EP1326798B1 - Kran oder bagger zum umschlagen von einer an einem lastseil hängenden last mit lastpendelungsdämpfung - Google Patents

Kran oder bagger zum umschlagen von einer an einem lastseil hängenden last mit lastpendelungsdämpfung Download PDF

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Publication number
EP1326798B1
EP1326798B1 EP01987730A EP01987730A EP1326798B1 EP 1326798 B1 EP1326798 B1 EP 1326798B1 EP 01987730 A EP01987730 A EP 01987730A EP 01987730 A EP01987730 A EP 01987730A EP 1326798 B1 EP1326798 B1 EP 1326798B1
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EP
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Prior art keywords
load
crane
control
excavator according
controller
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German (de)
English (en)
French (fr)
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EP1326798A1 (de
Inventor
Oliver Sawodny
Jörg KÜMPEL
Cristina Tarin-Sauer
Harald Aschemann
E. P. Hofer
Klaus Schneider
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Liebherr Werk Nenzing GmbH
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Liebherr Werk Nenzing GmbH
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C13/00—Other constructional features or details
    • B66C13/04—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack
    • B66C13/06—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for minimising or preventing longitudinal or transverse swinging of loads
    • B66C13/063—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for minimising or preventing longitudinal or transverse swinging of loads electrical
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C13/00—Other constructional features or details
    • B66C13/04—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack
    • B66C13/08—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for depositing loads in desired attitudes or positions
    • B66C13/085—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for depositing loads in desired attitudes or positions electrical

Definitions

  • the invention relates to a crane or excavator for handling a load suspended on a load rope, which has a computer-controlled control for damping the load oscillation.
  • the invention is concerned with the load swing damping in cranes or excavators which allows movement of the load suspended on a rope in at least three degrees of freedom.
  • Such cranes or excavators have a slewing gear, which can be mounted on a chassis, which serves for rotating the crane or excavator.
  • a luffing mechanism for erecting or tilting a boom is available.
  • the crane or excavator includes a hoist for lifting and lowering the load suspended on the rope.
  • Such cranes or excavators are used in various designs. Exemplary here are mobile harbor cranes, ship cranes, offshore cranes, crawler cranes and crawler excavators.
  • DE 127 80 79 describes an arrangement for the automatic suppression of oscillations of a hanging by means of a rope at a level movable rope suspension point load on movement of Seilauf fatigues in at least one horizontal coordinate, in which the speed of Seilauf fatigues in the horizontal plane by a control loop is influenced in dependence on a derived from the deflection angle of the load cable against the Endlot size.
  • DE 20 22 745 shows an arrangement for the suppression of pendulum vibrations of a load suspended by means of a rope on the cat of a crane, the drive of which is equipped with a speeding device and a travel control device, with a control arrangement which takes the cat into consideration during the oscillation period of a first part of the path traveled by the cat so accelerated and delayed during a last part of this way so that the movement of the cat and the vibration of the load at the destination are equal to zero.
  • DE 322 83 02 proposes to control the speed of the drive motor of the trolley by means of a computer so that the trolley and the load carrier are moved during the steady drive at the same speed and the pendulum damping be achieved in no time.
  • the computer known from DE 322 83 02 works according to a computer program for solving the differential equations applicable to the undamped two-mass vibration system formed from trolley and load body, whereby the coulomb and speed-proportional friction of the cat or bridge drives are not taken into account.
  • the known from DE 39 33 527 method for damping of load oscillations oscillations comprises a normal speed position control.
  • DE 691 19 913 deals with a method for controlling the adjustment of a swinging load, in which the deviation between the theoretical and the actual position of the load is formed in a first control loop. This is derived, multiplied by a correction factor and added to the theoretical position of the mobile carrier. In a second control loop, the theoretical position of the mobile carrier is compared with the actual position, multiplied by a constant and added to the theoretical speed of the mobile carrier.
  • DE 44 02 563 deals with a method for the regulation of electric traction drives of hoists with a load suspended from a rope, the equations describing the dynamic behavior of the setpoint course of the speed the trolley generated and gives to a speed and current controller. Furthermore, the computing device can be extended by a position controller for the load.
  • the method of DE 44 02 563 in the basic version also requires at least the crane paw speed. Also in DE 20 22 745 several sensors are required for the load oscillation damping. Thus, in DE 20 22 745 at least one speed and position measurement of the trolley must be made.
  • the object of the present invention is to develop a crane or excavator for transferring from a load suspended on a load rope, which can move the load at least over three degrees of freedom of movement, such that during the movement actively occurring pendulum movement of the load can be damped and the load can be performed as accurately on a given path.
  • this object is achieved by a crane or excavator with the features of claim 1. Accordingly, the crane or excavator on a computer-controlled control for damping the load oscillation, which has a Bahn doctrinesmodul, a Zentripetalkraftkompensations announced and at least one axis controller for the slewing, an axle controller for the luffing and an axis controller for the hoist.
  • the path control with active damping of the pendulum motion is based on the basic idea of initially modeling the dynamic behavior of the mechanical and hydraulic system of the crane or excavator in a dynamic model based on differential equations. Based on this dynamic model, a feedforward control can be designed which, under these idealized conceptions of the dynamic model, suppresses oscillations when the load is moved by the slewing gear, luffing gear and hoist and guides the load exactly in the given path.
  • Prerequisite for the precontrol is first the generation of the web in the work space, which is made by the path planning module.
  • the path planning module generates the path, which is given in the form of time functions for the load position, speed, acceleration, jerk and possibly the derivative of the jerk to the feedforward, from the specification of the desired speed proportional to the deflection of the hand lever in the case of semi-automatic operation or from set points in the case of fully automatic operation.
  • the system of feedforward and trajectory planning module may be assisted by a state controller in the event of large deviations from the idealized dynamic model (e.g., due to disturbances such as wind effects, etc.). This then performs at least one of the measured variables: pendulum angle in the radial and tangential direction, Aufrichtwinkel, rotation angle, boom bending in the horizontal and vertical direction and their derivative and the load mass back.
  • a decentralized control concept is based on a spatially decoupled dynamic model in which an independent control algorithm is assigned to each individual movement direction.
  • the present invention provides a particularly efficient and easy to maintain control for a crane or excavator of the type mentioned.
  • FIG. 1 The basic mechanical structure of a mobile harbor crane is shown.
  • the mobile harbor crane is usually mounted on a chassis 1.
  • To position the load 3 in the working space of the boom 5 can be tilted with the hydraulic cylinder of the luffing mechanism 7 by the angle ⁇ A.
  • the rope length l S can be varied.
  • the tower 11 allows the rotation of the boom by the angle ⁇ D about the vertical axis.
  • With the load pivot 9, the load at the target point can be rotated by the angle ⁇ red .
  • Fig. 2 shows the interaction of hydraulic control and path control 31.
  • 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 circuit, and an engine 27 or cylinder 29 as a working machine.
  • a delivery flow Q FD , Q FA , Q FL , Q FR is thus set, independent of the load pressure.
  • the Poportionalventile are controlled by the signals U StD, StA U, U StL, U st.
  • the hydraulic control is usually equipped with a subordinate flow control.
  • control voltages u StD , U StA , U StL , U StR are implemented on the proportional valves by the subordinate flow control in this proportional flow rates Q FD , Q FA , Q FL , Q FR in the corresponding hydraulic circuit.
  • the basis for this is a dynamic model of the crane with the help of this based on the sensor data at least one of the variables w v , w h , l S , ⁇ A , ⁇ D , ⁇ red , ⁇ Stm , ⁇ Srm , and the guide specifications q ⁇ target or q Goal this task is solved.
  • the overall structure of the web control 31 will be explained with reference to FIG.
  • the operator 33 inputs the target speeds or the target points either via the hand levers 35 at the control stations or via a set point matrix 37 which was stored in the computer in a previous trip of the crane.
  • the fully automatic or semi-automatic path planning module 39 or 41 calculates, taking into account the kinematic limitations (maximum speed, acceleration and jerk) of the crane, the time functions of the target load position with respect to the luffing, luffing, lifting and load swinging mechanism and their derivatives, which are in the vectors ⁇ Dref , ⁇ Aref , l ref , ⁇ Rref are summarized.
  • the setpoint position vectors are applied to the axis controllers 43,45,47 and 49, which are then evaluated by evaluating at least one of the sensor values ⁇ A , ⁇ D , W v , W h , l s , ⁇ red , ⁇ Stn , ⁇ Srm , (see 2) calculate the drive functions u StD , u StA , u StL , u StR for the proportional valves 25 of the hydraulic drive system 21.
  • a compensation trajectory for the luffing gear is generated from the guidance specification for the slewing gear in the module for Zentripetalkraftkompensation 150, so that the caused by the Zentripetalbevantung Auswandem of the load is compensated.
  • the compensation movement of the luffing gear is synchronized with the hoist movement.
  • a permissible cable deflection ⁇ SrZul due to the rotational movement is calculated for the luffing mechanism controller .
  • the time functions are calculated so that none of the predetermined kinematic restrictions, such as the maximum speeds ⁇ D max , ⁇ LA max , the maximum accelerations ⁇ D max , r ⁇ LA max or the maximum jerk . is exceeded.
  • the movement is divided into three phases.
  • An acceleration phase I a phase of constant speed II, which may also be omitted, and a braking phase III.
  • phases I and III a third-order polynomial is assumed as the time function for the jerk.
  • a time function for the phase II a constant speed is assumed.
  • the remaining free coefficients in the time functions are determined by the boundary conditions at the start of the movement, at the transition points to the next or previous movement phase or at the target point and the kinematic restrictions, with respect to each axis, all kinematic conditions must be checked.
  • the kinematic limitation of the maximum acceleration ⁇ D max and the jerk for the axis of rotation limiting effective in Phase II the maximum speed of the luffing mechanism Rotary axis ⁇ LA max .
  • the other axes are synchronized to the movement time limiting axis.
  • the time optimization of the movement is achieved by determining the minimum total travel time by varying the proportion of the acceleration and deceleration phase in the overall movement in an optimization run.
  • the semi-automatic path planner consists of steepness limiters, which are assigned to the individual directions of movement.
  • Fig. 6 shows the transconductance limiter 60 for the rotational movement.
  • the target speed of the load 3 by the hand lever of the operating state of .phi Dzie ⁇ is the input signal. This is first normalized to the value range of the maximum achievable speed ⁇ D max .
  • the slope limiter itself consists of two limiter boundary blocks with different parameterization, one for the normal operation 61 and one for the quick stop 63, between which can be switched back and forth via the switching logic 67.
  • the time functions at the output are formed by integration 65.
  • the signal flow in the slope limiter will now be explained with reference to FIG.
  • a setpoint-actual value difference between the target speed ⁇ DZiel and the current setpoint speed ⁇ Dref is first formed.
  • the difference is amplified by the constant K S1 (block 613) and gives the target acceleration ⁇ D target .
  • a downstream limiting element 69 limits the value to the maximum acceleration ⁇ ⁇ D max .
  • the target acceleration ⁇ Dref the target speed ⁇ Dref and the target position ⁇ Dref are determined.
  • the derivative of the target jerk is by differentiation in block 65 and simultaneous filtering from the target jerk certainly.
  • the kinematic constraints .phi..sub.D max and and the proportional gain K S1 predetermined so that results in a subjectively pleasant and gentle dynamic behavior for crane operators. This means that maximum jerk and acceleration are set slightly lower than the mechanical system would allow. However, especially at high speeds, the wake of the system is high. This means that the operator sets the target speed 0 at full speed, so the load takes a few seconds to come to a standstill.
  • a second operating mode is introduced, which provides a quick stop of the crane.
  • a second transconductance limiter block 63 structurally identical in construction, is connected in parallel with the transconductance limiter block for the nominal operation 61.
  • the parameters that determine the caster are increased up to the mechanical load limit of the crane. Therefore this block with the maximum rapid stop acceleration ⁇ D max2 and the maximum quick stop pressure is and the rapid stop proportional gain K S2 are parameterized.
  • a switching logic 67 which identifies the emergency stop from the hand lever signal.
  • Output of the quick-stop Steibheitsbegrenzer 63 is like the slope limiter for the Nor malbeitreb the target jerk , The calculation of the other time functions takes place in the same way as in normal operation in block 65.
  • the time functions for the setpoint position of the load in the direction of rotation and its derivation are available taking into account the kinematic restrictions.
  • this steepness limiter it is also possible to use a structure in which the speed setpoint signal, limited to the maximum speed in the steepness of the rising and falling edge in block (691), is limited to a defined value corresponding to the maximum acceleration (FIG. 6 aa). This signal is then differentiated and filtered. The result is the desired acceleration ⁇ Dref . To calculate the setpoint speed ⁇ Dref and setpoint position ⁇ Dref , this signal is integrated, for the calculation of again differentiated in real terms.
  • the slope limiter from the semi-automatic path planner can also be used for the fully automated path planner ( Figure 6a).
  • This is advantageous since, in particular during the movement in the radial direction, the kinematic limitations are dependent on the erection angle. Therefore, in a block depending on the position of the boom position on the kinematics of the luffing gear (See also FIG. 11) calculates the kinematic constraints ⁇ LA max and r ⁇ LA max and tracks the limits (block 617). This will shorten the journey time.
  • an extension can be introduced for fully automatic operation (block 621). New input is the target position instead of the target speed.
  • a position vector is calculated from the start and end point, which indicates the direction for the desired movement.
  • the load will always move on this orbit in the direction of the location vector if and only if the current velocity direction vector always points in the same direction as the position vector.
  • the current velocity vector is influenced by the proportionality factors p D , p r , p L ; that is, by targeted modification of these proportionality factors, the synchronization task is solved.
  • the time functions are given to the axis controllers.
  • the structure of the Achsregiers for the slewing with reference to FIG. 7 will be explained.
  • the output functions of the path planning module in the form of the target position of the load in the direction of rotation and their derivatives (speed, acceleration, jerk, and derivative of the jerk) are given to the pre-control block 71.
  • these functions are so amplified that results in a web-accurate driving the load with respect to the rotation angle without vibrations under the idealized conditions of the dynamic model.
  • the basis for determining the feedforward gains is the dynamic model derived in the following sections for rotary motion.
  • the feedforward control can be supplemented by a conditioner control block 73.
  • a conditioner control block 73 At least one of the measured quantities rotational angle ⁇ D , rotational angular velocity ⁇ D , bending of the cantilever in the horizontal direction (direction of rotation) W h , derivative of the bend ⁇ h , rope angle ⁇ St or the Seilwinkei Marie ⁇ St amplified and returned to the control input.
  • the derivatives of the measured quantities ⁇ D and w h are formed numerically in the microprocessor control.
  • the cable angle can be detected, for example, via a gyroscopic sensor, an acceleration sensor on the load hook, a Hallmeßrahmen, an image processing system or the strain gauges on the boom. Since each of these measurement methods does not directly determine the rope angle, the measurement signal is processed in a disturbance observer module (block 77). The example of the Meßsignalaufpung for the measurement signal of a gyroscope on the load hook this is exemplified. In the interference observer, the relevant part of the dynamic model is stored for this purpose and, by comparing the measured variables with the calculated value from the idealized model, estimation variables for the measured variable and their interference components are formed, so that thereafter a noise-compensated measured variable can be reconstructed.
  • a disturbance observer module block 77.
  • the relevant part of the dynamic model is stored for this purpose and, by comparing the measured variables with the calculated value from the idealized model, estimation variables for the measured variable and their interference components are formed, so that thereafter a noise-compensated measured variable can be
  • FIG. 8 gives explanations of the definition of the model variables.
  • Essential here is the relationship shown there between the rotational position ⁇ D of the crane tower and the load position ⁇ LD in the direction of rotation.
  • the boom is assumed to be rigid and thus neglects the bending w h of the boom.
  • ⁇ A is the current upright angle of the luffing gear
  • l A is the length of the boom
  • ⁇ St is the current rope angle in the tangential direction.
  • the first equation of (4) essentially describes the equation of motion for the cantilever crane tower, taking into account the feedback due to the load oscillation.
  • the second equation of (4) is the equation of motion which describes the load oscillation by the angle ⁇ St , the excitation of the load oscillation caused by the rotation of the tower over the angular acceleration of the tower or an external disturbance expressed by initial conditions for these differential equations ,
  • Q F D K P D u S t D
  • i D is the gear ratio between engine speed and tower rotation speed
  • V is the displacement of the hydraulic motors
  • ⁇ p D is the pressure drop across the hydraulic drive motor
  • ⁇ is the oil compressibility
  • Q FD is the flow in the hydraulic circuit for turning
  • K PD is the Proportionality constant
  • a ⁇ D [ 0 1 0 0 0 - c e a e - b 2 f b a e - b 2 0 0 0 1 0 c b a e - b 2 - a f a e - b 2 0 ]
  • a J T + ( J A Z + m A S A 2 + m L l A 2 ) cos ( ⁇ A ) 2
  • b m L l A l S cos ( ⁇ A )
  • the dynamic model of the slewing gear is conceived as a parameter-variable system with regard to the cable length l S , the righting angle ⁇ A , the load mass m L.
  • Equations (6) to (12) are the basis for the now described design of the feedforward control 71, the state controller 73 and the disturbance observer 77.
  • Input variables of the pilot control block 71 are the desired angular position ⁇ Dref , the target angular velocity ⁇ Dref , the target angular acceleration ⁇ Dref , the target jerk and if necessary, the derivative of the desired jerk ⁇ (4) Dref ⁇
  • pre-control block 71 the components of W D are weighted with feedforward gains K VD0 to K VD4 and their sum is given to the set input.
  • the axis controller for the rotation axis does not include a state controller block 73, then the size U Dvorst from the feedforward block is equal to the reference drive voltage u dref , which is given after compensation of the hydraulic non-linearity as drive voltage U StD on the proportional valve.
  • U Dvorst is the uncorrected target drive voltage for the proportional valve based on the idealized model.
  • u Dvorst K VD 0 ⁇ Dref + K VD 1 ⁇ ⁇ Dref + K VD 2 ⁇ ⁇ Dref + K VD 3 ⁇ ⁇ Dref + K VD 4 ⁇ Dref ( I V )
  • the K VD0 to K VD4 are the Vorticianungsverstärkache which are calculated as a function of the current Aufrichtwinkels ⁇ A , the rope length l s and the load mass m L , so that the load without vibrations track exactly the desired trajectory.
  • the feedforward gains K VD0 to K VD4 are calculated as follows.
  • the feedforward block must be considered in the transfer function.
  • the change of model parameters such as the pitch angle ⁇ A , the load mass m L and the rope length l s can be taken into account immediately in the change of the pilot gains.
  • these can always be tracked depending on the measured values of ⁇ A , m L and l S. That is, the rope length is changed with the hoist, then automatically change the Vorêtungsver reinforcements of the slewing, so that as a result, always keep the pendulum damping Ver pre-control in the process of the load is maintained.
  • the parameters K PD , i D , V, ⁇ , J T , J AZ , m A , s A and l A are available from the data sheet of the technical data. Basically, as variable system parameters, the parameters l s , ⁇ A and m L are determined from sensor data.
  • the parameters J T , J AZ are known from FEM investigations.
  • the attenuation parameter b D is determined from frequency response measurements.
  • the dynamic model is only an abstract representation of the real dynamic conditions.
  • external disturbances such as strong wind attack or the like.
  • the feedforward block 71 is supported by a state controller 73.
  • the state controller at least one of the measured variables ⁇ St, St .phi, ⁇ D, .phi..sub.D is weighted with a controller gain and fed back to the control input.
  • the difference between the output value of the feedforward block 71 and the output value of the state energizing block 73 is formed. If the state controller block is present, this must be taken into account in the calculation of the feed forward gains.
  • K VD 0 k 1
  • K VD 1 c + d k 2 d
  • K VD 2 - cos ( ⁇ A ) l A f a + cos ( ⁇ A ) l A b d k 3 - d l S b k 1 cos ( ⁇ A ) l A d f ⁇ ( - 1 )
  • K VD 3 - ( cos ( ⁇ A ) l A d k 4 - l S c - l S d k 2 ) b cos ( ⁇ A ) l A d f
  • K VD 4 ( ( e cos ( ⁇ A ) 2 l A 2 d k 3 - e cos ( ⁇ A ) l A d l S k 1 + l S cos ( ⁇ A A )
  • the regulator feedback 73 is designed as a complete state controller.
  • a complete state controller is characterized in that each state variable, that is, each component of the state vector x D is weighted with a control gain k iD and fed back to the set input of the path. The control gains k iD are combined to the control vector K D.
  • the dynamic behavior of the system is determined by the position of the eigenvalues of the system matrix A D , which are also poles of the transfer function in the frequency domain.
  • the poles r i are to be chosen so that the system is stable, the control operates sufficiently fast with good damping and the manipulated variable limitation is not achieved for typical occurring control deviations.
  • the r i can be determined before commissioning in simulations according to these criteria.
  • the controller gains from the analytic expressions of Eq. 36 are calculated, also possible for individual poles during operation i r as a function of measured values such as load mass m L, rope length l s or of elevation ⁇ A. to be changed. This results in a very advantageous dynamic behavior.
  • variable system parameters m L , l S and ⁇ A are checked numerically. Since this can only be done numerically, the entire space spanned by the variable system parameters must be detected. In this case, these would be the variable system parameters m L , l S and ⁇ A. These parameters vary in the interval [ m Lmin , m Lmax ] , [ l Smin , l Smax ] and [ ⁇ Amin , ⁇ Amax ] .
  • a state variable is not measurable, it can be reconstructed from other measurands in an observer. In this case, caused by the measurement principle disturbances can be eliminated. In Fig. 7, this module is referred to as Störbeobachter 77.
  • the interference observer is suitable to configure. If, for example, an acceleration sensor is used, then the observer must estimate the pendulum angle from the pendulum dynamics and the acceleration signal of the load. In an image processing system, it is necessary that the oscillations of the cantilever be compensated by the observer so that a usable signal can be detected.
  • the signal from the retro-active bending of the cantilever to extract the observer.
  • the reconstruction of the cable angle and the cable angular velocity will be shown on the basis of the measurement with a gyroscope sensor on the load hook.
  • the disturbances are first to be modeled as differential equations.
  • the offset error ⁇ Offset, D is introduced as a disturbance variable.
  • the disturbance is assumed to be constant as sections.
  • the state space representation of the submodel for the slewing gear according to Eq. 6-12 is extended by the fault model. In the present case, a complete observer is derived.
  • H ⁇ D z [ H 11 D H 12 D H 13 D H 21 D H 22 D H 23 D H 31 D H 32 D H 33 D H 41 D H 42 D H 43 D H 51 D H 52 D H 53 D H 61 D H 62 D H 63 D H 71 D H 72 D H 73 D ]
  • the determination of the observer gains h ljD is carried out either by transformation into observation normal form or by the Riccati design method . It is essential that in the observer also variable rope length, righting angle and load mass are taken into account by adapting the observer differential equation and the observer reinforcements.
  • the estimation may advantageously also be based on a reduced model.
  • ⁇ D The input of the observer is defined as ⁇ D , which can be calculated either from the measured quantity or U Dref (see equation 40).
  • a ⁇ DZred [ 0 1 0 0 0 - a f a e - b 2 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 - w 1 2 0 ]
  • B ⁇ dZred [ 0 m L ⁇ l A ⁇ cos ⁇ A m L l S 0 0 0 ]
  • H dZred [ H 1 red H 2 red H 3 red H 4 red H 5 red ]
  • x ⁇ DZred [ ⁇ ⁇ S t ⁇ ⁇ ⁇ S t ⁇ ⁇ offset .
  • the observer gains are determined via pole specification as in the controller design (Eq. 29 ff.).
  • the resulting structure for the two-stage reduced observer is shown in Figure 7a. This variant guarantees an even better compensation of the offset on the measured value and a better estimation for ⁇ St and ⁇ St.
  • Fig. 9 shows the basic structure of the axis controller for the luffing mechanism.
  • the output functions of the path planning module in the form of the Sollastposition, in the radial direction, and their derivatives (speed, acceleration, jerk, and derivative of the jerk) are given to the feedforward block 91 (block 71 in the slewing gear).
  • these functions are so amplified that results in a web-accurate driving the load without vibrations under the idealized conditions of the dynamic model.
  • the basis for determining the feedforward gains is the dynamic model derived in the following sections for the luffing gear.
  • the feedforward can optionally be supplemented by a state control block 93 (see slewing gear 73) for compensating for disturbances (eg wind influences) and compensating for model errors.
  • a state control block 93 for compensating for disturbances (eg wind influences) and compensating for model errors.
  • this block at least one of the measured values embarkrichtwinkel ⁇ A , Aufrichtwinkel aus ⁇ A , bending of the boom in the vertical direction w v , the derivation of the vertical bend ⁇ v , the radial cable angle ⁇ Sr or the radial cable angular velocity ⁇ Sr amplified and back to the control input recycled.
  • the derivative of the measured quantities ⁇ A , ⁇ Sr and w v is formed numerically in the microprocessor control.
  • FIG. 10 gives explanations of the definition of the model variables.
  • the first equation of (4) essentially describes the equation of motion of the boom with the driving hydraulic cylinder, taking into account the retroactivity of the pendulum of the load. In this case, the proportion acting through the gravity of the boom and the viscous friction in the drive is taken into account.
  • the second equation of (4) is the equation of motion describing the load swing ⁇ Sr , where the excitation of the vibration is caused by the canting of the cantilever over the angular acceleration of the cantilever or an external perturbation expressed by 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 as the load rotates with the slewing gear.
  • M M A F Zyl d b cos ⁇ p ( ⁇ A )
  • Q F A K P A u S t A
  • F Zyl is the force of the hydraulic cylinder on the piston rod
  • p Zyl is the pressure in the cylinder (depending on the direction of movement piston or ring side)
  • a Zyl is the cross-sectional area of the cylinder (depending on the direction of movement piston or ring side)
  • ⁇ is the oil compressibility
  • V Zyl is the cylinder volume
  • Q FA is the flow rate in the hydraulic circuit for the luffing gear
  • K PA is the proportionality constant, which indicates the relationship between the flow rate and the control voltage of the proportional valve. Dynamic effects of subordinate flow control are neglected.
  • the relevant cylinder volume is assumed to be half the total volume of the hydraulic cylinder.
  • z Zyl , ⁇ Zyl are the position or speed of the cylinder rod.
  • FIG. 11 shows the erecting kinematics of the luffing mechanism.
  • the hydraulic cylinder is anchored to the lower end of the crane tower. From design data, the distance d a between this point and the pivot point of the boom can be taken. The piston rod of the hydraulic cylinder is attached to the boom at a distance d b .
  • ⁇ 0 is also known from design data. from that can derive the following relationship between Aufrichtwinkel ⁇ A and hydraulic cylinder z zyl position .
  • z Zyl d a 2 + d b 2 - 2 d b d a cos ( ⁇ A + ⁇ 0 )
  • Equation 46 For a compact notation, in Eq. 51, the auxiliary variables h 1 and h 2 is inserted. This can be done in the Eqs. 46-51 described dynamic model of the luffing gear now in the state space representation (see also O. Föllinger: control technology, 7th ed., Weghig Verlag, Heidelberg, 1992) to be transformed. Since linearity is assumed, first the centripetal force coupling term with the slewing gear due to the rotational speed ⁇ D is neglected. In addition, the components of Equation 46, which are due to gravitation, are set to zero. The result is the following state space representation of the system.
  • the dynamic model of the luffing gear is considered as a parameter variable system with respect to the rope length l s and the trigonometric function components of the boom angle ⁇ A and the load mass m L
  • the equations (52) to (58) are the basis for the now described design of the pilot control 91, the state controller 93 and the interference observer 97.
  • Input variables of the pilot control block 91 are the desired position r LA , the target speed ⁇ LA , the target acceleration r ⁇ LA , the target jerk and the derivative of the target jerk r L A ( I V ) ,
  • the components of W A are weighted with the feedforward gains K VA0 to K VA4 and their sum is given to the set input.
  • the axis controller for the Aufrichtachse does not include a state controller block 93, then the size U Avorst from the feedforward block equal to the reference drive voltage U Aref , which is given after compensation of the hydraulic non-linearity as drive voltage U StA on the proportional valve.
  • u Avor is the uncorrected target drive voltage for the proportional valve based on the idealized model.
  • u Avorst K VA 0 r LAREF + K VA 1 r ⁇ LAREF + K VA 2 r ⁇ LAREF + K VA 3 r ⁇ LAREF + K VA 4 r LAREF ( I V )
  • the K VA0 to K VA4 are the Vorticianungsverstärkache which are calculated as a function of the current Aufrichtwinkels ⁇ A , the load mass m L and the rope length l s , so that the load without vibrations track exactly the desired trajectory.
  • the feedforward gains K VA0 to K VA4 are calculated as follows.
  • Eq. (63) the transfer function between output pilot block and load position are calculated.
  • K VA 0 0
  • K VA 1 - c e l A sin ( ⁇ A 0 )
  • K VA 2 - a G G ( a f - b 2 ) e l A sin ⁇ A 0 ( f a G G - b 2 G )
  • K VA 3 - b ( l S b 2 c - l S a f c ) ( e l A 2 sin ( ⁇ A 0 ) 2 ( f a G G - b 2 G ) )
  • K VA 4 b ( a 2 f 2 l A sin ( ⁇ A ) b G - l S a 3 f 2 G G - l S b 4 a G G + 2 l S b 2 a 2 f G G - 2
  • the change of model parameters such as the righting angle ⁇ A , the load mass m L and the rope length l s can be taken into account immediately in the change of the pilot gains. So they can always be tracked depending on the measured values. That is, when the hoist another rope length l s approached, so automatically change the Vor Kunststoffungsverstärkungen, so that as a result always the pendulum damping behavior of the feedforward control is maintained during the process of the load.
  • the parameters J AY , m A , s A , I A , K PA , A Zyl , V Zyl , ⁇ , d b and d a are available from the data sheet of the technical data. Basically, as variable system parameters, the parameters / S , m L and ⁇ A are determined from sensor data. The attenuation parameter b A is determined from frequency response measurements.
  • the feedforward block 91 is supported by a state controller 93.
  • the state controller at least one of the measured variables ⁇ A , ⁇ A , ⁇ Sr , ⁇ Sr is weighted with a controller gain and fed back to the actuating input. There, the difference between the output value of the pre-control block 91 and the output value of the state-control block 93 is formed. If the state controller block is present, it must be taken into account when calculating the feed forward gains.
  • K A is the matrix of the controller gains of the state controller of the luffing gear analogous to the controller matrix K D in the slewing gear.
  • the descriptive transfer function changes too
  • G AR ( s ) r LA ( s )
  • u Avorst ( s ) C ⁇ A ( s I ⁇ - A ⁇ A + B ⁇ A K ⁇ A ) - 1 B ⁇ A
  • the quantities ⁇ A , ⁇ A , ⁇ SR , ⁇ Sr can be returned.
  • the corresponding governing gains of K A are k 1A , k 2A , k 3A , k 4A .
  • the pilot gains K VAi K VA0 to K VA4 ) can be calculated according to the condition of Eq. 21 are calculated.
  • K VA 0 k 1 A l A sin ( ⁇ A 0 ) ⁇ ( - 1 )
  • K VA 1 c + e k 2 A e l A sin ( ⁇ A 0 ) ⁇ ( - 1 )
  • K VA 2 - ( a f b e k 3 A l A sin ( ⁇ A ) - b 2 a G G l A sin ( ⁇ A ) - b 3 e k 3 A l A sin ( ⁇ A ) + a 2 f G G G l A sin ( ⁇ A ) - e l S b 3 k 1 A + e l S b a f k 1 A ) ( e l A 2 sin ( ⁇ A 0 ) 2 ( f a G G G G l A sin ( ⁇ A ) - e l S b 3 k 1 A + e l S b a f k 1 A ) (
  • the regulator feedback 93 is designed as a state controller.
  • the controller gains are calculated analogously to the calculation method of Eq. 29 to 39 at the turning.
  • the components of the state vector x A are weighted with control gains k iA the controller matrix K A and fed back to the control input of the route.
  • the poles r i of the Polvorgabepolynoms be chosen so that the system is stable, the control operates sufficiently fast with good damping and the manipulated variable limitation is not reached at typical occurring deviations.
  • the r i can be determined before commissioning in simulations according to these criteria.
  • control can also be executed as output feedback. In doing so, individual k iA become zero. The calculation then takes place analogously to Eq. 37 to 38 in the slewing gear.
  • interference observer 97 this module is referred to as interference observer 97.
  • the interference observer is suitable to configure.
  • the measurement is again carried out with a gyroscope sensor on the load hook and the reconstruction of the cable angle and the cable angular velocity are shown. In this case occurs as an additional problem, the excitation of pitching vibrations of the load hook, which must also be eliminated by the observer or suitable filter techniques.
  • the state space representation of the submodel for the luffing gear according to Eq. 52-58 is extended by the fault model. In the present case, a complete observer is derived.
  • H ⁇ A z [ H 11 A H 12 A H 13 A H 21 A H 22 A H 23 A H 31 A H 32 A H 33 A H 41 A H 42 A H 43 A H 51 A H 52 A H 53 A H 61 A H 62 A H 63 A H 71 A H 72 A H 73 A ]
  • an improved offset compensation can be achieved in that in a second observer, the remaining offset on the angle signal ⁇ Sr , by the additional disturbance variable estimated and eliminated and the then estimated angle signal is used for the state control.
  • the determination of the observer gains h ijD is carried out either by transformation into observational normal form or by the Riccati or Polvorgabe design method . It is essential that in the observer also variable rope length, righting angle and load mass are taken into account by adapting the observer differential equation and the observer reinforcements.
  • the estimated values ⁇ Sr returned to the state controller. This results in the output of the state regulator block 93 when ⁇ A , ⁇ A ⁇ Sr is returned , respectively.
  • u Arück k 1 A ⁇ A + k 2 A ⁇ ⁇ A + k 3 A ⁇ ⁇ S r + k 4 A ⁇ ⁇ ⁇ S r
  • non-linearities of the hydraulics can be compensated in block 95 of the hydraulic compensation, resulting in a linear system behavior with respect to the system input.
  • correction factors for the drive voltage of the righting angle ⁇ A and for the gain factor K PA and the relevant cylinder diameter A Zyl can be provided in addition to the valve output and the hysteresis.
  • a direction-dependent structure changeover of the axis controller can be avoided.
  • the combination of the path planning module and the Wippwerk axis controller fulfills the requirement of a vibration-free and pin-accurate movement of the load when erecting and tilting the boom.
  • the module 150 for compensating the centripetal force now has the task of achieving this by simultaneously compensating movement of the luffing mechanism and the lifting mechanism Compensate for deviation as a function of the rotational movement.
  • the target rotational speed of the load ⁇ Dref generated in the path planning module is used.
  • the desired position to be set in the radial direction or the angular position of the cantilever to be set is then calculated from the equations (78 ac), so that the original radius is traversed by the load position.
  • R ges R 1 [ 1 + ⁇ ⁇ Dref 2 G ⁇ l s ]
  • a then permissible Seilaustenkung for ⁇ Sr must be introduced.
  • the pendulum motion of the load can be described taking into account the centrifugal force by the following differential equation, the influence on the pendulum motion by ⁇ A deliberately was not considered here, because one aims exclusively at the sole effect of centrifugal force.
  • m L l s 2 ⁇ ⁇ ⁇ S r z F Z ⁇ l S ⁇ cos ⁇ S r z - m G ⁇ l S ⁇ sin ⁇ S r z
  • the luffing gear controller is set so that it can be equated with a damping coefficient d R in the above differential equation. This is reflected in Eq. 78jd inserted.
  • This differential equation can now be used with the measured variable ⁇ ⁇ D 2 or the target size ⁇ ⁇ Dref 2 be simulated as input during crane operation. It delivers the expected rope angles due to the centrifugal force, with the parameters of the rope length l S and Aufrichtwinkel ⁇ A are always tracked.
  • the higher derivatives are formed accordingly.
  • the simulated angle ⁇ Srz caused by the centrifugal force, is weighted compensated by k 3A to the control input.
  • Eq. 781 and 78n respectively, becomes Eq. 78o or 78p used. Then these equations can be transformed according to the moment to be applied.
  • M D a 1 a 4 ( a 6 ⁇ ⁇ D 2 ⁇ S t - a 5 ⁇ S t - a 3 ⁇ ⁇ D ) + a 0 ⁇ ⁇ D + a 2 ⁇ ⁇ D
  • M A b 1 b 5 ( b 7 ⁇ ⁇ A 2 ⁇ S r - b 6 ⁇ S r - b 4 ⁇ ⁇ A ) + b 0 ⁇ ⁇ A + b 2 ⁇ ⁇ A
  • the P 10 , P 11 , P 20 , P 21 are to be chosen so that the scheme works with high dynamics with sufficient damping.
  • the structure of the axis controller for the hoist is shown in FIG.
  • the axis controller for the hoist 47 since this axis shows little tendency to oscillate, equipped with a conventional cascade control with an outer loop for the position and an inner for the speed.
  • the position control loop controller 123 may be implemented as a proportional controller (P controller).
  • the control gain is to be determined according to the criteria stability and sufficient damping of the closed loop.
  • Output of regulator 123 is the ideal drive voltage of the proportional valve.
  • the nonlinearities of the hydraulics are compensated in a compensation block 125.
  • the calculation is the same as for turning (equations 42-44).
  • the output variable is the corrected drive voltage of the proportional valve u StL .
  • Internal control loop for the speed is the subordinate flow control of the hydraulic circuit.
  • the last direction of movement is the turning of the load on the load hook itself by the load pivot mechanism.
  • a corresponding description of this regulation results from the German patent application DE 100 29 579 from 15.06.2000, on the Content is expressly referred to here.
  • the rotation of the load is made via the arranged between a hanging on the rope bottom block and a load receiving device load swing mechanism. In this case occurring torsional vibrations are suppressed. Thus, in most cases, just not rotationally symmetric load can be accurately recorded, moved by a corresponding bottleneck and discontinued.
  • this direction of movement is integrated in the path planning module, as shown for example with reference to the overview in Fig. 3.
  • the load can be moved here after picking during transport through the air in the corresponding desired pivot position by means of the load pivoting mechanism, in which case the individual pumps and motors are controlled synchronously.
  • a mode for a rotation-independent orientation can be selected.
  • the path control allows a web-accurate method of the load with all axes and actively suppresses vibrations and oscillations.

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Control And Safety Of Cranes (AREA)
  • Jib Cranes (AREA)
  • Load-Engaging Elements For Cranes (AREA)
EP01987730A 2000-10-19 2001-10-18 Kran oder bagger zum umschlagen von einer an einem lastseil hängenden last mit lastpendelungsdämpfung Expired - Lifetime EP1326798B1 (de)

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DE10064182 2000-12-22
DE10064182A DE10064182A1 (de) 2000-10-19 2000-12-22 Kran oder Bagger zum Umschlagen von einer an einem Lastseil hängenden Last mit Lastpendelungsdämpfung
PCT/EP2001/012080 WO2002032805A1 (de) 2000-10-19 2001-10-18 Kran oder bagger zum umschlagen von einer an einem lastseil hängenden last mit lastpendelungsdämpfung

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US7627393B2 (en) 2009-12-01
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