EP2272786A1 - Crane control for controlling a crane's hoisting gear - Google Patents

Abstract

The crane controller has a lifting unit, in which the oscillation-dynamics are allowed by the crane controller. The crane controller reduces the oscillation-dynamics by proper controlling to the lifting unit. The oscillation-dynamics are based on the flexibility of a hoist rope (3). The drive speed of the lifting unit is limited for limiting the overshooting of a maximum drive speed. An independent claim is also included for a method for controlling a lifting unit of a crane by a crane controller.

Description

The present invention relates to a crane control for controlling a hoist of a crane. In particular, this is an electronic crane control, which determines drive signals for the hoist of a crane from the input signals entered by an operator by means of input elements, in particular by means of hand levers. Alternatively, the input signals can also be generated by an automation system.

When the load is lifted by the crane, besides the static loads, which unavoidably affect the rope and the crane due to the weight of the load, further dynamic loads result from the movement of the load. In order to be able to absorb these dynamic loads as well, the crane structure must be made correspondingly more stable or the static maximum load correspondingly reduced.

In known crane controls, the operator determines the speed of the hoist by the operation of the hand lever. With appropriate operation, therefore, considerable dynamic loads can occur, which by a According stable (and therefore expensive) construction of the crane must be considered.

The object of the present invention is to provide an improved crane control system.

This object is achieved by a crane control according to claim 1. The present invention thus provides a crane control for controlling a hoist of a crane available, which takes into account the based on the extensibility of the hoist rope vibration dynamics in the control of the hoist and reduced or damped by suitable control of the hoist. In particular, the vibration dynamics of the system of rope and load is taken into account. Furthermore advantageously, the hoist and / or the crane structure can be taken into account. This makes it possible to reduce the dynamic loads acting on the rope and the crane structure by using the crane control according to the invention. As a result, the crane structure can be built correspondingly lighter or operated with higher static loads. In particular, the crane control according to the invention can limit the lifting force acting on the crane structure to a maximum permissible value by taking into account the vibration dynamics of the system comprising the hoist, rope and load.

The crane control according to the invention advantageously comprises a vibration reduction operation, in which the based on the extensibility of the hoisting rope vibration dynamics is taken into account, while any movements of the support region on which the crane structure is supported, are not taken into account in the control of the hoist. The control thus starts in the vibration reduction operation of a stationary support area. The control according to the invention must therefore take into account only vibrations which arise through the hoisting rope and / or the hoisting gear and / or the crane structure. Movements of the support area, as z. B. in a floating crane by wave motion incurred, remain unconsidered in the vibration reduction operation. The crane control can be made considerably simpler.

The crane control according to the invention can be used in a crane, which is actually supported on a stationary support area during the lift with the crane structure, in particular on the ground. However, the crane control according to the invention can also be used in a floating crane, but does not take into account the movements of the floating body in the vibration reduction mode. If the crane control system has an operating mode with active coasting sequence, the vibration reduction operation accordingly takes place without simultaneous active coasting sequence operation.

Further advantageously, the method according to the invention in transportable and / or mobile cranes is used. The crane advantageously has support means via which it can be supported at different lifting locations. Further advantageously, the method is used in port cranes, especially in mobile harbor cranes, crawler cranes, vehicle cranes, etc. used.

The hoist of the crane according to the invention can be hydraulically driven. Alternatively, a drive via an electric motor is possible.

The crane control according to the invention advantageously determines from the input signals input by an operator by means of input elements, in particular by means of hand levers, for the hoisting gear of a crane, the vibration dynamics of the system of hoisting gear, cable and load based on the extensibility of the hoisting cable being taken into account in the determination of the control signals to limit the dynamic forces acting on the rope and the crane structure. Alternatively or additionally, the crane control system may have an automation system which predetermines a desired lifting movement. Advantageously, the drive speed of the hoist for limiting overshoots in at least one operating phase, in particular during the cancellation and / or discontinuation of the load is limited to a maximum permissible drive speed. The maximum permissible drive speed can also be zero, so that the crane control stops the hoist. Advantageously, however, the crane control limits the drive speed to a speed greater than zero, so that the lifting movement is not interrupted.

The present invention makes it possible to limit overshoots of the lifting force beyond the static load to a certain extent. Advantageously, the overshoots can be limited to a fixed factor dependent on the boom position maximum load.

The consideration of the vibration dynamics or the limitation of the drive speed is advantageously carried out at least in those operating phases, which are particularly relevant for the dynamic loads of the system of hoist winch, hoisting rope and load. It can be provided in particular that the drive speed is limited only in certain operating phases, in contrast, is released in other phases of operation, in order not to unnecessarily restrict an operator. In particular, it may be provided that the drive speed is limited only during the cancellation and / or discontinuation of the load and otherwise released.

Advantageously, it is further provided that the drive speed of the hoist is determined as long as the input signals, as the drive speed is below the maximum allowable drive speed. Only when the drive speed determined from the input signals of the operator would be above the maximum permissible drive speed, the drive speed is limited to this maximum permissible drive speed. As long as the operator so the maximum allowable Drive speed does not exceed, they can control the hoist freely as in known crane controls.

Advantageously, the crane control determines the maximum permissible drive speed of the hoist dynamically based on crane data. So no fixed maximum drive speed is given, but this is currently determined based on the situation. As a result, the maximum permissible drive speed can be continuously adapted to the respective stroke situation. This has the advantage that the drive speed of the hoist does not need to be unnecessarily limited.

Advantageously, the unloading of the crane enters the maximum permissible drive speed. In turn, the crane's outreach determines the maximum force that the crane structure can absorb, and thus the maximum permissible dynamic forces. If the crane is a boom that can be augmented by a horizontal rocking axis, then the rocking angle of the boom is used to determine the maximum permissible drive speed.

In a further advantageous manner, the maximum permissible drive speed of the lifting mechanism is determined as a function of a currently measured lifting force. This makes it possible to limit the overshoot of the lifting force to a certain value of the maximum allowable static lifting force. Advantageously, the maximum permissible drive speed decreases with increasing lifting force. In particular, the maximum permissible drive speed is advantageously inversely proportional to the root of the currently measured lifting force. The lifting force can be determined via a load mass sensor.

In a further advantageous manner, the maximum permissible drive speed of the hoist is determined as a function of the rope length. The rope length has an influence on the rigidity of the hoisting rope and thus on the dynamics of the hoist, rope and load system. The rope length is advantageously determined via a measurement of the movement of the hoist or via the control data of the hoist.

In a further advantageous manner, the calculation of the maximum permissible drive speed continues to include certain constants which depend on the structure of the crane and the cable.

Advantageously, the maximum permissible drive speed of the hoist is determined on the basis of a physical model which describes the vibration dynamics of the system comprising hoist, rope and load. This makes it possible to achieve a precise limitation of the maximum permissible drive speed. In addition, the crane control is easier to adapt to other crane models.

Since the dynamic loads of the crane and the crane rope in the different phases of a stroke are very different, it is advantageous if the crane control is controlled in the different phases with a respectively suitable control program.

The crane control according to the invention therefore advantageously has a situation detection, based on which the crane control determines the control behavior. In particular, the crane control according to the invention has a state machine which determines the activation behavior of the crane control on the basis of the situation recognition. In particular, this is advantageously a discrete state machine which recognizes discrete states and in each of these states executes predetermined drive programs for the hoist.

Advantageously, the situation recognition recognizes a lifting state in which the drive speed of the hoist is limited to avoid overshooting. For this purpose, the state machine advantageously has a lift-off state, in which the drive speed of the Hoist is limited to avoid overshoots. By releasing a load, the greatest dynamic stresses of the rope and the crane arise, so that it is important that in this phase, the drive speed of the hoist is inventively limited to avoid overshoot.

Advantageously, it is changed to the Aufhebezustand when the situation recognizes that a resting on the ground load is raised. As long as the load is still resting on the ground, the hoisting rope is first tensioned by winding the hoisting rope until the load then lifts off the ground. During this phase, the drive speed of the hoist is limited to avoid overshooting the load after lifting the load.

Advantageously, the situation detection detects a lifting state by monitoring the change in the measured lifting force. Advantageously, the derivation of the lifting force enters the situation detection. In particular, it can be queried whether the derivative of the lifting force over time exceeds a certain predetermined minimum value. Furthermore, the absolute value of the force can enter into the situation recognition. Advantageously, the difference between the currently measured lifting force and the last determined static lifting force, which is solely caused by the static weight of the load, is considered. It can be queried whether this difference exceeds a certain predetermined value. By also taking into account the absolute values of the force, it is possible to prevent a lifting state from being detected even though the load hangs freely on the hook and does not threaten too much overshoot.

In a further advantageous manner, the situation recognition recognizes a release state in which the drive speed of the hoist is released, advantageously a release state is detected when the load has been raised and now hangs freely on the crane cable. Advantageously, the state machine for this purpose has a release state in which the drive speed of the Hoist is released. This makes it possible that in such operating phases in which an overshoot of the lifting force need not be expected, the operator is not restricted by the crane control according to the invention. Rather, the hoist can be operated freely by the operator in these phases, without the crane control limits the drive speed of the hoist.

Advantageously, it is changed to the release state when the situation recognizes that the load has been raised and now hangs freely on the crane cable. In this situation, no decisive dynamic processes are to be expected, so that the operator can now operate the hoist freely.

Advantageously, data on the movement of the hoisting gear enter into the situation recognition in order to detect whether the load has been lifted. In particular, the situation detection determined from the measured lifting force and data on the expansion behavior of the rope, from when the hoist has already wound enough rope to lift the load from the ground.

In a further advantageous manner, the situation recognition recognizes a AblegeZustand in which the drive speed of the hoist is limited in order to avoid that unnecessarily much rope is handled when placing the load. Advantageously, the state machine for this purpose has a storage state in which the drive speed of the hoist is limited in order to avoid that unnecessarily much rope is unwound when placing the load. When setting down the load no limitations are necessary with regard to the stability of the crane structure. However, in order to prevent the crane operator unwinding too much slack when he sets down the load on the ground, the crane control according to the invention also intervenes in such situations.

The embodiments of the crane controls according to the invention described so far intervene essentially in those phases of the stroke in the control of the hoist, in which the load is either raised or stored. This is based on the consideration that in these phases, the largest dynamic effects occur, so that by limiting the speed, in particular by a load-dependent limitation of the speed, overshoot can be effectively reduced. While the load hangs freely on the crane hook, the control previously shown advantageously does not intervene or limits it only in exceptional situations.

The present invention now comprises a further control variant, which is advantageously used during phases in which the load hangs freely on the crane cable. In these phases, the crane control is used to avoid natural vibrations of the rope and / or the crane structure, which can also be stressful for the ropes and the crane structure.

In this case, the present invention comprises a crane control, for which a desired lifting movement of the load serves as an input quantity, on the basis of which a control variable for controlling the lifting mechanism is calculated. In the calculation of the control variable, the crane control according to the invention takes into account the vibration dynamics which arise due to the extensibility of the hoist rope. As a result, natural vibrations of the system rope and load can be damped. From the input signals of the operator and / or an automation system, a set stroke movement of the load is initially generated, which now serves as the input variable of the crane control according to the invention. Based on this input quantity and taking into account the vibration dynamics, a control variable for controlling the hoist is then calculated in order to dampen natural oscillations.

Advantageously, in addition to the extensibility of the hoisting rope in the calculation of the control variable and the vibration dynamics of the hoist due to the compressibility of the hydraulic fluid is taken into account. This factor can also cause natural oscillations of the system of hoist, rope and load, which burden the crane structure.

Advantageously, the variable cable length of the hoisting rope is included in the calculation of the control variable. The rope length of the hoist affects the rigidity of the rope and thus its dynamics. In a further advantageous manner, the measured lifting force or the weight determined therefrom of the load hanging on the load cable enters into the calculation of the control variable. The weight of the load hanging on the load rope thereby significantly influences the dynamics of the system of hoisting rope, hoist and load.

Advantageously, the control of the hoist is carried out on the basis of a physical model, which describes the lifting movement of the load as a function of the control variable of the hoist. This makes it possible to achieve a very good vibration damping. In addition, the use of a physical model allows rapid adaptation of the crane control according to the invention to other cranes. In particular, such an adjustment can be made on the basis of simple calculations and data of the crane. The model advantageously starts from a stationary support location for the crane.

Advantageously, the control of the lifting mechanism takes place on the basis of an inversion of the physical model. By inverting the physical model, the control quantity of the hoisting gear is obtained as a function of the lifting movement of the load, which can thus be used as the input variable of the control.

Furthermore, it is conceivable to combine the two variants for a crane control according to the invention. In particular, a limitation of the speed of the hoist can take place when the state machine is in the lifting state, and the control of the hoist based on the Sollhubbewegung the load done when the state machine has changed to the release state.

The present invention further comprises a method for controlling a hoist of a crane by means of a crane control, wherein in the control of the

Hubwerks considered based on the extensibility of the hoist rope vibration dynamics of the system of hoist, rope and load and is reduced or damped by a suitable control of the hoist by the crane control. In particular, the control of the hoist is carried out by means of a crane control according to the invention, as shown above.

Furthermore, the present invention includes a crane with a crane control as set forth above.

Figur 1

das Überschwingen in der Kraftmessachse des Hubwerks beim Anheben einer Last mit und ohne Einsatz einer Kransteuerung gemäß der vorlie- genden Erfindung,

Figur 2:

ein erstes Ausführungsbeispiel eines Krans, bei welchem eine erfin- dungsgemäße Kransteuerung zum Einsatz kommt,

Figur 3:

eine Prinzipdarstellung eines ersten Ausführungsbeispiels einer erfin- dungsgemäßen Kransteuerung mit Situationserkennung und einer Be- grenzung der Antriebsgeschwindigkeit des Hubwerks während einem Anhebezustand,

Figur 4:

eine Prinzipdarstellung des Zustandsautomaten des ersten Ausfüh- rungsbeispiels,

Figur 5:

die Antriebsgeschwindigkeit eines Hubwerks beim Anheben einer Last mit und ohne Einsatz einer erfindungsgemäßen Kransteuerung gemäß dem ersten Ausführungsbeispiel,

Figur 6:

die Hubkraft, welche bei der in Figur 5 dargestellten Ansteuerung des Hubwerks auftritt, wiederum mit und ohne Verwendung einer erfindungs- gemäßen Kransteuerung gemäß dem ersten Ausführungsbeispiel,

Figur 7:

eine Prinzipdarstellung des hydraulischen Antriebs eines Hubwerks, und

Figur 8:

eine Prinzipdarstellung des physikalischen Modells, welches in einem zweiten Ausführungsbeispiel für das System aus Hubwerk, Seil und Last herangezogen wird.

The present invention will now be described in more detail with reference to embodiments and drawings. Showing:

FIG. 1

the overshoot in the force measuring axis of the hoist when lifting a load with and without the use of a crane control according to the present invention,

FIG. 2:

A first embodiment of a crane in which a crane control according to the invention is used,

FIG. 3:

1 is a schematic representation of a first exemplary embodiment of a crane control according to the invention with situation recognition and a limitation of the drive speed of the lifting mechanism during a lifting state,

FIG. 4:

3 is a schematic representation of the state machine of the first embodiment,

FIG. 5:

The drive speed of a hoist when lifting a load with and without the use of a crane control according to the invention according to the first embodiment,

FIG. 6:

the lifting force, which at the in FIG. 5 shown control of the lifting mechanism occurs, again with and without using a crane control according to the invention according to the first embodiment,

FIG. 7:

a schematic diagram of the hydraulic drive a hoist, and

FIG. 8:

a schematic diagram of the physical model, which is used in a second embodiment of the system of hoist, rope and load.

In FIG. 2 an embodiment of the crane according to the invention is shown, which is equipped with an embodiment of a crane control according to the invention. The crane has a boom 1, which is pivoted about a horizontal rocking axis on the tower 2. For lifting and rocking the boom 1 in the rocker plane while a hydraulic cylinder 10 is provided, which is articulated between the boom 1 and the tower 2. The tower 2 is rotatably mounted about a vertical axis of rotation. The tower 2 is arranged for this purpose on an upper carriage 7, which can be rotated by a slewing gear relative to a lower carriage 8. In the embodiment, this is a movable crane, for which the undercarriage 8 is equipped with a chassis 9. At the hub of the crane can then be supported by support members 71.

The lifting of the load takes place via a hoist rope 3, on which a load-receiving element 4, in this case a crane hook, is arranged. The hoist rope 3 is guided over pulleys on the jib tip 5 and on the tower top 6 to the hoist 30 on the superstructure over which the length of the hoist rope can be changed. The hoist 30 is designed as a hoist winch.

According to the invention, the crane control takes into account the dynamics of the system of hoist, hoist rope and load in the control of the hoist to reduce vibrations due to the extensibility (or elasticity) of the hoisting rope.

In the following, a first exemplary embodiment of a control method implemented in a crane control according to the invention is shown in more detail:

1 Introduction to the first embodiment

According to DIN EN 13001-2 and DIN EN 14985, the steel construction of a boom slewing crane can be reduced as long as a maximum overshoot in the force measuring axis of the hoist can be guaranteed. In this case, the maximum permissible discharge-dependent lifting force may only be exceeded by the p- fold value due to the dynamic overshoot when lifting a load from the ground. To guarantee such a maximum overshoot, an automatic lift can be used.

Fig. 1 shows the measured lifting force when lifting a load without lifting automatics and with an automatic lifting system, which guarantees a maximum overshooting by p times. The automatic lifting system presented below guarantees that the maximum permissible maximum load-dependent maximum force in the hoisting gear is never exceeded by more than the p- fold value when lifting a load from the ground. In addition, the automatic lifting system discussed here reduces the hoist speed when depositing a load on the ground. Thus, it should be prevented that the crane operator unwinds too much slack when he drops a load on the ground.

2 crane model in the first embodiment

wobei l₁ , l₂ und l₃ die Teillängen von der Hubwinde zum Turm, vom Turm zum Auslegerkopf und vom Auslegerkopf zum Lastaufnahmemittel sind.In the following, the crane model, which is used in the first embodiment for the development of the lifting mechanism is described. Figure 2 shows the complete construction of a mobile harbor crane. The load with the mass m _l is lifted by the crane by means of the lifting device and is connected to the lifting hoist via the rope with the total length l _s . The rope is deflected from the load handler via a respective deflection roller on the boom head and tower. It should be noted that the rope is not deflected directly from the boom head to the hoist winch but it is deflected from the boom head to the tower, back to the boom head and then over the hoist winch tower (see Fig. 2 ). This results in the entire rope length too $$l_s\left(t\right)=l_1\left(t\right)+3l_2\left(t\right)+l_3\left(t\right).$$

where l ₁ , l ₂ and l _{3 are} the partial lengths from the hoist winch to the tower, from the tower to the boom head and from the boom head to the load handler.

hierbei sind E_s und A_s das Elastizitätsmodul und die Querschnittsfläche des Seils. Da am Hafenmobilkran n_s parallele Seile die Last anheben (vgl. Fig. 2) ergibt sich die Federsteifigkeit c_seil der Seile zu $$c_{\mathit{seil}}=n_s{c}_s\mathrm{.}$$

Now it is assumed that the crane behaves like a spring-mass-damper system when lifting a load. The overall spring stiffness of the crane when lifting a load consists of the spring stiffness of the ropes and the spring stiffness of the crane (deflection of the tower, jib, etc.). The spring stiffness of a rope results to $$c_s=\frac{e_s{A}_s}{l_s}$$

Here, E _s and A _{s are} the elastic modulus and the cross-sectional area of the rope. Since the mobile harbor crane n _s parallel ropes the load lift (see FIG. Fig. 2 ) results in the spring stiffness c _{rope of} the ropes $$c_{\mathit{rope}}=n_s{c}_s\mathrm{,}$$

To calculate the total spring stiffness, it is assumed that the stiffnesses of the crane and the cables are connected in series, ie $$c_{\mathit{total}}=\frac{{\mathit{c}}_{\mathit{crane}}{\mathit{c}}_{\mathit{eil}}}{{\mathit{c}}_{\mathit{crane}}+{\mathit{c}}_{\mathit{eil}}}\mathrm{,}$$

3 lifting mechanism in the first embodiment

The lifting mechanism presented here is based on an event-discrete state machine, which should detect the lifting of a load. As soon as a load is lifted, the lifting speed should be reduced to a predetermined value, thus guaranteeing a maximum overshoot of the dynamic lifting force. After the load has lifted completely off the ground, the hoist speed is to be released again by the automatic hoist. In addition, the automatic lifting should detect a settling of the load and also reduce the hoist speed. Again, the hoist should be released again after discontinuation.

The scheme of automatic lifting is in Fig. 3 shown. Within the block "Default v _up , v _down ", the permitted maximum speeds for load release and load offset are calculated or specified. The exact calculation is described in the following section. The "Situation detection" block detects whether a load is picked up from the ground or set down on the ground or whether the crane is in normal operating mode. Based on the current situation, the corresponding desired speed v set _{is then} selected. This decision is based on an event discrete state machine as described above.

In the following description it should be noted that the z-axis is directed downwards to the load movement (see Fig. 2 ). As a result, the load is lowered by a positive hoist speed v _hw and raised by a negative hoist speed v _hw .

3.1 Default v _on , v _off

wobei F_const = m_lg die konstante Lastkraft auf Grund der Schwerkraft ist. Die dynamische Hubkraft F_dyn wird durch die dynamische Federkraft des Feder-Masse Schwingers beschrieben $${\mathit{F}}_{\mathit{dyn}}\mathit{=}{\mathit{m}}_{\mathit{l}}{\ddot{\mathit{z}}}_{\mathit{dyn}},$$

wobei z̈_dyn die Beschleunigung der Last (ohne die Erdbeschleunigung) ist. Die Differentialgleichung für das ungedämpfte Feder-Masse System lautet $${\mathit{m}}_{\mathit{l}}{\ddot{\mathit{z}}}_{\mathit{dyn}}+c_{\mathit{gesamt}}{z}_{\mathit{dyn}}=0.$$

Within this block, the maximum lift speed _V is calculated upon release of the load from the ground. This speed depends on _total of the currently measured lifting force F _L, the ausladungsabhängigen maximum lifting load m _max and the total spring stiffness C. For calculation it is assumed that the lifting movement of the load occurs shortly after lifting off the ground composed of a continuous lifting movement and a superimposed oscillation. The vibration here is described by an undamped spring-mass system. The measured lifting force thus results $${\mathit{F}}_{\mathit{l}}\mathit{=}{\mathit{F}}_{\mathit{const}}\mathit{+}{\mathit{F}}_{\mathit{dyn}}\mathit{.}$$

where F _const = m _l g is the constant load force due to gravity. The dynamic lifting force F _dyn is described by the dynamic spring force of the spring-mass oscillator $${\mathit{F}}_{\mathit{dyn}}\mathit{=}{\mathit{m}}_{\mathit{l}}{\ddot{\mathit{z}}}_{\mathit{dyn}}.$$

where z̈ _{dyn is} the acceleration of the load (without gravitational acceleration). The differential equation for the undamped spring-mass system is $${\mathit{m}}_{\mathit{l}}{\ddot{\mathit{z}}}_{\mathit{dyn}}+c_{\mathit{total}}{z}_{\mathit{dyn}}=\mathrm{0th}$$

da F_dyn (0) = m_lz̈_dyn (0) = -c _gesamtz_dyn (0) = 0 und $${\dot{z}}_{\mathit{dyn}}\left(0\right)=-v_{\mathit{auf}},$$

da die Last mit der Geschwindigkeit -v_auf vom Boden abheben soll (z ist nach unten positiv gerichtet). Die allgemeine Lösung von (7) ist durch $$z\left(t\right)=A\sin \left(\omega t\right)+B\cos \left(\omega t\right)$$

gegeben. Die Koeffizienten A und B können durch die Anfangsbedingungen (8) und (9) berechnet werden und ergeben sich zu $$A=-\frac{v_{\mathit{auf}}}{\omega },$$

$$B=0$$

mit $\omega =\sqrt{\frac{c_{\mathit{gesamt}}}{m_l}}\mathrm{.}$

Somit ergibt sich der Zeitverlauf der dynamischen Kraft zu $$F_{\mathit{dyn}}\left(t\right)=m_l{v}_{\mathit{auf}}\omega \sin \left(\omega \mathit{t}\right)$$

und daher $$\max \left(F_{\mathit{dyn}}\left(t\right)\right)=m_l{v}_{\mathit{auf}}\sqrt{\frac{c_{\mathit{gesamt}}}{m_l}},$$

da -1≤sin(ωt)≤1. Nun soll das maximale Überschwingen in der Hubkraft pm _max g betragen, daher ergibt sich für die maximal erlaubte Hubgeschwindigkeit beim Abheben $$\mathit{p}{\mathit{m}}_{\max }\mathit{g}\mathit{=}{\mathit{m}}_{\mathit{l}}{\mathit{v}}_{\mathit{auf}}\sqrt{\frac{c_{\mathit{gesamt}}}{m_l}},$$

$$v_{\mathit{auf}}=\frac{{\mathit{pm}}_{\max }g}{\sqrt{c_{\mathit{gesamt}}{m}_l}}\mathrm{.}$$

The initial conditions for (7) are too $${\mathrm{<figure-callout\; id="0"\; label="z\; dyn"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">z\; </figure-callout>}}_{\mathit{dyn}}\left(0\right)=0.$$

since F _dyn (0) = m _l z̈ _dyn (0) = -c _total z _dyn (0) = 0 and $${\dot{z}}_{\mathit{<figure-callout\; id="0"\; label="dyn"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">dyn</figure-callout>}}\left(0\right)=-v_{\mathit{on}}.$$

because the load is to lift off from the ground _at the -v speed (z is positive down). The general solution of (7) is by $$z\left(t\right)=A\sin \left(\omega t\right)+B\cos \left(\omega t\right)$$

given. The coefficients A and B can be calculated by the initial conditions (8) and (9) and result in $$A=-\frac{v_{\mathit{on}}}{\omega }.$$

$$B=0$$

With $\omega =\sqrt{\frac{c_{\mathit{total}}}{m_l}}\mathrm{,}$

This results in the time course of the dynamic force $$F_{\mathit{dyn}}\left(t\right)=m_l{v}_{\mathit{on}}\omega \sin \left(\omega \mathit{t}\right)$$

and therefore $$\mathrm{Max}\left(F_{\mathit{dyn}}\left(t\right)\right)=m_l{v}_{\mathit{on}}\sqrt{\frac{c_{\mathit{total}}}{m_l}}.$$

as -1≤sin (ω t) ≤1. Now, the maximum overshoot in the lifting force pm _max g should be, therefore, results for the maximum permitted lifting speed when lifting $$\mathit{p}{\mathit{m}}_{\mathrm{Max}}\mathit{G}\mathit{=}{\mathit{m}}_{\mathit{l}}{\mathit{v}}_{\mathit{on}}\sqrt{\frac{c_{\mathit{total}}}{m_l}}.$$

$$v_{\mathit{on}}=\frac{{\mathit{pm}}_{\mathrm{Max}}G}{\sqrt{c_{\mathit{total}}{m}_l}}\mathrm{,}$$

und somit $$m_l=\frac{F_l}{g}\mathrm{.}$$

The current hoisting load m _l during lifting (load not yet lifted) can be calculated by the measured load force. Because at this time there is no dynamic force F _dyn yet. It applies during the so-called tensioning of the hoist train $$F_l=F_{\mathit{const}}$$

and thus $$m_l=\frac{F_l}{G}\mathrm{,}$$

In addition, within this block, the maximum permissible Hubwerksgeschwindigkeit when discontinuing the load v _from specified. This can be chosen to be a constant value, since no restrictions due to standards have to be met. Braking to this speed should only serve for Schlappseilsicherung.

3.2 Situation detection

In this block, the corresponding setpoint speed is selected on the basis of the current situation by means of an event-discrete state machine. The state machine used here is in Fig. 4 shown. The associated transitions and actions in each state are described below. The individual variables are summarized in Table 1.

3.2.1 General calculations

The calculations described in this section are performed independently of the condition. In the following, the measured load mass m _l is understood to mean the load mass measured by the force measuring axis on the hook, neglecting the dynamic forces, ie m _l = F _l / g .

Calculation of Ḟ _l :

This is the time derivative of the currently measured lifting force.

Calculation of Δm _on :

This is the absolute difference of the measured load mass in comparison to the measured load mass in the last low point of the measurement signal, which is referred to below as m _{0, on} . In addition, m _{0, is} updated to ( m _{0, on} = m _l ) when the transition 2 is passed in the state machine. This is the case when it is detected after a load lifting that the load is lifted off the ground.

Calculation of Δ m _from :

This is the absolute difference of the measured load mass compared to the measured load mass in the last high point of the measurement signal, which is referred to below as m _{0, ab} . In addition, m _{0, ab is} updated ( m _{0, ab} = m _l ) when the transition 6 is passed in the state machine. This is the case when the hoist is released again after a load has been released.

Calculation of Δ m _{on , det} :

This is the threshold value which of Δ _m must be exceeded in order for a detection of the load canceling is possible. This threshold value depends on the particular crane type and the measurement signal in the last low point m _{0, on} .

Calculation of Δ m _{ab , det} :

This is the threshold value which must be m below _from Δ, so that a detection of the load deposition is possible. This threshold value depends on the particular crane type and the measurement signal in the last low point m _{0, ab} .

Calculation of Ḟ _threshold :

wobei m_max die ausladungsabhängige maximal zulässige Hublast ist.This is the threshold value which must be exceeded by Ḟ _l to detect a possible load cancellation. This threshold value depends on the respective crane type, the total spring stiffness C _total, the permissible overshoot p in the force measuring axis and the ratio of $\frac{m_l}{m_{\mathrm{Max}}}$

where m _{max is} the discharge-dependent maximum allowable lifting load.

3.2.2 Description of the states State 1 (release hoist):

Within this state, the hoist is released and can be operated by default. The system starts after initialization (starting the crane) in this state.

Actions and calculations when entering I:

$$\mathrm{\Delta }l=0$$

Actions and calculation while staying in I:

Since the hand lever is released within this state applies $${\mathit{v}}_{\mathit{should}}\mathit{=}{\mathit{v}}_{\mathit{hh}}\mathit{,}$$

Condition II (cancel):

In this state, the system is located after it has been detected that a load is being lifted. When passing the transition to this state, l ₀ and m ₀ with / _rel
and m _l initialized. / _rel is the relative value of the angle encoder of the hoist winch converted into meters and m _l is the currently measured load mass on the hook.

Actions and calculations while staying in II:

$$\mathrm{\Delta }{l}_{\mathit{ab}}=\frac{\left(m_l-m_0+m_{\mathit{sicher}}\right)g}{c_{\mathit{gesamt}}}\mathrm{.}$$

Once the system is in this state, the calculation of the relative to l ₀ wound rope length and the theoretically required rope length for lifting is performed at each time step Δ l _from $$\mathrm{\Delta }l=l_0-l_{\mathit{rel}}$$

$$\mathrm{\Delta }{l}_{\mathit{from}}=\frac{\left(m_l-{\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">m</figure-callout>}}_0+m_{\mathit{for\; sure}}\right)G}{c_{\mathit{total}}}\mathrm{,}$$

Here m is _certainly a safety factor, so that more rope than necessary to be wound before this state can be left.

• 1. (v_hh < v_auf )
  In diesem Fall liegt die Handhebelgeschwindigkeit außerhalb des erlaubten Bereichs, daher gilt: $${\mathit{v}}_{\mathit{soll}}\mathit{=}{\mathit{v}}_{\mathit{auf}}\mathit{.}$$
  
• 2. (v _hh > v_auf )
  In diesem Fall liegt die Handhebelgeschwindigkeit im erlaubten Bereich, daher gilt $${\mathit{v}}_{\mathit{soll}}\mathit{=}{\mathit{v}}_{\mathit{hh}}\mathit{.}$$
  

In the calculation of the drive signal, two cases must be distinguished in this state. The current speed of the hand lever is used to distinguish these cases _hh v and the maximum allowed lifting gear speed v when picked _up (16). It should be noted that a negative v stands for lifting and a positive v for lowering. The two cases are:

• 1. ( v _hh < v _on )
  In this case, the hand lever speed is outside the permitted range, therefore: $${\mathit{v}}_{\mathit{should}}\mathit{=}{\mathit{v}}_{\mathit{on}}\mathit{,}$$
  
• 2. (v _hh > v _up )
  In this case, the hand lever speed is within the allowed range, therefore $${\mathit{v}}_{\mathit{should}}\mathit{=}{\mathit{v}}_{\mathit{hh}}\mathit{,}$$
  

Condition III (discontinuation):

The system comes into this state as soon as the load is detected. When passing the transition to this state, l _{0 is} initialized with / _rel .

Actions and calculations while staying in III:

As soon as the system is in this state, the calculation of the length of rope unwound relative to l ₀ takes place in each time step $$\mathrm{\Delta }l=l_0-l_{\mathit{rel}}\mathrm{,}$$

When calculating the drive signal, two cases must be distinguished. to

• 1. (v _hh > v_ab )
  In diesem Fall liegt die Handhebelgeschwindigkeit außerhalb des erlaubten Bereichs, daher gilt: $${\mathit{v}}_{\mathit{soll}}\mathit{=}{\mathit{v}}_{\mathit{ab}}\mathit{.}$$
  
• 2. (v_hh < v_ab )
  In diesem Fall liegt die Handhebelgeschwindigkeit im erlaubten Bereich, daher gilt $${\mathit{v}}_{\mathit{soll}}\mathit{=}{\mathit{v}}_{\mathit{hh}}\mathit{.}$$
  

Distinguish these cases serve v _hh and the maximum permitted lifting gear at weaning v _from the current hand lever speed. It should be noted that a negative v stands for lifting and a positive v for lowering. The two cases are:

• 1. (v _hh > v _from )
  In this case, the hand lever speed is outside the permitted range, therefore: $${\mathit{v}}_{\mathit{should}}\mathit{=}{\mathit{v}}_{\mathit{from}}\mathit{,}$$
  
• 2. ( v _hh < v _from )
  In this case, the hand lever speed is within the allowed range, therefore $${\mathit{v}}_{\mathit{should}}\mathit{=}{\mathit{v}}_{\mathit{hh}}\mathit{,}$$
  

3.2.3 Description of the transitions

• ein negatives v_hw bedeutet, dass die Winde Heben fährt,
• ein positives v_hw bedeutet, dass die Winde Senken fährt.

In the following it should be noted that the currently measured wind speed v _hw
is defined as follows:

• a negative v _hw means that the winch is lifting,
• a positive v _hw means the winch is lowering.

Transition 1:

Is activated as soon as a lifting of the load is detected from the ground in the "Release hoist" status. The following event activates this transition: $$\left(\dot{F_l}>{\dot{F}}_{\mathit{schwell}}\right)\&\&\left(\mathrm{\Delta }{m}_{\mathit{on}}>\mathrm{\Delta }{m}_{\mathit{on}.\det }\right)\&\&\left(v_{\mathit{hw}}<0\right)\mathrm{,}$$

$$m_0=m_l$$

The following calculations are performed when passing this transition: $${\mathrm{<figure-callout\; id="0"\; label="l"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">l</figure-callout>}}_0=l_{\mathit{rel}}$$

$$m_0=m_l$$

Transition 2:

Will be active as soon as the hoist is lowering when lifting the load. And the previously relatively wound rope length Δ l was completely unwound again. Thus located the system returns to its original state before the lifting has been detected. The following event activates this transition: $$\left(v_{\mathit{hw}}>0\right)\&\&\left(\mathrm{\Delta }l<0\right)\mathrm{,}$$

The following calculations are performed when passing this transition: $${\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">m</figure-callout>}}_0=0$$

Transition 3:

Is activated as soon as the load is lifted off the ground and the load is lifted off the ground. The following event activates this transition: $$\mathrm{\Delta }l>\mathrm{\Delta }{l}_{\mathit{from}}\mathrm{,}$$

The following calculations are performed when passing this transition: $${\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">m</figure-callout>}}_0=\mathrm{0th}$$

In addition, _to set in the calculation of Δ m _on the currently measured load mass ml is when passing this transition m is _0, (see 3.2.1).

Transition 4:

Is activated as soon as the load is detected in the "cancel" state or the measured load falls below a certain empty weight of the load-handling device. The following event activates this transition: $$\left(v_{\mathit{hw}}>0\right)\&\&\left(\left(\mathrm{\Delta }{m}_{\mathit{from}}<\mathrm{\Delta }{m}_{\mathit{from}.\det }\right)\Vert \left(m_l<m_{\mathit{empty}}\right)\right)$$

$$m_0=0$$

The following calculations are performed when passing this transition: $${\mathrm{<figure-callout\; id="0"\; label="l"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">l</figure-callout>}}_0=l_{\mathit{rel}}$$

$$m_0=0$$

Transition 5:

It becomes active as soon as a lifting of the load is detected from the ground in the condition "settling".

The following event activates this transition: $$\left(\dot{F_l}>{\dot{F}}_{\mathit{schwell}}\right)\&\&\left(\mathrm{\Delta }{m}_{\mathit{on}}>\mathrm{\Delta }{m}_{\mathit{on}.\det }\right)\&\&\left(v_{\mathit{hw}}<0\right)\mathrm{,}$$

$$m_0=m_l$$

The following calculations are performed when passing this transition: $${\mathrm{<figure-callout\; id="0"\; label="l"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">l</figure-callout>}}_0=l_{\mathit{rel}}$$

$$m_0=m_l$$

Transition 6:

Is activated as soon as it is detected in the "settling" state that the relatively wound wire length Δ l is again in the initial state (before transition 7 has been passed). The following event activates this transition: $$\mathrm{\Delta }l>0$$

When this transition occurs, m _{0, ab is set} to the currently measured load mass m _l for the calculation of Δ m _ab (see 3.2.1).

Transition 7:

Is activated as soon as the load is detected in the "Release hoist" status or the measured load falls below a certain empty weight of the load handler. The following event activates this transition: $$\left(v_{\mathit{hw}}>0\right)\&\&\left(\left(\mathrm{\Delta }{m}_{\mathit{from}}<\mathrm{\Delta }{m}_{\mathit{from}.\det }\right)\Vert \left(m_l<m_{\mathit{empty}}\right)\right)$$

The following calculations are performed when passing this transition: $${\mathrm{<figure-callout\; id="0"\; label="l"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">l</figure-callout>}}_0=l_{\mathit{rel}}$$

4 results of the crane control according to the first embodiment

Exemplary are in FIGS. 5 and 6 Results of a measurement in which 60 tons of load were lifted with slack rope off the ground. The figures each include the measurement with and without the automatic lifting according to the first embodiment of the present invention. <b> Table 1: </ b> Description of the variables from automatic lifting variable name description v _should Target speed which is sent to the hoist control. A positive value corresponds to sinks, a negative value corresponds to lifting. v _on Calculated permitted absolute speed when canceling. Calculation according to (16). v _from Prescribed permissible absolute speed at weaning. v _hh Target speed specified by the hand lever. F _l Force measured in the hoist train in N. F _const Constant force component in the hoist train in N. F _dyn Dynamic force component in the hoist train in N. m _l Is the load mass measured by the force measuring axis on the hook neglecting the dynamic forces. We have m _l = F _l / g . Ḟ _l Time derivative of F _l in N / s. Δm _on Absolute difference of m _l with respect to the last low point in the measurement of m _l in kg. m _{0, up} Last low point in the measurement signal from m _l to kg. Δ m _from Absolute difference of m _l with respect to the last high point in the measurement of m _l in kg. m _{0, from} Last high point in the measurement signal of m _l kg. Δ m _{on , det} Threshold in kg, which must be exceeded by Δ m _to detect a possible load cancellation. Δ m _{from , det} Threshold in kg, which must be fallen below by Δ m _{from in} order to detect a possible load settling. m _max Discharge-dependent approved maximum load in kg. F _max Shutter-dependent permitted maximum force in N. F _max = m _max g Ḟ _threshold Threshold, which must be exceeded by Ḟ _l to detect a load cancellation. Δ l Relative cable length after detecting a load release or a load release. We have Δ l = l ₀ - l _rel . l ₀ Initial value for calculating the relative rope length Δ l . Will happen when the transitions 1, 4, 5, 7. m ₀ Measured load mass m _l when detecting a load lifting in kg. Needed to calculate the theoretical rope length until take-off Δ l _ab . m _sure Safety factor in calculating Δ l _from in kg. Δ l _from Theoretical rope length in m until lifting of the load after a lifting has been detected. v _hw Measured hoist speed at the winch in m / s. Positive corresponds to sinks, negative corresponds to lifting. m _empty Empty weight of the lifting device in kg. _rel Relative rope length measured in m by the relative incremental encoder on the hoist winch.

5 Introduction to the second embodiment

In the following, a second embodiment of a control method implemented in a crane control according to the invention will now be described in which the dynamics of the system of hoist, hoisting rope and load, which is based on the compressibility of the hydraulic fluid and the extensibility of the load, are taken into account.

FIG. 7 shows a schematic diagram of the hydraulics of the hoist. Here is z. B. a diesel or electric motor 25 is provided, which drives a variable displacement pump 26. This variable displacement pump 26 forms with a hydraulic motor 27 a hydraulic circuit and drives it. Also, the hydraulic motor 27 is designed as an adjusting motor. Alternatively, a constant motor could be used. About the hydraulic motor 27, the hoist winch is then driven.

In FIG. 8 is the physical model through which the dynamics of the system of hoist winch, load cable 3 and the load in the second embodiment is described in more detail. The system of load rope and load is considered as a damped spring pendulum, with a spring constant C and a damping constant D. In the spring constant C is the length of the hoist rope L, which either determined based on measured values or due to the control the hoist winch is calculated. Furthermore, the mass M of the load, which is measured via a load mass sensor, enters into the control.

Also, the second embodiment is used to control a mobile harbor crane, as in FIG. 2 is shown. Here, the boom, the tower and the hoist winch are set in motion by hydraulic drives. The hydraulic drives which set the hoist winch of the crane generate natural vibrations due to the inherent dynamics of the hydraulic systems and / or the hoisting rope. The resulting force vibrations affect the long-term fatigue of the ropes and the entire crane structure, resulting in increased maintenance. According to the invention, therefore, a tax law is provided which suppresses caused by strokes of the crane natural oscillations and thereby reduces the stress cycles within the Wöhlerdiagramms. A reduction in the stress cycles logically increases the service life of the crane structure.

In the derivation of the tax law of the second embodiment, returns are to be avoided because they require sensor signals, which must meet certain safety requirements within industrial applications and thereby lead to higher costs.

Therefore, the design of a pure pilot control without feedback is necessary. Within this paper, a flatness-based feedforward control, which inverts the system dynamics, is derived for the hoist.

6 hoist winch

The hoist winch of the crane shown in the embodiment is driven by a hydraulically operated rotary motor. The dynamic model and the hoist winch control law are derived in the following section.

6.1 Dynamic Model

wobei l₁ , l₂ und l₃ die Teillängen von der Hubwinde zum Turm, vom Turm zum Ende des Auslegers und vom Ende des Auslegers zum Haken bezeichnen. Das Hubsystem des Krans, das aus der Hubwinde, dem Seil und der Nutzlast besteht, wird im Folgenden als Feder-Masse-Dämpfer-System betrachtet und ist in Figur 8 dargestellt. Das Verwenden des Verfahrens von Newton-Euler ergibt die Bewegungsgleichung für die Nutzlast: $$m_p{\ddot{z}}_p=m_{p}g-\underset{F_s}{\underbrace{\left(c\left(z_p-r_w{\phi }_w\right)+d\left({\dot{z}}_p-r_w{\dot{\phi }}_w\right)\right)}},z_p\left(0\right)=z_{p0},{\dot{z}}_p\left(0\right)=0$$

mit der Gravitationskonstante g, der Federkonstante c, der Dämpfungskonstante d, dem Radius der Hubwinde r_w , dem Winkel ϕ_w der Hubwinde, der Winkelgeschwindigkeit ϕ̇ _w , der Nutzlastposition z_p , der Nutzlastgeschwindigkeit ż_p und der Nutzlastbeschleunigung z̈_p. Die Seillänge l_r ist gegeben durch $$l_r\left(t\right)=r_w{\phi }_w\left(t\right)$$

mit $${\phi }_w\left(0\right)={\phi }_{w0}=\frac{l_1\left(0\right)+3l_2\left(0\right)+l_3\left(0\right)}{r_w}$$

Since the lifting force is directly influenced by the payload movement, the dynamics of the payload movement must be taken into account. As in FIG. 2 illustrated, the payload with the mass m _{p is} attached to a hook and can be raised or lowered by the crane by means of a rope of length l _r . The rope is deflected by a pulley on the jib tip and on the tower. However, the rope is not deflected directly from the end of the boom to the hoist winch, but from the end of the boom to the tower, from there back to the end of the boom and then over the tower to the hoist winch (see FIG. 2 ). Thus, the entire rope length is given by: $$l_r={\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="imgf0001.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+3{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="imgf0003.png"\; state="\{\{state\}\}">l</figure-callout>}}_3$$

where l ₁ , l ₂ and l ₃ denote the partial lengths of the hoist winch to the tower, from the tower to the end of the boom and from the end of the boom to the hook. The lifting system of the crane, which consists of the hoist winch, the rope and the payload, is considered below as a spring-mass-damper system and is in FIG. 8 shown. Using the Newton-Euler method yields the equation of motion for the payload: $$m_p{\ddot{z}}_p=m_{p}G-\underset{F_s}{\underset{\}}{\left(c\left(z_p-r_w{\phi }_w\right)+d\left({\dot{z}}_p-r_w{\dot{\phi }}_w\right)\right)}}.{\mathrm{<figure-callout\; id="0"\; label="z\; p"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">z\; </figure-callout>}}_p\left(0\right)=z_{p0}.{\dot{z}}_{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">p</figure-callout>}}\left(0\right)=0$$

with the gravitational constant g, the spring constant c, the damping constant d, the radius of the hoist winch r _w, the angle φ _w of the hoist winch, the angular velocity .phi _w, the payload position z _p, the payload speed z _p and the payload acceleration Z _p. The rope length l _r is given by $$l_r\left(t\right)=r_w{\phi }_w\left(t\right)$$

With $${\mathrm{<figure-callout\; id="0"\; label="\phi \; w"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">\phi \; </figure-callout>}}_w\left(0\right)={\phi }_{w0}=\frac{{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="imgf0001.png"\; state="\{\{state\}\}">l</figure-callout>}}_1\left(0\right)+3{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">l</figure-callout>}}_2\left(0\right)+{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="imgf0003.png"\; state="\{\{state\}\}">l</figure-callout>}}_3\left(0\right)}{r_w}$$

wobei E_r und A_r das Elastizitätsmodul und die Schnittfläche des Seils bezeichnen.The spring constant c _{r of} a rope of length l _r is given by Hooke's law and can be written as $$c_r=\frac{e_r{A}_r}{l_r}$$

where E _r and A _r denote the modulus of elasticity and the sectional area of the rope.

The crane has n _r parallel ropes (see FIG. 2 ), so the spring constant of the crane's hoist is given by: $$c=n_r{c}_r$$

The damping constant d can be specified using Lehr's damping factor D. $$d=2D\sqrt{{\mathit{cm}}_p}$$

The differential equation for the rotational movement of the hoist winch is given by the method of Newton-Euler as $$\left(J_w+i_{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">w</figure-callout>}}^2{J}_m\right){\ddot{\phi }}_w=i_w{D}_m\mathrm{\Delta }{p}_w+r_w{F}_s.{\mathrm{<figure-callout\; id="0"\; label="\phi \; w"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">\phi \; </figure-callout>}}_w\left(0\right)={\phi }_{w0}.{\dot{\phi }}_{\mathrm{<figure-callout\; id="0"\; label="w"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">w</figure-callout>}}\left(0\right)=0$$

where J _w and J _m denote the moment of inertia of the winch and the motor, i _{w is} the gear ratio between the engine and the winch, Δ p _{w is} the pressure difference between high and low pressure chambers of the engine, D _{m is} the displacement of the hydraulic motor, and F _{s is} the spring force given in (39). The initial condition φ _w0 for the angle of the _{hoist winch} is given by (41). The hydraulic circuit for the hoist winch is in FIG. 7 shown. The pressure difference Δp _w between both pressure chambers of the engine is described by the pressure build-up assuming that no internal or external leakage occurs. In addition, in the following, the small volume change due to the motor angle φ _{w is} neglected. Thus, the volume in both pressure chambers is assumed to be constant and denoted by V _m . With the help of these assumptions, the pressure build-up equation can be described as $$\mathrm{\Delta }{\dot{p}}_w=\frac{4}{V_m\beta }\left(q_w-D_m{i}_w{\dot{\phi }}_w\right).\mathrm{\Delta }{\mathrm{<figure-callout\; id="0"\; label="p\; w"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">p\; </figure-callout>}}_w\left(0\right)=\mathrm{\Delta }{p}_{w0}$$

wobei u_w und K_w der Ansteuerstrom des Pumpenwinkels und der Proportionalitätsfaktor sind.Write, where β is the compressibility of the oil. The oil flow rate q _w is controlled by the pump angle and is given by $$q_w=K_w{u}_w$$

where u _w and K _{w are} the drive current of the pump angle and the proportionality factor.

6.2 Tax Law

wobei $$\mathbf{f}\left(\mathbf{x}\right)=\left[\begin{array}{c}{x}_2\\ \frac{\begin{array}{c}1\end{array}}{J_w+i_w^2{J}_m}\left(i_w{D}_m{x}_5+r_w\left(\frac{E_r{A}_r{n}_r}{r_w{x}_1}\left(x_3-r_w{x}_1\right)\right)\right)\\ x_4\\ g-\frac{E_r{A}_r{n}_r}{r_w{x}_1{m}_p}\left(x_3-r_w{x}_1\right)\\ \frac{\begin{array}{c}-4D_m{i}_w{x}_2\end{array}}{V_m\beta }\end{array}\right]$$

$$\mathbf{g}\left(\mathbf{x}\right)=\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ \frac{\begin{array}{c}4K_w\end{array}}{V_m\beta }\end{array}\right]$$

$$h\left(\mathbf{x}\right)=x_3$$

und u = u_w .In the following, the dynamic model for the hoist winch is transformed into the state space to design a flatness-based feedforward control. The derivation of the tax law neglects the damping, therefore D = 0. The state vector of the crane's hoist is defined as x = [φ _w , φ _w , z _p , ¿ _p , Δ p _w ] ^T. Thus, the dynamic model consisting of (39), (40), (43), (45), (46) and (47) can be written as a system of first order differential equations given by: $$\dot{\mathbf{x}}\mathbf{=}\mathbf{f}\left(\mathbf{x}\right)+\mathbf{G}\left(\mathbf{x}\right)u.{}_{}y=H\left(\mathbf{x}\right).\mathbf{x}\left(0\right)={\mathbf{x}}_0.t\ge 0$$

in which $$\mathbf{f}\left(\mathbf{x}\right)=\left[\begin{array}{c}{x}_2\\ \frac{\begin{array}{c}1\end{array}}{J_w+i_{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">w</figure-callout>}}^2{J}_m}\left(i_w{D}_m{x}_5+r_w\left(\frac{e_r{A}_r{n}_r}{r_w{x}_1}\left(x_3-r_w{x}_1\right)\right)\right)\\ x_4\\ G-\frac{e_r{A}_r{n}_r}{r_w{x}_1{m}_p}\left(x_3-r_w{x}_1\right)\\ \frac{\begin{array}{c}-4D_m{i}_w{x}_2\end{array}}{V_m\beta }\end{array}\right]$$

$$\mathbf{G}\left(\mathbf{x}\right)=\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ \frac{\begin{array}{c}4K_w\end{array}}{V_m\beta }\end{array}\right]$$

$$H\left(\mathbf{x}\right)=x_3$$

and u = u _w .

For the design of a flatness-based feedforward, the relative degree r with respect to the system output must be equal to the order n of the system. Therefore, the relative degree of the system under consideration (48) will be examined below.

The relative degree of system output is determined by the following conditions: $$\begin{array}{l}{L}_{\mathrm{G}}{L}_{\mathrm{f}}^{i}H\left(\mathbf{x}\right)=0\\ L_{\mathrm{G}}{L}_{\mathrm{f}}^{r-1}H\left(\mathbf{x}\right)\ne 0\end{array}\begin{array}{l}\forall i=0.....r-2\\ \forall \mathrm{x}\in {\mathrm{R}}^n\end{array}$$

The operators L _f and L _g represent the Lie derivatives along the vector fields f and g , respectively. Using (52) gives r = n = 5, so the system (48) is (49), (50) and (51) flat and a flatness-based feedforward for D = 0 can be designed.

$$\dot{y}=\frac{\partial h\left(\mathbf{x}\right)}{\partial \mathbf{x}}\frac{\partial \mathbf{x}}{\partial t}=L_{\mathrm{f}}h\left(\mathbf{x}\right)+\underset{=0}{\underbrace{L_{g}h\left(\mathbf{x}\right)u}}$$

$$\ddot{y}=\frac{\partial L_{\mathrm{f}}h\left(\mathbf{x}\right)}{\partial \mathbf{x}}\frac{\partial \mathbf{x}}{\partial t}=L_{\mathrm{f}}^{2}h\left(\mathbf{x}\right)+\underset{=0}{\underbrace{L_g{L}_{\mathrm{f}}h\left(\mathbf{x}\right)}}u$$

$$\stackrel{\dot{}¨}{y}=\frac{\partial L_{\mathrm{f}}^{2}h\left(\mathbf{x}\right)}{\partial \mathbf{x}}\frac{\partial \mathbf{x}}{\partial t}=L_{\mathrm{f}}^{3}h\left(\mathbf{x}\right)+\underset{=0}{\underbrace{L_g{L}_{\mathrm{f}}^{2}h\left(\mathbf{x}\right)}}u$$

$$\stackrel{\left(4\right)}{y}=\frac{\partial L_{\mathrm{f}}^{3}h\left(\mathbf{x}\right)}{\partial \mathbf{x}}\frac{\partial \mathbf{x}}{\partial t}=L_{\mathrm{f}}^{4}h\left(\mathbf{x}\right)+\underset{=0}{\underbrace{L_g{L}_{\mathrm{f}}^{3}h\left(\mathbf{x}\right)}}u$$

$$\stackrel{\left(5\right)}{y}=\frac{\partial L_{\mathrm{f}}^{4}h\left(\mathbf{x}\right)}{\partial \mathbf{x}}\frac{\partial \mathbf{x}}{\partial t}=L_{\mathrm{f}}^{5}h\left(\mathbf{x}\right)+L_g{L}_{\mathrm{f}}^{4}h\left(\mathbf{x}\right)u$$

The system output (51) and its time derivatives are used to invert the system dynamics, as was done for the seesaw and slewing gear. The derivatives are given by the Lie derivatives, so $$y=H\left(\mathbf{x}\right)$$

$$\dot{y}=\frac{\partial H\left(\mathbf{x}\right)}{\partial \mathbf{x}}\frac{\partial \mathbf{x}}{\partial t}=L_{\mathrm{f}}H\left(\mathbf{x}\right)+\underset{=0}{\underset{\}}{L_{G}H\left(\mathbf{x}\right)u}}$$

$$\ddot{y}=\frac{\partial L_{\mathrm{f}}H\left(\mathbf{x}\right)}{\partial \mathbf{x}}\frac{\partial \mathbf{x}}{\partial t}={\mathrm{<figure-callout\; id="2"\; label="L\; f"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_{\mathrm{f}}^{\mathrm{}}H\left(\mathbf{x}\right)+\underset{=0}{\underset{\}}{L_G{L}_{\mathrm{f}}H\left(\mathbf{x}\right)}}u$$

$$\stackrel{\dot{}¨}{y}=\frac{\partial {\mathrm{<figure-callout\; id="2"\; label="L\; f"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_{\mathrm{f}}^{\mathrm{}}H\left(\mathbf{x}\right)}{\partial \mathbf{x}}\frac{\partial \mathbf{x}}{\partial t}={\mathrm{<figure-callout\; id="3"\; label="L\; f"\; filenames="imgf0003.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_{\mathrm{f}}^{\mathrm{}}H\left(\mathbf{x}\right)+\underset{=0}{\underset{\}}{L_G<figure-callout\; id="2"\; label="\; L\; f"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">\; </figure-callout>L_{\mathrm{f}}^{}{\mathrm{}}_2^{}H\left(\mathbf{x}\right)}}\mathrm{<figure-callout\; id="4"\; label="u\; y"\; filenames="imgf0003.png"\; state="\{\{state\}\}">u\; </figure-callout>}$$

$$\stackrel{}{y}$$$$\stackrel{\left(4\right)}{}=\frac{\partial {\mathrm{<figure-callout\; id="3"\; label="L\; f"\; filenames="imgf0003.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_{\mathrm{f}}^{\mathrm{}}H\left(\mathbf{x}\right)}{\partial \mathbf{x}}\frac{\partial \mathbf{x}}{\partial t}={\mathrm{<figure-callout\; id="4"\; label="L\; f"\; filenames="imgf0003.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_{\mathrm{f}}^{\mathrm{}}H\left(\mathbf{x}\right)+\underset{=0}{\underset{\}}{L_G<figure-callout\; id="3"\; label="\; L\; f"\; filenames="imgf0003.png"\; state="\{\{state\}\}">\; </figure-callout>L_{\mathrm{f}}^{}{\mathrm{}}_3^{}H\left(\mathbf{x}\right)}}\mathrm{<figure-callout\; id="5"\; label="u\; y"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">u\; </figure-callout>}$$

$$\stackrel{}{y}$$$$\stackrel{\left(5\right)}{}=\frac{\partial {\mathrm{<figure-callout\; id="4"\; label="L\; f"\; filenames="imgf0003.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_{\mathrm{f}}^{\mathrm{}}H\left(\mathbf{x}\right)}{\partial \mathbf{x}}\frac{\partial \mathbf{x}}{\partial t}={\mathrm{<figure-callout\; id="5"\; label="L\; f"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_{\mathrm{f}}^{\mathrm{}}H\left(\mathbf{x}\right)+L_G<figure-callout\; id="4"\; label="\; L\; f"\; filenames="imgf0003.png"\; state="\{\{state\}\}">\; </figure-callout>L_{\mathrm{f}}^{}{\mathrm{}}_4^{}H\left(\mathbf{x}\right)u$$

$$x_2=x_2\left(y\dot{y}\ddot{y}\stackrel{\dot{}¨}{y}\right)$$

$$x_3=y$$

$$x_4=\ddot{y}$$

$$x_5=x_5\left(y\dot{y}\ddot{y}\stackrel{\dot{}¨}{y}\stackrel{\left(4\right)}{y}\right)$$

The states depending on the system output and its derivatives follow from (53), (54), (55), (56) and (57) and can be written as: $$x_1=\frac{A_r{e}_r{n}_{r}y}{r_w\left({\mathit{gm}}_p+A_r{e}_r{n}_r-m_p\ddot{y}\right)}$$

$$x_2=x_2\left(y\dot{y}\ddot{y}\stackrel{\dot{}¨}{y}\right)$$

$$x_3=y$$

$$x_4=\ddot{y}$$

$$x_5=x_5\left(y\dot{y}\ddot{y}\stackrel{\dot{}¨}{y}\stackrel{\left(4\right)}{y}\right)$$

welche die Systemdynamik invertiert. Das Referenzsignal y und seine Ableitungen werden durch eine numerische Trajektoriengenerierung aus dem Handhebelsignal des Kranbedieners gewonnen.Solving (58) for system input u , using (59), (60), (61), (62), and (63), provides the control law for flatness-based feedforward control for the hoist $$u_w=f\left(y\dot{y}\ddot{y}\stackrel{\dot{}¨}{y}\stackrel{\left(4\right)}{y}\stackrel{\left(5\right)}{\mathrm{<figure-callout\; id="5"\; label="y"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">y</figure-callout>}}\right)$$

which inverts the system dynamics. The reference signal y and its derivatives are obtained by a numerical trajectory generation from the hand lever signal of the crane operator.

Claims (15)

Crane control for controlling a hoist of a crane, which takes into account the based on the extensibility of the hoist rope vibration dynamics in the control of the hoist and reduced by suitable control of the hoist. Crane control according to claim 1, wherein the drive speed of the hoist for limiting overshoots is limited to a maximum allowable drive speed. Crane control according to claim 2, wherein the maximum permissible drive speed of the hoist is determined dynamically based on crane data. Crane control according to claim 2 or 3, wherein the maximum permissible drive speed of the hoist in dependence on a currently measured Lifting force is determined and / or determined as a function of the rope length. Crane control according to one of claims 2 to 4, wherein the maximum permissible drive speed of the hoist is determined on the basis of a physical model, which describes the vibration dynamics of the system of hoist, rope and load. Crane control according to one of the preceding claims, with a situation detection, based on which the crane control determines the driving behavior. A crane controller according to claim 6, wherein the situation recognition recognizes a lift-off condition in which the drive speed of the hoist is limited to avoid overshoot, advantageously the situation detection recognizes a lift-off condition when an overlying load is lifted. Crane control according to claim 6, wherein the situation recognition detects a release state in which the drive speed of the hoist is released, advantageously a release state is detected when the load has been raised and now hangs freely on the crane cable. Crane control according to claim 6, wherein the situation detection detects a storage state in which the drive speed of the hoist is limited, to avoid that unnecessarily much rope is unwound when placing the load. Crane control according to one of the preceding claims, wherein a target stroke of the load serves as input, on the basis of which a control variable for controlling the hoist is calculated, wherein in the calculation of the control variable, the vibration dynamics due to the extensibility of the hoist rope is taken into account in order to reduce natural vibrations. Crane control according to claim 10, wherein the hoist is hydraulically driven and in the calculation of the control variable, the vibration dynamics due to the compressibility of the hydraulic fluid is taken into account. Crane control according to claim 10 or 11, wherein the variable cable length of the hoisting rope and / or the measured lifting force is included in the calculation of the control variable. Crane control according to one of claims 10 to 12, wherein the control of the hoist based on a physical model of the crane, which describes the lifting movement of the load as a function of the control amount of the hoist, wherein advantageously the control of the hoist on the inversion of the physical model based. Method for controlling a hoist of a crane by means of a crane control according to one of claims 1 to 13, which takes into account in the control of the hoist based on the extensibility of the hoist rope vibration dynamics and reduced by suitable control of the hoist. Crane with a crane control according to one of claims 1 to 13.

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