EP1628902A1

EP1628902A1 - Crane or excavator for handling a cable-suspended load provided with optimised motion guidance

Info

Publication number: EP1628902A1
Application number: EP04739403A
Authority: EP
Inventors: Klaus Schneider; Oliver Sawodny; Eckard Arnold
Original assignee: Liebherr Werk Nenzing GmbH
Current assignee: Liebherr Werk Nenzing GmbH
Priority date: 2003-05-30
Filing date: 2004-05-27
Publication date: 2006-03-01
Anticipated expiration: 2024-05-27
Also published as: DE502004005274D1; WO2004106215A1; EP1628902B1; JP4795228B2; DE10324692A1; ES2293271T3; KR20060021866A; JP2006525928A; US7426423B2; US20060074517A1

Abstract

The invention relates to a crane or excavator for handling a cable-suspended load (3) comprising a rotation system for rotating the crane or excavator, a rocker system (7) for lifting or tilting a crane arm (5) and a lifting system for lifting or lowering the cable-suspended load (3) which is provided with a drive system. According to said invention, the crane or excavator comprises a continuous control system (31) whose output values are directly or indirectly used for input values for adjusting the position or speed of the crane or excavator, the control guiding values being generated in the continuous control system (31) in such a way that the amplitude of pendulum swing of the load is minimised.

Description

Crane or excavator for handling a load hanging on a load rope with optimized motion control

The invention relates to a crane or excavator for handling a load suspended from a load rope according to the preamble of claim 1.

In detail], the invention is concerned with the generation of command variables as control functions in cranes or excavators, which allows the load suspended on a rope to be moved in at least three degrees of freedom. Such cranes or excavators have a slewing gear, which can be mounted on a trolley, which is used to turn the crane or excavator. There is also a luffing gear for raising or tilting a boom and a slewing gear. Finally, the crane or excavator comprises a hoist for lifting or lowering the load suspended on the rope. Such cranes or excavators are used in a wide variety of designs. Examples include mobile harbor cranes, ship cranes, offshore cranes, crawler cranes or cable excavators.

When a load hanging on a rope is handled by means of a crane or excavator of this type, pendulum movements of the load occur which affect the movements. the crane or excavator itself. Efforts have already been made in the past to reduce or suppress pendulum vibrations in load cranes.

WO 02/32805 A1 describes a crane or excavator for handling a load hanging on a load rope with a computer-controlled regulation for damping the load oscillation, which has a path planning module, a centripetal force compensation device and at least one axis controller for the slewing gear, one axis controller for the luffing gear and one Has axis controller for the hoist. Only the kinematic limits of the system are taken into account in the path planning module. The dynamic behavior is only taken into account when designing the control.

The object of the invention is to further optimize the motion control of the load hanging on the load rope.

To solve this task, a generic crane or excavator has a control system in which the reference variables for the control system are generated in such a way that there is an optimized movement with minimized pendulum deflections. The traversed path of the oscillating load can also be forecast and a collision avoidance strategy can be implemented based on this.

Advantageous refinements of the invention result from the subclaims following the main claim.

It is particularly advantageous that optimal control trajectories are calculated and updated online in the path control of the present invention. The model-based optimal control trajectories can be created based on a model linearized around reference trajectories. Alternatively, the model-based optimal control trajectories can be based on a non-linear model approach. The model-based optimal control trajectories can be determined with feedback from all state variables.

Alternatively, the model-based optimal control trajectories can be determined by tracing at least one measured variable and estimating the remaining state variables.

Again, alternatively, the model-based optimal control trajectories can be determined by tracing at least one measured variable and tracking the remaining state variables by means of model-based forward control.

The path control can advantageously be carried out as fully automatic or else as semi-automatic.

In connection with a regulation for load oscillation damping, this results in an optimized movement behavior with reduced residual oscillation and lower pendulum deflections while driving. The required sensors on the crane can be reduced without the regulation of load oscillation damping. Fully automatic operation, in which the start and finish point are fixed, can be implemented, as can hand lever operation, which is referred to below as semi-automatic operation.

In contrast to WO 02/32805 A1, the desired functions are now generated in the present invention in such a way that the dynamic behavior of the crane is taken into account even before the control is switched on. The control only has the task of compensating for model deviations and disturbance variables, which results in improved driving behavior. In addition, if the positional accuracy and the tolerable residual oscillation allow, the control can be omitted entirely and the crane can be operated with this optimized control function. However, the behavior will be somewhat less favorable than when operating with the control, since the model does not agree in all details with the actual circumstances. The process provides two modes of operation. The hand lever operation, in which the operator specifies a target speed of the load through the hand lever deflection, and the fully automatic operation, in which the start and destination points are specified.

In addition, the optimized control function calculation can be operated alone or in connection with a regulation for load oscillation damping.

Further details and advantages of the invention will be explained with reference to an embodiment shown in the drawing. As a typical representative of a crane or excavator of the type mentioned at the outset, the invention is described here using a mobile harbor crane.

Show it:

Fig. 1: Basic mechanical structure of a mobile harbor crane

Fig. 2: Interaction of hydraulic control and path control with module for optimized movement control as a control function of the crane

Fig. 3: Structure of the path control with module for optimized motion control with regulation for load pendulum damping

Fig. 4: Structure of the path control with module for optimized motion control as a control function without regulation for load swing damping (if necessary with subordinate position controllers for the drives)

Fig. 5: Mechanical structure of the slewing gear and definition of model variables

Fig. 6: Mechanical structure of the luffing gear and definition of model variables

Fig. 7: Erection kinematics of the luffing gear Fig. 8: Flow chart for the calculation of the optimized control variable in fully automatic operation

Fig. 9: Flow chart for the calculation of the optimized control variable in semi-automatic operation

Fig. 10: Exemplary generation of reference variables in fully automatic operation

Fig. 11: Exemplary time profiles of control variables and control variables in hand lever operation

The basic mechanical structure of a mobile harbor crane is shown in FIG. The mobile harbor crane is usually mounted on a chassis 1. To position the load 3 in the work area, the boom 5 can be tilted by the angle φ _A with the hydraulic cylinder of the luffing gear 7. The rope length Is can be varied with the hoist. The tower 11 enables the rotation of the boom by the angle φ _D about the vertical axis. With the load swivel 9, the load at the target point can be rotated by the angle φ _red .

Fig. 2 shows the interaction of hydraulic control and path control 31 with a module for optimized movement control. As a rule, the mobile harbor crane has a hydraulic drive system 21. An internal combustion engine 23 feeds the hydraulic control circuits via a transfer case. The hydraulic control circuits each consist of a variable displacement pump 25, which is controlled via a proportional valve in the pilot control circuit, and a motor 27 or cylinder 29 as the working machine. A flow rate Q _F D, QFA, QFL, QFR is set via the proportional valve independently of the load pressure. The proportional valves are controlled via the signals UstD, Us _A , UstL, Ust _R. The hydraulic control is usually equipped with a subordinate flow control. It is essential that the control voltages usto, UstA, Ust UstR at the proportional valves are converted by the subordinate flow control into flow rates QFD, QFA, QFL, QFR proportional to this in the corresponding hydraulic circuit.

The structure of the path control is now shown in FIGS. 3 and 4. Figure 3 shows the path control with the module for optimized motion control with Regulation for load oscillation damping and Figure 4 the path control with the module for optimized motion control without regulation for load oscillation damping. This load sway damping can be designed, for example, according to PCT / EP01 / 12080. Therefore, the content disclosed there is fully incorporated into this document.

It is now essential that the time functions for the control voltages of the proportional valves are no longer derived directly from the hand levers, for example via ramp functions or a path planner that takes into account the kinematic restrictions of the system, but are calculated in path control 31 such that when the crane is moved little or no pendulum movements of the load occur and the load follows the desired path in the work area. That When calculating the optimized control variable, not only the kinematic description but also the dynamic description of the system is taken into account.

The input variables of the module 37 are a target point matrix 35 for the position and orientation of the load, which in the simplest case consists of the start and end point. The position is usually described for slewing cranes by polar coordinates (Ψ _LD , r _LA ,) ■ Since this does not completely describe the position of the extended body (e.g. a container) in space, another angle size can be added (angle of rotation γ _L around the Vertical axis, which is parallel to the rope). The target position variables φwziei, r aa, kiei, iei are summarized in the vector gziei.

The input variables of the module 39 are the current positions of the hand levers 34 for controlling the crane. The deflection of the hand lever corresponds to the desired target speed of the load in the respective direction of movement. Accordingly, the target speeds ψ LDTarget ^zurf] Target speed ^vector q summarized. In the case of the module for optimized motion control in fully automatic operation 37, the optimal control problem can be solved from this information about the stored model for describing the dynamic behavior and the selected boundary and secondary conditions. The output variables are then the time functions u _{out> D} , u _out , _A , u _0Ut , ι, u _0UtιR , which are at the same time input variables of the subordinate regulation for load oscillation damping 36 or the subordinate regulation for position or speed of the crane 41. Also a direct control 41 of the crane without subordinate regulation is possible if the equations in 37 are formulated accordingly. In fully automatic operation, the hand lever value can be used to change the secondary condition of the maximum permissible speed in the optimal control problem. This is particularly advantageous in that even in fully automatic operation, the user has the possibility of influencing the speed of the fully automatic process online. The changes made are immediately adopted and taken into account in the next run of the algorithm.

In the case of the module for optimized movement control in semi-automatic operation 39, however, the current system status, in addition to the boundary and secondary conditions, is required as further information for information about the currently desired target speed of the load through the hand lever position. Therefore, in semiautomatic mode, the measured variables of the position of the crane and the load must be continuously fed back to the module 39. In detail, these are:

- slewing gear angle φ _D ,

- luffing gear angle φ _A ,

- rope length l _s , and

- relative load hook position c

and the angles to describe the load position:

- tangential rope angle φ _St ,

- radial rope angle φ _Sr , and - absolute rotation angle of the load γ _L.

In particular, the last-mentioned measured variables for rope angle and absolute rotation angle of the load can only be measured with great effort. For the realization of a load swing damping, however, these are absolutely necessary to compensate for disturbances. This means that very high positioning accuracy can be achieved with low residual sway even under the influence of disturbance variables (such as wind). In the case of Fig. 3, these sizes are all available.

However, if the method is used in a system in which there are no sensors for the rope angle measurement and the absolute rotation angle, these variables must be reconstructed for the module for optimized motion control in semi-automatic operation. Model-based estimation methods 43, such as observer structures, are suitable here. In this case, the missing state variables are estimated or tracked from the measured variables of the crane position and the control functions u _0UtιD , u _0U t, A, u _out , u _out , κ in a stored dynamic model (see FIG. 4).

The basis for the process of optimized motion control is the process of dynamic optimization. To do this, the dynamic behavior of the crane must be mapped in a differential equation model. Either the Lagrangian formalism or the Newton-Euler method can be used to derive the model equations.

In the following, several possible model approaches are presented. 5 and 6, the definition of the model variables is carried out first. For better clarity, FIG. 5 shows the model variables, the model variables related to the rotary movement, and FIG. 6 shows the model variables for the radial movement.

5 is explained in detail first. What is important here is the relationship shown there between the rotational position φ _{D of} the crane tower and the load position ΨLD in the direction of rotation. The load rotation angle position corrected by the pendulum angle is then calculated

Ψ _L D (1)

Is is the resulting rope length from the boom head to the center of the load. Ψ is the current righting angle of the luffing gear, l _A is the length of the boom, φ _S t is the current rope angle in the tangential direction (since φst is small, can be approximated).

The dynamic system for the movement of the load in the direction of rotation can be described by the following differential equations.

JT + { _JÄ Z + ^m A ^s A + m _L fy cos ² φ _A ψ _D + m _L l _A l _s cόsφ _A φ _st + b _D φ _D = M _MD - ^ (2) m _L l _A l _s cos ^ φ _D + m _L i φ _st + m _L gl _s φ _st = 0 (3)

designations:

m _L load mass ls rope length m _A mass of the boom

JAZ moment of inertia of the boom with respect to the center of gravity at

Rotation around the vertical axis

IA length of the boom

SA center of gravity of the boom

JT mass moment of inertia of the tower b _D viscous damping in the drive

M _M D drive torque

M _RD friction torque (2) essentially describes the equation of motion for the crane tower with jib, taking into account the retroactive effect of the load swing. (3) is the equation of motion that describes the load oscillation by the angle φs _t , the excitation of the load oscillation being caused by the rotation of the tower, the angular acceleration of the tower or an external disturbance expressed by the initial conditions for these differential equations.

The hydraulic drive is described by the following equations.

^M MD ^{= i} D - zπ PD

Q.FD - ^K PD ^and StD

i _D is the gear ratio between the engine speed and the rotating speed of the tower, V is the absorption volume of the hydraulic motors, Δ o is the pressure drop across the hydraulic drive motor, ß is the oil compressibility, QFD is the flow rate in the hydraulic circuit for turning and K _PD is the proportionality constant, which indicates the relationship between the flow rate and the control voltage of the proportional valve. Dynamic effects of the subordinate flow control are neglected.

As an alternative to this, the transmission behavior of the drive units can be represented by an approximate relationship as a delay element of the 1st or higher order instead of using equation 4. The approximation with a delay element of the 1st order is shown below. Then the transfer function results

sΦ _D (s) = ~ ^ -U _StD (s) (5)

'- ^{+ 1} DAιιtr ^S or in the time domain ψ _D - ^~ - _D ^^ - ^ _StD (6)

* ^■ DAntr DAntr

In this way, an adequate model description can also be built from equations (6) and (3); Equation (2) is not needed. T _DAntr is the approximate (time constant determined from measurements to describe the deceleration _{behavior of} the drives. K _{PDAntr is} the resulting amplification between the control voltage and the resulting speed in the stationary case.

With an insignificant time constant with regard to the drive dynamics, a proportionality between the speed and the control voltage of the proportional valve can be assumed directly.

ΨD = ^K PDdirekt ^u StD ( ⁷ )

Here, too, an adequate model description can be built from equations (7) and (3).

For the radial movement shown in FIG. 6, the equations of motion can be set up analogously to equations (2) and (3). 6 gives explanations for the definition of the model variables. What is important here is the relationship shown there between the righting angle position φ _{A of} the boom and the load position in the radial direction ΓLA

^r LA = ^l A ^C0S PA + ^l S ⁽ Psr ( ⁸ )

The dynamic system can then be described by applying the Newton-Euler method using the following differential equations. φ _5r

+ b _A φ _A - m _A s _A g smφ _A - <p _A (9) M _M A - ^M RA - ^m A ^s A g ∞sφ ^

- m _L l _A l _s sinφ ^ φ ^ + m _L i <p _sr + m _L l _s g φ _sr = m _L l _s φ _j (l _s φ _sr + l _A cosφ ^)

(10)

designations:

m _L load mass ls rope length m _A mass of the boom

JAY mass moment of inertia with respect to the center of gravity when rotating around a horizontal axis including the drive train

IA length of the boom

SA center of gravity of the boom b _A viscous damping

M _M A drive torque

MRA friction torque

Equation (9) essentially describes the equation of motion of the boom with the driving hydraulic cylinder, whereby the reaction is taken into account by the swaying of the load. This also takes into account the portion affected by the gravity of the boom and the viscous friction in the drive. Equation (10) is the equation of motion that describes the load oscillation φs _r , the excitation of the vibration being caused by the erection or inclination of the boom via the angular acceleration of the boom or an external disturbance, expressed by the initial conditions for these differential equations. The term on the right side of the differential equation describes the influence of the centripetal force on the load when the load rotates with the slewing gear. This describes a problem that is typical of a slewing crane, since it provides a coupling between the slewing gear and the luffing gear. clear this problem can be described by the fact that a slewing gear movement with a quadratic rotational speed dependency also causes an angular deflection in the radial direction.

The hydraulic drive is described by the following equations.

^M MA = ^F Cyl ^d b ^{C0S (} Pp (PA)

^F cyl = Pzyl ^A cyl

pcyl VZYL

QFA = ^κ PA ^u stA

F _Z yi is the force of the hydraulic cylinder on the piston rod, pz _y ι is the pressure in the cylinder (depending on the direction of movement on the piston or ring side), Az _y ι is the cross-sectional area of the cylinder (depending on the direction of movement on the piston or ring side), ß is the oil compressibility, V _Zy ι is the cylinder volume, QFA is the flow rate in the hydraulic circuit for the luffing gear and K _PA is the proportionality constant, which indicates the relationship between flow rate and control voltage of the proportional valve. Dynamic effects of the subordinate flow control will be; neglected. With oil compression in the cylinder, half of the total volume of the hydraulic cylinder is assumed to be the relevant cylinder volume. z _Zy ι, z _Zy ι smd the position or the speed of the cylinder rod. Like the geometric parameters db and φ _p, these are dependent on the righting kinematics.

In Fig. 7 the erection kinematics of the luffing gear is shown. As an example, the hydraulic cylinder is anchored to the crane tower above the pivot point of the boom. The distance d _a between this point and the pivot point of the boom can be taken from design data. The piston rod of the hydraulic cylinder is attached to the boom at a distance d _b . The correction angle φo takes into account the deviations of the fastening points from the boom or tower axis and is also known from design data. The following relationship between the righting angle φ _A and the hydraulic cylinder position z _{Zy / can be} derived from this.

^Z cyl = ^d l + ^d l ^{~ 2d} b ^d a ^{sin (~} <Pθ) (12)

Since only the righting angle φ _{A is a} measured variable, the inverse relation of (12) and the dependency between piston rod speed z _cyl and righting speed φ _{A are} also of interest.

dφ _Ä . 4 ^d a ^{+ d} b - ^2d b ^d a ^sm (P _A - <PÖ). v

<PΛ = - dz -, ^z z ≠ = - d -z _b -d, _a cos; (φ _A - φ ₀ ) ^z z _y ι (14)

To calculate the effective moment on the boom, the projection angle φ _p must also be calculated.

Alternatively, instead of the hydraulic equations (11), an approximation for the dynamics of the drives can be provided with an approximate relationship as a delay element of the 1st or higher order. This gives you an example

sZ _≠ (s) = - ^ - U _slA (s) (16)

or in the time domain

In this way, an adequate model description can also be built from equations (17), (14) and (10); Equation (9) is not required. T _ΛAntr is the approximate (time constant determined from measurements to describe the deceleration _{behavior of} the drives. K _PAAnt r the resulting gain between the control _voltage and the resulting speed in the stationary case. With an insignificant time constant with regard to the drive _dynamics, a proportionality between the speed and the control _{voltage of the proportional valve} can be assumed directly become.

^z Zyl = ^K PAdirekt ^u StA 0 ⁸ )

Here, too, an adequate model description can be constructed from equations (18), (10) and (14).

The last direction of movement is the turning of the load on the load hook itself by the load slewing gear. A corresponding description of this regulation results from the German patent application DE 100 29 579 dated June 15, 2000, the content of which is expressly referred to here. The rotation of the load is carried out via the load swiveling mechanism arranged between a bottom block hanging from the rope and a load suspension device. Torsional vibrations are suppressed. In most cases, this means that the load, which is not rotationally symmetrical, can be picked up in an accurate position, moved and offset by a corresponding bottleneck. Of course, this direction of movement is also integrated in the module for optimized movement control, as is shown for example on the basis of the overview in FIG. 3. In a particularly advantageous manner, the load can already be moved into the correspondingly desired swiveling position by means of the load swiveling mechanism after being picked up during transport through the air, the individual pumps and motors being controlled synchronously here. Optionally, a mode for a rotation angle-independent orientation can also be selected. This results in the equation of motion listed below. The variable designation corresponds to DE 100 29 579 from June 15, 2000. No linearization was carried out.

(®LC + ®UC) J drill (19)

Differential equations for the description of the drive dynamics for improving the function as for the rotary movement can now also be taken into account for the load slewing gear. A detailed description is not to be given here.

The dynamics of the hoist are neglected, since the dynamics of the hoist movement is fast compared to the system dynamics of the load swinging of the crane. As with the load slewing gear, however, the corresponding dynamic equations for describing the hoist dynamics can be supplemented at any time if required.

The remaining equations for describing the system behavior are now to be brought into a nonlinear representation of state space according to Isidori, Nonlinear Control Systems Springer Verlag 1995. This is done, for example, based on equations (2), (3), (9), (10), (14), (15). The rotation axis of the load around the vertical axis and the hoist axis is not taken into account in this example that follows. However, it is not difficult to include these in the model description. For the present application, a crane without an automatic load slewing gear is assumed; the lifting gear is operated manually by the crane operator for safety reasons. Accordingly you get:

x = a (x) + b (x) u representation of the state space:, (20) y = £ ( ^χ ) with: State vector: ^χ = [φ _D ΦD ΨA ΨA Ψst Φst <Psr Φ _Ä - Pz _y ιf

(21)

Control variable: H = [ ^u st _D ^U S _I AY (22)

Output variable: y = [φ _LD r _LA ] (23)

The vectors a (χ), b (χ), c (x) result from transforming the equations (2) - (4), (8) - (15).

In the operation of the module for optimized motion control without subordinate load oscillation damping, the problem arises in semi-automatic operation that state x must be completely present as a measurement vector. However, since no pendulum angle sensors are installed in this case, the pendulum angle variables φs _t> Ψst _> ΨSr _> Ψsr ^from the control variables UΆD, u _StA and the measured variables ψD _> Ψ'D _> ΨA _> ΨA _> Pzyl have to be reconstructed as examples become. For this purpose, the nonlinear model is linearized according to equation (20-23) and, for example, a parameter-adaptive state observer (see also FIG. 4 block 43) is designed. In the case of reduced accuracy requirements, the condition of the rope angle values can also be simplified, based on the model equations and the known courses of the input values and the measurable state variables.

The target curves for the input signals (control variables) u _stD (t), u _stA (t) are solved by solving an optimal control problem, i.e. a task of dynamic optimization. For this purpose, the intended reduction of the load sway is recorded in a target function. Boundary conditions and trajectory restrictions of the optimal control problem result from the railway data, the technical restrictions of the crane system (e.g. limited drive power, as well as restrictions due to dynamic load torque restrictions to prevent the crane from tipping) and expanded requirements for the movement of the load. For example, with the method described below, it is possible for the first time to precisely predict in advance the rail corridor that the load requires when the calculated control functions are activated. This provides automation options that were not previously possible. Such a formulation of the optimal control problem is given in the following by way of example both for the fully automatic operation of the system with a predetermined start and end point of the load path and for hand lever operation.

In the case of fully automatic operation, the entire movement from the specified start to the specified destination is considered. In the target functional of the optimal control problem, the load pendulum angles are evaluated quadratically. The minimization of this target functional therefore provides a movement with reduced load oscillation. An additional evaluation of the load pendulum angle velocities with a time-variant penalty (increasing at the end of the optimization horizon) results in a calming of the load movement at the end of the optimization horizon. A regularization term with a quadratic evaluation of the amplitudes of the control variables can favorably influence the numerical condition of the task.

J = jfe (0 + () + Pu (stD (> «SU (0)) ()

Ό

Designations: to Specified start time t _f Specified end time p (t) Time variant penalty coefficient

Pu (ustD, UstA) regularization term (quadratic evaluation of the control variables)

In hand lever operation, however, the entire load movement between the specified start and finish point is not considered, but the optimal control problem is based on a time window that moves with the dynamic process [t ₀ , t _f ] considered. The start time of the optimization horizon t _Q is the current one

Time, and in the optimal control problem, the dynamics of the crane system in the forecast horizon up to t _{f is} considered. This time horizon is an essential tuning parameter of the method and is limited by the period of oscillation of the load pendulum movement.

In the target function of the optimal control problem, in addition to the intended reduction in load swing, the deviation of the actual load speed from the target speeds specified by the hand lever positions must be taken into account.

ΦLD (- ΦLD, I +

J = 1 PLD (SCII J + PIA ^ ^' LA (0 ^~ ^ A dt (25) ⁱ +' φ 1 l (+ φl (0 + P (S, (+ Φl () + p _u ⁽ um (0, u _stA (t))

Designations: t ₀ Specified start time of the optimization horizon t _f Specified end time of the forecast period

PL _D weighting coefficient deviation of load angular velocity φ _LD set load rotational speed given by hand lever position PIA weighting coefficient deviation radial load speed r _{LA soU} radial load _{speed given} by hand lever position

In fully automatic operation with a given start and finish point, the boundary conditions for the optimal control problem result from their coordinates and the requirements for a rest position in the start and finish position. ΨD fto) ⁼ Φofi »<PD (f _f ) = <PD Φι _> (t ₀ ) = 0, φ _D (t _f ) = 0

Φ _A (t ₀ ) = 0, φ _A (t _f ) = 0 (26) <Ps _t (o) = ⁰ ><Pst ( ^t f) = ⁰ φ _Sr ( ^t ₀ ) = ⁰ > ⁽ PsΛt _f ) = ^Q

Designations: φ _Dι o Starting point slewing gear _angle

Φo _{, f} end point slewing gear angle

Γ _L A _{, O} start point load position rt_, f end point load position

The boundary conditions for the pressure in the cylinder result from the stationary values at the start and end point according to equation (11).

In contrast, in hand lever operation, the boundary conditions must take into account that the movement does not start from a rest position and generally does not end in a rest position. The boundary conditions at the start of the optimization _horizon t ₀ result from the current system state χ (t _ϋ ), which is measured or, via a model carried, from the control _variables u _SιtD , u _{S! A} and the measured variables §D 'D _> $ A _> '$ A _> PZyl is reconstructed using a parameter-adaptive state observer.

The boundary conditions at the end of the optimization horizon t _f are free.

Due to the technical parameters of the crane system, there are a number of restrictions that must be taken into account in the optimal control problem regardless of the operating mode. So the drive power is limited. This can be about A maximum flow rate in the hydraulic drives can be described and included in the optimal control problem via amplitude restrictions for the control variables.

- u stD, max <u _stD (t) ≤ u stD, mm.

(27) ≤ u _SfA (t) ≤ u _s

In order to avoid stresses on the system due to abrupt load changes, the consequences of which are not recorded in the simplified dynamic model described above, the rate of change of the control variables is limited. The mechanical stress can thus be limited in a defined manner.

^U StD, max - ^U StD (≤ ^u StD, max _{/ <} -> o _\

^U StA, max - ^U StA ~ ^U SlA, nmx

In addition, it can be required that the control variables as functions of time should be constant and have constant first derivatives with respect to time.

The erection angle is limited due to the crane construction

designations:

UstD, maχ Maximum value control function slewing gear

" _{ÄD, Π»} Maximum rate of change control function slewing gear

UstA, max maximum value control function ^luffing gear ^ύ s _{tΛ, ma.} Maximum rate of change control function luffing gear

.Phi.A. _{WIΠ Minimum} erection _angle value max. Maximum erection _angle value Additional restrictions result from further requirements regarding the movement of the load. In fully automatic operation, in which the entire load movement from the start to the destination is considered, a monotonous change in the angle of rotation can be required.

Φ _D (t) {φn (t _f ) ~ φ _D (t ₀ )) ≥ ^Q (30)

Railway corridors can be included in the calculation of the optimal control in the fully automatic as well as in the hand lever operation by means of the analytical description of the permissible load positions with the help of inequality restrictions.

Smm ≤ g (<PLD (0, ^r LA (0) ≤ g _m , x (31)

With the help of these inequality conditions, a path is forced inside a permissible range, here the rail corridor, the limits of this permissible range limit the load movement and thus represent 'virtual walls'.

If the path to be traveled does not only consist of the start and finish point, but if further points have to be traveled in a given order, this can be included in the optimal control problem by internal boundary conditions.

ΨD (', ^■ ) = ΨD, i »ΨA (U) = (32)

Designations: tj (free) time of reaching the specified path point i φ _DιJ rotation angle _{coordinate of} the specified path point i

JTIA) Radial position of the given path point i The claim is not tied to a specific method for numerically calculating the optimal controls. The claim expressly also relates to an approximate solution to the optimal control problems specified above, in which only a solution of sufficient (not maximum) accuracy is determined in view of a reduced computing effort when using online. In addition, for reasons of effectiveness, a number of the hard constraints formulated above (boundary conditions or trajectory inequality constraints) can be treated numerically as a soft constraint by evaluating the constraint violation in the target functional.

As an example, however, the numerical solution using multi-level control parameterization is to be explained here.

For an approximate numerical solution of the optimal control problem, the optimization horizon is discretized.

t ₀ = t ° <t '<•• <t ^κ = t _t (33)

The length of the partial intervals τ, ^ ⁺ can be adapted to the dynamics of the problem. A larger number of subintervals usually leads to an improvement of the approximation solution, but also to an increased calculation effort.

At each of these subintervals, the time profile of the control variables is approximated by an approach function U ^k with a fixed number of parameters u ^k (control parameters).

u (t) _* u _app (t) t ^k ≤ t ≤ t ^M (34)

Now the state differential equation of the dynamic model can be numerically integrated and the target function can be evaluated, using the approximated time profiles instead of the control variables. As a result, the target functional is obtained as a function of the control parameters u ^k , k = 0, ..., K-1. The Boundary conditions and the trajectory restrictions can also be understood as functions of the control parameters.

In this way, the optimal control problem is approximated by a nonlinear optimization problem in the control parameters, whereby the target function calculation and the evaluation of the limitation of the nonlinear optimization problem each require the numerical integration of the dynamic model taking into account the approximation approach according to equation (34). This limited nonlinear optimization problem can now be solved numerically, for which purpose a conventional method of sequential quadratic programming (SQP) is used, in which the solution of the nonlinear problem is determined via a sequence of linear quadratic approximations. The efficiency of the numerical solution can be increased considerably if, in addition to the control parameters of the interval k, the initial state is also increased

x ^k x (t ^k ), k = ö, ..., K (35)

of the respective interval is considered as a variable of the nonlinear optimization problem. The continuity of the approximated state trajectories must be ensured by suitable equation restrictions. This increases the dimension of the nonlinear optimization problem. However, there is a considerable simplification in the coupling of the problem variables and also a strong structuring of the nonlinear optimization problem. Therefore, the solution effort in many cases drops considerably, provided that the problem structure is used appropriately in the solution algorithm.

An additional significant reduction in the computational effort to solve the optimal control problem is achieved by approximation using linearization of the system equations. The original nonlinear state differential equations and algebraic output equations (20) are linearized along an initially arbitrary system trajectory (x _ref (t), u _ref (t)) that fulfills the state differential equations. Δx = A (t) Δx + B (t) Δu

(36) ky = C (t) Δx

The variables Ax, Δu, Δy denote the deviations from the reference curve of the respective variable

Aχ = xx _ref , Δu = u -u _ref , y = yy _ref x _ιef = a (x _ιef ) + b (x, _ef ) ^■ u _ref (37)

The time-variant matrices A (t), B (t), C (t) result from the Jacobi matrices

dc (x _rpf (t))

_A (t) b ( _{X> ef} (t)), c (= ^{re /} ; .. (38)

Now the optimal control task in the variables

Formulated Aχ, Δu, there is a limited linear-quadratic optimal control problem. With a suitable choice of the application functions U ^k , the state differential equation can be solved analytically via the associated equation of motion at each subinterval [t, ^ ¹ ], and the complex numerical integration is eliminated.

The optimal control task is thus approximated by a finite-dimensional quadratic optimization problem with linear equation and inequality restrictions, which can be solved numerically using an adapted standard procedure. The numerical effort for this is again significantly less than for the nonlinear optimization problem described above. The linearization approach described is particularly suitable for the approximate solution of the optimal control problems with hand lever operation, because in this case the inaccuracies caused by the linearization have a smaller effect due to the shorter optimization horizon (time window [to.ty]) and the other with the in each case calculated previous time step suitable reference trajectories are available for optimal control and status changes.

As a solution to the optimal control problem, the optimal time profiles of both the control variables and the state variables of the dynamic model are obtained. When operated with a subordinate control, these are activated as manipulated and reference variables. Since the dynamic behavior of the crane is taken into account in these target functions, the control only has to compensate for disturbance variables and model deviations.

In the case of operation without a subordinate control, on the other hand, the optimal courses of the control variables are directly applied as control variables.

Furthermore, the solution to the optimal control problem provides a prognosis of the path of the oscillating load, which can be used for extended measures for collision avoidance.

8 shows the flow chart for the calculation of the optimized control variable in fully automatic operation. This is supported by module 37 from FIG. 3. Starting from the starting and target points of the load movement determined by the target point matrix, the optimal control problem is defined by including the specification of the permissible range and the technical parameters. The numerical solution of the optimal control problem provides optimal time profiles of the control and state variables. In the case of a subordinate regulation for load oscillation damping, these are applied as manipulated and command variables. Alternatively, a realization without subordinate regulation - then with direct connection of the optimal control functions to the hydraulics - can be realized.

Fig. 9 shows the interaction of state reconstruction and calculation of the optimal control in the case of hand lever operation. The state of the dynamic crane model is tracked using the available measured variables. By solving the optimal control problem, such time profiles of the control functions are determined which - based on this current state - when the Reduced load swing brings the load speed up to the setpoints specified by the hand lever.

Once an optimal control has been calculated, it is not implemented over the full time horizon [t ₀ , t _f ], but continuously adapted to the current system status and the current setpoints. The frequency of this adaptation is limited by the computing time required to recalculate the optimal control.

10 shows exemplary results for optimal time profiles of the control variables in fully automatic operation. A time horizon of 30 s was specified. The control functions are continuous functions of time with continuous 1st derivatives.

11 shows exemplary time profiles of control variables and control variables in simulated hand lever operation. The setpoints for the load speed (the hand lever specifications) are varied in the form of staggered rectangular pulses. The optimal control is updated with a sampling time of 0.2 s.

Claims

1.Crane or excavator for handling a load hanging on a load rope with a slewing gear for rotating the crane or excavator, a luffing mechanism for raising or tilting a boom and a hoist for lifting or lowering the load suspended on the rope with a drive system .

marked by

a path control (31) whose output variables (u _0U tD, u _0U tA, u _0U tL, u _0U tR) are used directly or indirectly as input variables in the regulation for the position or the speed of the crane (41) or excavator, the Command variables for the control in the path control (31) are generated so that there is a load movement with minimized pendulum deflections. - 2 -

2. Crane or excavator according to claim 1, characterized in that in the path control (31) model-based optimal control trajectories are calculated and updated online.

3. Crane or excavator according to claim 2 characterized by model-based optimal control trajectories based on a model linearized around reference trajectories.

4. Crane or excavator according to claim 2 characterized by model-based optimal control trajectories based on a non-linear model approach.

5. Crane or excavator according to one of claims 1 to 4 characterized by model-based optimal control trajectories with feedback from all state variables.

6. Crane or excavator according to one of claims 1 to 4 characterized by model-based optimal control trajectories with feedback of at least one measurement variable and an estimate of the remaining state variables.

7. crane or excavator according to one of claims 1 to 4 characterized by model-based optimal control trajectories with feedback of at least one measurement variable and tracking of the remaining state variables by model-based forward control.

8. Crane or excavator according to one of claims 1 to 7, characterized in that the path control (31) can be carried out as fully automatic or as semi-automatic.

9. Crane or excavator according to one of the preceding claims, characterized in that a target point matrix (35) for the position and orientation of the load can be entered in the path control (31) as an input variable. - 3 -

10. Crane or excavator according to one of the preceding claims, characterized in that the target point matrix (35) consists of the start and end point.

11. Crane or excavator one of the preceding claims, characterized in that in the case of a semi-automatic operation, the desired target speed of the load can also be entered by the position of the hand lever (34) in the path control (31).

12. Crane or excavator according to claim 11, characterized in that the measured variables of the positions of the crane and load can be detected in semiautomatic operation and can be traced back into the path control (31).

13. Crane or excavator according to claim 11, characterized in that the positions of crane and load in a module for the model-based estimation method (43) can be estimated and returned to the path control (31) in semi-automatic operation.

14. Crane or excavator according to one of the preceding claims, characterized in that the output variables (u _0U tD, u _0U tA, u _out L, u _0Ut ) are first performed in a subordinate control with load swing damping.

15. Crane or excavator according to claim 14, characterized in that the load swing damping has a path planning module, a centripetal force compensation device and at least one axis controller for the slewing gear, an axis controller for the luffing gear, an axis controller for the lifting mechanism and an axis controller for the pivoting mechanism.

16. Crane or excavator according to one of the preceding claims, characterized in that by means of the path control (31) the movement path of the load can be determined such that predetermined free areas cannot be left by the oscillating load.