbewegung des Seilaufhängepunkts $Z_a^h\left(s\right)\mathrm{.}$

Jedoch erfolgt keine direkte Stabilisierung der Windenposition durch eine Rückführung von Y_h (s). Dies erfolgt indirekt durch die Rückführung des gemessenen Kraftsignals.The precontrol F (s) of the two-degree-of-freedom structure is identical to that for active sea state compensation and given by (2.2) or (2.3). However, in the constant voltage mode, the hand lever signal is not applied, which is why the reference trajectory only from the negative target speed and - acceleration $-{\dot{y}}_a^{*}$

and $-{\ddot{y}}_a^{*}$

exists for the compensation movement. The pilot control component initially compensates for the vertical movement of the cable suspension point $Z_a^H\left(s\right)\mathrm{,}$

However, there is no direct stabilization of the winch position by a return of Y _h ( s ). This is done indirectly by the return of the measured force signal.

mit den beiden Übertragungsfunktionen $$G_{\mathrm{CT},1}\left(s\right)=\frac{G_{s,F}\left(s\right)}{1+K_s\left(s\right)G_h\left(s\right)G_{s,F}\left(s\right)},$$

$$G_{\mathrm{CT},2}\left(s\right)=\frac{K_s\left(s\right)G_h\left(s\right)G_{s,F}\left(s\right)}{1+K_s\left(s\right)G_h\left(s\right)G_{s,F}\left(s\right)},$$

wobei die Übertragungsfunktion des Seilsystems für eine am Boden stehende Last aus (2.12) folgt: $$G_{s,F}\left(s\right)=-k_c\mathrm{.}$$

The measured output F _c ( s ) results from Fig. 11 to $$F_c\left(s\right)=G_{\mathrm{CT}.1}\left(s\right)\underset{e_a\left(s\right)}{\underset{\}}{\left[Y_a^{*}\left(s\right)F\left(s\right)G_H\left(s\right)+Z_a^H\left(s\right)\right]}}+G_{\mathrm{CT}.2}\left(s\right)F_c^{*}\left(s\right)$$

with the two transfer functions $$G_{\mathrm{CT}.1}\left(s\right)=\frac{G_{s.F}\left(s\right)}{1+K_s\left(s\right)G_H\left(s\right)G_{s.F}\left(s\right)}.$$

$$G_{\mathrm{CT}.2}\left(s\right)=\frac{K_s\left(s\right)G_H\left(s\right)G_{s.F}\left(s\right)}{1+K_s\left(s\right)G_H\left(s\right)G_{s.F}\left(s\right)}.$$

where the transfer function of the rope system for a grounded load (2.12) follows: $$G_{s.F}\left(s\right)=-k_c\mathrm{,}$$

welches nach einer Übergangsphase durch die konstante Sollkraft $F_c^{*}$

aus (2.21) gegeben ist. Zur Vermeidung einer stationären Regelabweichung bei solch einer konstanten Führungsgröße muss die offene Kette K_s(s)G_h(s)G_s,F(s) /-Verhalten besitzen. Da die Übertragungsfunktion der Winde G_h(s) solch ein Verhalten schon implizit aufweist, lässt sich diese Anforderung mit einer P-Rückführung realisieren; somit gilt: $$K_s\left(s\right)=-\frac{T_h}{K_h{r}_h\left(j_l\right)}{\kappa }_{\mathrm{CT}},{\kappa }_{\mathrm{CT}}>0.$$

As can be seen from (2.22), the compensation error E _a ( s ) is compensated by a stable transfer function G _{CT, 1} ( s ) and the wind position stabilized indirectly. The request to the controller K _s ( s ) also results in this case from the expected command signal $F_c^{*}\left(s\right).$

which after a transitional phase by the constant desired force $F_c^{*}$

from (2.21). To avoid a steady-state deviation at such a constant reference variable, the open chain must have K _s (s) G _h (s) G _{s, F} (s) / behaviors. Since the transfer function of the wind G _h (s) implicitly has such a behavior, this requirement can be realized with a P return; thus: $$K_s\left(s\right)=-\frac{T_H}{K_H{r}_H\left(j_l\right)}{\kappa }_{\mathrm{CT}}.{\kappa }_{\mathrm{CT}}>\mathrm{0th}$$

Claims (15)

Crane control for a crane having a hoist for lifting a load suspended from a rope,
characterized,
in that the crane control system has a cable force mode in which the crane control activates the lifting mechanism in such a way that a desired value of the cable force is established. Crane control according to claim 1, wherein the speed and / or position of the winch is controlled in particular taking into account the elasticity of the system so that adjusts the desired value of the cable force. Crane control according to claim 1 or 2, wherein the cable force can be maintained in the cable force mode at a constant setpoint, wherein advantageously a cable force determining unit is provided which an actual value of Cable force determined, the control is advantageously carried out on the basis of a comparison of the actual value and the desired value of the cable force. Crane control according to one of the preceding claims, wherein the cable force is controlled in the cable force mode by returning at least one measured value, advantageously a cable force determining unit is provided which determines an actual value of the cable force based on a measurement signal of a cable force sensor, wherein the cable force sensor is advantageously arranged on the hoist, in particular on an attachment of the hoist winch and / or attachment of a pulley. Crane control according to one of the preceding claims, wherein a cable force determination unit is provided which determines the actual value of the cable force via a filtering of measured values or a model-based estimate. Crane control according to one of the preceding claims, with a desired force determination unit which determines the desired value of the cable force on the basis of measured values and / or control signals and / or inputs of a user. Crane control according to claim 6, wherein the desired force determination unit determines the static force acting on the rope during a stroke and / or wherein the rope length is included in the desired force determination unit, wherein advantageously the desired force determination unit takes into account the weight of the unwound rope and / or wherein the crane control comprises an input element, about which the crane operator can change the setpoint of the cable force, wherein advantageously a factor can be entered, which determines the ratio between the desired value of the cable force and the static force during a stroke. Crane control according to one of the preceding claims, wherein the crane control in the cable force mode comprises a pilot control part, which the Taken into account dynamics of the rope, and a return part, over which the determined by the cable force determination unit cable force is returned. Crane control according to one of the preceding claims, with a state detection, wherein the crane control automatically switches on the basis of the state detection in and / or from the cable force mode, wherein the state detection can advantageously detect a settling and / or receiving the load. Crane control according to one of the preceding claims, with a lifting mode in which the hoist is controlled on the basis of a desired value of the load position and / or load speed and / or cable position and / or rope speed, wherein advantageously a control is provided, which in the lifting mode an actual value of the load position and / or load speed and / or rope position and / or rope speed. Crane control according to one of the preceding claims, with an active sea state compensation, which at least partially compensates for the movement of the cable suspension point and / or a Lastabsetzpunktes due to the sea state by a control of the hoist. Crane with a crane control according to one of the preceding claims, in particular ship crane, port crane, offshore crane or crawler crane, in particular mobile harbor crane. Use of a crane or a crane control according to one of the preceding claims under lifting conditions in which the cable suspension point and / or the Lastabsetzpunkt is moved by external forces, and / or use with stored load. Method for controlling a crane, which has a lifting mechanism for lifting a load suspended on a cable, in particular by means of a crane control according to one of claims 1 to 12,
characterized,
that the hoist is controlled based on a setpoint of the cable force. Software with code for carrying out a method according to claim 14.

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