EP1880971B1 - Method for controlling the orientation of a crane load - Google Patents

Description

The present invention relates to a method for controlling the orientation of a crane load, wherein a manipulator for handling the load by a rotator means is connected to a hook hanging on ropes and the angle of rotation φ _{L of} the load by a control device using the moment of inertia J _{L of} the load as most important parameter is controlled.

In DE 100 64 182 and DE 103 24 692 Whose content is incorporated by reference into the present application, control and automation concepts for mobile harbor cranes are disclosed. In these rotary luffing cranes, the manipulator hangs to accommodate the load on ropes, and positioning the manipulator to pick up containers causes ball pendulum movements. The control concepts use trajectory tracking control to control the movement of the load and automatically avoid jogging, thereby improving the efficiency of the cargo handling process.

For such control systems, a method of controlling the orientation of the crane load is off DE 100 29 579 the entire contents of which are incorporated by reference into the present invention. There, the hanging on ropes hook on a hydraulic drive containing rotator device, so that the Manipulator for picking up containers can be rotated about a vertical axis. This makes it possible to change the orientation of the crane loads. When the crane operator or the automatic controller gives a signal for rotating the manipulator and thereby the load about the vertical axis, the hydraulic motors of the rotator device are actuated, and a resulting flow causes a torque. If the hook hangs on ropes, the torque would result in torsional vibration of the manipulator and the load. To position the load at a specific angle φ _L , this torsional vibration must be compensated.

The known control method uses a dynamic model of the system based on the equations of motion of a physical model of the crane, the known anti-torsional vibration control consisting of a path planning module and a trajectory tracking module. The path planning module calculates the path of the variables describing the state of the system and generates a reference function. Trajectory tracking control can be subdivided into noise suppression, feedforward control, and state feedback control. The parameters used by the controller are the mass of the load and, above all, the moment of inertia of the load.

However, the mass distribution in the load, eg a container, is not known, and therefore the moment of inertia of the load is also unknown. Therefore, the moment of inertia J _{L of} the load must be estimated. In the known control system, this is done by assuming a homogeneous mass distribution in the load and calculating an estimated moment of inertia J _{L of} the load solely from the mass of the container and the known dimensions of the container.

However, the load distribution in a container is usually anything but homogeneous, so that the estimated value of the load J _{L is} only a very inaccurate approximation. Since the controller uses the moment of inertia J _{L of} the load as a parameter for controlling the orientation of the crane load, the difference between the true one Value of the moment of inertia J _L and the rough estimate of inaccuracy in controlling the orientation of the load.

From the DE 199 07 989 A1 is a method for rail control of cranes and a device for accurate pathway of a load known. For the path control also the moment of inertia of the load is used.

The object of the present invention is therefore to provide a method for controlling the orientation of the crane load, which has a better accuracy.

This object is realized by a method of controlling the orientation of a crane load according to claim 1, wherein the control means for controlling the rotation angle φ _{L of} the load is an adaptive control means, wherein the moment of inertia J _{L of} the load during crane operation is determined from data which by measuring the system condition.

Thereby, the moment of inertia J _{L of} the load can be determined, which leads to a better accuracy in this important parameter, which is used by the control device for controlling the orientation of the crane load. The controller is adjusted during crane operation by using a corrected value of the moment of inertia J _{L determined} during crane operation from the data obtained by measuring the system state as a parameter. Therefore, the controller does not use a once-estimated fixed value, but a value that is adjusted with the help of further information obtained during crane operation.

In the method according to the invention for controlling the rotation of the crane, the angle of rotation φ _{L of} the load is advantageously controlled by means of an adaptive trajectory tracking control. This allows effective control of the movements of the crane load. For example, an auxiliary control law may be used to calculate the orbits of the system variables based on forward integration of the equations of motion of the system, and a state feedback control may use data obtained by measuring the system state.

In the method according to the invention for controlling the rotation of a crane load, it is advantageous to use a dynamic model of the system for calculating data describing the system condition, i. the paths of the system variables. This data can then form the basis for controlling the rotation of the crane load, the dynamic model of the system allowing a precise description of the system and therefore precise control of the orientation of the crane load.

In a further development of the method according to the invention for controlling the orientation of a crane load, the difference φ _C between the angle of rotation φ _{L of} the load and the angle of rotation φ _{H of} the hook can be changed by the rotator device. This advantageously takes place by using a hydraulic motor for the rotator device, so that torque can be applied by the rotator device. This permits rotation of the manipulator and thereby the load about a vertical axis, thereby allowing orientation of the load in any desired direction.

In a further development of the method according to the invention for controlling the orientation of a crane load, torsional vibrations are avoided by an anti-vibration device using the data calculated by the dynamic model. This anti-torsional vibration device uses the data calculated by the dynamic model to control the rotator device to avoid vibrations of the load. Thereby, the anti-torsional vibrator may generate control signals that counteract the possible predicted potential vibrations of the load from the dynamic model. When a hydraulic motor is used for the rotator, the anti-vibration device may generate signals for actuating the hydraulic motor, thereby applying a torque generated by the resulting flow.

In a further development of the method according to the invention for controlling the orientation of a crane load, the difference φ _C between the angle of rotation φ _{L of} the load and the angle of rotation φ _{H of} the hook by one with the rotator device measured transmitter. This transmitter allows the exact measurement of the difference φ _C and thus helps to control the orientation of the load.

In a further development of the method according to the invention for controlling the orientation of a crane load, the movements of a cardan element guided through the cable are measured in order to obtain data by which the angle of rotation φ _{H of} the hook and / or the angle of rotation φ _{L of} the load can be determined. The cardanic element is preferably connected by gimbal connection to the jib head of the crane and follows the movements of the rope on which it is guided by rollers. By measuring the movements of the gimbal, the movements of the rope can be determined. Since the hook usually hangs on several ropes, preferably at least two gimbal elements are provided to determine the movements of at least two of these ropes. The angle of rotation φ _H of the hook hanging on the ropes and / or the angle of rotation φ _{L of} the load can then be determined from the data obtained by measuring the movements of the gimbals.

In the method according to the invention for controlling the orientation of a crane load, a gyroscope is used to obtain data by which the angle of rotation φ _{H of} the hook and / or the angle of rotation φ _{L of} the load can be determined. The use of a gyroscope is a particularly effective way to obtain this data with sufficient precision. The gyroscope can be attached to different locations on the crane. If cardanic elements are used, the gyroscope can be attached to the gimbals to measure their movements, but it is also possible to attach the gyroscope directly to the hook or to the manipulator.

In a further development of the method according to the invention for controlling the orientation of a crane load, the change φ̇ _{H of} the angle of rotation φ _{H of} the hook and / or the change φ̇ _H , of the angle of rotation φ _{L of} the load is measured by a gyroscope. The gyroscope can be mounted either on the hook or on the manipulator be, but preferably on the hook. Gyroscopes can measure the angular velocities φ̇ _H and φ̇ _I , which enables a determination of the angle of rotation φ _{H of} the hook and of φ _L. If .phi _H is measured by the gyroscope, φ _H can be determined by integration. The rotational angle φ _{L of} the load can then be calculated by using the difference φ _C between the rotational angle φ _{L of} the load and the rotational angle φ _{H of} the hook measured by the transducer. Since the value of φ̇ _H measured by the gyroscope contains noise and an offset, direct integration would result in summation of these errors, which would lead to poor accuracy results. Therefore, advantageously, an observer is used to compensate for the offset. This allows a more stable estimate of the rotation angle φ _L from the angular velocity φ̇ _H.

In a further development of the method according to the invention for controlling the orientation of a crane load, the dynamic model of the system is based on the equations of motion of a physical model of at least the ropes, the hook and the load. In such a physical model, the hook and the load hanging on the ropes form a torsion pendulum whose equations of motion are determined by means of e.g. of the Lagrange formalism can be determined. This allows a realistic description of the system and therefore precise path planning and control.

Advantageously, the moment of inertia J _{H of} the hook and J _{Sp of} the manipulator are used as parameters for the control of the angle of rotation φ _{L of} the load. Even though the moment of inertia J _{H of} the hook and J _{Sp of} the manipulator are usually smaller than the inertia element J _{L of} the load, they nevertheless contribute to the rotational behavior of the system and should be taken into account in the calculations and the physical model.

In a further development of the method according to the invention for controlling the orientation of a crane load, a torque is applied to the load and / or the hook during operation of the crane. By measuring the system condition while applying a torque to the hook and / or the load obtained data allow the estimation of the moment of inertia J _{L of} the load, eg by using an observer.

Advantageously, the data obtained by measuring the system state comprises at least the change φ _{H of} the angle of rotation φ _{H of} the hook and / or the change φ̇ _I , the angle of rotation φ _{L of} the load in response to the torque applied to the load and / or the hook. This data can then be used to estimate the moment of inertia J _{L of} the load, eg by comparing the data calculated from the dynamic model with the measured data.

In a further development of the method according to the invention for controlling the orientation of a crane load, a value of the moment of inertia J _L0 , which is estimated on the basis of the mass and the dimensions of the load alone, is used as the output value for J _L , and corrected values J _Lk are in one iterative process is determined to determine the moment of inertia J _L. This gives a rough estimate of the output value for J _L "from the data that is readily available while better estimates are made during crane operation based on the additional data obtained by measuring the system condition.

In a further development of the method according to the invention for controlling the orientation of a crane load during crane operation, data describing the system state are calculated from the dynamic model based on a value J _{L, k-1 of} the moment of inertia J _L , and a corrected value J _{Lk of} the moment of inertia J _L is determined from the calculated data and the data obtained by measuring the system state to determine the moment of inertia J _L. This allows a much better estimate of the moment of inertia J _L than the use of mass and the dimensions of the load alone.

The moment of inertia J _L is determined according to the invention with the help of an observer. This method of estimating the moment of inertia J _L uses data computed by the dynamic model and combines it with data, obtained by measuring the system state to estimate the parameter J _{L of} the dynamic model. The use of an observer to determine variables of the system, such as the angle of rotation φ _{H of} the hook from the angular velocity φ _H measured by the gyroscope, was already known. Here, however, a parameter of the model is determined with the aid of an observer, which leads to an adaptive control.

When a parameter of the model is estimated by the observer, the problem becomes non-linear, so that the moment of inertia J _{L is} advantageously determined by means of a non-linear observer. There are various ways to implement a nonlinear observer, especially in time-variant models, for example a high-gain approach or the extended Kalman filter.

The last possibility offers a very stable system for rapidly estimating parameters of the system, so that the moment of inertia J _{L can} advantageously be determined with the aid of an extended Kalman filter.

In a further development of the method according to the invention for controlling the orientation of a crane load, a homogeneous distribution of mass in the load is assumed for the estimation of an output value J _{L0 of} the moment of inertia J _{L of} the load. This allows a quick calculation that requires only the mass and dimensions of the load as input.

In a further development of the method according to the invention for controlling the orientation of a crane load, noise in the data obtained by measurements is taken into account in the determination of the moment of inertia J _L. This leads to more precision in the estimation of the moment of inertia J _L , which is based on the measured data and therefore influenced by noise in the measurements.

Advantageously, the noise in the data obtained by measurements is modeled by covariance matrices. This allows a quantitative description influence of noise and can minimize the errors resulting from noise.

These covariance matrices are advantageously determined experimentally. By testing the control system with different values for the covariance matrices, the best values for a fast and stable estimation of the moment of inertia J _L can be determined and used for the observer.

The present invention further includes a system for controlling the orientation of a crane load using one of the methods described above. Such a control system comprises a control device for controlling the rotation angle φ _{L of} the load. The control device includes a web planning device and a web control device and an observer for estimating the moment of inertia J _L.

The present invention further comprises a crane, in particular a jib crane, comprising a system for controlling the rotation of a crane load by means of one of the methods described above. Such a crane comprises a hook-hanging hook, a rotator device and a manipulator. Advantageously, the crane also includes an anti-sway control system which cooperates with the system for controlling the rotation of a crane. When the crane is a jib crane, it comprises a boom that can be swung up and down about a horizontal axis and rotated by a tower about a vertical axis. Furthermore, the length of the rope can be changed.

Fig. 1a

eine Seitenansicht und eine Draufsicht eines Hafenmobilkrans,

Fig. 1b

eine Seitenansicht eines Auslegerkopfes des Hafenmobilkrans mit einem kardanischen Element,

Fig. 2

den Steueraufbau des Hafenmobilkrans,

Fig. 3

den Aufbau der Antitorsionsschwingungssteuerung,

Fig. 4

eine an einem Seil hängende Rotatoreinrichtung mit Manipulator und Last,

Fig. 5

den Aufbau eines Simulationsumfelds,

Fig. 6

die Ermittlungsleistung des erweiterten Kalman-Filters abhängig von der Wahrscheinlichkeitsmatrix P₀,

Fig. 7

die Bestimmung von J_L mit falschem Ausgangswert,

Fig. 8

die Bestimmung von J_L mit richtigem Ausgangswert.

Now, the present invention will be described in detail with reference to the following drawings. Show in it

Fig. 1a

a side view and a top view of a mobile harbor crane,

Fig. 1b

a side view of a jib head of the mobile harbor crane with a gimbal element,

Fig. 2

the control structure of the mobile harbor crane,

Fig. 3

the structure of the anti-torsional vibration control,

Fig. 4

a rotator device with manipulator and load hanging from a cable,

Fig. 5

the construction of a simulation environment,

Fig. 6

the determination performance of the extended Kalman filter as a function of the probability matrix P ₀ ,

Fig. 7

the determination of J _L with the wrong initial value,

Fig. 8

the determination of J _L with the correct initial value.

Jib cranes are often used to handle cargo handling operations in ports. Such a mobile harbor crane will be in Fig. 1 a shown. The crane has a load capacity of up to 140 t and a rope length of up to 80 m. It comprises a boom 1, which can be pivoted up and down about a horizontal axis, which is formed by the hinge axis 2, with which it is attached to a tower 3. The tower 3 can be rotated about a vertical axis, whereby the boom 3 is rotated with this. The tower 3 is attached to a mounted on wheels 7 undercarriage 6. The length of the rope 8 can be changed by winds. The load 10 may be received by a manipulator or spreader 20 which may be rotated by rotator means 15 mounted in a hook hanging on the rope 8. The load 10 is rotated either by rotating the tower and thereby the whole crane or by using the rotator means 15. In practice, both rotations must be used simultaneously to align the load in a desired position.

For the sake of simplicity, only the rotation of a load which hangs on an otherwise immovable crane will be explained here. However, the control concept of the invention can be easily integrated into a control concept for the entire crane.

Especially for container handling was the DE 100 64 182 and DE 103 24 692 already known Antipendelsteuerung extended by a control and automation concept for container orientation based on the dynamic model of the system to prevent unwanted vibration of the load. This control concept for container orientation is in DE 100 29 579 discloses where the moment of inertia of the crane load is estimated based on the assumption that the mass distribution in the container is homogeneous.

Since the spreader / rotator system can be considered a flexible arm robot with slow dynamic behavior, an adaptive and model-based method of manipulating the manipulator is used. In order to improve the performance of this control concept, the parameters of the dynamic model of the system and in particular the moment of inertia of the load must be known as accurately as possible. The present invention discloses a determination method for improving these control and automation concepts of a mobile harbor crane, which in DE 10064182 . DE 10324692 and DE 10029579 as in O. Sawodny, H. Aschemann, J. Kümpel, C. Tarin, K. Schneider, Anti-Sway Control for Boom Cares, American Control Conference, Anchorage USA, Proc. Pages 244-249, 2002 ; O. Sawodny, A. Hildebrandt, K. Schneider, Control Design for the Crane Loads for Boom Cranes, International Conference on Robotics & Automation, Taipei Taiwan, Proc. Pages 2182-2187, 2003 and J. Neupert, A. Hildebrandt, O. Sawodny, K. Schneider, A Trajectory Planning Strategy for Large Serving Robots, SICE Annual Conference, Okayama Japan, Proc. Pages 2180-2185, 2005 , to be discribed.

Due to the unusually inhomogeneous distribution of the load in the container, the estimated moment of inertia based on the assumption that the distribution of load is homogeneous is only a very rough approximation to this parameter, resulting in an inaccurate control of the orientation of the container. Therefore, the present invention discloses a method of determining the moment of inertia of the load during crane operation based on data obtained by measuring the system. This type of estimation of the moment of inertia of the load with the aid of an observer approach leads to a better accuracy of the control method.

The data on which the determination of the moment of inertia of the load is based can be obtained by various methods. Fig. 1b shows a gimbal element 35 which is attached to the boom head 30 of a boom 1 by gimbals 32 and 33 under the main role 31. The gimbal element 35 has rollers 36, by which it is guided on the rope 8, so that it follows the movements of the rope 8. The gimbals 32 and 33 allow the gimbal element 35 to freely move about a horizontal and a vertical axis, but prevent rotational movements. The movements of the gimbal and thus the movements of the rope can be measured. In this embodiment, two gimbals 35 are provided, which are guided on the two cables to which the hook hangs. These data can then be used to calculate the torsion of the cables and the angle φ _{H of} the torsion of the hook. For this purpose, a gyroscope can be attached to the gimbals. If no gimbals are used, a gyroscope can also be attached directly to the hook or manipulator to determine its rotation angle.

In the present invention, various observer methods for determining the moment of inertia of the load during crane operation can be used based on data obtained by measuring the system.

By applying the least squares method to the measured input / output data, system parameters can be estimated. However, the standard least squares method is unsatisfactory in estimating time-varying parameters. To solve this problem, an exponential forgetting of the older data can be used. The so-called forgetting factor can be chosen such that the resulting gain matrix keeps a constant track. This approach can be further developed into the gain-fit forgetting method in which the forgetting factor is constantly changed according to the Gain Matrix norm.

Another method for determining the parameters of dynamic systems is the extended Kalman filter used in the embodiment of the present invention. There are several advantages to using this technique, which will be discussed later.

Fig. 2 shows a known adaptive control concept for managing the orientation of the load (of the container). This in ( O. Sawodny, A. Hildebrandt, K. Schneider, Control Design for the Crane Loads for Boom Cranes, International Conference on Robotics & Automation, Taipei Taiwan, Proc. Pages 2182-2187, 2003 ) and also in DE 10029579 The disclosed control concept, the contents of which are incorporated by reference in this application, consists of a trajectory tracking control, an observer and a state feedback control to prevent torsional vibrations. To control the load orientation, the torsion angle is reconstructed from the angular velocity measured by a gyroscope in the hook. The angle between the hook and the container is measured by a transducer. The load orientation is obtained by summing both angles. Due to the fact that all parts of the control concept are model-based algorithms, they must be adapted to parameter changes. Most parameters can be measured directly, but the distribution of the load mass in the container and thus the moment of inertia of the container is unknown.

Since this parameter has a great influence on the dynamic behavior of the torsional oscillator and thus on the performance of the anti-vibration control, it must be determined on-line.

Dynamic model for the rope-hanging manipulator

For handling the containers, the jib crane is equipped with a special manipulator, the so-called spreader. The manipulator can be rotated about the vertical axis by a rotator device containing a hydraulic drive. As in FIG. 4 is shown, this device is installed in the hook.

The hook is attached to two ropes, where r and I _s indicate the effective distance between the two parallel ropes or the rope length. The system consists of three extended bodies. The load (container), characterized by the moment of inertia J _L , and the mass m _L , the manipulator (container spreader) and the hook. J _Sp and J _H indicate the moment of inertia of the spreader and the hook, m _Sp and m _H respectively indicate the mass of the two bodies. The angle of rotation of the spreader with load is referred to as φ _L. The second angle φ _H indicates the torsion angle.

To derive the equations of motion of the considered mechanical system, the Lagrangian formulation is used L. Sciavicco, B. Siciliano, Modeling and Control of Robotic Manipulators, Springer-Verlag London, United Kingdom, 2001 ). $$\frac{d}{dt}\frac{\partial L}{\partial {\dot{q}}_{\mathit{i}}}-\frac{\partial L}{\partial q_{\mathit{i}}}={\xi }_{\mathit{i}}$$

The Lagrange function L is defined as the difference between the kinetic energy T and the potential energy U of the system. $$L=T-U$$

Assuming that hook, spreader and load (container) are combined into an expanded body with the total moment of inertia J _total = J _H + J _Sp + J _L , the kinetic and potential energies are obtained as follows: $$T=\frac{J_{\mathit{total}}}{2}{\dot{\phi }}_H^2;U=\frac{c_{\mathit{T}}}{2}{\phi }_H^2$$

c _T describes the linearized torsional rigidity of the two parallel ropes as a function of the parameters M _total = m _H + m _Sp + m _L and I _s , (- is the gravitational constant): $$c_{\mathit{T}}=\frac{m_{\mathit{total}}{\mathit{gr}}^2}{4l_{\mathit{S}}}$$

Solving equation (1) with the resulting Lagrange function and the generalized coordinate q = φ _H results in the dynamic model of the rotator with load. $$J_{\mathit{total}}{\ddot{\phi }}_H+c_{\mathit{T}}{\phi }_H=\xi$$

wobei ϕ̇ _C die relative Winkelbeschleunigung zwischen dem Haken und dem Spreader ist $$\left({\ddot{\varphi }}_{\mathit{C}}={\ddot{\varphi }}_{\mathit{L}}-{\ddot{\mathrm{\varphi }}}_H\right)\mathrm{.}$$

The generalized force is the moment of the hydraulic motor and can be defined as $$\xi =-\left(J_{\mathit{sp}}+J_{\mathit{L}}\right){\ddot{\phi }}_C$$

where φ̇ _{C is} the relative angular acceleration between the hook and the spreader $$\left({\ddot{\phi }}_{\mathit{C}}={\ddot{\phi }}_{\mathit{L}}-{\ddot{\mathrm{\phi }}}_H\right)\mathrm{,}$$

For the determination method, the continuous model (equations (5) and (6)) is converted into a discrete state space model with the following form: $$\begin{array}{cc}\hfill {\underset{}{x}}_{k+1}& =\underset{}{\mathrm{\Phi }}{\underset{}{x}}_k+\underset{}{H}{\underset{}{u}}_k\hfill \\ \hfill {\underset{}{y}}_k& =\underset{}{C}{\underset{}{x}}_k\hfill \end{array}$$

wobei $$a=\sqrt{\frac{c_{\mathit{T}}}{J_{\mathit{total}}}}$$

und die Abtastzeit T.The system matrices, the state vector, and the input vector are obtained: $$\begin{array}{l}\underset{}{\mathrm{\Phi }}\left(T\right)=\left[\begin{array}{cc}\cos \left(\mathit{at}\right)& \frac{1}{a}\sin \left(\mathit{at}\right)\\ -a\sin \left(\mathit{at}\right)& \cos \left(\mathit{at}\right)\end{array}\right]\\ \underset{}{H}\left(T\right)=\left[\begin{array}{c}\frac{J_{\mathit{sp}}+J_l}{c_{\mathit{T}}}\left[\cos \left(\mathit{at}\right)-1\right]\\ -\frac{J_{\mathit{sp}}+J_{\mathit{L}}}{a{J}_{\mathit{total}}}\sin \left(\mathit{at}\right)\end{array}\right]\\ \underset{}{C}=\left[\begin{array}{cc}0& 1\end{array}\right]\\ {\underset{}{x}}_k={\left[\begin{array}{cc}{\phi }_{\mathit{Hk}}& {\dot{\phi }}_{\mathit{Hk}}\end{array}\right]}^I:u_k={\ddot{\phi }}_{\mathit{ck}}\end{array}$$

in which $$a=\sqrt{\frac{c_{\mathit{T}}}{J_{\mathit{total}}}}$$

and the sampling time T.

Determination of the uncertain parameter

For the given application, the moment of inertia of the container during crane operation must be determined in order to adapt the model-based control concept. Due to this fact, the inertial moment determination algorithm must be iterative so that each time an accurate measurement of input / output data is obtained, a new parameter estimate is generated. In the past, a number of system determination methods were discussed. One of the methods for online parameter determination is the extended Kalman filter.

To estimate the unknown moment of inertia of the container, the state vector x _{k of} the discrete state space model (equations (7) and (8)) is extended by the unknown parameter J _L ( CK Chui, G. Chen, Kalman Filtering with Real-Time Application, Springer-Verlag Berlin Heidelberg, Germany, 3rd edition, 1999 ). $${\underset{}{\tilde{x}}}_k={\left[\begin{array}{ccc}{\phi }_{\mathit{Hk}}& {\dot{\phi }}_{\mathit{Hk}}& J_{\mathit{lk}}\end{array}\right]}^T$$

wobei v_k eine Sequenz weißen Gaußschen Rauschens mit null Mittelwert ist, um das reale System präziser zu beschreiben. Das Systemrauschen wird durch die folgende Kovarianzmatrix charakterisiert $$\underline{Q}=E\left(v_k{v}_k^T\right)$$

This extension results in a nonlinear discrete model of the following form: $${\underset{}{\tilde{x}}}_{k+1}=\underset{}{f}\left({\underset{}{\tilde{x}}}_k,u_k\right)+{\underset{}{G}}_k{v}_k$$

where v _{k is} a sequence of zero mean zero Gaussian noise to more accurately describe the real system. The system noise is characterized by the following covariance matrix $$\underset{}{Q}=e\left(v_k{v}_k^T\right)$$

The vector-valued functions f and g are obtained by: $$\begin{array}{cc}\hfill \underset{}{f}\left(\widetilde{{\underset{}{x}}_k},u_k\right)& =\left[\begin{array}{c}\underset{}{\mathrm{\Phi }}\left(J_{\mathit{lk}}\right){\underset{}{x}}_k+\underset{}{H}\left(J_{\mathit{lk}}\right){\underset{}{u}}_k\\ J_{\mathit{lk}}\end{array}\right]\hfill \\ \hfill {\underset{}{G}}_k& =\left[\begin{array}{c}\underset{}{H}\left(J_{\mathit{lk}}\right)\\ 0\end{array}\right]\hfill \end{array}$$

wobei $$\underline{h}=\left[\begin{array}{ccc}0& 1& 0\end{array}\right]$$

und w_k ein weißes Gaußsches Rauschen mit null Mittelwert mit der folgenden Kovarianzmatrix ist $$\underline{R}=E\left(w_k{w_k}^{\mathit{T}}\right)$$

As explained in section 1, the angle of rotation of the hook φ _H can not be measured directly. It has to be reconstructed from the angular velocity φ̇ _Hgyro , which is measured by a gyroscope in the hook. Since the gyroscope signal is disturbed, the measurement noise must be taken into account, resulting in a system output that can be modeled as: $${\tilde{y}}_k=\underset{}{H}{\underset{}{\tilde{x}}}_k+w_k$$

in which $$\underset{}{H}=\left[\begin{array}{ccc}0& 1& 0\end{array}\right]$$

and w _{k is} a white zero Gaussian noise with the following covariance matrix $$\underset{}{R}=e\left(w_k{w_k}^{\mathit{T}}\right)$$

wobei F die Jacobische Matrix von f mit den folgenden Koeffizienten ist: $$F_{\mathit{ij}}=\frac{\partial f_{\mathit{i}}\left(\underline{\tilde{x}},u\right)}{\partial {\underline{\tilde{x}}}_{\mathit{j}}}$$

To apply the Kalman filter to the obtained nonlinear system, it must be linearized using a linear Taylor approximation to the estimate of the previous state x _k : $$\begin{array}{ll}{\underset{}{\tilde{x}}}_{k+1}\square & \underset{}{f}\left({\underset{}{\hat{\tilde{x}}}}_k,u_k\right)+\underset{}{F}\left({\underset{}{\hat{\tilde{x}}}}_k,u_k\right)\left({\widetilde{\underset{}{x}}}_k-{\underset{}{\hat{\tilde{x}}}}_k\right)\\ & +\underset{}{G}\left({\hat{J}}_{\mathit{Luke}}\right)v_k\end{array}$$

where F is the Jacobian matrix of f with the following coefficients: $$F_{\mathit{ij}}=\frac{\partial f_{\mathit{i}}\left(\underset{}{\tilde{x}},u\right)}{\partial {\underset{}{\tilde{x}}}_{\mathit{j}}}$$

By calculating the coefficients for i, j = 1, ..., 3 , the Jacobian matrix is obtained as: $$\underset{}{F}=\left[\begin{array}{cc}\underset{}{\mathrm{\Phi }}\left(J_{\mathit{lk}}\right)& \frac{\partial }{\partial J_{\mathit{lk}}}\left(\underset{}{\mathrm{\Phi }}\left(J_{\mathit{lk}}\right){\underset{}{x}}_k+\underset{}{H}\left(J_{\mathit{lk}}\right){\underset{}{u}}_k\right)\\ 0& 1\end{array}\right]$$

1. 1. Schritt: Die Vorhersage der Zustände [ϕ _Hk ϕ̇ _Hk ] und des Parameters J_Lk wird aus der Eingabe u_k und den geschätzten nicht gestörten Zuständen xk berechnet. $${{\underline{x}}^{*}}_{k+1}=\underline{\mathrm{\Phi }}\left({\hat{J}}_{\mathit{Lk}}\right){\underline{\hat{x}}}_k+\underline{H}\left({\hat{J}}_{\mathit{Lk}}\right){\underline{u}}_k$$
   
2. 2. Schritt: Die Kovarianzmatrizen des Vorhersagefehlers M _k+1 und der Schätzungsfehler P _k+1 sowie die Kalman-Gain-Matrix K _k+1 werden mit Hilfe von Folgendem berechnet (I ist die Identitätsmatrix): $$\begin{array}{ll}{\underline{M}}_{k+1}& =\underline{F}\left({\underline{\hat{\tilde{x}}}}_k,u_k\right){\underline{P}}_k\underline{F}{\left({\underline{\hat{\tilde{x}}}}_k,u_k\right)}^{\mathit{T}}\\ & +\underline{g}\left({\hat{J}}_{\mathit{Lk}}\right)\underline{Q}\underline{g}{\left({\hat{J}}_{\mathit{Lk}}\right)}^{\mathit{T}}\end{array}$$
   
   $${\underline{K}}_{k+1}={\underline{M}}_{k+1}{\underline{C}}^{\mathit{T}}{\left(\underline{C}{\underline{M}}_{k+1}{\underline{C}}^{\mathit{T}}+\underline{R}\right)}^{-1}$$
   
   $${\underline{P}}_{k+1}=\left(\underline{I}-{\underline{K}}_{k+1}\underline{C}\right){\underline{M}}_{k+1}$$
   
3. 3. Schritt: Die Schätzung des Zustandsvektors und des Trägheitsmoments des Containers werden durch Korrigieren der vorhergesagten Werte mit der gewichteten Differenz zwischen der gemessenen und der vorhergesagten Winkelgeschwindigkeit des Hakens erhalten.

$$\left[\begin{array}{c}{\underline{\hat{x}}}_{k+1}\\ {\hat{J}}_{\mathit{Lk}+1}\end{array}\right]=\left[\begin{array}{c}{\underline{x}}_{k+1}^{*}\\ {\hat{J}}_{\mathit{Lk}}\end{array}\right]+{\underline{K}}_{k+1}\left({\dot{\varphi }}_{\mathit{Hgyro}}-{\left[\begin{array}{c}0\\ 1\end{array}\right]}^T{\underline{x}}_{k+1}^{*}\right)$$

With the linearized model and the covariance matrices Q and R , the optimal Kalman filter algorithm can be derived in the following way ( T. Iwasaki, T. Kataoka, Application Of An Extended Kalman Filter To Parameter Identification Of An Induction Motor, Industry Applications Society Annual Meeting, Vol. 1, pp. 248-253, 1989 ):

1. 1st step: The prediction of the states [φ _Hk φ̇ _Hk ] and the parameter J _Lk is calculated from the input u _k and the estimated undisturbed states x k . $${{\underset{}{x}}^{*}}_{k+1}=\underset{}{\mathrm{\Phi }}\left({\hat{J}}_{\mathit{lk}}\right){\underset{}{\hat{x}}}_k+\underset{}{H}\left({\hat{J}}_{\mathit{lk}}\right){\underset{}{u}}_k$$
   
2. 2nd step: The covariance matrices of the prediction error M _{k + 1} and the estimation error P _{k + 1} and the Kalman gain matrix K _{k + 1} are calculated using (I is the identity matrix): $$\begin{array}{ll}{\underset{}{M}}_{k+1}& =\underset{}{F}\left({\underset{}{\hat{\tilde{x}}}}_k,u_k\right){\underset{}{P}}_k\underset{}{F}{\left({\underset{}{\hat{\tilde{x}}}}_k,u_k\right)}^{\mathit{T}}\\ & +\underset{}{G}\left({\hat{J}}_{\mathit{lk}}\right)\underset{}{Q}\underset{}{G}{\left({\hat{J}}_{\mathit{lk}}\right)}^{\mathit{T}}\end{array}$$
   
   $${\underset{}{K}}_{k+1}={\underset{}{M}}_{k+1}{\underset{}{C}}^{\mathit{T}}{\left(\underset{}{C}{\underset{}{M}}_{k+1}{\underset{}{C}}^{\mathit{T}}+\underset{}{R}\right)}^{-1}$$
   
   $${\underset{}{P}}_{k+1}=\left(\underset{}{I}-{\underset{}{K}}_{k+1}\underset{}{C}\right){\underset{}{M}}_{k+1}$$
   
3. 3rd step: The estimation of the state vector and the moment of inertia of the container are obtained by correcting the predicted values with the weighted difference between the measured and the predicted angular velocity of the hook.

$$\left[\begin{array}{c}{\underset{}{\hat{x}}}_{k+1}\\ {\hat{J}}_{\mathit{lk}+1}\end{array}\right]=\left[\begin{array}{c}{\underset{}{x}}_{k+1}^{*}\\ {\hat{J}}_{\mathit{lk}}\end{array}\right]+{\underset{}{K}}_{k+1}\left({\dot{\phi }}_{\mathit{Hgyro}}-{\left[\begin{array}{c}0\\ 1\end{array}\right]}^T{\underset{}{x}}_{k+1}^{*}\right)$$

The described algorithm is executed each time a new measurement of input / output data is available ( k = 1,2 , ...). To initialize the extended Kalman filter, a start pulse is generated at the moment a container is picked up. The states observed by the observer [φ _H φ _H ] at this moment are the initial estimate x ₀ for the filter algorithm. The initial moment of inertia of the container Ĵ _L0 can be obtained by assuming that the container has a uniformly distributed mass. Since the length I _container and the mass m _{L of} the container can be measured and the width is constant ( b _container = 2.4m ), the moment of inertia can be calculated as follows: $${\hat{J}}_{\mathit{L}0}=\frac{m_L}{12}\left(l_{\mathrm{Container}}^2+b_{\mathrm{Container}}^2\right)$$

The output covariance matrix for the estimation error P ₀ is used to tune the determination algorithm (see Section 4).

Results simulation

In order to find good elements of the covariance matrix for the estimation error P ₀ , the determination algorithm is implemented in a simulated environment. As in FIG. 5 is shown, the simulation model is _terminated by the measurement signal φ̈ _{c_measured} from the real system. Furthermore, a sequence of white noise is added to the output of the simulation model.

The parameters and the initial conditions of the simulation are as follows: $$\begin{array}{l}{\hat{J}}_{\mathit{L}0}=0.8\cdot J_{\mathit{L}\mathrm{model}}:J_{\mathit{L}\mathrm{model}}=36000{\mathit{kgm}}^2\\ {\underset{}{x}}_0={\left[\begin{array}{cc}0& 0\end{array}\right]}^{\mathit{T}};\underset{}{Q}={10}^{-10};\underset{}{R}={10}^{-6}\\ T=0025s;c_{\mathit{T}}=3750;J_H=940{\mathit{kgm}}^2\end{array}$$

In the FIG. 6 The simulation results shown are obtained by using this configuration. The three curves represented the results obtained by using three different initial values for the covariance matrix of the estimation error. The higher the values of this matrix, the faster the estimated moment of inertia of the container reaches the reference value J _Lmodel .

The results show that even with simulation there is an upper limit for the output value of the covariance matrix of the estimation error when the simulation _{model is} terminated by the measurement signal φ̈ _{c_measured} . This means that the determination algorithm responds strongly to disregarded system input perturbations when the output covariance matrix P _{0 ij} = 2 * 10 ¹⁰ δ _ij ; i, j = 1,2,3 (δ _ij is the Kronecker delta) or greater.

Experimental investigations

In order to evaluate the performance of the extended Kalman filter, the algorithm is implemented in the control and automation concept of the boom crane, in particular in the adaptive anti-torsional vibration control part, as in FIG. 3 is set out. The obtained experimental results are obtained online calculates the algorithm for the extended Kalman filter during crane operation. The experiments show that the best output value of the covariance matrix P _{0 ij} = 7 · 10 ² δ _ij ; i, j = 1,2,3. This is much smaller than in the simulation due to model uncertainties and disregarded input / output signal disturbances. FIG. 7 shows, however, that the estimate of the moment of inertia of the load approaches the reference value of 36,000kgm ² .

The initial value for the moment of inertia Ĵ _L0 was 47 . 000kgm ² , and the remaining parameters and initial conditions were the same as the simulation configuration . Since the excitation of the torsional motion was stopped at 150 seconds, there is a residual deviation between the estimated J _L and the reference value. Given the slow dynamic behavior of the flexible system, the estimated moment of inertia quickly approaches the values in the tolerance range around the reference value. A deviation of ± 5% between Ĵ _I and the reference value of the moment of inertia has no great effect on the performance of the anti-torsional vibration control. FIG. 8 shows the estimated moment of inertia of the load when the output value Ĵ _{L0 is} equal to the reference value. In this case, the mass of the container is evenly distributed (see equation (24)).

The obtained determination result of the parameter J _L shows the robustness of the algorithm of the extended Kalman filter, since no estimates are calculated outside the tolerance range of ± 5%. The small deviations between the estimated parameter and the reference value are caused by model uncertainties.

conclusion

The present invention discloses an extension of a control and automation concept for the orientation of a crane load. Because this concept is an adaptive model-based algorithm, the parameters of the dynamic model must be known as precisely as possible. Most parameters can be measured directly, but the moment of inertia of the crane load (container) must be determined based on the unknown distribution of mass during crane operation. The determination method used, the extended Kalman filter algorithm, is derived from the dynamic model of the manipulator hanging from the cable. This parameter determination method is integrated into the anti-torsional vibration control and tested on a LIEBHERR LHM 402 mobile harbor crane. The obtained measurement results show the fast approach and the robustness of estimating the unknown moment of inertia of the crane load.

Claims (22)

1. A method for controlling the orientation of a crane load, wherein a manipulator for manipulating the load is connected by a rotator unit to a hook suspended on ropes and the rotational angle ϕ _L of the load is controlled by a control unit using the moment of inertia J_L of the load as most important parameter, wherein the control unit is an adaptive control unit, wherein the moment of inertia J_L of the load is identified during operation of the crane based on at least one of the following variables obtained by measuring the state of the system: rotational angle ϕ _H of the hook, rotational angle ϕ _L of the load, change ϕ̇ _H in the rotational angle ϕ _H of the hook and/or change ϕ̇ _I in the rotational angle ϕ_L of the load,
   characterized in that,
   a gyroscope is used to obtain data by which the rotational angle ϕ_H of the hook and/or the rotational angle ϕ _L of the load can be determined, wherein the moment of inertia J_L is identified using an observer.
2. The method for controlling the orientation of a crane load according to claim 1, wherein the rotational angle ϕ _L of the load is controlled using an adaptive trajectory tracking control.
3. The method for controlling the orientation of a crane load according to claim 1, wherein a dynamic model of the system is used to calculate data describing the state of the system.
4. The method for controlling the orientation of a crane load according to claim 3, wherein torsional oscillations are avoided by a anti-torsional oscillation unit using the data calculated by the dynamical model.
5. The method for controlling the orientation of a crane load according to claim 1, wherein the difference ϕ _C between the rotational angle ϕ _L of the load and the rotational angle ϕ _H of the hook can be varied by the rotator unit.
6. The method for controlling the orientation of a crane load according to claim 1, wherein the difference ϕ _C between the rotational angle ϕ _L of the load and the rotational angle ϕ _H of the hook is measured by an encoder connected to the rotator unit.
7. The method for controlling the orientation of a crane load according to claim 1, wherein the movements of a cardanic element guided by the rope are measured to obtain data by which the rotational angle ϕ _H of the hook and/or the rotational angle ϕ _L of the load can be determined.
8. The method for controlling the orientation of a crane load according to claim 1, wherein the change ϕ̇ _H in the rotational angle ϕ _H of the hook and/or the change ϕ̇ _I in the rotational angle ϕ _L of the load are measured by a gyroscope.
9. The method for controlling the orientation of a crane load according to claim 3, wherein the dynamical model of the system is based on the equations of motion of a physical model of at least the ropes, the hook and the load.
10. The method for controlling the orientation of a crane load according to claim 1 or 3, wherein the moment of inertia J_H of the hook and J_Sp of the manipulator are used as parameters.
11. The method for controlling the orientation of a crane load according to claim 1, wherein during the operation of the crane a torque is applied to the load and/or the hook.
12. The method for controlling the orientation of a crane load according to claim 11, wherein the data obtained by measuring the state of the system at least comprise the change ϕ̇ _H in the rotational angle ϕ _H of the hook and/or the change ϕ̇ _I in the rotational angle ϕ _L of the load in reaction to the torque applied to the load and/or the hook.
13. The method for controlling the orientation of a crane load according to claim 1, wherein a value of the moment of inertia J_L0 estimated only on the basis of the mass and the dimensions of the load is used as an initial value for J_L and corrected values J_Lk are determined in an iterative process in order to identify the moment of inertia J_L .
14. The method for controlling the orientation of a crane load according to claim 3, wherein during operation of the crane data describing the state of the system are calculated by the dynamical model based on a value J_L,K-1 of the moment of inertia J_L and a corrected value J_Lk of the moment of inertia J_L is determined based on the calculated data and the data obtained by measuring the state of the system in order to identify the moment of inertia J_L .
15. The method for controlling the orientation of a crane load according to claim 1, wherein the moment of inertia J_L is identified using a non-linear observer.
16. The method for controlling the orientation of a crane load according to claim 1, wherein the moment of inertia J_L is identified using an extended Kalman filter.
17. The method for controlling the orientation of a crane load according to claim 1, wherein a homogeneous distribution of mass inside the load is assumed for an estimation of an initial value J_L0 of the moment of inertia J_L of the load.
18. The method for controlling the orientation of a crane load according to claim 1, wherein noise in the data obtained by measurements is taken into account in the identification of the moment of inertia J_L .
19. The method for controlling the orientation of a crane load according to claim 18, wherein the noise in the data obtained by measurements is modelled by covariance matrices.
20. The method for controlling the orientation of a crane load according to claim 19, wherein the covariance matrices are determined experimentally.
21. System for controlling the orientation of a crane load according to the method of any one of the preceding claims, comprising a control unit for controlling the rotational angle ϕ _L of the load and a gyroscope for receiving data by which the rotational angle ϕ _H of the hook and/or the rotational angle ϕ _L of the load are determined, wherein the control unit includes a trajectory planning unit and a trajectory control unit as well as an observer for estimating the moment of inertia J_L .
22. A crane, especially a boom crane, comprising the system for controlling the rotation of a crane load according to claim 21.

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