CRANE AND METHOD FOR CONTROLLING SUCH A CRANE

Abstract

The invention relates to a crane, in particular a revolving tower crane or boom crane, having a hoisting cable which extends from a crane boom and carries a load hook, wherein a sling having a load fixed thereto is rigged to the load hook, which load hangs down, spaced apart from the load hook by the sling, and having a determination device for determining the position and/or excursion of the load, and an electronic control apparatus for controlling drive devices for moving crane elements and relocating the load hook according to the detected position and/or excursion of the load, wherein the determination device has first determining means for determining a position and/or excursion of the load hook and furthermore an inertial measurement unit which is attached to the sling and/or the load and which has acceleration and rotation rate sensor means for providing acceleration and rotation rate signals and second determination means for determining and/or estimating an excursion and/or position of the load from the acceleration and rotation rate signals of the inertial measurement unit, which is attached to the sling and/or to the load, and from the signals of the indicated first determination means which characterize the position and/or excursion of the load hook.

Claims

1. A revolving tower crane or boom crane comprising: a hoisting cable extending from a crane boom and carries a load hook; a sling having a load fixed thereto is rigged to the load hook, wherein the load hangs down, spaced apart from the load hook by the sling; a determination device for determining the position and/or deflection of the load, wherein the determination device has a first determiner for determining a position and/or deflection of the load hook; an electronic control apparatus for controlling drive devices for moving crane elements and relocating the load hook according to the detected position and/or deflection of the load; and an inertial measurement device attached to the sling and/or the load, wherein the inertial measurement device comprises acceleration and rotation rate sensors for providing acceleration and rotation rate signals and a second determiner for determining and/or estimating a deflection and/or position of the load from the acceleration and rotation rate signals of the inertial measurement device, which is attached to the sling and/or to the load, and from the signals of the first determiner which characterize the position and/or deflection of the load hook.

2. The crane of claim 1, wherein the inertial measurement device on the sling and/or on the load comprises a wireless communication module to wirelessly transmit measuring signals and/or signals derived therefrom to a receiver, wherein the communication module and the receiver are connectable to each other via a Bluetooth or WLAN connection, and wherein the receiver is arranged on a trolley from which the hoisting cable extends.

3. The crane of claim 1, wherein the inertial measurement device on the sling and/or on the load has an energy accumulator comprising a rechargeable battery.

4. The crane of claim 1, wherein the inertial measurement device comprises a releasable fastener comprising a magnet device and/or a clamping device, wherein the releasable fastener is on the sling and/or on the load for releasable fastening to the load and/or to the sling.

5. The crane of claim 4, wherein the inertial measurement device is firmly integrated in the sling as a chain link.

6. The crane of claim 1, wherein the sling comprises at least one sling rope and/or sling chain.

7. The crane of claim 1, wherein the second determiner comprises a filter and/or observer device which is configured to take into account as an input variable a determined deflection and/or tilt of the sling and/or the load and determine the deflection of the sling and/or load relative to vertical from an inertial acceleration at the load and/or the sling.

8. The crane of claim 7, wherein the filter and/or observer device comprises an extended and/or unscented Kalman filter.

9. The crane of claim 1, wherein the first determiner for determining the position and/or deflection of the crane hook comprises an imaging sensor system comprising camera, which looks down substantially vertically in the region of a trolley having a suspension point of the hoisting cable, further comprising an image evaluation device for evaluating an image provided by the imaging sensor system with respect to the position of the load hook in the image provided and determining the deflection of the load hook and/or of the hoisting cable and/or the deflection speed with respect to vertical.

10. The crane of claim 9, wherein the first determiner comprises an inertial measurement device mounted on the load hook and having acceleration and rotation rate sensors for providing acceleration and rotation rate signals characterizing a translational acceleration and a rotation rate of the load hook.

11. The crane of claim 1, wherein the load hook is articulated to the hoisting cable in such a way that the deflection of the load hook corresponds to the deflection of the sling, wherein an inertial measurement device with acceleration and rotation rate sensors for providing acceleration and rotation rate signals is provided on the load hook and the determiner are configured for this purpose, determine and/or estimate the deflection and/or position of the load attached to the sling from the acceleration and rotation rate signals of said inertial measurement device on the load hook.

12. The crane of claim 11, wherein only the inertial measurement device is provided on the load hook and the determination and/or estimation of the deflection and/or position of the load rigged to the sling is performed without an inertial measurement device on the sling and the load.

13. The crane of claim 11, wherein a length of the sling is estimated and/or input and/or transferred via an external interface, wherein the deflection of the sling and/or the load relative to vertical is determined from the estimation of an orientation filter configured as a complementary filter.

14. A method for controlling a revolving tower crane or boom crane, on which on the load hook attached to a hoisting cable there is rigged a sling with a load attached thereto, comprising: determining by a determining device the position and/or deflection of the load in dependence on the determined load position and/or deflection drive devices for moving crane elements; controlling by an electronic control apparatus deflection drive devices for moving crane elements; determining by the first determiner the position and/or deflection of the load hook; determining by at least one inertial measurement device with acceleration and rotation rate sensors attached to the sling and/or on the load acceleration and rotation rate signals the translational accelerations and the rotation rates at the sling and/or at the load; transmitting the translational accelerations and the rotation rates at the sling and/or at the load wirelessly to the control apparatus; and determining by the first determiner a position and/or deflection of the load from the acceleration and rotation rate signals of the inertial measurement device and the position and/or deflection of the load hook.

15. The method of claim 14, wherein the deflection of the load and/or of the sling relative to vertical from an inertial acceleration at the load and/or at the sling by a filter and/or observer device to which the determined deflection of the load and/or of the sling is supplied as an input variable.

16. The method of claim 14, wherein the acceleration signals indicating the translational accelerations at the load and/or at the sling are determined with respect to three spatial axes and the rotation rate signals indicating the rotation rates at the load and/or the sling are detected with respect to at least two spatial axes.

17. The method of claim 14, wherein the load hook is articulated to the hoisting cable and is deflected with the same pendulum angle as the sling with respect to vertical; providing by an inertial measurement device with acceleration and rotation rate sensors attached to the load hook acceleration and rotation rate signals indicating the translational accelerations and the rotation rates at the load hook; transmitting wirelessly to the control apparatus the acceleration and rotation rate signals indicating the translational accelerations and the rotation rates at the load hook; and determining a position and/or deflection of the sling and of the load from the acceleration and rotation rate signals of the inertial measurement device at the load hook.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The invention is explained in more detail below on the basis of a preferred exemplary embodiment and the corresponding drawings. The drawings show:

[0045] FIG. 1 shows a schematic representation of a revolving tower crane in which a hoisting cable extends from a trolley which can be moved on a boom and on which a load hook is articulated, wherein on the load hook there is suspended a sling, wherein the double pendulum movements possible through this are shown with different deflection angles of the hoisting cable and the sling;

[0046] FIG. 2 shows a schematic representation of the double pendulum from FIG. 1 and its hinging to a crane trolley, wherein the travel movements of the trolley, the length changes of the hoisting cable and the resulting pendulum angles are entered;

[0047] FIG. 3 shows a possible tilting of the load hook with respect to the hoisting cable; and

[0048] FIG. 4 shows a schematic representation of a revolving tower crane and the double pendulum comprising the hoisting cable and the sling hinged to the load hook, wherein the load hook is connected to the hoisting cable by an articulated connection and the deflection of the load hook corresponds to the def of the sling.

DETAILED DESCRIPTION

[0049] As FIG. 1 shows, the crane 10 can be configured as a revolving tower crane. The revolving tower crane shown in FIG. 1 can, for example, have a tower 1 in a manner known per se that carries a boom 2 that is balanced by a counter-boom 4 at which a counter-weight can be provided. Said boom 2 can be rotated by a slewing gear together with the counter-boom 4 about an upright axis of rotation 5 that can be coaxial to the longitudinal tower axis. A trolley 6 can be traveled at the boom 2 by a trolley drive, with a hoisting cable 7 to which a load hook 8 is fastened extending from the trolley 6.

[0050] As FIG. 1 likewise shows, the crane 2 can—obviously also as well as a development as a bridge crane or another crane—here have an electronic control apparatus 3 that can comprise a control processor arranged at the crane itself. Said control apparatus 3 can here control different adjustment members, hydraulic circuits, electric motors, drive apparatus, and other pieces of working equipment at the respective construction machine. In the crane shown, they can, for example, be its hoisting gear, its slewing gear, its trolley drive, its boom luffing drive—where present—or the like.

[0051] Said electronic control apparatus 3 can here communicate with an end device 9 that can be arranged at the control station or in the operator's cab and can, for example, have the form of a tablet with a touchscreen and/or joysticks, rotary knobs, slider switches, and similar operating elements so that, on the one hand, different information can be displayed by the control processor 3 at the end device 9 and conversely control commands can be input via the end device 9 into the control apparatus 3.

[0052] Said control apparatus 3 of the crane 10 can in particular be configured also to control said drive apparatuses of the hoisting gear, of the trolley, and of the slewing gear when an pendulum damping device 30 detects pendulum-relevant movement parameters.

[0053] For this purpose, the crane 1 can have a pendulum sensor or detection device 60 that detects an oblique pull of the hoisting cable 7 and/or deflections of the load hook 8 with respect to a vertical line 62 that passes through the suspension point of the load hook 8, i.e. the trolley 6. The cable pull angle β can in particular be detected with respect to the line of gravity effect, i.e. the vertical line 62, cf. FIG. 1.

[0054] In this regard, the pendulum sensor 60 may have a camera 63 or other imaging sensor system attached to the trolley 6 that looks perpendicularly downwardly from the trolley 6 so that, with a non-deflected load hook 8, its image reproduction is at the center of the image provided by the camera 63. If, however, the load hook 8 is deflected with respect to the vertical line 62, for example by a jerky traveling of the trolley 6 or by an abrupt braking of the slewing gear, the image reproduction of the load hook 8 moves out of the center of the camera image, which can be determined by an image evaluation device 61.

[0055] On the other hand the oblique pull β of the hoisting cable or the deflection of the load hook with respect to the vertical can also be achieved with the aid of an inertial measurement unit that is attached to the load hook 8 and that can preferably transmit its measurement signals wirelessly to a receiver at the trolley 6, cf. FIG. 1.

[0056] Furthermore, in order to detect the “lower” part of the double pendulum movements, more specifically the pendulum movements of the sling 12 and the load 11 attached thereto with respect to the load hook 8, the pendulum sensor 60 comprises an additional inertial measurement unit, which may be attached to said sling 12 or directly attached to the load 11. FIGS. 1 and 2 show an additional inertial measurement unit 66 on the sling 12 and another inertial measurement unit 67 attached directly to the load 11. By means of this at least one additional inertial measurement unit 66 and 67, in particular the deflection angle φ, which indicates the deflection of the sling 12 and the load 11 relative to the vertical 62 and thus relative to the load hook 8, can be determined.

[0057] Depending on the detected or determined deflections β and φ with respect to the vertical 62, in particular taking into account the direction and magnitude of the deflections, the control apparatus 3 can control the slewing gear drive and the trolley drive using the pendulum damping device 30 in order to bring the trolley 6 more or less precisely back over the load 11 and to compensate for double pendulum movements, or to reduce them, or to prevent them from occurring in the first place.

[0058] In particular, on the basis of the dynamics of the double pendulum, an observer can be determined, for example in the form of a Kalman filter, in particular an “unscented” Kalman filter, which can reliably determine the position of the load 11 and/or its deflection φ with the aid of the position of the load hook 8 or the measurements of said sensors in the form of the camera 63 and/or the inertial measurement unit 65 and the deflection β determined therefrom, on the one hand, and the additional pendulum sensor in the form of the inertial measurement unit 66 on the sling 12 and/or the inertial measurement unit 67 on the load 11, on the other hand. In particular, it is also possible to estimate the length of the sling 12 and thus the spacing of the load 11 from the load hook 8 as well as the angle φ between the vertical 62 and the sling 12 and to calculate the position of the load therefrom.

[0059] The basis for the observer is the mathematical description of the double pendulum. Taking into account the model shown in FIG. 2, the double pendulum dynamics can be derived with the help of the Euler-Lagrange equations. For simplicity, in the following there are considered only a pendulum plane and a crane without slewing gear, e.g. a bridge crane. However, the derivation can easily be extended to include another vibration plane and other drives such as a luffing or slewing gear.

[0060] First, the trolley position s.sub.x(t) the cable length l(t) as well as the upper and lower pendulum angle β(t) and φ(t) are defined as a function of time t, wherein in the following, for better readability, the time dependence is no longer specified specifically by the term (t). The position of the hook

[00001] $\begin{matrix} r_{H} = [\begin{matrix} s_{x} - l \sin (β) \\ - l \cos (β) \end{matrix}] & (1) \end{matrix}$

and the load

[00002] $\begin{matrix} r_{L} = r_{H} + [\begin{matrix} - l_{A} \sin (φ) \\ l_{A} \cos (φ) \end{matrix}] & (2) \end{matrix}$

and the associated velocities

[00003] $\begin{matrix} {\dot{r}}_{H} = [\begin{matrix} {\dot{s}}_{x} - \dot{l} \sin (β) - l \dot{β} \cos (β) \\ l \dot{β} \sin (β) - \dot{l} \cos (β) \end{matrix}] and & (3) \\ {\dot{r}}_{L} = [\begin{matrix} {\dot{s}}_{x} - \dot{l} \sin (β) - l \dot{β} \cos (β) - \dot{φ} l_{A} \cos (φ) \\ l \dot{β} \sin (β) - \dot{l} \cos (β) + \dot{φ} l_{A} \sin (φ) \end{matrix}] & (4) \end{matrix}$

can be defined depending on these variables. The parameter l.sub.A indicates the length of the sling. Depending on the design of the filter, this parameter can also be estimated online with, as will be explained later. The accelerations

[00004] $\begin{matrix} {\overset{.Math.}{r}}_{H} = [\begin{matrix} {\overset{.Math.}{s}}_{x} - \sin (β) \overset{.Math.}{l} - 2 \dot{l} \dot{β} \cos (β) - \overset{.Math.}{β} \cos (β) l + \dot{β^{2}} l \sin (β) \\ - \overset{.Math.}{l} \cos (β) + 2 \sin (β) \dot{β} \dot{l} + \cos (β) l \dot{β^{2}} + \overset{.Math.}{β} l \sin (β) \end{matrix}] and & (5) \\ {\overset{.Math.}{r}}_{L} = [\begin{matrix} {\overset{.Math.}{s}}_{x} - \overset{.Math.}{φ} l_{A} \cos (φ) - \sin (β) \overset{.Math.}{l} - 2 \dot{l} \dot{β} \cos (β) + {\dot{φ}}^{2} l_{A} \sin (φ) - \overset{.Math.}{β} \cos (β) l + \dot{β^{2}} l \sin (β) \\ - \overset{.Math.}{l} \cos (β) + 2 \sin (β) \dot{β} \dot{l} + \cos (β) l \dot{β^{2}} + l_{A} \cos (φ) {\dot{φ}}^{2} + \overset{.Math.}{φ} l_{a} \sin (φ) + \overset{.Math.}{β} l \sin (β) \end{matrix}] & (6) \end{matrix}$

are not needed to derive the double pendulum dynamics, but can be used in the later observer design. With the help of the kinetic energy

T=½m.sub.H{dot over (r)}.sub.H.sup.T{dot over (r)}.sub.H+½m.sub.L{dot over (r)}.sub.L.sup.T{dot over (r)}.sub.L (7)

and the potential energy

V=[0g](m.sub.Hr.sub.H+m.sub.Lr.sub.L) (8)

via the solution of the Euler-Lagrange equation

[00005] $\begin{matrix} \frac{d}{d t} \frac{\partial T}{\partial \dot{q}} - \frac{\partial T}{\partial q} + \frac{\partial V}{\partial q} = 0 & (9) \end{matrix}$

there can be derived the double pendulum dynamics with generalized coordinates q=[β,φ].sup.T. Due to the elongated expression, an explicit specification of the terms of {umlaut over (β)} and {umlaut over (φ)} is omitted. In a next step, from this there can be set up a nonlinear system in the state space

{dot over (x)}=ƒ(x,u)+w

y=h(x,u)+v (10)

with the states x=[β, {dot over (β)}, φ, {dot over (φ)}, l.sub.A].sup.T, the inputs u=[s.sub.x, l, {dot over (s)}.sub.x, {dot over (l)}, {umlaut over (s)}.sub.x, {umlaut over (l)}].sup.T as well as with the system noise w=N(0, Q) and measurement noise v=N(0, R) assumed to be normally distributed over the covariance matrices Q and R. If the accelerations of the trolley {umlaut over (s)}.sub.x and the hoisting cable {umlaut over (l)} are not available directly from the control system or via measurements or estimates as input for the observer, they can also be determined via a PT-1 approximation, as explained for example in WO 2019/007541. The outputs y depend on the available sensors. In the case of IMUs on the hook (65) and the load (67), for example, the accelerations y=[{umlaut over (r)}.sub.H, {umlaut over (r)}.sub.L].sup.T are suitable. In the case of the camera (63) and an IMU (67), the hook swing angle and the load acceleration determined via the camera can be used as output y=[β.sub.H, {umlaut over (r)}.sub.L].sup.T. Alternatively or additionally, the rotation rate signals of the IMUs can be used in the outputs.

[0061] In this formulation, the system dynamics ƒ contains, in addition to the double pendulum dynamics, a random walk approach for the simultaneous estimation of the length of the sling with {dot over (l)}.sub.A=0. For this system with the accelerations of the hook and the load in inertial coordinates, a stationary wheel observer can now be designed. In the nonlinear case, for example, an unscented or extended Kalman filter can be used. Depending on the system, the desired accuracy and the available computing power, a simplifying linearization in combination with a linear observer, e.g. a simple Kalman filter, can also be useful.

[0062] The following is an example of the procedure for an unscented Kalman filter using the hook and load acceleration as output y=[{umlaut over (r)}.sub.H, {umlaut over (r)}.sub.L].sup.T. First, at time step k, suitable sigma points χ=[χ.sub.0, . . . , χ.sub.2n] and suitable weighting factors W=[W.sub.0, . . . , W.sub.2n]

[00006] $\begin{matrix} χ_{0} (k) = \hat{x} (k), W_{0} = \frac{κ}{n + κ} χ_{i} (k) = \hat{x} (k) + {(\sqrt{(n + κ) P (k)})}_{i}, W_{i + n} = \frac{1}{2 (n + κ)}; i = (1, .Math., n) χ_{i + n} (k) = \hat{x} (k) - {(\sqrt{(n + κ) P (k)})}_{i}, W_{i + n} = \frac{1}{2 (n + κ)} & (11) \end{matrix}$

must be determined using the expected value {circumflex over (x)} of the system state x, the covariance matrix P, the design parameter κ and the system state n=5. The root of the matrix in equation (11) is not uniquely defined and must be determined via a Cholesky decomposition. Depending on the approach, the i-th column or i-th row is to be used in equation (11). Subsequently, the sigma points of the next sampling step k+1

χ.sub.i(k+1|k)=ƒ(χ.sub.i(k),u(k)) (12)

are predicted by applying the system equation (10). The predicted expected value is given by

{circumflex over (x)}(k+1|k)=Σ.sub.i=0.sup.2nW.sub.iχ.sub.i(k+1|k). (13)

[0063] The estimation error covariance matrix is then obtained with the covariance of the process noise Q to give

[00007] $\begin{matrix} P (k + 1 | k) = {.Math.}_{i = 0}^{2 n} W_{i} (χ_{i} (k + 1 | k) - \hat{x} (k + 1 | k)) {(χ_{i} (k + 1 | k) - \hat{x} (k + 1 | k))}^{T} Q . & (14) \end{matrix}$

[0064] The new Sigma points χ.sub.i(k+1|k) and weights W.sub.i can now be determined via equation (11) using P(k+1|k) and {circumflex over (x)}(k+1|k) instead of P(k) and {circumflex over (x)}(k). The sigma points predicted in this way can now be entered into the measuring range using the output equation (10),

Z.sub.i(k+1|k)=h(χ.sub.i(k+1|k),u(k)) (15)

thereby predicting the measurements via the formation of the expected value

[00008] $\begin{matrix} \hat{z} (k + 1 | k) = {.Math.}_{i = 0}^{2 n} W_{i} Z_{i} (k + 1 | k) & (16) \end{matrix}$

Subsequently, the covariance matrix of the measurement noise R is used to determine the innovation covariance matrix

[00009] $\begin{matrix} S (k + 1) = {.Math.}_{i = 0}^{2 n} W_{i} (Z_{i} (k + 1 | k) - \hat{z} (k + 1 | k)) {(Z_{i} (k + 1 | k) - \hat{z} (k + 1 | k))}^{T} R . & (17) \end{matrix}$

[0065] With this and the cross-correlation matrix

[00010] $\begin{matrix} T (k + 1) = {.Math.}_{i = 0}^{2 n} W_{i} (χ_{i} (k + 1 | k) - \hat{x} (k + 1 | k)) {(Z_{i} (k + 1 | k) - \hat{z} (k + 1 | k))}^{T} R, & (18) \end{matrix}$

the Kalman matrix

K(k+1)=T(k+1)S.sup.−1(k+1) (19)

can be determined and, together with the measured values z(k+1) the innovation of the expected value

{circumflex over (x)}(k+1|k+1)={circumflex over (x)}(k+1|k)+K(k+1)(z(k+1)−{circumflex over (z)}(k+1|k)) (20)

and the estimation error covariance

P(k+1|k+1)=P(k+1|k)−K(k+1)S(k+1)K(k+1).sup.T (21)

can be carried out. With the estimated expected value of the states {circumflex over (x)}(k+1|k+1) the position of the hook and the load can be determined using equations (1) and (2).

[0066] The measured values z(k+1) used in equation (20) can, as mentioned at the beginning of the filter description, be the accelerations of the hook {umlaut over (r)}.sub.H and the load {umlaut over (r)}.sub.L can be. In general, however, the measured accelerations of the IMUs (65) and (67) cannot be used directly, since the IMUs may be installed at an angle, or the load hook may be tilted by the angle ε.sub.β, cf. FIG. 3. For this reason, the measured accelerations must be transposed into the inertial system. Orientation filters, which can be designed as EKF or complementary filters, are suitable for this purpose. An approach using a complementary filter is described, for example, in WO 2019/007541 and is roughly outlined again here for completeness.

[0067] The IMU measures all the signals in the co-moving, co-rotating body coordinate system of the load hook, which is characterized by the index K while vectors in inertial coordinates are characterized by I or also remain fully without an index. As soon as ϵ.sub.β has been estimated, the measured acceleration a.sub.K=[a.sub.K,x, a.sub.K,z].sup.T in load hook coordinates can be transformed into a.sub.I in inertial coordinates, using

[00011] $\begin{matrix} a_{I} = {[\begin{matrix} \cos (ϵ_{β}) & \sin (ϵ_{β}) \\ - \sin (ϵ_{β}) & \cos (ϵ_{β}) \end{matrix}]}^{T} a_{K} . & (22) \end{matrix}$

[0068] The inertial acceleration can then be used as a measured variable of the observer z or as output y of the system (10). In itself, the tilt could be estimated using a model corresponding to the simple integrator

{dot over (ϵ)}.sub.β=ω.sub.β (23)

from the measured rotation rate ω.sub.β to the tilt angle. However, in the case of gyroscopic measurement of the rotation rate or tilt speed, the gyroscope signals have a time-variable offset and are superimposed by measurement noise, so the method described is not useful. Advantageously, it is therefore possible to work with an orientation filter.

[0069] The accelerometer is therefore used to provide a reference value for angle ϵ.sub.β in that the acceleration due to gravity constant (that occurs in the signal having a low frequency) is evaluated and is known in inertial coordinates as

g.sub.I=[0,−g].sup.T (24)

and can be transformed in load hook coordinates

g.sub.K=−g[−sin(ϵ.sub.β)cos(ϵ.sub.β)].sup.T (25)

The measured acceleration results as the sum of (103) and (112)

a.sub.K={umlaut over (r)}.sub.K−g.sub.K (26)

[0070] The negative sign of g.sub.K here results from the circumstance that the acceleration due to gravity is measured as a fictitious upward acceleration due to the sensor principle. Since all the components of {umlaut over (r)}.sub.K are generally significantly smaller than g and oscillate about zero, the use of a lowpass filter having a sufficiently low masking frequency permits the approximation

a.sub.K≈−g.sub.K (27)

[0071] If the x-component a.sub.K,x is divided by the z-component a.sub.K,z, the reference tilt angle for low frequencies is obtained as

[00012] $\begin{matrix} ϵ_{β} = \arctan (\frac{a_{K, x}}{a_{K, z}}) & (28) \end{matrix}$

[0072] The simple structure of the equations (23) and (28) permits the use of various filters to estimate the orientation. One option is a complementary filter, that can be set with respect to its frequency characteristic by a selection of the highpass and lowpass transfer functions.

[0073] A highpass filtering of the gyroscope signal ω.sub.β with G.sub.hp(s) produces the offset-free rotational rate {tilde over (ω)}.sub.β and, after integration, a first tilt angle estimate ϵ.sub.β,ω. The further estimation ϵ.sub.β,a comes from equation (28) based on the accelerometer. A simple highpass filter having the transfer function

[00013] $\begin{matrix} G_{h p} (s) = \frac{s}{s + ω_{0}} & (29) \end{matrix}$

and very low masking frequency ω.sub.0 can in particular be applied to the gyro signal ω.sub.β to eliminate the constant measurement offset. Integration produces the gyroscope based tilt angle estimate ϵ.sub.β,ω that is relatively exact for high frequencies, but is relatively inexact for low frequencies. The underlying idea of the complementary filter is to sum up ϵ.sub.β,ω and ϵ.sub.β,a or to link them to one another, with the high frequencies of ϵ.sub.6β,ω being weighted more by the use of highpass filter, and the low frequencies of ϵ.sub.β,a being weighted more by the use of the lowpass filter

[00014] $\begin{matrix} G_{lp} (s) = \frac{ω_{0}}{s + ω_{0}} & (30) \end{matrix}$

since (28) represents a good estimate for low frequencies. The transfer functions can be selected as simple first order filters, where the masking frequency ω.sub.0 is selected as lower than the pendulum frequency. Since

G.sub.hp(s)+G.sub.lp(s)=1 (31)

applies to all the frequencies, the estimate of ϵ.sub.β is not incorrectly scaled.

[0074] The inertial acceleration a.sub.I of the load hook can be determined on the basis of the estimated load hook orientation from the measurement of a.sub.K and indeed while using (22), which permits the design of an observer on the basis of the double pendulum dynamics (10)

a.sub.I={umlaut over (r)}.sub.I−g.sub.I (32)

[0075] Although both components of this equation can equally be used for the estimate of the pendulum angle, good results can also be obtained only using the x component that is independent of g.

[0076] The evaluation of the inertial measurement unit 65 and 66 or 67, which is attached to the sling 12 or directly to the load 11, can be carried out in an analogous manner as has just been explained. To avoid repetition, reference may be made to the statements just made.

[0077] Thus, the additional inertial measurement unit 66 or 67 on the sling 12 or the load 11 allows the position of the load 11 to be precisely determined even during double pendulum movements.

[0078] Depending on the type of crane and the design of the bottom hook block or load hook, the connection between the hoisting cable and the bottom hook block can be modeled using a pivot joint (70) and at the same time the connection between the load sling and the crane hook can be assumed to be fixed, as FIG. 4 shows. In this case, the tilting of the crane hook corresponds ϵ.sub.β exactly to the lower pendulum angle φ. Consequently, in this constellation with a single IMU on the load hook, the position or pendulum angles of both the load hook and the length of the sling, and thus the position or pendulum angles of the load itself, can be determined. If necessary, the installation angle of the IMU must also be taken into account if its axes are not exactly aligned.

[0079] The tilt ϵ.sub.β or the lower pendulum angle φ follows directly from the estimation of the orientation filter, which can be implemented e.g. as explained by a complementary filter. With regard to the observer, two implementations are conceivable depending on the quality of the orientation filter.

[0080] If the tilt ϵ.sub.β estimated by the orientation filter is inaccurate or confused, it is advisable to use the entire double pendulum model (10) with the states x=[β, {dot over (β)}, φ, {dot over (φ)}, l.sub.A].sup.T in the observer. In this constellation the outputs of the model y=[{umlaut over (r)}.sub.H, φ, {dot over (φ)}].sup.T can comprise, in addition to the accelerations of the hook, the tilt of the hook ϵ.sub.β=φ as well as the rotation rate of the hook, which corresponds to the lower pendulum angular velocity, ω.sub.β={dot over (φ)} and serve as measurement variables z for the observer.

[0081] If the quality of the orientation filter is sufficiently high, the observer can be reduced. In this case, the state x=[β, {dot over (β)}, l.sub.A].sup.T to be estimated is reduced to the upper pendulum angle β, the pendulum angular velocity {dot over (β)} and the length of the sling l.sub.A. The lower pendulum angle φ and the angular velocity {dot over (φ)} are not states but inputs of the system. These thus result in u=[s.sub.x, l, {dot over (s)}.sub.x, {dot over (l)}, {umlaut over (s)}.sub.x, {umlaut over (l)}, φ, {dot over (φ)}].sup.T. The outputs of the model y=[{umlaut over (r)}.sub.H].sup.T can comprise the accelerations of the hook in this constellation and serve as measurement variables z for the observer. At this point it should be noted again that additionally or alternatively the rotation rates of the hook in the inertial system could be used.

[0082] Again, the length of the sling is estimated using a random walk approach. Alternatively, the length can also be transferred to the observer directly from outside or from a higher-level software module or by the user.

[0083] In advantageous further development, the described approach for describing the double pendulum dynamics and the indicated observers can be combined with a structural model of the crane, such as described in WO 2019/007541. The states determined in this way can be used for stabilization and to suppress unnecessary pendulums. For this purpose, a nonlinear control, e.g. a model predictive control (MPC), can be designed. For a simpler representation, a crane with a swing plane, e.g. a bridge crane, is used here as well. However, the method can easily be extended to include other vibration levels, e.g. a slewing gear, and structural elasticities.

[0084] In terms of model predictive control, the behavior of the crane is predicted using a mathematical model over a certain period of time and the manipulated variables are varied in such a way that a cost functional J, which describes the control objectives, is minimized.

[0085] This requires a mathematical model of the crane. However, in addition to the pendulum dynamics and any structural elasticities, this must also take into account the drive dynamics. Assuming a fast superimposed speed control of the inverters, the drive dynamics for the bridge crane considered for simplification results in

[00015] $\begin{matrix} f_{c o n t} (x, u, l_{A}) = [\begin{matrix} {\dot{s}}_{x} \\ {\overset{.Math.}{s}}_{x} \\ \dot{l} \\ \overset{.Math.}{l} \\ \dot{β} \\ f_{1} (x, u, l_{A}) \\ \dot{φ} \\ f_{2} (x, u, l_{A}) \end{matrix}] & (33) \end{matrix}$

with the states x.sub.des=[s.sub.x, {dot over (s)}.sub.x, l, {dot over (l)}, β, {dot over (β)}, φ, {dot over (φ)}].sup.T and the inputs u.sub.des=[{umlaut over (s)}.sub.x, {umlaut over (l)}].sup.T. The functions ƒ.sub.1(x, u) and ƒ.sub.2 (x, u) describe the acceleration of the double pendulum angles analogous to the system (10). In addition, the structural dynamics of the crane could also be considered in (33).

[0086] A possible design of the cost functional

J(u;x.sub.k)=∫.sub.0.sup.T.sup.hor(x−x.sub.des).sup.TQ(x−x.sub.des)+(u−u.sub.des).sup.TR(u−u.sub.des)dt (34)

provides for x.sub.des=[˜, {dot over (s)}.sub.x,des, ˜, {dot over (l)}.sub.des, 0,0,0,0].sup.T and u.sub.des=[0,0].sup.T the penalization of the pendulum angles, the pendulum angle speed and the deviation of the trolley and hoist speeds from the desired target speeds {dot over (s)}.sub.x,des and {dot over (l)}.sub.des depending on the weighting matrices Q and R. The tilde indicates that no target values are specified for the trolley position and the hoisting cable length. Alternatively, other formulations are also conceivable, e.g. penalizing the deviation of the load or hook speed from a target. Formulations that penalize the deviation of the position of the hook, load or individual drives to a target position can also be implemented. On this basis it is possible to formulate the dynamic optimization problem

[00016] $\begin{matrix} \min_{u (.Math.)} J (u; x_{k}, l_{A}) u . B . v . \dot{x} = f_{c o n t} (x (t), u (t), l_{A}), x (t_{k}) = x_{k} u_{\min} \leq u (t) \leq u_{\max}, x_{\min} \leq x (t) \leq x_{\max} & (35) \end{matrix}$

This is solved in each sampling step via a numerical procedure, e.g. via common software tools such as ACADO or GRAMPC. The first part of the manipulated variable trajectory u(t) serves as input and is passed on to the inverters of the drives as setpoint speed after integration. In addition to the system dynamics, the optimization problem (35) directly includes the possibly time-varying constraints of the drives in the form of maximum and minimum acceleration in the manipulated variable constraints u.sub.max=[{umlaut over (s)}.sub.x,max, {umlaut over (l)}.sub.max].sup.T and u.sub.min=[{umlaut over (s)}.sub.x,min, {umlaut over (l)}.sub.min].sup.T as well as the maximum and minimum velocity and positions in the state constraints x.sub.min=[s.sub.x,min, {dot over (s)}.sub.x,min, l.sub.min, {dot over (l)}.sub.min, ˜, ˜, ˜, ˜].sup.T and x.sub.max=[s.sub.x,max, {dot over (s)}.sub.x,max, l.sub.max, {dot over (l)}.sub.max, ˜, ˜, ˜, ˜].sup.T. This is a particular advantage of the MPC.

[0087] However, MPC involves a high computational cost, so that as an alternative to nonlinear control based on linearization of the model (33), a linear controller with gain scheduling, for example in the form of linear-quadratic control (LQR), can also be determined. Advantageously, this control can be combined with a trajectory generation and a feedforward control to form a two-degree-of-freedom control, as shown for example in WO 2019/007541 for a single pendulum.

CRANE AND METHOD FOR CONTROLLING SUCH A CRANE

Assignee

Inventors

Cpc classification

Classification Explorer

B66C13/063

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B66C13/085

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

G06T7/70

PHYSICS

Classification Explorer

G01P15/08

PHYSICS

Classification Explorer

G01C19/00

PHYSICS

International classification

Classification Explorer

B66C13/06

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B66C13/08

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

G01C19/00

PHYSICS

Classification Explorer

G01P15/08

PHYSICS

Classification Explorer

G06T7/70

PHYSICS

Abstract

Claims

Description