JP2012041180A - Method of controlling crane - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method of controlling a crane, inhibiting more effectively residual vibration of a suspended load when varying the length of a rope of the suspended load.SOLUTION: The method of controlling the crane includes a carrying process of making a turn in the order of an acceleration section, an equal angular velocity section and a deceleration section. In the carrying process, coordinate transformation is performed so that symmetry (symmetric relationship in which equality is achieved if turning back) is made in half the carrying time required from a carrying start position to a target position, and acceleration and deceleration control of turning speed is performed based on the turn acceleration and deceleration pattern calculated according to change in the length of a wire and variation in the rise and fall speed of the suspended load.

Description

  The present invention relates to a crane control method that suppresses the swinging (loading) of a suspended load when the length of the rope of the suspended load is varied.

  A tower crane for a dam (hereinafter simply referred to as a crane) is a large cargo handling machine that transports ready-mixed concrete to a predetermined position by turning and raising and lowering a boom and lifting or lowering a suspended load.

  For example, in a concrete placement facility for dam construction, as shown in FIG. 1, a bucket in which fresh concrete conveyed from a concrete kneading plant 101 by a transfer car 102 is suspended from the tip of a boom 105 of a crane C via a wire 104. (Example of suspended load) After receiving the wire 103, the bucket 103 is lifted by winding the wire 104.

  Next, the boom 105 of the crane C is turned, and the bucket 103 is transported over the destination point on the placement surface of the dam dam body 200.

  Then, after unwinding the wire 104 until the bucket 103 reaches a predetermined height of the destination point, the gate of the bucket 103 is opened, and the ready-mixed concrete in the bucket 103 is placed at the destination point of the dam dam body 200. .

  Moreover, in addition to the operator of the crane C, an operator is also required for the concrete placement in the ready-mixed concrete mixing plant 101 side and the destination point.

  In the crane C as described above, in order to ensure the safety of work, the boom 105 is swung so that the bucket 103 does not swing as much as possible, and the bucket 103 suspended by the wire 104 on the destination point does not swing. There is a request to do.

  Furthermore, there is a demand for making the crane C turn as fast as possible in order to shorten the construction period and reduce the cost.

  Therefore, in order to satisfy the above two requirements, there is a situation that skill is required for the operations of turning, undulating, winding and unwinding of the boom 105 of the crane C.

  However, in the construction industry, there is a fact that there are fewer skilled workers who can perform advanced operations as described above, and it takes time and costs to train skilled crane operators. There is also.

  On the other hand, the concrete placement as described above requires not only the operator of the crane C but also the workers (concrete kneading plant side and destination point side) who follow the movement of the crane C. is there.

  Therefore, the influence of the cycle time of the crane C determined by the skill level of the above-described operation on the cost such as the construction period and labor cost is very large.

  In particular, in the dam construction as described above, a huge amount of ready-mixed concrete is placed in one day, so the influence of the cycle time of the crane C does not affect the construction process and becomes more serious.

  By the way, the tip of the boom 105 of the crane C draws an arc-shaped trajectory, and the suspended load 103 becomes a two-dimensional motion because of the circumferential acceleration in the turning direction and the centrifugal force acting in the radial direction, and its operation (dynamics). Is very different from traveling cranes.

  In particular, in order to shorten the transport cycle time, it is necessary to wind or unload the suspended load in parallel with the turning, and the dynamics of the suspended load become more complicated.

  As mentioned above, shortening the concrete placement cycle time is an important issue, and in order to improve it, it is necessary to suppress the occurrence of residual vibration at the placement position. Therefore, it is a difficult task to suppress shake.

  Here, various techniques for suppressing residual vibration in the crane have been proposed.

  For example, in Japanese Patent No. 3241491, a boom type crane having a boom that can be swung and raised and lowered is used in a crane control method that transports a suspended load from a transportation start point to a destination point while suspending a suspended load with a wire. The wire is wound or unwound between the start of acceleration and the end of acceleration, and the suspension is based on the period of the pendulum movement of the suspended load based on the suspension length of the wire at the start of acceleration and the suspension length of the wire at the end of acceleration. During a time that is an integral multiple of the average value of the load pendulum movement period, the boom is swung at the same time, and the boom is raised and lowered only in this accelerated turning section. Next, turn the boom at a constant speed at the turning angular velocity at the end of acceleration while maintaining the turning radius of the destination point, and then turn the boom. The wire is wound up or down between the start of deceleration and the end of deceleration, and the suspended load is based on the pendulum movement cycle based on the suspended length of the wire at the start of deceleration and the suspended length of the wire at the end of deceleration. A crane control method is disclosed in which the boom is turned while decelerating for a time that is an integral multiple of the average value of the pendulum movement period, and the suspended load is stopped at the destination point.

Japanese Patent No. 3224191

  However, it has been found that it is difficult to sufficiently suppress the swing of the suspended load when the length of the rope of the suspended load is fluctuated even by the conventional technique.

  Then, an object of this invention is to provide the control method of the crane which can suppress the residual vibration of a suspended load more effectively when the length of the rope of a suspended load is fluctuated.

  In order to solve the above-mentioned problem, the crane control method according to the invention of claim 1 is configured to convey a suspended load suspended from the wire from a conveyance start position to a target position while turning the boom and changing the length of the wire. A crane control method for performing steadying control for converging residual vibration of the suspended load at the target position accompanying the turning of the boom, wherein the boom turning radius is constant, an acceleration section, It has a transporting process that turns in the order of an equiangular velocity section and a deceleration section, and in this transporting process, it is symmetric (equal to the case of folding) at half the transport time required from the transport start position to the target position. (Symmetry relation) and coordinate conversion is performed, and the turning acceleration and deceleration patterns calculated according to the change in the length of the wire and the change in the lifting speed of the suspended load Based on, and performs acceleration and deceleration control of the turning speed.

  The crane control method according to the invention of claim 2 sets a time scale so that the natural period of the crane does not change when performing acceleration / deceleration control of the turning speed in the invention of claim 1. The acceleration / deceleration of the turning speed is converted.

  According to a third aspect of the present invention, the crane control method according to the first or second aspect of the present invention uniquely determines the turning acceleration / deceleration pattern based on the turning speed in the equiangular velocity section. It is characterized by doing.

  The crane control method according to the invention of claim 4 is the crane control method according to claim 3, wherein the angle (turning angle) of the boom from the X axis is α, the turning speed is dα / dt, and the X axis of the pendulum is used. When the direction angle is Ψ, the swing angle of the suspended load is θ, the horizontal distance between point B (boom tip) and point O (turning center) is r, the crane turning radius is r, and the suspended rope length is l,

Substituting the α into the following equation,

  The turning acceleration / deceleration pattern is calculated.

  According to the present invention, the following effects can be obtained.

  That is, according to the first aspect of the present invention, even if the turning speed (turning angle) from the transport start position to the target position is changed, the residual vibration of the suspended load when the length of the rope of the suspended load is changed. It can be effectively suppressed.

  According to the second aspect of the present invention, the time scale is set so that the natural period of the crane does not change, and the acceleration / deceleration of the turning speed is converted. The residual vibration of the load can be more effectively suppressed.

  According to the third aspect of the present invention, the turning acceleration / deceleration pattern can be uniquely determined based on the turning speed in the equiangular velocity section, so that the turning acceleration / deceleration pattern can be efficiently obtained.

  According to the invention described in claim 4, simply by substituting the angle α from the X-axis of the boom or the turning speed dα / dt, the turning acceleration / deceleration pattern can be obtained easily and quickly, and the remaining efficiently. Vibration can be suppressed.

It is explanatory drawing which shows the crane C of a construction state. It is explanatory drawing which shows the movement state from a conveyance start position (S) to a target position (E). It is explanatory drawing which shows the position of the concrete bucket from a conveyance start position (S) to a target position (E). It is explanatory drawing which shows the model of a tower crane. It is explanatory drawing which shows the model of a tower crane. It is explanatory drawing which shows the position of the concrete bucket from a conveyance start position (S) to a target position (E). It is explanatory drawing which shows the speed control signal of turning and winding (lowering) of concrete conveyance from S point to E point. It is explanatory drawing which shows the comparison of the track | orbit obtained by projecting the motion of a boom tip and a pendulum on XY plane. It is explanatory drawing which shows the comparison of the simulation result and measurement result of the height direction of a pendulum. It is a graph which shows the comparison of the simulation result of the time change of the X, Y coordinate of a pendulum, and a measurement result. It is a graph which shows the comparison of the simulation result of the time change of the X, Y coordinate of a pendulum, and a measurement result. It is a graph which shows the swing angle of a pendulum when the length of a pendulum is constant. It is a graph which shows the swing angle of a pendulum in case the length of a pendulum fluctuates, and the acceleration of turning. It is a graph which shows the acceleration of the X and Y direction of a boom front-end | tip. It is a graph which shows the swing angle of the pendulum when changing the acceleration in the turning direction. It is a graph which shows the swing angle of the pendulum when carrying time is lengthened. It is explanatory drawing which shows a locus | trajectory when the dimensionless relative motion from the boom front-end | tip of a concrete bucket is projected on XY plane. It is explanatory drawing which shows the speed pattern of the turning and winding (lowering) for making the track | orbit of a pendulum into the track | orbit shown in FIG. It is a graph which shows the trajectory of a pendulum at the time of inputting the acceleration input pattern of turning. It is the graph which compared the motion of the pendulum at the time of applying the "control method 1" which concerns on this invention, and the conventional "control method 2". It is the graph which compared the motion of the pendulum at the time of applying the "control method 1" which concerns on this invention, and the conventional "control method 2". It is the graph which expanded the section of 120s-180s. It is the graph which expanded the section of 120s-180s. It is a block diagram of the drive control apparatus of the boom type crane which concerns on one Embodiment of this invention. It is the top view which looked at the crane C from upper direction. It is explanatory drawing which shows a conveyance pattern (cases 1-3). It is a flowchart which shows the process sequence of a calculation process.

  Hereinafter, an embodiment as an example of the present invention will be described in detail with reference to the drawings. Here, in the accompanying drawings, the same reference numerals are given to the same members, and duplicate descriptions are omitted. In addition, since description here is the best form by which this invention is implemented, this invention is not limited to the said form.

  Here, before explaining the crane control method according to the present embodiment, the process until the present invention is completed will be described.

  First, in the past, a tower crane was modeled and it was verified that gain-scheduled control was effective for suspended load positioning control and steady-state control when the suspended rope length fluctuated (TAKAGI, K., (NISHIMURA, H., Gain-Scheduled Control A Tower Crane Considering Varying Load-RopeLength, the Japan Society of Mechanical 98, No. 126, Sr. 6).

  In another conventional technique, a feedforward input is obtained by terminal state control so that the suspended load and the tower portion are stationary at the target position, and a two-degree-of-freedom control system including feedback control without using a load deflection angle sensor is configured. It has been verified that vibration control of suspended loads, boom hoisting / turning angle positioning control, and tower vibration control can be performed (TAKAGI, K., NISHIMUURA, H., UCHIDA, Y., Controllof A Tower Crane without). Sensor for Load-RopeAngle (2DOF Control Using Final-State Control Methodology Error Learning), the Japan Society of MechanicalE gineers, Series C, Vol.67, No.656, (2001), pp.103-111.).

  Further, in another prior art, when the length of the pendulum varies, a function corresponding to the energy of the pendulum is defined, and a control law for steadying by moving the center of gravity so that the value becomes small is derived (YOSHIDA , Y., FUKAO, T., TSUGE, T., Positioning and Vibration Control of a Containr Crane Sustained Load, The Japan Society of Mec. 155.). This control law can be applied to swing control of a crane-type pendulum in which the pendulum moves up and down.

  Furthermore, in another conventional technique, a feedback control system in which pole fixed variable gain control is applied to the position tracking control of a suspended load is constructed for an overhead crane (KANESHIGE, A., TERASHIMA, K., MUNETOSHI, H ., SADAMORI, T., Modeling and Transferring Control ofan Overhead Traveling Crane based on the informationof Object Position (2nd Report, Design of Object-PositionFeedback Controller Considering the Change of Rope-Length), the Japan Societ of Mechanichal Engineers, Series C, Vol.64, No.628, (1998), pp.253-260.).

  Still another prior art deals with the shortest time control problem related to the steady vibration control and the movement of the suspended load in the linear transfer system by simultaneous movement of the swing crane, undulation and hoisting (lowering), and shortens the transfer time. It has been shown that residual vibrations can be suppressed (SHEN, Y., TERASHIMA, K., YANO, K., SUZUKI, K., Minimum Time Control of the Rotor-Through Transfer Trans-Transfer Transfer Transform, Control Engineers Industrial Thesis Collection, Vol. 3, No. 10, (2004), pp. 70-79. ).

  By the way, in the research considering the fluctuation of the rope length of these suspended loads, the control method is induced on the assumption that the feedback control can be applied.

  However, feedback control is not suitable in the field considering the cost of the system and the failure of the measuring device, and operation by an open loop is required.

  Therefore, the present inventor has eagerly studied a turning acceleration method that applies a non-linear time scale and suppresses the occurrence of residual vibration at the target position for the case where the rope length of the suspended load of the tower crane fluctuates. The invention has been completed.

  The effectiveness of the present invention is shown below in comparison with simulation results.

  First, the steadying method by variable transformation of independent variables will be described.

  Considering a crane as shown in FIG. 2, the crane operation accelerates the trolley while lifting (lowering) the suspended load so that the maximum speed is reached at point O from the conveyance start position at point S. Thereafter, when the vehicle is driven at the maximum speed and approaches the concrete placement position, deceleration starts at point P, stops at the concrete placement position at point E, and returns to point S again after completion of concrete placement. It is necessary to reduce the runout of the concrete bucket when reaching the placement position of point E for shortening the drawing amount time and safety.

  As shown in FIG. 2, such a crane is regarded as a pendulum in which the fulcrum of the pendulum is displaced in the horizontal direction and the length is changed, and an acceleration pattern in which no residual vibration remains after the end of acceleration / deceleration of the fulcrum is obtained analytically.

The equation of motion is shown in Equation 3.

  Assuming that the swing angle θ of the suspended load is very small, sin θ≈θ, cos θ≈1, the suspended rope is massless and rigid, and the suspended load is assumed to be a material point, and viscous damping is ignored.

  Here, θ is the swing angle, l is the length of the pendulum, X is the position of the trolley, and g is the acceleration of gravity.

In Equation (1), if l0 is the reference length of the pendulum and l = lOl ^* , X = lOX ^* , t = Tt ^* (T = √ (l0 / g), then Equation 1 becomes non-dimensional and Equation 4 Become.

  Next, application of the nonlinear scale will be described.

In the initial state t ^* = 0, the deflection angle θ and the angular velocity dθ / dt ^* are set.

A new time scale (corresponding to the pendulum phase) φ is introduced, the acceleration start time is φ = 0, the acceleration end time is φ = 2π, and the acceleration input d of the trolley in which the swing angle θ changes as shown in Equation 5 ² X ^* / dt ^{* 2} is derived.

In this case, θ = dθ / dφ = 0 at the end of acceleration, and if the relationship between φ and t ^* is set as described later, θ = dθ / dt ^* = 0 at the end of acceleration, so no residual vibration remains.

In Equation 5, θ ₀ is determined so that the maximum value of the acceleration input to the trolley is less than or equal to the maximum acceleration of the trolley determined from the crane specifications.

If φ is regarded as a function of t ^* ,

Thus, the differential of t5 with respect to t ^* is as in Eqs. 8 and 9.

Substituting Equation 5, Equation 8, and Equation 9 into the left side of Equation 4, the acceleration input d ² X ^* / dt ^{* 2} to the trolley for realizing the shake of Equation 5 is obtained as shown in Equation 10 below.

Using Equations 6 and 7, the left side of Equation 4 is represented, the acceleration input is represented by Equation 10, the right side of Equation 4 is represented, and both sides are divided by (dφ / dt ^* ) ² to obtain Equation 11.

  Note that the general solution of Equation 11 is Equation 5.

  Here, the coefficient of the third term on the left side of Equation 11 represents the equivalent stiffness of the pendulum when viewed on a new time scale φ.

If the relationship as shown in Equation 12 is made between the time t ^* and the new time scale φ so that this does not change and takes a constant value 1, the natural frequency becomes 1.

That is, φ is set as shown in Equation 13.

At this time, the time t ^* and the new time φ are not proportional, and φ becomes a non-linear time scale.

Further, the number 10 of the input acceleration is simplified as shown in the following Expression 14.

Further, since Expressions 15 and 16 are established from Expression 12, the expression representing the acceleration input can be rewritten as Expression 17.

Here, the winding speed v ^* _r was set as shown in Equation 18.

By calculating d ² X ² / dt ^{* 2} for φ = 0 to 2π from Equation 17, and converting the result from φ to t ^* using the relational expression of t ^* and φ (Equation 13) The acceleration input to be given at each time t ^* is obtained.

The response waveform of the swing angle of the pendulum in the time domain is expressed by t ^* by applying Equation 13 to θ = θ ₀ (1-cos φ) defined by the nonlinear time scale φ (expanded in the time axis direction) ) The waveform is as shown in Equation 19.

  That is, it can be seen that the pendulum trajectory when the pendulum length changes can be obtained without integrating Equation 2 by applying a non-linear time scale to enlarge or reduce the waveform in the time axis direction.

  Next, an analysis model and equation of motion of a tower crane related to the basis of the present invention will be described.

  First, the operation method of a tower crane is demonstrated.

  An outline of the operation method of the crane C is shown in FIG.

  In FIG. 3A, O is the turning center, and SPO'QE is the locus of the boom.

  FIG. 3B is a development of the arcuate track at the tip of the boom shown in FIG.

  The operation of the crane C accelerates the turning while lifting (lowering) the suspended load so as to reach the maximum turning speed at the point P from the transportation start position at the point S.

  After that, when the vehicle is driven at the maximum turning speed and approaches the target position, it starts decelerating at point Q, stops at the concrete pouring position at point E, and returns to point S again after the concrete pouring is completed.

  In the acceleration region between SPs and the deceleration region between QEs, the Coriolis force due to the fluctuation of the pendulum length acts on the concrete bucket 103 in addition to the acceleration in the turning direction and the centrifugal force.

  Further, centrifugal force and Coriolis force act in the constant speed section of the turn between PQs.

  As shown in FIG. 3, the driving method is an open control in which turning is divided into acceleration, steady speed, and deceleration areas, and a calculation method of a turning acceleration pattern that suppresses the occurrence of residual vibration at the target position is considered.

  Next, the equation of motion will be described.

  Here, modeling as shown in FIGS. 4 and 5 is used.

  FIG. 5 shows a case where the concrete bucket is raised and lowered by changing the length of the rope.

  The crane body and boom are handled as rigid bodies, suspended loads are handled as mass points, and ropes are handled as rigid bodies ignoring mass.

  Point O represents the turning center, point B represents the boom tip, and the dam axis is the X axis.

  Ψ is the direction angle of the concrete bucket from the X-axis, θ is the swing angle of the suspended load, α is the angle from the X-axis of the boom (turning angle), r is the horizontal distance between point B and point O, and the crane turns The radius, l is the suspended rope length.

  Here, the movement of the suspended load of the tower crane is modeled as a conical pendulum with the B point as a fulcrum.

  Hereinafter, the concrete bucket is referred to as a “pendulum”.

In FIG. 4, the coordinates of the turning center (O) are (x _O , y _O , z _O ), the coordinates of the boom tip (B) are (x _B , y _B , z _B ), and the pendulum coordinates are (x _C , Y _C , z _C ), the coordinates of the pendulum are as shown in equations 20 and 21.

  Next, the kinetic energy of the pendulum is calculated from the speed obtained by differentiating the equations 20 and 21 with respect to time to obtain the Lagrangian.

By making Euler's differential equation from Lagrangian, the equation of motion of the pendulum becomes as shown in Equations 22 and 23.

Also, as shown in FIG. 4, since the fulcrum of the pendulum is at the tip of the boom, the external force acting on the pendulum is given by the movement of the tip of the boom, and the coordinates of the tip of the boom can be expressed as Equations 24 and 25.

Then, assuming that the turning radius is constant, accelerations in the X and Y directions at the boom tip are as shown in Equations 26 and 27.

Here, l ₀ is the reference length of the pendulum, and l = l ₀ l ^* , x = l ₀ x ^* , t = Tt ^* (T = √ (l ₀ / g)), v ^* _r = Tvr / l ₀ In other words, the dimensionless length of the pendulum can be expressed as Equation 28.

Also, assuming that d ² Z _B / dt ^{* 2} = 0, θ is minute, and assuming that sin θ≈θ and cos θ≈1, substituting Equations 26 and 27 into Equations 22 and 23, and considering Equation 28, The equations of motion of a conical pendulum with varying pendulum length are as shown in Equations 29 and 30.

  For the examination of the control method for suppressing the residual vibration after reaching the target position of the tower crane C, the dimensionless equations 29 and 30 are applied.

  Thus, in the present invention, since the change in the length of the pendulum is taken into consideration, the second term on the left side of Equation 29 and the second term on the left side of Equation 30 exist.

  Next, we discuss the validity of modeling by comparison with measured values.

  First, the transportation method will be described.

  The validity of the tower crane modeling is evaluated by comparing the measured values of the concrete bucket trajectory when placing concrete with automatic operation of the actual tower crane and the simulation results using Equations 29 and 30.

  The method of automatic operation is as follows.

  That is, when the length of the pendulum does not change, residual vibration of the pendulum does not occur if the trolley is brought to a steady speed by applying a constant acceleration during the natural period.

  Utilizing this fact, the acceleration pattern of turning when the pendulum length changes is set as follows.

That is, the time obtained by averaging the natural period at the start of acceleration and the natural period at the end of acceleration is defined as an acceleration time T ^* _A.

The length 1 of the pendulum at the start of acceleration is 1, and the length 1 of the pendulum after time T ^* _A is 1 + v ^* rT ^* _A , so the acceleration time T ^* _A is as shown in Equation 31.

When the acceleration time T ^* _A is obtained from Equation 31, Equation 32 is obtained.

This is a method of setting the following acceleration A ^* _i using this T ^* _A.

Here, the above control method is referred to as “control method 2”.

Here, α _v is the turning speed during steady operation.

Further, since the speed of the turning and hoisting (lowering) motors of the actual tower crane is controlled, when the relationship between the input signal to the motor and the rotational speed is modeled by a first-order lag system, d ² α / dt of Equations 29 and 30 are used. ^{* 2} becomes like 34.

Here, T ^* _α is a time constant of turning.

Further, the turning speed control signal α ^S can be expressed as in Expression 35.

  Next, comparison with actual measurement values will be described.

  Here, the measured value of the trajectory of the pendulum and the simulation result when transported from point S (transport start position) to point E (concrete placement position) shown in FIG. 6 are compared.

Table 1 shows the coordinates of point S and point E.

  In Table 1, the dam axis is the X axis, and the Z coordinate represents the altitude.

  This is a case where the turning angle from the point S to the point E is about 205 degrees and the case turns clockwise.

  FIG. 6B is an unfolded arc-shaped cross section of a swivel, and a line connecting SDFE represents a pendulum intrusion prohibited region for avoiding an obstacle during concrete transportation.

  Therefore, the pendulum is controlled so as to pass through a trajectory higher than the intrusion prohibited area.

  Then, a tracking mirror was attached to the pendulum, and its three-dimensional coordinates were measured by an automatic tracking transition.

  FIG. 7 shows speed control signals for turning and winding (lowering) the concrete transport from point S to point E.

  The turning speed is positive in the counterclockwise direction, and the winding (lowering) is positive in the lowering.

  As shown in FIG. 7, the winding starts from 25 seconds, and the turning starts when the bucket reaches a predetermined height.

  Also, the winding starts from about 90 seconds.

  At this time, the pendulum has a higher trajectory than the intrusion prohibited area shown in FIG.

  FIG. 8 shows a comparison of trajectories obtained by projecting the motion of the boom tip and the pendulum onto the XY plane.

  The trajectory of the boom tip is a value calculated from the boom length and the undulation angle.

  The coordinates of the measured pendulum overlap with the coordinates obtained by simulation.

  The pendulum vibrates in the radial direction through the outer track by centrifugal force from the track at the tip of the boom.

  FIG. 9 shows a comparison between the simulation result in the height direction of the pendulum obtained by developing the arc-shaped cross section shown in FIG. 8 and the measurement result.

  In FIG. 9, the horizontal axis is the turning angle, and the vertical axis is the altitude.

  Winding starts as soon as transport starts, and when it reaches a height that avoids obstacles, the winding (lowering) stops, and when it exceeds the obstacles, it becomes a trajectory that rolls down.

  The pendulum trajectory obtained from the simulation and the measured trajectory overlap.

  Next, FIGS. 10 and 11 show a comparison between the simulation result of the time change of the X and Y coordinates of the pendulum and the measurement result.

  FIG. 11 is an enlarged view of 180 seconds from 120 seconds in FIG.

  As shown in FIG. 10, the coordinates obtained from the simulation overlap with the measured coordinates.

  Further, FIG. 11 is an enlarged view of the measurement at the target position of the pendulum and the simulation. Although the phases are slightly different, the simulation result simulates the measurement result, and the above modeling is considered appropriate.

  Therefore, Formula 29 and Formula 30 are used to construct a control method using open control that suppresses residual vibration at the target position of the tower crane.

  Next, a method for stabilizing the suspended load will be described.

  In the case where the length of the pendulum changes, an acceleration pattern that suppresses the occurrence of residual vibration at the target position is obtained as follows.

  First, in the case where the pendulum length does not change by the above-described method, a turning acceleration pattern is obtained on a non-linear time scale.

  That is, when acceleration from the transport start position S to the P point with a constant acceleration, a constant turning speed at the P point, and when the Q point near the transport target position is reached, the turning deceleration starts and the turning stops at the E point. An acceleration pattern in which no residual vibration occurs is obtained.

When the length of the pendulum changes, a new nonlinear time scale φ shown in Equation 36 that relates time and a new time scale is applied so that the equivalent stiffness of the motion equation of the pendulum changing with time does not change. Convert to an acceleration pattern when the pendulum length changes.

Here, when the winding (lowering) speed is constant, the conversion from the non-linear time scale φ to the time t ^* is as shown in Expression 36 and Expression 28 to Expression 37.

  The residual vibration at the target position can be suppressed by inputting an acceleration pattern converted from a nonlinear time scale to dimensionless real time (actually converted to dimensional time) using Equation 37.

  A simulation was performed to evaluate the validity of the above control method (control method 1).

Table 2 shows the conditions.

  In Table 2, the cases from C1 to C3 are cases where the input acceleration of turning is changed, and C4 and C5 are cases where the transportation time is lengthened.

In the table, d ² α / dt ^{* 2} represents acceleration, and v ^* r represents the winding (lowering) speed.

C1-1, C2-1, C3-1, C4-1, in the case where there is no wind-up is C5-1 of the case (down), P point from the point S, Q point, the time ^T φ _P to reach the point E, T ^φ _Q and T ^φ _E are represented by a nonlinear time scale φ.

Moreover, their time when the length of the other pendulum changes, is the number ^{_{35 T φ P, T φ Q}} , T φ E and hoisting (lowering) the speed v time calculated by substituting the ^* _r .

  Next, a case where the length of the pendulum is constant will be described.

  FIG. 12 shows the swing angle of the pendulum when the length of the pendulum is constant.

  12A shows the case where the acceleration in the turning acceleration region is changed, and FIG. 12B shows the case where the transportation time is changed.

  From FIG. 12A, the swing angle of the pendulum increases as the acceleration increases.

  From (b) of FIG. 12, since the acceleration in the acceleration region is equal, the maximum deflection angle is equal. Thus, it can be seen that no residual vibration occurs at the target position even if the transportation time is increased.

  Next, a case where the length of the pendulum changes will be described.

The swing angle of the pendulum and the turning acceleration when d ² α / dt ^{* 2} = 0.015, v ^* _r = 0.0, 0.0226, 0.0452, −0.0226, −0.0452 are set. As shown in FIG.

  The transportation time is longer in the case of lowering and shorter in the case of winding than when the length of the pendulum does not change.

  In the case of winding down, the maximum value of the swing angle is small, and in the case of winding up, the maximum value is large.

  When the pendulum length does not change, the occurrence of residual vibration after the end of deceleration can be suppressed. However, when the pendulum length changes, a shake of about θ = 0.0025 occurs.

  Further, as the lowering speed increases, the amplitude of residual vibration also increases.

In the case where the acceleration in the turning direction is d ² α / dt ^{* 2} = 0.015, the acceleration / deceleration time due to the difference in the winding (lowering) speed is compared.

  The acceleration time is 6.99 for C2-1 without winding (lowering), 6.71 for C2-4 for winding, and 7.27 for C2-2 for winding.

  Similarly, the deceleration time is 6.99, 5.76, and 8.22.

  FIG. 14 shows the acceleration in the X and Y directions at the boom tip for each case.

When there is no hoisting (lowering), it is symmetrical in the X direction at t ^* = 9.25 and point symmetric in the Y direction, but when there is hoisting (lowering), the length of the pendulum changes. Therefore, it can be seen that the input acceleration calculated on the non-linear time scale is expanded and contracted in the time direction and the input acceleration becomes asymmetric.

Next, FIG. 15 shows the swing angle of the pendulum when the hoisting / lowering speed is a constant value v ^* _r = 0.0226 and the acceleration in the turning direction is changed.

  As the acceleration increases, the maximum deflection angle increases proportionally.

  The magnitude of the residual vibration is almost equal.

  In carrying work using a tower crane, the maximum turning angle to the target position is π. Therefore, it is necessary to confirm that the occurrence of residual vibration at the target position is suppressed when the turning angle is increased, that is, when the transportation time is increased.

When the transport time becomes longer, the hoisting (lowering) speed is set to be smaller in the actual machine, so the hoisting (lowering) speed is set to v ^* _r = 0.113.

  FIG. 16 shows the swing angle of the pendulum when the transport time is increased.

  Further, the case shown in FIG. 16 corresponds to a turning angle of about π.

  In either case, the amplitude of the residual vibration at the target position is about 0.002.

  Next, FIG. 17 shows a trajectory when the dimensionless relative motion from the boom tip of the concrete bucket is projected onto the XY plane.

  Here, the origin is the boom tip position.

  The maximum amplitude is 0.04, and the amplitude at the target position is about 0.002.

  For example, assuming that the pendulum length is 50 m, the maximum amplitude is 2 m, and the residual amplitude at the target position is 0.1 m.

  This amplitude is practically no problem considering that the diameter of the concrete bucket is 2.0 to 2.5 m.

  Next, confirmation of the validity of the control method according to the present invention will be described.

  Compared with the above-mentioned “Control Method 2” and the above-mentioned “Control Method 1” by taking as an example the case where the concrete transport start position and concrete placement position shown in Table 1 and FIG. The usefulness of the invention is shown.

  In FIG. 6, the point S is the start position of transport, the point E is the concrete placement position, the point DF is a position set to transport the concrete while avoiding obstacles, and the pendulum trajectory from the line connecting the SDFE points. Need to be high.

  FIG. 18 shows a speed pattern of turning and winding (lowering) for changing the pendulum trajectory into the trajectory shown in FIG.

It accelerates to point S ~P point (a) of FIG. 18, then operating at a steady rate alpha _v to point Q, and stops at point E starting deceleration from the Q point.

The winding (lowering) is performed at a speed v ^* _{r1 from the} point S to the point D, and the winding is stopped at the point D.

Next, at the point F, lowering is started at the speed v ^* _r2 , and the concrete pouring position E is reached.

  In order to suppress the residual vibration at the target position, the speed pattern of turning and hoisting shown in FIG. 18 is obtained as follows.

First, the time from point S to point D, point D to point F, and point F to point E is defined as t ^* ₁ , t ^* ₂ , and t ^* ₃ .

Also, assuming that the acceleration time from the S point to the P point is T ^* _A , the time during which the turning speed from the P point to the Q point is steady is T ^* _ST , and the deceleration time from the Q point to the E point is T ^* _D , FIG. From FIG. 18, the turning angle and the winding (lowering) are in the relationship of Equations 38-42.

Here, α _SD , α _DF , α _FE are S-point to D-point, D-point to F-point, F-point to E-point turning angle, D ^* _SD and D ^* _FE are S-point to D-point, F-point to This is the length of winding (lowering) to point E.

  The turning speed is made equal to suppress the occurrence of pendulum shake due to the change in the turning speed when the suspended load is wound (lowered).

Therefore, when the turning speed α _V is obtained from the equations 38 and 39 and set equal to each other, and t ^* ₁ and t ^* ₃ are obtained from the equations 41 and 42 and substituted, the equation 43 is obtained.

In Equation 43, the winding (lowering) speeds v ^* _r1 and v ^* _r2 are unknown numbers.

  Next, the acceleration pattern in the time domain is obtained by associating the acceleration pattern that suppresses the occurrence of residual vibration at the target position defined by the nonlinear time scale with the equations 38 to 43 defined in the time domain.

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９）ｔ^＊ _１、ｔ^＊ _２、ｔ^＊ _３から数４５を適用して求めたＴ^φｔ _ＥとＴ^φ _Ｅが一致することを確認する。

End time of acceleration time nonlinear time scale, as ^{_{T φ P, T φ Q,}} T φ E as shown in Table 2, supra deceleration start time and deceleration end time, obtaining the acceleration pattern the following procedure.
1) Assuming a hoisting (lowering) speed.
Request 2) winding up or down speed, S point, the length of the pendulum of the point ^{_{E, T φ A = T φ P}} , T φ D = T φ E -T φ Q acceleration and deceleration times from ^T _* ^A, the ^T _{* D} .
3) The above two items are repeated until Equation 41 is established to obtain v ^* _r1 and v ^* _r2 .
4) Find t ^* ₁ and t ^* ₃ from Equations 41 and 42.
Since 5) winding speed is ^{_{sought, T φ P, T φ Q}} , corresponding to ^T φ _E T _* ^P, can be determined _{^T *} ^Q, _T * _E.
6) Obtain α _V from Equation 38.
7) If the turning angle from the transport start position to the target position is α _TOT , the time T ^* _ST of the steady turning speed is obtained from Equation 44.

8) The time for stopping the winding is t ^* ₂ = T ^* _A + T ^* _ST + T ^* _D- t ^* _1- t ^* ₃ .
_{^{9) t * 1, t *}} 2, t * 3 T were determined by applying the number 45 from ^.phi.t _E and T ^phi _E is confirmed consistencies.

  FIG. 19 shows a pendulum trajectory when a turning acceleration input pattern obtained by the above method is input.

  The pendulum is in a trajectory that passes over the SDFE and avoids obstacles.

  FIG. 20 and FIG. 21 show a comparison of the movement of the pendulum when the “control method 1” according to the present invention and the conventional “control method 2” are applied.

  22 and 23 are enlarged views of 120s to 180s in FIGS. The alternate long and short dash line in the figure indicates the target position.

  The target position in the X direction is 63.508 m, the control method 2 is 62.8 to 64 m, the “control method 1” is 63.4 to 63.9 m, and the Y direction is the target position 24.191 m. On the other hand, in the case of the “control method 2”, it vibrates between 23.8 to 24.8 m, and in the case of the control method 1, it vibrates between 23.2 to 23.7 m.

  In “Control Method 2”, the amplitude in the X direction is 1.2 m and the amplitude in the Y direction is 1.0 m, whereas in “Control Method 1”, the amplitude is reduced to 0.5 m and 0.3 m, respectively. I understand that.

  Therefore, considering that the diameter of a normal concrete bucket is 2.0 m to 2.5 m, the concrete can be placed at the same time as reaching the concrete placing position. The time loss is reduced, and the use of “control method 1” has an excellent effect that the cycle time can be shortened.

  Here, with reference to FIG. 24 and FIG. 25, the structural example of the crane C which concerns on this Embodiment is demonstrated.

  FIG. 24 is a principal block diagram of a drive control device for a boom type crane according to an embodiment of the present invention. Further, the crane has the same configuration as the crane C used in the concrete placing facility shown in FIG. 1 except for the drive control device. In addition, the same code | symbol is attached | subjected about the same structure part and description is abbreviate | omitted.

  24, 11 is a data input unit for inputting data such as a transportation start point and a three-dimensional coordinate of a destination point, and 12 is a turning angle and a undulation angle of the boom 105 shown in FIG. 1 based on the output of the data input unit 11. And the like. 13 is a control unit composed of a microcomputer or the like for controlling the turning and undulation of the boom 5 based on the output of the calculation unit 12, and 14 is a boom based on the control signal of the control unit 13. A boom turning motor as a driving means for turning 105, 15 is a boom raising / lowering motor for raising / lowering the boom 105 based on a control signal of the control unit 13, and 16 is a suspension shown in FIG. 1 based on a control signal of the control unit 13. This is a wire winding motor that winds / unwinds a wire 104 that suspends a bucket 103 as a load.

  The data input unit 11, the calculation unit 12, the control unit 13, the boom turning motor 14, the boom hoisting motor 15, and the wire winding motor 16 constitute a drive control device 300.

  FIG. 25 is a plan view of the turning operation (turning center O, turning angle θ) of the crane C as viewed from above.

  24A to 24C show transport patterns (cases 1 to 3) by the crane according to the present embodiment.

  Next, a processing procedure of calculation processing executed by the drive control device 300 will be described with reference to the flowchart of FIG.

  When this process is started, first, in step S10, assuming a winding (lowering) speed, the process proceeds to step S11.

In step S11, the take-up and down speed, S point, the length of the pendulum of the point ^{_{E, T φ A = T φ P}} , T φ D = T φ E -T φ Q acceleration and deceleration times from ^T _* ^{A, T} _{* D} Is obtained and then the process proceeds to step S12.

In step S12, the above two items are repeated until Equation 43 is established, and v ^* _r1 and v ^* _r2 are obtained, and the process _proceeds to step S13.

In step S13, t ^* ₁ and t ^* ₃ are obtained from equations 41 and 42, and the process proceeds to step S14.

In step S14, since the winding speed is ^{_{demanded, T φ P, T φ Q}} , T φ T * P corresponding to _{^E, T} * ^Q, decide ^T _{* E} proceeds to step S15.

In step S15, seeking a few 38 alpha _V proceeds to step S16.

In step S16, if the turning angle from the transport start position to the target position is α _TOT , the time T ^* _ST of the steady turning speed is obtained from equation 42, and the process proceeds to step S17.

In step S17, the time for stopping the winding is calculated as t ^* ₂ = T ^* _A + T ^* _ST + T ^* _D- t ^* _1- t ^* _3, and the process proceeds to step S18.

In step ^{_{S18, t * 1, t *}} 2, t * 3 T were determined by applying the number 45 from ^.phi.t _E and T ^phi _E is finished check and process to be consistent.

  As described above, according to the present invention, it is possible to provide a turning acceleration method capable of suppressing the amplitude of residual vibration after reaching the target position when the length of the suspended load rope varies for a tower crane. can do.

  In this way, by using the acceleration input pattern converted to the acceleration input pattern when the suspension rope length fluctuates by applying a nonlinear time scale to the acceleration input pattern with a constant suspension rope length, the concrete placement position Control by an open loop that suppresses residual vibration in the case becomes possible.

  Moreover, when the control method according to the present invention was applied, it was confirmed by simulation using an analysis model that was experimentally confirmed that the occurrence of residual vibration at the target position could be suppressed.

  As can be seen from the above derivation process, the proposed turning acceleration pattern for various hoisting and lowering patterns of the suspended rope length can be set easily and in a short time, and the safety of concrete placement work using a tower crane and This can contribute to labor saving.

  Although the invention made by the present inventor has been specifically described based on the embodiments, the embodiments disclosed herein are illustrative in all respects and are not limited to the disclosed technology. Should not be considered. That is, the technical scope of the present invention should not be construed restrictively based on the description in the above embodiment, but should be construed according to the description of the scope of claims. All modifications that fall within the scope of the claims and the equivalent technology are included.

  When using a program, it can be provided via a network or stored in a recording medium such as a CD-ROM.

  That is, the predetermined program including the image processing program is not limited to being recorded in a storage device such as a hard disk as a recording medium, and the predetermined program can be provided as follows.

  For example, a predetermined program may be stored in the ROM, and the CPU may load the predetermined program from the ROM to the main storage device and execute it.

  Further, the predetermined program may be stored and distributed in a computer-readable recording medium such as a DVD-ROM, CD-ROM, MO (magneto-optical disk), or flexible disk.

  The crane control method according to the present invention can be applied to tower cranes and other cranes applied to dam construction.

101 Concrete kneading plant 102 Transfer car 103 Concrete bucket 104 Wire (rope)
105 Boom 200 Dam Dam Body 300 Drive Control Device

Claims (4)

A crane that pivots a boom and changes the length of the wire while transporting a suspended load suspended from the wire from a conveyance start position to a target position. A crane control method that performs steady rest control to converge residual vibration,
The boom has a constant turning radius, and has a transportation process of turning in the order of an acceleration section, a constant angular speed section, and a deceleration section,
In the transporting process, coordinate conversion is performed so that it is symmetric (a symmetric relationship that is equal when folded) at a time half of the transporting time required from the transport start position to the target position, and the length of the wire A crane control method, wherein acceleration / deceleration control of a turning speed is performed on the basis of a turning acceleration / deceleration pattern calculated according to a change in height and a change in a lifting speed of the suspended load.   2. The crane according to claim 1, wherein when performing acceleration / deceleration control of the turning speed, a time scale is set so that the natural period of the crane does not change, and acceleration / deceleration of the turning speed is converted. Control method.   3. The crane control method according to claim 1, wherein the turning acceleration / deceleration pattern is uniquely determined based on a turning speed in the equiangular speed section. 4. The angle of the boom from the X axis (turning angle) is α, the turning speed is dα / dt, the direction angle of the pendulum from the X axis is ψ, the swing angle of the suspended load is θ, and point B (the tip of the boom) When the turning radius of the crane is r and the suspended rope length is l at the horizontal distance of point O (turning center),
Substituting the α into the following equation,

The crane control method according to claim 3, wherein the turning acceleration and deceleration patterns are calculated.

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