EP2272784A1 - Crane for covering a load suspended on a load rope - Google Patents

Abstract

The crane has a rotating mechanism and a luffing mechanism which is provided for luffing a cantilever arm. A lifting unit is provided lowering and lifting the load (9) hanging on a load cable. The calculation of the control instructions for controlling the rotating mechanism, luffing mechanism and lifting unit takes place on the basis of a reference-movement specified in Cartesian coordinate.

Description

The present invention relates to a crane for handling a load suspended on a load rope with a slewing gear for rotating the crane, a luffing mechanism for luffing the boom and a hoist for lowering or lifting the load hanging on the load rope. The crane has a control unit for calculating the control of slewing gear, luffing gear and / or hoist on. Advantageously, the control unit in this case comprises a load oscillation damping, which damps oscillation of the load during a movement of the crane by suitable control of slewing gear, luffing gear and / or hoist.

Such a crane is for example off DE 100 64 182 known. In this case, the input of the control commands, the generation of the desired trajectories and the calculation of the control of slewing gear, luffing gear and hoist in cylindrical coordinates. The calculation of the appropriate control of slewing gear, luffing gear and / or hoist for load oscillation damping is complex and relatively inaccurate.

The object of the present invention is to provide a crane for handling a load suspended on a load rope with an improved crane control.

This object is achieved by a crane according to claim 1. The crane according to the invention comprises a slewing gear for turning the crane, a luffing gear for luffing the boom and a hoist for lowering or lifting the load suspended on the load rope. The crane has a crane control with a control unit for calculating the control of slewing gear, luffing gear and / or hoist on. Advantageously, the control unit comprises a load oscillation damping. According to the invention, the control unit is designed so that the calculation of the control commands for the control of slewing gear, luffing gear and / or hoisting gear is effected on the basis of a specified movement of the load in Cartesian coordinates. This has the advantage that the calculation based on the desired movement in Cartesian coordinates is considerably simplified and improved. In particular, based on the desired movement of the load in Cartesian coordinates a simpler or more effective load oscillation damping can be realized.

Advantageously, the load oscillation damping of the control unit is based on the inversion of a physical model of the load hanging on the load rope and the crane, wherein the inverted physical model converts a predetermined movement of the load hanging rope load in Cartesian coordinates in control signals for the slewing, luffing and / or hoist , The physical model encompasses the dynamics of the load hanging on the load rope, in particular the pendulum vibration dynamics, so that an extremely effective load oscillation damping can be realized by inverting the model. The calculation in Cartesian coordinates allows a quasi-static decoupling of the lifting movement in the z-direction of the movements in the horizontal, ie in the x and γ direction. This allows easier inversion of the model.

The crane according to the invention advantageously comprises one or more sensors for determining one or more measured variables for the position and / or movement of the load and / or the crane, in particular for determining one or more of the parameters rope angle radial, rope angle tangential, rocking angle, rotation angle, rope length and their Derivatives, where the measurand or measures are in the inversion of the physical model. In particular, several of these variables, advantageously all of these variables, enter into the inversion of the physical model. The feedback of the measured state variables allows an inversion of the physical model, which otherwise would only be at great expense or not at all invertible.

The crane according to the invention further advantageously comprises one or more sensors for determining one or more measured variables for the position and / or movement of the load and / or the crane, in particular for determining one or more of the parameters rope angle radial, rope angle tangential, rocking angle, rotation angle, rope length and their derivatives, wherein the measured variable or the measured variables are fed back into the control unit. The feedback of the measured state variables is also independent of the inversion of the model of great advantage to stabilize the control.

Advantageously, a first transformation unit is provided which calculates the actual position and / or actual movement of the load in Cartesian coordinates on the basis of the measured variable or the measured variables, in particular one or more of the variables position in x, y and z, velocity in x, y and z, acceleration in x and y, jerk in x and y. The first transformation unit thus permits a comparison of the actual position and / or actual movement of the load with the desired position present in Cartesian coordinates and / or the desired movement of the load. In addition to the actual position of the load, the actual speed of the load and possibly higher derivatives in Cartesian coordinates are advantageously calculated.

The sensor signals correspond to measured values in crane coordinates or in rope coordinates such. B. the sizes rope angle radially, rope angle tangential, rocking angle, rotation angle and pitch and their derivatives, from which the actual position and / or actual movement of the load is calculated in Cartesian coordinates by the first transformation unit. The rocking angle and the angle of rotation are present as measured variables in crane coordinates. By contrast, the cable angles are in the form of cable coordinates, which are measured with respect to a vertical axis directed downwards from the boom head. The first transformation unit requires a transformation of these coordinate systems into Cartesian coordinates of the load.

The crane according to the present invention advantageously comprises one or more cable angle sensors, wherein the measured values of the cable angle sensor (s) are fed back into the control unit. The cable angle sensors thereby enable a return of the pendulum movement in the control unit and in particular in the pendulum damping. This results in a closed control loop, by which the control unit according to the invention and in particular the load oscillation damping is stabilized.

In particular, the first transformation unit calculates the actual position and / or the actual movement of the load in Cartesian coordinates on the basis of the measured values measured by the cable angle sensor (s). In addition to the actual position of the load, it is also possible to calculate the derivation of the actual position and optionally further derivations. In this case, further measured quantities can be included in the calculation of the actual position and / or actual movement of the load. In particular, the rocking angle, the angle of rotation and / or the length of the cable and, if appropriate, its derivatives can be taken into account as measured variables.

The crane control advantageously further comprises an input unit for inputting control commands by an operator and / or by an automation system, wherein a second transformation unit is provided between input unit and control unit, which calculates the target movement of the load in Cartesian coordinates on the basis of the control commands. The input of the control commands thus continues to be in crane coordinates. The crane coordinates thereby advantageously comprise the angle of rotation of the crane, the rocking angle of the boom or the projection and the lifting height. These coordinates represent the natural coordinate system of the crane according to the invention, so that an input of the control commands in these coordinates is intuitively possible. The second transformation unit therefore transforms a desired movement of the load in crane coordinates into a desired movement of the load in Cartesian coordinates.

Alternatively, however, an input of the desired movement of the load in Cartesian coordinates is possible. In particular, if the crane is controlled via a remote control, an input in Cartesian coordinates may be easier for the operator, especially if they are e.g. stops at the hub. The second transformation unit can thus be omitted.

Further advantageously, the crane according to the invention has one or more sensors for determining measured variables with respect to the position and / or movement of cranes, in particular for determining the rocking angle and / or the rotational angle, wherein the second transformation unit is initialized on the basis of the measured variable or the measured variables. This ensures that a correct transformation of the crane coordinates into Cartesian coordinates takes place. The initialization of the second transformation unit based on the measured variable or measured variables can be z. B. in each case when switching on the crane control.

The crane control of the crane according to the invention further advantageously comprises a path plan module which generates trajectories from the control commands of the input unit, which serve as input variables for the control unit. The path planning module therefore calculates a desired movement of the load from the control commands entered by an operator.

Advantageously, the trajectories are generated in crane coordinates, so that the second transformation unit is arranged between the track plan module and the control unit. The crane coordinates are advantageously the cylindrical coordinates of the crane, ie the angle of rotation, the rocking angle or the discharge and the lifting height. In these coordinates, the generation of the trajectories is particularly easy, since the system restrictions are present in these coordinates.

Advantageously, the trajectories in the railway plan module are generated optimally from the control commands taking into account the system limitations.

Advantageously, the control unit further takes into account the dynamics of the load hanging on the load rope to dampen vibrations of the load. This can be done in particular in the load oscillation damping of the control unit to dampen pendulum vibrations of the load. In addition, if necessary, vibrations of the load in the stroke direction can also be taken into account and damped.

Advantageously, the control unit is based on the inversion of a physical model of the load hanging on the load rope and the crane. The physical model advantageously describes the movement of the load as a function of the control of slewing gear, luffing gear and / or hoisting gear. The inversion of the model results in the control of the respective works on the basis of a target trajectory of the load.

The model takes into account advantageously the vibration dynamics of the load hanging on the load rope. This results in an effective damping of vibrations of the load, in particular an effective load oscillation damping. In addition, the control unit can be easily adapted to different cranes.

Advantageously, the physical model is non-linear. This is important because many of the key effects in load swing damping are nonlinear.

Advantageously, the model allows in Cartesian coordinates a quasi-static decoupling of the vertical movement of the load. Through this quasi-static decoupling of the vertical movement of the load in the stroke direction of the Movement of the load in horizontal directions makes a simplified and improved calculation of the control of slewing gear, luffing gear and / or hoist possible. In particular, this allows a simpler load oscillation damping.

The quasi-static decoupling of the vertical movement of the load also makes it possible to control the vertical movement of the load directly, while the horizontal movement is controlled by the load swing damping.

In the crane according to the invention can therefore be provided that the control unit controls the hoist directly on the basis of control commands of an operator and / or an automation system, while the control of the slewing and the luffing takes place via the load swing damping. As a result, the control system according to the invention can be realized simpler and cheaper. In addition, higher safety standards are met, since the lifting movement has different safety requirements than the movement of the load in the horizontal direction. The operator and / or the automation system can therefore according to the invention directly control the speed of the hoist, while for the control of the slewing gear and the luffing gear from the inputs of the operator and / or the automation system initially a desired movement of the load is generated, from which the Lastpendeldämpfung calculates a control of the hoist and the luffing, which avoids or dampens load oscillations.

In the drives of the crane according to the invention, it may be z. B. act to hydraulic drives. Likewise, the use of electric drives is possible. The luffing can z. B. be realized via a hydraulic cylinder, or via a retractor, which moves the boom via a stranding.

The present invention further comprises, in addition to the crane, a crane control for controlling the slewing gear, the luffing gear and / or the hoisting gear of a crane. The crane control has a control unit for calculating the control of slewing gear, luffing gear and / or hoist on. The control unit points advantageously further on a load oscillation damping. According to the invention, the control unit is designed such that the calculation of the control commands for the control of slewing gear, luffing gear and / or hoisting gear is effected on the basis of a setpoint load movement indicated in Cartesian coordinates.

The crane control is advantageously carried out as already shown above with respect to the crane. Advantageously, the crane control is a computer-implemented crane control.

The present invention further comprises a corresponding method for controlling a crane.

In particular, the present invention comprises a method for controlling a crane for handling a load suspended on a load rope with a slewing gear for rotating the crane, a luffing mechanism for luffing the boom and a hoist for lowering or lifting the load hanging on the rope, wherein the Calculation of the control commands for the control of slewing gear, luffing gear and / or hoist on the basis of specified in cartesian coordinates target load movement takes place. As already described with respect to the crane, the calculation of the control commands based on a specified in Cartesian coordinates Solllastbewegung allows a simplified and improved control. In particular, in the calculation of the control commands for the control of slewing gear, luffing gear and / or hoist a load oscillation damping can be made by which oscillating movements of the load are damped. The load oscillation damping takes place advantageously taking into account the dynamics of the load hanging on the load rope, in particular taking into account the pendulum dynamics of the load rope hanging load to dampen spherical oscillations of the load by a suitable control of slewing and luffing gear.

Advantageously, the method is carried out in the same manner as was described in more detail above with respect to the crane or crane control. Especially the method according to the invention is a method for controlling a crane, as has been described above.

Figur 1:

die Struktur des zur Ansteuerung herangezogenen physikalischen Mo- dells,

Figur 2:

eine Prinzipdarstellung des Krans sowie der am Lastseil hängenden Last unter Angabe der relevanten Koordinaten,

Figur 3:

eine Prinzipdarstellung der Steuerungsstruktur einer erfindungsgemäßen Kransteuerung,

Figur 4:

einen Ausschnitt aus der erfindungsgemäßen Steuerungsstruktur, wel- che die Rückführung von Meßwerten anhand einer zweiten Transforma- tionseinheit näher darstellt,

Figur 5:

die maximale Geschwindigkeit des Auslegerkopfes in radialer Richtung in Abhängigkeit von der Ausladung des Auslegers,

Figur 6:

die radiale Position der Last bei einer Wippbewegung des Auslegers,

Figur 7:

die entsprechende Position der Last in x- bzw. y-Richtung während der Wippbewegung,

Figur 8:

die Position, Geschwindigkeit und Beschleunigung der Last in Drehrich- tung während einer Drehbewegung des Krans,

Figur 9:

die Position der Last in radialer Richtung während der Drehbewegung des Krans und

Figur 10:

die entsprechende Position der Last in x- und γ-Richtung während der Drehbewegung des Krans.

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

FIG. 1:

the structure of the physical model used for the control,

FIG. 2:

a schematic representation of the crane as well as the load hanging on the load rope with indication of the relevant coordinates,

FIG. 3:

a schematic representation of the control structure of a crane control according to the invention,

FIG. 4:

2 shows a detail of the control structure according to the invention, which represents in more detail the feedback of measured values on the basis of a second transformation unit,

FIG. 5:

the maximum speed of the boom head in the radial direction as a function of the projection of the boom,

FIG. 6:

the radial position of the load during a rocking motion of the boom,

FIG. 7:

the corresponding position of the load in the x or y direction during the rocking movement,

FIG. 8:

the position, velocity and acceleration of the load in the direction of rotation during a rotation of the crane,

FIG. 9:

the position of the load in the radial direction during the rotation of the crane and

FIG. 10:

the corresponding position of the load in x- and γ-direction during the rotation of the crane.

An embodiment of a crane according to the invention, a method for controlling the crane and a corresponding crane control, in which this method is implemented, will now be described in more detail below.

The essential control tasks in the automation of crane operation according to the method of controlling a crane according to the invention are load-swing damping and load-speed following control. For this purpose, a nonlinear dynamic crane model is used, which combines the equations of motion of the cable-guided load and the simplified drive dynamics. Based on the flatness characteristic of the crane model, a linearizing tax law is obtained by state feedback. The generation of smooth and realizable reference trajectories is formulated as an optimal control problem. The control system is integrated into the software of a crane, in particular a mobile harbor crane.

The essential goals of crane automation according to the present invention are thereby increasing the efficiency and safety during loading processes. Crane operation and external disturbances cause weakly damped load pendulum movements. Another problem with the control of slewing cranes compared to gantry cranes is the non-linear coupling of the turning and rocking movements. An active load swing damping and a precise sequence of the desired load speeds, which are given by the hand lever signals of the operator, are the essential control tasks for the mobile harbor crane.

The problem of trajectory succession is solved by deriving control laws that linearize the nonlinear crane system based on state information (state feedback linearization). When designing the control, the flatness characteristic of the MIMO system is verified and used. The resulting linearized system is additionally stabilized by asymptotic output controls. Due to the model-based controller design, all parameters are represented analytically, and the control concept can be easily adapted to different configurations and crane types.

The application of model-based, non-linear design techniques requires sufficiently smooth reference trajectories that are feasible with respect to the input and state constraints of the system. Therefore, the follow-up problem is formulated as an optimal control problem solved online to generate the viable reference trajectories for the exactly linearized system. Trajectory generation can be considered as Model Predictive Control (MPC). The formulation of the problem of optimal control in the flat coordinates reduces the effort in the numerical solution.

In the following section, a dynamic model of the crane is derived from the equations of motion of the load suspended from a cable and from approximations of the drive dynamics. Subsequently, the differential flatness of the crane model is shown and a non-linear flatness-based control law is derived. The formulation and numerical solution of the problem of trajectory generation as an optimal control problem is shown. The measurement results from the implementation of the control strategy on a mobile harbor crane are presented in the last section.

Dynamic crane model

The present invention is used in a crane with a boom 1, which is pivoted about a horizontal rocking axis on the tower 2 of the crane. To rock the boom 1 while a boom cylinder between the tower and the boom is arranged. The tower is rotatable about a vertical axis of rotation. For this purpose, the tower is arranged on an upper carriage, which is rotatable about a slewing gear with respect to a lower carriage about the vertical axis of rotation. At the superstructure Furthermore, the hoist is arranged to lift the load. The hoist rope is guided by the lifting hoist arranged on the superstructure via deflection rollers on the tower top and on the jib tip 3 to the load. The undercarriage has in the embodiment of a chassis, so that the crane is movable. This is in the embodiment of a mobile harbor crane. This has z. B. a load capacity of up to 200 t, a maximum radius of 60 m and a rope length of up to 80 m.

The dynamic model of the jib crane is derived by subdividing the entire system into two subsystems, see Fig. 1 , The first subsystem is the rigid crane structure 5 consisting of the crane tower 2 and the boom 1. This submodel has two degrees of freedom. The angle of rotation φ _s and the righting angle φ _I. The second subsystem 6 represents the load hanging on the rope. The suspension point is the tip of the boom. As in Fig. 1 shown, crane structure acts on the cable-guided load by movements of the boom tip, which leads to spherical load pendulum movements. The physical model of the crane structure uses the input signals 7 for the drives to describe the movement 8 of the cantilever tip, the physical model of the crane rope-dependent load describes the movement of the load 9 by means of the movement 8 of the cantilever tip, where the model takes account of pendulum movements of the load.

Dynamics of the crane structure

The crane structure is set in motion by hydraulic motors for rotary motion and a hydraulic cylinder for rocking the boom. Assuming that the hydraulic pump has a first-order lag behavior and the rotational speed φ _{s is} proportional to the oil flow delivered by the pump, the equation of motion for rotation results $$\ddot{\phi }+\frac{1}{T_s}{\dot{\phi }}_s=\frac{2{\mathit{\pi K}}_s}{\underset{d}{\underset{\}}{i_s{\mathit{VT}}_s}}}{u}_s$$

mit der Zeitkonstante T_I, der Proportionalkonstante K_I , der Querschnittfläche A und den geometrischen Konstanten C₁ und C₂ .The parameters of equation (1) are the time constant T _s , the proportional constant K _s between the input signal u _s and the oil flow rate, the transmission ratio i _s and the engine volume V. The derivation of the dynamic model of the rocking motion is again based on the assumption of the first order lag response between the input signal u _I and the pump flow rate. The dynamics of the hydraulic cylinder can be neglected, but the actuator kinematics must be considered. The resulting equation of motion is: $$\ddot{{\phi }_l}+\frac{1}{T_l}{\dot{\phi }}_l-\frac{C_2}{\underset{e}{\underset{\}}{{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="imgf0006.png"\; state="\{\{state\}\}">C</figure-callout>}}_1^2}}}{\dot{\phi }}_1^2=\frac{K_l{C}_1}{\underset{k}{\underset{\}}{T_{l}A}}}{u}_l$$

with the time constant T _I , the proportional constant K _I , the cross-sectional area A and the geometric constants C ₁ and C ₂ .

Dynamics of the rope hanging on the rope

ergeben sich die folgenden Bewegungsgleichungen: $$a_0+a_1{\ddot{\phi }}_t+a_2{\ddot{\phi }}_s+a_3{\ddot{\phi }}_l+a_4{\dot{\phi }}_s^2+a_5{\dot{\phi }}_l^2+a_6{\dot{\phi }}_s{\dot{\phi }}_l+a_7{\dot{\phi }}_r{\dot{\phi }}_s+a_8{\dot{\phi }}_t{\dot{\phi }}_l+a_9{\dot{\phi }}_t{\dot{l}}_R+a_{10}{\dot{\phi }}_s{\dot{l}}_R+a_{11}{\dot{\phi }}_r{\dot{\phi }}_t=0$$

$$b_0+b_1{\ddot{\phi }}_r+b_2{\ddot{\phi }}_s+b_3{\ddot{\phi }}_l+b_4{\phi }_s^2+b_5{\dot{\phi }}_l^2+b_6{\dot{\phi }}_s{\dot{\phi }}_l+b_7{\dot{\phi }}_t{\dot{\phi }}_s+b_8{\dot{\phi }}_r{\dot{\phi }}_l+b_9{\dot{\phi }}_r{\dot{l}}_R+b_{10}{\dot{\phi }}_s{\dot{l}}_R+b_{11}{\dot{\phi }}_t^2=0$$

$$\ddot{l}+c_1{\ddot{\phi }}_s+c_2{\ddot{\phi }}_l+c_3{\dot{\phi }}_s^2+c_4{\dot{\phi }}_l^2+c_5{\dot{\phi }}_s{\dot{\phi }}_l+c_6{\dot{\phi }}_t{\dot{\phi }}_s+c_7{\dot{\phi }}_r{\dot{\phi }}_s+c_8{\dot{\phi }}_t^2+c_9{\dot{\phi }}_r^2-c_0=\left(\frac{F_R}{m_L}\right)$$

The second subsystem represents a spherical pendulum attached to the cantilever tip. Pendulum motions can be triggered either by movements of the crane structure (first subsystem) or by external forces. As in Fig. 2 shown, the load position in relation to the cantilever tip of the Cardan rope angles φ _t and φ _r and the rope length I _R depends. To derive the equations of motion for the load hanging on the rope, the Euler / Lagrange formalism is used. If the generalized coordinates are defined as $$\mathrm{q}={\left[{\phi }_t{\phi }_r{l}_R\right]}^T$$

The following equations of motion result: $$a_0+a_1{\ddot{\phi }}_t+a_2{\ddot{\phi }}_s+a_3{\ddot{\phi }}_l+a_4{\dot{\phi }}_s^2+a_5{\dot{\phi }}_l^2+a_6{\dot{\phi }}_s{\dot{\phi }}_l+a_7{\dot{\phi }}_r{\dot{\phi }}_s+a_{\mathrm{8th}}{\dot{\phi }}_t{\dot{\phi }}_l+a_9{\dot{\phi }}_t{\dot{l}}_R+a_{10}{\dot{\phi }}_s{\dot{l}}_R+a_{11}{\dot{\phi }}_r{\dot{\phi }}_t=0$$

$$b_0+b_1{\ddot{\phi }}_r+b_2{\ddot{\phi }}_s+b_3{\ddot{\phi }}_l+b_4{\phi }_s^2+b_5{\dot{\phi }}_l^2+b_6{\dot{\phi }}_s{\dot{\phi }}_l+b_7{\dot{\phi }}_t{\dot{\phi }}_s+b_{\mathrm{8th}}{\dot{\phi }}_r{\dot{\phi }}_l+b_9{\dot{\phi }}_r{\dot{l}}_R+b_{10}{\dot{\phi }}_s{\dot{l}}_R+b_{11}{\dot{\phi }}_t^2=0$$

$$\ddot{l}+c_1{\ddot{\phi }}_s+c_2{\ddot{\phi }}_l+c_3{\dot{\phi }}_s^2+c_4{\dot{\phi }}_l^2+c_5{\dot{\phi }}_s{\dot{\phi }}_l+c_6{\dot{\phi }}_t{\dot{\phi }}_s+c_7{\dot{\phi }}_r{\dot{\phi }}_s+c_{\mathrm{8th}}{\dot{\phi }}_t^2+c_9{\dot{\phi }}_r^2-c_0=\left(\frac{F_R}{m_L}\right)$$

The coefficients a _i , b _i and c _j (0 ≦ i ≦ 11, 0 ≦ j ≦ 9) are complex expressions that depend on the system parameters, the pitch angle φ _i and the generalized coordinates (3). However, equations (4) - (6) show the complexity of the dynamic submodel with coupling terms such as centrifugal and Coriolis accelerations. In equation (6), a third input F _R , which is the force of the winch, is taken into account. With the winch, the rope length and thus the height of the load with the mass m _{L can be} changed.

Input-affine system representation

mit dem Eingangsvektor u = [u_s u_l F_R ]^T und dem folgenden Zustandsvektor: $$x={\left[{\phi }_s{\dot{\phi }}_s{\phi }_l{\dot{\phi }}_l{\phi }_t{\dot{\phi }}_t{\phi }_r{\dot{\phi }}_r{l}_R{\dot{l}}_R\right]}^T$$

The two subsystems are now combined into an input-affine nonlinear system of the following form: $$\mathrm{x}\mathrm{=}\mathrm{f}\left(\mathrm{x}\right)\mathrm{+}\mathrm{G}\left(\mathrm{x}\right)\mathrm{u}{\mathrm{x}}_{\mathrm{0}}\mathrm{=}\mathrm{x}\left({\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="imgf0005.png,imgf0006.png"\; state="\{\{state\}\}">t</figure-callout>}}_0\right)$$

with the input vector u = [ u _s u _l F _R ] ^T and the following state vector: $$x={\left[{\phi }_s{\dot{\phi }}_s{\phi }_l{\dot{\phi }}_l{\phi }_t{\dot{\phi }}_t{\phi }_r{\dot{\phi }}_r{l}_R{\dot{l}}_R\right]}^T$$

wobei $$f_6\left(\mathrm{x}\right)=\frac{1}{a_1}\left(\frac{a_2}{T_s}{x}_2+a_3\left(\frac{1}{T_l}{x}_4-e{x}_4^2\right)-a_4{x}_2^2-a_5{x}_4^2-a_6{x}_2{x}_4-a_7{x}_8{x}_2-a_8{x}_6{x}_4-a_9{x}_6{x}_{10}-a_{10}{x}_2{x}_{10}-a_{11}{x}_8{x}_6+a_0\right)$$

$$f_8\left(\mathrm{x}\right)=\frac{1}{b_1}\left(\frac{b_2}{T_s}{x}_2+b_3\left(\frac{1}{T_l}{x}_4-e{x}_4^2\right)-b_4{x}_2^2-b_5{x}_4^2-b_6{x}_2{x}_4-b_7{x}_6{x}_2-b_8{x}_8{x}_4-b_9{x}_8{x}_{10}-b_{10}{x}_2{x}_{10}-b_{11}{x}_6^2+b_0\right)$$

$$f_{10}\left(\mathrm{x}\right)=\frac{c_1}{T_s}{x}_2+c_2\left(\frac{1}{T_l}{x}_4-e{x}_4^2\right)-c_3{x}_2^2-c_4{x}_4^2-\left(c_5{x}_4+c_6{x}_6+c_7{x}_6\right)x_2-x_8{x}_6^2-c_9{x}_8^2-c_0$$

With the equations of motion (1), (2) and (4) - (6) one obtains the vector fields f and g : $$\mathrm{f}\left(\mathrm{x}\right)=\left[\begin{array}{c}{x}_2\\ -\frac{1}{T_s}{x}_2\\ x_4\\ -\frac{1}{T_l}{x}_4+e{x}_4^2\\ x_6\\ f_6\left(\mathrm{x}\right)\\ x_{\mathrm{8th}}\\ f_{\mathrm{8th}}\left(\mathrm{x}\right)\\ x_{10}\\ f_{10}\left(\mathrm{x}\right)\end{array}\right]\mathrm{G}\left(\mathrm{x}\right)=\left[\begin{array}{ccc}0& 0& 0\\ \mathrm{<figure-callout\; id="0"\; label="O"\; filenames="imgf0005.png,imgf0006.png"\; state="\{\{state\}\}">O</figure-callout>}& 0& 0\\ 0& 0& 0\\ 0& \mathrm{<figure-callout\; id="0"\; label="e"\; filenames="imgf0005.png,imgf0006.png"\; state="\{\{state\}\}">e</figure-callout>}& 0\\ 0& 0& 0\\ & -\frac{a_2}{a_1}d-\frac{a_3}{a_1}k0& \\ & -\frac{b_2}{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="imgf0006.png"\; state="\{\{state\}\}">b</figure-callout>}}_1}d-\frac{b_3}{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="imgf0006.png"\; state="\{\{state\}\}">b</figure-callout>}}_1}k0& \\ & -{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0006.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1}d-{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0004.png"\; state="\{\{state\}\}">c</figure-callout>}}_{2}k\frac{1}{m_L}& \end{array}\right]$$

in which $$f_6\left(\mathrm{x}\right)=\frac{1}{a_1}\left(\frac{a_2}{T_s}{x}_2+a_3\left(\frac{1}{T_l}{x}_4-e{x}_4^2\right)-a_4{x}_2^2-a_5{x}_4^2-a_6{x}_2{x}_4-a_7{x}_{\mathrm{8th}}{x}_2-a_{\mathrm{8th}}{x}_6{x}_4-a_9{x}_6{x}_{10}-a_{10}{x}_2{x}_{10}-a_{11}{x}_{\mathrm{8th}}{x}_6+a_0\right)$$

$$f_{\mathrm{8th}}\left(\mathrm{x}\right)=\frac{1}{b_1}\left(\frac{b_2}{T_s}{x}_2+b_3\left(\frac{1}{T_l}{x}_4-e{x}_4^2\right)-b_4{x}_2^2-b_5{x}_4^2-b_6{x}_2{x}_4-b_7{x}_6{x}_2-b_{\mathrm{8th}}{x}_{\mathrm{8th}}{x}_4-b_9{x}_{\mathrm{8th}}{x}_{10}-b_{10}{x}_2{x}_{10}-b_{11}{x}_6^2+b_0\right)$$

$$f_{10}\left(\mathrm{x}\right)=\frac{c_1}{T_s}{x}_2+c_2\left(\frac{1}{T_l}{x}_4-e{x}_4^2\right)-c_3{x}_2^2-c_4{x}_4^2-\left(c_5{x}_4+c_6{x}_6+c_7{x}_6\right)x_2-x_{\mathrm{8th}}{x}_6^2-c_9{x}_{\mathrm{8th}}^2-c_0$$

wobei I_B , die Länge des Auslegers, I_T die Höhe des Befestigungspunkts des Auslegers und I_P die Länge des sphärischen Pendels sind. Bei dem betrachteten Kransystem hängt die Pendellänge I_P von der Seillänge I_R und von dem Aufrichtwinkel ϕ_I ab. $$l_P=l_R+l_B\sin {\phi }_l$$

The outputs of the nonlinear system are the three elements of the load position in Cartesian coordinates. Thus, the output vector is defined as: $$\begin{array}{l}\mathrm{y}\mathrm{=}{\mathrm{r}}_L={\left[y_x{y}_y{y}_z\right]}^T=\mathrm{H}\left(\mathrm{x}\right)\\ =\left[\begin{array}{l}\cos {\phi }_s\left(\sin {\phi }_r{l}_P+\cos {\phi }_l{l}_B\right)-\sin {\phi }_s\sin {\phi }_t\cos {\phi }_r{l}_P\\ -\sin {\phi }_s\left(\sin {\phi }_r{l}_P+\cos {\phi }_l{l}_B\right)-\cos {\phi }_s\sin {\phi }_t\cos {\phi }_r{l}_P\\ -\cos {\phi }_t\cos {\phi }_r{l}_P+\sin {\phi }_l{l}_B+l_T\end{array}\right]\end{array}$$

where I _B , the length of the cantilever, I _{T is} the height of the attachment point of the cantilever and I _{P is} the length of the spherical pendulum. In the crane system considered, the pendulum length I _P depends on the cable length I _R and on the angle of elevation φ _I. $$l_P=l_R+l_B\sin {\phi }_l$$

control concept

This section presents the realization of a boom deflection and trajectory concept for jib cranes. As in Fig. 3 an input unit 10 is provided through which an operator can input control commands, e.g. B. via hand lever. Alternatively, the control commands can also be generated by a higher-level automation system, which autonomously controls the crane. From the control commands, 11 reference trajectories are generated in a path plan module 11. ω _t and ω _r are the target speeds of the load associated with the turning and rocking motion of the crane. ω _z denotes the target stroke speed of the load. The reference trajectories y _{t, ref} and y _r , _ref are generated based on a model predictive control (MPC) 12.

Due to the fact that the tax law is derived based on the non-linear model (7), which is in Cartesian coordinates, these reference trajectories must be transformed from the polar representation to the Cartesian representation. The transformation P implemented by a second transformation unit 14 according to the present invention takes into account not only the position but also higher-order derivatives. The reference trajectory for the height of the load y _{z, ref} is generated from the hand lever signal ω _z by an integrating filter 13 of sufficient order. The tax law, which consists of a linearizing and a stabilizing part, calculates the input signals of the jib crane. The calculation takes place in a calculation unit 15 of the control unit. The tax jurisdiction is based on a flatness-based approach.

The control unit controls the drives of the crane 20. Sensors arranged on the crane measure a state x of the crane and load system, the measurement signals being fed back into the controller via a first transformation unit 16.

draft regulation

$$\begin{array}{cc}{L}_{g_j}{L}_{\mathrm{f}}^{r_i-1}{h}_i\left({\mathrm{x}}_0\right)\ne 0& \forall 1\le i\le m\hfill \\ & \mathrm{für\; mindestens\; ein}j\in \left\{1\dots m\right\}\hfill \end{array}$$

und (iii) die m x m Matrix: $$\mathrm{R}\left(\mathrm{x}\right)=\left[\begin{array}{ccc}{L}_{g_1}{L}_{\mathrm{f}}^{r_1-1}{h}_1\left(\mathrm{x}\right)& L_{g_2}{L}_{\mathrm{f}}^{r_1-1}{h}_1\left(\mathrm{x}\right)\cdots & L_{\mathit{gm}}{L}_{\mathrm{f}}^{r_1-1}{h}_1\left(\mathrm{x}\right)\\ L_{g_1}{L}_{\mathrm{f}}^{r_2-1}{h}_2\left(\mathrm{x}\right)& L_{g_2}{L}_{\mathrm{f}}^{r_2-1}{h}_2\left(\mathrm{x}\right)\cdots & L_{\mathit{gm}}{L}_{\mathrm{f}}^{r_2-1}{h}_2\left(\mathrm{x}\right)\\ ⋮& ⋮& ⋮\\ L_{g_1}{L}_{\mathrm{f}}^{r_m-1}{h}_m\left(\mathrm{x}\right)& L_{g_2}{L}_{\mathrm{f}}^{r_m-1}{h}_m\left(\mathrm{x}\right)\cdots & L_{\mathit{gm}}{L}_{\mathrm{f}}^{r_m-1}{h}_m\left(\mathrm{x}\right)\end{array}\right]$$

regulär ist, d.h. Rang R (x ₀) = m, [5]. Mit System (7) und m = 3 wird die Matrix (15) erhalten als: $$\mathrm{R}\left(\mathrm{x}\right)=\left[\begin{array}{cc}00& \frac{\cos {\phi }_s\sin {\phi }_r-\sin {\phi }_s\sin {\phi }_t\cos {\phi }_r}{m_L}\\ 00& -\frac{\sin {\phi }_s\sin {\phi }_r+\cos {\phi }_s\sin {\phi }_t\cos {\phi }_r}{m_L}\\ 00& -\frac{\cos {\phi }_{\mathit{St}}\cos {\phi }_{\mathit{Sr}}}{m_L}\end{array}\right]$$

First, the relative degree of the system (7) is determined to check for its differential flatness. A MIMO system with m inputs and outputs has the vectorial relative degree r = { r ₁ , ..., r _m } for all x in the neighborhood of x _o , if: $$\begin{array}{cc}{L}_{G_j}{L}_{\mathrm{f}}^k{H}_i\left({\mathrm{x}}_0\right)=0& \forall 1\le j\le m\\ & \forall 1\le i\le m\\ & \forall k\le r_i-2\end{array}$$

$$\begin{array}{cc}{L}_{G_j}{L}_{\mathrm{f}}^{r_i-1}{H}_i\left({\mathrm{x}}_0\right)\ne 0& \forall 1\le i\le m\hfill \\ & \mathrm{for\; at\; least\; one}j\in \left\{1...m\right\}\hfill \end{array}$$

and (iii) the mxm matrix: $$\mathrm{R}\left(\mathrm{x}\right)=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="1"\; label="L\; G"\; filenames="imgf0006.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_{G_{}}{L}_{\mathrm{f}}^{r_1-1}{H}_1\left(\mathrm{<figure-callout\; id="2"\; label="x\; L\; G"\; filenames="imgf0004.png"\; state="\{\{state\}\}">x\; </figure-callout>},\right)& L_{G_{}}{{}_2}_{}{L}_{\mathrm{f}}^{r_1-1}{H}_1\left(\mathrm{x}\right)\cdots & L_{\mathit{gm}}{L}_{\mathrm{f}}^{r_1-1}{H}_1\left(\mathrm{<figure-callout\; id="1"\; label="x\; L\; G"\; filenames="imgf0006.png"\; state="\{\{state\}\}">x\; </figure-callout>},\right)& \\ L_{G_{}}{{}_1}_{}{L}_{\mathrm{f}}^{r_2-1}{H}_2\left(\mathrm{<figure-callout\; id="2"\; label="x\; L\; G"\; filenames="imgf0004.png"\; state="\{\{state\}\}">x\; </figure-callout>},\right)& L_{G_{}}{{}_2}_{}{L}_{\mathrm{f}}^{r_2-1}{H}_2\left(\mathrm{x}\right)\cdots & L_{\mathit{gm}}{L}_{\mathrm{f}}^{r_2-1}{H}_2\left(\mathrm{x}\right)\\ ⋮& ⋮& ⋮\\ L_{{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="imgf0006.png"\; state="\{\{state\}\}">G</figure-callout>}}_1}{L}_{\mathrm{f}}^{r_m-1}{H}_m\left(\mathrm{<figure-callout\; id="2"\; label="x\; L\; G"\; filenames="imgf0004.png"\; state="\{\{state\}\}">x\; </figure-callout>},\right)& L_{G_{}}{{}_2}_{}{L}_{\mathrm{f}}^{r_m-1}{H}_m\left(\mathrm{x}\right)\cdots & L_{\mathit{gm}}{L}_{\mathrm{f}}^{r_m-1}{H}_m\left(\mathrm{x}\right)\end{array}\right]$$

is regular, ie rank R ( x ₀ ) = m, [5]. With system (7) and m = 3, the matrix (15) is obtained as: $$\mathrm{R}\left(\mathrm{x}\right)=\left[\begin{array}{cc}00& \frac{\cos {\phi }_s\sin {\phi }_r-\sin {\phi }_s\sin {\phi }_t\cos {\phi }_r}{m_L}\\ 00& -\frac{\sin {\phi }_s\sin {\phi }_r+\cos {\phi }_s\sin {\phi }_t\cos {\phi }_r}{m_L}\\ 00& -\frac{\cos {\phi }_{\mathit{St}}\cos {\phi }_{\mathit{sr}}}{m_L}\end{array}\right]$$

$${\ddot{y}}_x=\frac{\sin {\phi }_s\sin {\phi }_r+\cos {\phi }_s\sin {\phi }_t\cos {\phi }_r}{m_L}{F}_R$$

$${\ddot{y}}_z=-g-\frac{\cos {\phi }_t\cos {\phi }_r}{m_L}{F}_R$$

Since the matrix (16) is not regular, the vectorial relative degree r is not well defined and static decoupling is not possible. But for all three outputs, only the third input F _{R appears} in the second derivative. Thus, a quasi-static decoupling can be achieved. Therefore, the second derivatives of the outputs are determined as: $${\ddot{y}}_x=\frac{\cos {\phi }_s\sin {\phi }_r-\sin {\phi }_s\sin {\phi }_t\cos {\phi }_r}{m_L}{F}_R$$

$${\ddot{y}}_x=\frac{\sin {\phi }_s\sin {\phi }_r+\cos {\phi }_s\sin {\phi }_t\cos {\phi }_r}{m_L}{F}_R$$

$${\ddot{y}}_z=-G-\frac{\cos {\phi }_t\cos {\phi }_r}{m_L}{F}_R$$

With equation (19) the control is given for the hoist winch as: $$F_R\left(\mathrm{x}{\ddot{y}}_z\right)=\frac{-m_L}{\cos {\phi }_t\cos {\phi }_r}\left({\ddot{y}}_z+G\right)$$

By replacing the force of the hoist winch F _R in Equation (17) and (18) by the relationship in Equation (20), the second derivatives of the outputs y _x and y _{y are} independent of u, but depend on ÿ _z . Further differentiation of the outputs up to the fourth derivatives gives: $$\left[\begin{array}{c}{\stackrel{\dot{}\dot{}¨}{y}}_x\\ {\stackrel{\dot{}\dot{}¨}{y}}_y\end{array}\right]=\mathrm{F}\left(\mathrm{x}{u}_s{u}_l{\ddot{y}}_z{\stackrel{\dot{}¨}{y}}_{\mathit{z}}{\stackrel{\dot{}\dot{}¨}{y}}_z\right)$$

Since the first two inputs u _s and u _{l appear} in the fourth derivatives of the outputs, the vectorial relative degree of system (7) is: $$\mathrm{r}=\left\{r_x=4.r_y=4.r_z=2\right\}$$

mit $$v_l={\stackrel{\left(\mathit{ri}\right)}{y}}_{i,\mathit{ref}}-v_{i,\mathit{stab}}i\in \left\{xyz\right\}$$

The sum of the elements of the vectorial relative degree is 10, which is equal to the order of the system. This means that the system (7) is differentially flat. Solving equation (21) for the inputs and replacing the outputs with the new inputs of the resulting integrator chains gives the following control laws: $$\left[\begin{array}{c}{u}_s\\ u_l\end{array}\right]={\mathrm{F}}^{-1}\left(\mathrm{x}.v_x.v_y.v{.}_z.{\stackrel{\dot{}¨}{y}}_{z.\mathit{ref}}.{\stackrel{\dot{}\dot{}¨}{y}}_{z.\mathit{ref}}\right)$$

With $$v_l={\stackrel{\left(\mathit{ri}\right)}{y}}_{i.\mathit{ref}}-v_{i.\mathit{Rod}}i\in \left\{xyz\right\}$$

In Equation (20), ÿ _{z is} also replaced by the new input v _z . However, although the relative degree of output y _{z is} two, the reference trajectory y _{z, ref} must contain the third and fourth derivative of the reference position. Therefore, the filter used to generate this trajectory is of fourth order.

und den entsprechenden Zuständen der sich ergebenden entkoppelten Integratorketten ${\tilde{\mathbf{y}}}_{\mathit{i}}=\left[\begin{array}{c}{y}_{\mathit{i}}\end{array}\cdots {\stackrel{\left({\mathit{r}}_i-1\right)}{y}}_{\mathit{i}}\right]$

mittels der Rückführmatrizen K_i (i ∈ {x,y,z}) in der Stabilisierung 17 zurückgeführt. Somit sind die stabilisierenden Teile der neuen Eingänge gegeben durch: $$v_{i,\mathit{stab}}={\mathbf{K}}_i\left({\tilde{\mathbf{y}}}_{i,\mathit{ref}}-{\tilde{\mathbf{y}}}_{\mathit{i}}\right)i\in \left\{xyz\right\}$$

The linearizing part of the controller is now determined by equations (20) and (23). However, due to model and parameter uncertainties and external influences, a stabilizing feedback loop is constructed. As in Fig. 4 shown, the differences between the reference trajectories ${\tilde{\mathbf{y}}}_{i.\mathit{ref}}=\left[\begin{array}{c}{y}_{i.\mathit{ref}}\end{array}\cdots {\stackrel{\left({\mathit{r}}_i-1\right)}{y}}_{i.\mathit{ref}}\right]$

and the corresponding states of the resulting decoupled integrator chains ${\tilde{\mathbf{y}}}_{\mathit{i}}=\left[\begin{array}{c}{y}_{\mathit{i}}\end{array}\cdots {\stackrel{\left({\mathit{r}}_i-1\right)}{y}}_{\mathit{i}}\right]$

is returned by means of the feedback matrices K _i ( i ∈ { x, y, z }) in the stabilization 17. Thus, the stabilizing parts of the new inputs are given by: $$v_{i.\mathit{Rod}}={\mathbf{K}}_i\left({\tilde{\mathbf{y}}}_{i.\mathit{ref}}-{\tilde{\mathbf{y}}}_{\mathit{i}}\right)i\in \left\{xyz\right\}$$

The elements of the feedback matrices are determined by Polvorgabe. The poles are adjusted to the system dynamics by look-up tables that depend on the rope length. The output vectors ỹ _i are determined by the transformation T (x) . This transformation T (x) is implemented by the first transformation unit 16 according to the present invention. The transformation is based on the Byrnes / Isidori normal form representation.

trajectory

The basic idea is to formulate the problem of trajectory generation as a limited optimal control problem with finite horizon (open loop) for the integrator chains. The inputs of these integrator chains form the formal control variables for the optimal control problem. Because the limitations of the system given simple boundaries in polar coordinates ( y _t , y _r ), the optimal control problem is formulated in the variables ỹ _t , _ref , ỹ _r , _ref . The transformation P by the second transformation unit is subsequently performed in order to convert the optimal reference trajectories into Cartesian coordinates ỹ _x , _ref , ỹ _{y, ref} .

The problem of optimal control is solved numerically. In the sense of a model-predictive control, the solution procedure is repeated in the next scanning step with a shifted horizon in order to take account of changing specifications (nominal speeds of the load ω _t , ω _r ).

The model predictive trajectory generation algorithm deals with system variable constraints such as optimal control problem limitations. Restrictions result from the limited working space of the crane, which is given by the minimum and maximum outreach. In addition, limitations of radial velocity / acceleration and angular velocity / acceleration for the cantilever tip result from limitations of the hydraulic actuators. The maximum radial speed of the cantilever tip hangs as in Fig. 5 shown off the projection due to the cylinder kinematics and safety reasons. The boom tip constraints are designed as limitations on load movement in each direction in the optimal control problem. $$\left[\begin{array}{l}{y}_{r.\mathit{ref}.\min }\\ -{\dot{y}}_{r.\mathit{ref}.\mathrm{Max}}\left(y_r\right)\\ -{\ddot{y}}_{r.\mathit{ref}.\mathrm{Max}}\\ -{\dot{y}}_{t.\mathit{ref}.\mathrm{Max}}\\ -{\ddot{y}}_{t.\mathit{ref}.\mathrm{Max}}\end{array}\right]\le \left[\begin{array}{c}{y}_{r.\mathit{ref}}\\ {\dot{y}}_{r.\mathit{ref}}\\ {\ddot{y}}_{r.\mathit{ref}}\\ {\dot{y}}_{t.\mathit{ref}}\\ {\ddot{y}}_{t.\mathit{ref}}\end{array}\right]\le \left[\begin{array}{l}{y}_{r.\mathit{ref}.\mathrm{Max}}\\ {\dot{y}}_{r.\mathit{ref}.\mathrm{Max}}\left(y_r\right)\\ {\ddot{y}}_{r.\mathit{ref}.\mathrm{Max}}\\ {\dot{y}}_{t.\mathit{ref}.\mathrm{Max}}\\ {\ddot{y}}_{t.\mathit{ref}.\mathrm{Max}}\end{array}\right]$$

und ${\stackrel{\left(4\right)}{y}}_{r,\mathit{ref}}$

genutzt, um hochfrequente Anregungen des Systems zu vermeidenThe maximum radial speed, as in Fig. 5 shown depends on the projection, is approximated by piecewise linear functions. In addition, will be limited entrance change as a restriction for ${\stackrel{\left(4\right)}{y}}_{r.\mathit{ref}}$

and ${\stackrel{\left(4\right)}{y}}_{r.\mathit{ref}}$

used to avoid high-frequency excitations of the system

A standard quadratic objective function evaluates the quadratic deviation of the angular and radial position and velocity from their reference predictions as well as the rate of change of the input variables over the finite time horizon [ t ₀ , t _f ]. The optimization horizon is a setting parameter and should cover the essential dynamics of the system, which is determined by the period of load swinging. Reference forecasts are generated from the manual lever signals of the crane operator for the target load speed in tangential and radial directions (ω _t , ω _r ).

The continuous, constrained, linear-quadratic optimal control problem is discretized with K time steps and approximated by a quadratic program (QP) in the control and state variables that can be solved by a standard interior point algorithm. With this algorithm, the structure of the model equations in a Riccati-type approach is used to obtain a solution of Newton's step equation with O (K) operations, ie the computational effort increases linearly with the forecast horizon.

Measurement results

The illustrated control concept was implemented in a mobile harbor crane. As in Fig. 6 shown is the first scenario is a pure rocking motion. The load is converted by the rocker of the boom from a radius of 31 m to a radius of 17 m. It can be seen that the radial position of the load y _r , which is the distance between the crane mast and the load in the direction of the cantilever, follows the reference trajectory y _{r, ref} very precisely. The follow - up behavior of the regulated crane in Cartesian coordinates is in Fig. 7 shown.

For practical implementation, only the x and y directions are of interest in the exemplary embodiment. Due to safety reasons, it is not intended to automatically influence the z position of the load with the tax law (20). Therefore, only the control laws (23) are implemented on the LHM 280. As in Fig. 7 4, a radial reference trajectory with the transformation P leads to reference trajectories in the x and y directions if the rotation angle φ _{s is} not zero.

The second maneuver is a rotation from zero to 400 °. Fig. 8 shows the trajectory tracking behavior for the angular load position, velocity and acceleration. The reference trajectory is generated by the MPC algorithm considering the following constraints: $$\left|{\dot{y}}_{\mathrm{t}.\mathrm{ref}}\right|\le {\dot{y}}_{\mathrm{t}.\mathrm{ref}.\mathrm{Max}}=\mathrm{8th}.0°/\mathrm{s}.\left|{\ddot{y}}_{\mathrm{t}.\mathrm{ref}}\right|\le {\dot{y}}_{\mathrm{t}.\mathrm{ref}.\mathrm{Max}}=0.9°/{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="imgf0004.png"\; state="\{\{state\}\}">s</figure-callout>}}^2$$

The linearizing and stabilizing controller allows the load to follow very accurately without significantly overshooting this reference trajectory. The residual load oscillation is also sufficiently small. Of specific importance is the radial displacement of the load due to centrifugal forces during a rotary motion. In order to keep the load at a constant radius during rotational movements, the radial displacement is compensated by the Wippsteuergesetz u _l . As a result, the radial load position is nearly constant with errors between the reference trajectory and the measured load position of less than ± 0.5 m, see Fig. 9 ,

Since the controller concept is designed in Cartesian coordinates based on the flatness property of the nonlinear system with respect to the output vector Fig. 10 the measured load position in the x and y directions and their reference trajectories during the rotation. The quality of the control is as good as the quality in the rotational and rocker direction, since the Cartesian representation ( y _x , y _y ) is equivalent to the polar representation ( y _t , y _r ), where y _{t is} the rotation angle and y _{r is} the radius are the burden.

Claims (15)

Crane for handling a load suspended on a load rope with a slewing gear for turning the crane, a luffing mechanism for rocking the boom and a hoist for lowering or lifting the load hanging on the load rope, with a control unit for calculating the actuation of slewing gear, luffing gear and / or hoist, wherein the control unit advantageously has a load swing damping,
characterized,
that the calculation of the control commands for the control of slewing gear, luffing gear and / or hoisting gear takes place on the basis of a specified movement of the load in Cartesian coordinates. Crane according to claim 1, wherein the load oscillation damping of the control unit is based on the inversion of a physical model of the load hanging on the load rope and the crane, wherein the inverted physical model a predetermined movement of the load on the load rope in Cartesian coordinates in drive signals for the slewing, luffing and / or hoist converts. Crane according to claim 2, with one or more sensors for determining one or more measured variables for the position and / or movement of the load and / or the crane, in particular for determining one or more of the parameters rope angle radial, rope angle tangential, rocking angle, rotation angle, rope length and their derivatives, where the measured variable or the measured variables enter into the inversion of the physical model. Crane according to one of the preceding claims, with one or more sensors for determining one or more measured variables for position and / or movement of the load and / or the crane, in particular for determining one or more of the parameters rope angle radial, rope angle tangential, rocking angle, rotation angle, Rope length and their derivatives, with the measured variable or the measured variables are fed back into the control unit. Crane according to claim 4, wherein a first transformation unit is provided, which calculates the actual position and / or actual movement of the load in Cartesian coordinates based on the measured variable or the measured variables, in particular one or more of the variables position in x, y and z , Velocity in x, y and z, acceleration in x and y, jerk in x and y. Crane according to one of the preceding claims, with one or more cable angle sensors, wherein the measured values of the rope angle sensor (s) are fed back into the control unit. Crane according to one of the preceding claims, with an input unit for inputting control commands by an operator, wherein between the input unit and the control unit, a second transformation unit is provided which calculates the target movement of the load in Cartesian coordinates based on the control commands. Crane according to claim 7, with one or more sensors for determining measured variables with respect to the position and / or movement of cranes, in particular for determining the rocking angle and / or the rotational angle, wherein the second transformation unit is initialized on the basis of the measured variable or the measured variables. Crane according to one of the preceding claims, with a railway plan module, which generates trajectories from control commands of an operator and / or an automation system, which serve as input variables for the control unit. Crane according to claim 9, wherein the trajectories are generated in crane coordinates and the second transformation unit between the railway plan module and the control unit is arranged. Crane according to claim 9 or 10, wherein the trajectories are optimally generated in the railway plan module taking into account the system limitations of the control commands. Crane according to one of the preceding claims, wherein the control unit controls the hoist directly on the basis of control commands of an operator and / or an automation system, while the control of the slewing gear and the luffing gear takes place via the load swing damping. Crane control for a crane according to one of the preceding claims. Method for controlling a crane for handling a load suspended on a load rope with a slewing gear for turning the crane, a luffing mechanism for luffing the boom and a hoist for lowering or lifting the load hanging on the rope,
characterized,
that the calculation of the control commands for the control of slewing gear, luffing gear and / or hoisting gear is carried out on the basis of a set load movement specified in Cartesian coordinates. Method according to Claim 14 for controlling a crane according to one of Claims 1 to 12.

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