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Dynamics of an overhead crane under a wind disturbance condition

Dynamics of an overhead crane under a wind disturbance condition

Dynamics of an overhead crane under a wind disturbance condition

Jerzy Tomczyk,Jacek Cink ?,Andrzej Kosucki

Division of Working Machines,Drives and Control,Lodz University of Technology,Poland

a b s t r a c t

a r t i c l e i n f o Article history:

Received 14June 2012Revised 19February 2014Accepted 22February 2014Available online 17March 2014Keywords:

Automatic control State simulator Dynamics

Overhead crane Simulation tests

The following article discusses issues such as a crane control system with a state simulator,problems of load op-eration and positioning under different wind disturbances,the main elements of a dynamic model with a state simulator,a method of wind disturbance compensation and the results of simulation tests.

?2014Elsevier B.V.All rights reserved.

1.Introduction

Most cranes carry loads suspended on ropes.The load is suspended rigidly in a vertical direction and ?exibly in a horizontal direction,which causes load oscillations during working movement.Positioning of the load in a horizontal plane requires an optimum control of mech-anisms which control the motion of the rope suspension point.The mechanisms must contain continuous speed control and position ad-justment systems.

The conducted research included load sway limitation obtained by means of different methods of fuzzy control described in [6,9,10],as well as other methods using optimum or feedback control,e.g.[12,13].In [7],the UMC platform and Fieldbus are used for crane and hoist control.

Most of the presented dynamic models make use of simpli ?ed over-head crane laboratory models.Examples of such models are presented in [6,9,10].Similarly some papers do not take into consideration phe-nomena existing in real objects,e.g.beveling or different parameters of the pendulum for different directions of the bridge and carriage movement.Examples of these are:[8,11,12].

Some of the articles refer to the laboratory models of rotary and boom cranes.In [14]a dynamic model of a crane and methods of its open-loop control with load sway damping without the necessity of load inclination measurement is presented,but only through a proper shape of the control function.

In [16]a crane control system with partial-state feedback is present-ed,with an integrator allowing for simultaneous positioning and damping of load sway.

An experimentally veri ?ed sway-free system for a boom crane with disturbance observers and a trajectory generator which smoothes the reference trajectory online is presented in [17].The whole control sys-tem is implemented in a real harbor mobile crane.

A model of a crane with disturbances from sea-wave-induced ship motion and ship-motion-induced container sway is presented in [15].

In [18],a control system of the crane carriage movement under a dis-turbance condition (e.g.from wind or friction forces)with an observer is presented.The system gives large deviations from the reference tra-jectory during acceleration and deceleration with satisfactory position-ing at the end of a cycle.

References to papers that con ?rm the analogy of the motion of a load suspended to a carriage to a mathematical pendulum,as well as the pro-posal of a sway damping method during deceleration from a constant velocity motion to stop,based on the developed model of a pendulum are presented in [19].

The problem of optimum control was solved by moving the load along a horizontal straight line and dumping load oscillations after the starting and braking phases.A straight trajectory of the load was en-sured due to the simultaneous operation of traveling and traversing mechanisms in the case of a bridge crane,and slewing and jib mecha-nisms in the case of a jib crane.These methods of load positioning were veri ?ed through simulation and experimental tests [2–4].

The methods described above are not suitable for cranes working in the open air.A force caused by the wind acting on a ?exibly suspended load could change its determined trajectory.Our ?rst method [5]of eliminating wind disturbances requires knowledge of wind force acting on the load.To determine this factor,data such as the shape of the load or wind direction and velocity should be measured.This makes it possi-ble to calculate the correction of the load position which constitutes an input for the mechanism adjustment system.The rope suspension point

Automation in Construction 42(2014)100–111

?Corresponding author:Lodz University of Technology Division of Working Machines,Drives and Control K-111ul.Stefanowskiego 1/15,90-924?ód ?,Poland.

E-mail addresses:jerzy.tomczyk@p.lodz.pl (J.Tomczyk),jacek.cink@p.lodz.pl (J.Cink),andrzej.kosucki@p.lodz.pl (A.

Dynamics of an overhead crane under a wind disturbance condition

Kosucki).http://www.wendangku.net/doc/20b629c37cd184254a35356b.html/10.1016/j.autcon.2014.02.0130926-5805/?2014Elsevier B.V.All rights

Dynamics of an overhead crane under a wind disturbance condition

reserved.

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should be moved along the corrected trajectory,so that the real load trajectory should be compatible with the assumed one.The drawback of this method is the necessity of wind velocity and direction measurement.

The method presented in this paper uses a state simulator [1].One of the elements of the crane automatic control system is a real object whose mathematical model is called a state simulator,operating simul-taneously in real time.The real object and the state simulator have the

same input signals.In the case of the state simulator,calculations are carried out for windless conditions,whereas in the case of the real object the load suspended on ropes is under wind action.The action of wind disturbances changes the motion of the real object (load)and the time waveforms of the load position are different than the

Dynamics of an overhead crane under a wind disturbance condition

Fig.1.The dynamic model of a rope-suspended load.

Symbols used in Figs.1and 2:

S rope suspension point,v b velocity of point S along the direction of the bridge movement,v c velocity of point S along the direction of the carriage movement,v resultant velocity of the suspension point,L Q length of the ropes,Q force of wind action on the load,H horizontal component of the force in the rope,x Q displacement of the load along the direction of the bridge movement,y Q displacement of the load along the direction of the carriage movement,v Qx velocity of the load along the direction of the bridge movement,v Qy velocity of the load along the direction of the carriage movement,v Q resultant velocity of the load,m Q mass of the load,r relative horizontal position of the rope suspension point relative to the load,αangle de ?

Dynamics of an overhead crane under a wind disturbance condition

ning the direction of r and H vectors,βangle de ?ning the direction of the wind pressure force vector on the load,v w wind velocity,v wq relative velocity of the wind to the velocity of the load,αw angle de ?ning the direction of the wind velocity vector.

Fig.2.Relative air velocity with respect to the load.

ω

Fig.3.A physical model of overhead crane plane motion.

The symbols used in this model are described as follows:C center of the overhead crane mass,x l left co-ordinate of the center of the overhead crane mass,x r right co-ordinate of the center of the overhead crane mass,P l driving force of the left end carriage,P r driving force of the right end carriage,H horizontal component of the force in the rope,W l movement resistance force of the left end carriage,W r movement resistance force of the right end carriage,m cl mass of the left end carriage,m cr mass of the right end carriage,m b mass of the bridge,m c mass of the carriage,L ec length of the end carriage,L ecw wheelbase of the end carriage,l l location of the carriage from the left,l r location of the carriage from the right,L overhead crane span,v cb velocity of the overhead crane mass center,ωb angular velocity around the overhead crane mass center.

β

α

Fig.4.The de ?nition of points P and K and determination of the velocity of the suspension point.x p,start position of point S along the direction of the bridge movement,x k end position of point S along the direction of the bridge movement,y p start position of point S along the direction of the carriage movement,y k

end position of point S along the direction of the carriage movement,v bmax maximum permissible speed of the bridge traveling mechanism,v cmax

maximum permissible speed of the carriage traveling mechanism.

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J.Tomczyk et al./Automation in Construction 42(2014)100–111

theoretical ones(without disturbances).A deviation,i.e.the value of the difference between the theoretical and the real load position is entered into the regulator as a correction signal.The regulator determines the correction signal only for the real object control system as long as the deviation is limited to a minimal value.The presented method makes it possible to improve the accuracy of load movement without any knowledge of wind speed and direction.

2.A dynamic model of an overhead crane and a control system

The dynamic model of a load suspended on ropes is presented in Fig.1.

The determination of relative air velocity with respect to the load v wQ is shown in Fig.2.

The mathematical model of a load suspended on ropes in the space of state variables taking into account wind action is as follows:

dv Qx

dt

?

f Q

m Q

áv wQácosαw

eT?

f Q

m Q

áv Qxt

c Q

m Q

áx Qe1T

dv Qy

dt

?

f Q

m Q

áv wQásinαw

eT?

f Q

m Q

áv Qyt

c Q

m Q

áy Qe2T

dx Q

dt

??v Qxtv b?x l?l l

eTáωbe3T

dy Q

dt

??v Qytv ce4Twhere v Qx,v Qy,x Q and y Q are the de?ned state variables.

Fig.5.A diagram of the overhead crane control system with wind disturbance compensation.

a

b

Fig.6.Determination of the load position deviation a)and of the corrected position of the load rope suspension point b). 102J.Tomczyk et al./Automation in Construction42(2014)100–111

The inputs of this model are components determining the velocity of the rope suspension point S:v b and v c and the angular velocity of the bridge:ωb.

The state space method was used for a bridge and carriage dynamic description.A physical model of their elements was made.An example of an overhead crane physical model is presented in Fig.3.

Motion equations based on the assumption of rigid constraints with-out kinematic losses were used in the mathematical description of the overhead crane bridge and carriage plane motion.Examples of motion equations describing overhead crane dynamics in a general form are as follows:

–a motion equation of the mass center:

dv b

dt

?

X

Fe5

Dynamics of an overhead crane under a wind disturbance condition

Dynamics of an overhead crane under a wind disturbance condition

T

a) Compensation system awitched off

b) Compensation system awitched on

Fig.7.Load oscillation damping:v w wind velocity,v sg determined velocity of the load suspension point,ΔQ deviation of the model(state simulator)relative to the real load positions,ΔQ Sg load displacement relative to the determined load suspension point S g,ΔS displacement of the determined load suspension point S g relative to its real position S.

103

J.Tomczyk et al./Automation in Construction42(2014)100–111

–a rotational motion equation in a horizontal plane relative to the mass center:I á

d ωb ?X

T :e6T

The main task of the control system is to determine the control func-tion for moving the load from the initial point P (x p ,y p )to the terminal point K (x k ,y k )(Fig.4).The load rope suspension point S is moved along the horizontal straight line PK and the load oscillations are damped

before a steady motion and after stopping at point K as well.The wind disturbance compensation system operates continuously all the time,independently of the control system.

The main part of the overhead control system with wind disturbance compensation is presented in Fig.5.Load motion in a horizontal plane is possible owing to the overhead bridge crane traveling and traversing mechanisms.The input signals (Fig.5)are as follows:

–determined velocity of the bridge traveling mechanism v bg ,–determined velocity of the carriage traveling mechanism v cg .

a) Compensation system switched off

b)

Dynamics of an overhead crane under a wind disturbance condition

Dynamics of an overhead crane under a wind disturbance condition

Compensation system switched on

Fig.8.Trajectories:S g the given load suspension point trajectory,S the real load suspension point trajectory,Q the real load trajectory.

104J.Tomczyk et al./Automation in Construction 42(2014)100–111

These signals are sent to the continuously operating electronic con-troller which generates the determined position of the bridge x g and carriage y g,i.e.the determined coordinates of the rope suspension point S.Positions x g and y g are determined by the controller by integrat-ing the determined signals of bridge velocity v bg and carriage velocity v cg in real time:

x g?Z

v bgádty g?

Z

v cgádt:e7T

The determined x g and y g positions are compared with the real posi-

tion of point S(coordinates x and y).Signals of the determined velocities

of the load rope suspension point:v bg,v cg,x g and y g are simultaneously

transmitted to:

a)a block which simulates the load suspended on ropes(the state

simulator),

b)a correction block of the bridge and carriage velocity and position.

The state simulator solves the mathematical model of the load

suspended on ropes in real time.The model describes the load behavior

a) Compensation system switched off

b)

Dynamics of an overhead crane under a wind disturbance condition

Dynamics of an overhead crane under a wind disturbance condition

Compensation system switched on

Fig.9.Load oscillation damping:v w,v sg,ΔQ,ΔQS g andΔS—as in Fig.6.

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J.Tomczyk et al./Automation in Construction42(2014)100–111

without wind action and determines the theoretical load position given by the coordinates x Qt and y Qt .

The correction block,called the load position regulator,determines the corrected signals of the load suspension point S,both in the direc-tion of the bridge (velocity v bgc ,position x gc )and in the direction of the carriage relative to the bridge (velocity v cgc ,position y gc ).These sig-nals depend on the load position deviation εQ whose components are determined as follows:εQ x ?x Qt ?x Q

εQ y ?y Qt ?y Q

e8T

where x Q and y Q —the real load position components.

The aim of the wind disturbance compensation system is to reduce the load position deviation εQ to zero,which means that the load moves along the same trajectory as in the case of the absence of wind disturbances.The components of the load position deviation deter-mined by the measurement and control systems are transmitted as input signals to the position and velocity correction block of the load rope suspension point (Fig.5).

The method of determining the load position deviation error is shown in Fig.6a.A correction of the position of the load suspension point S causes the elimination of the load position deviation.The real load positions x Q and y Q are measured in real time.

a) Compensation system switched off

b)

Dynamics of an overhead crane under a wind disturbance condition

Dynamics of an overhead crane under a wind disturbance condition

Compensation system switched on

Fig.10.Trajectories:S g the given load suspension point trajectory,S the real load suspension point trajectory,Q the real load trajectory.

106J.Tomczyk et al./Automation in Construction 42(2014)100–111

The compensation system functions as a proportional regulator with a gain coef ?cient k,which determines the new position of the load sus-pension point S gc displaced relative to the theoretical position S g by the vector Δin a steady motion:ΔR ?k áεQ

εQ ?εQx tεQy :

e9T

The corrected velocity of point S is the same as the determined velocity (v sgc =v sg ).

3.Overhead crane dynamics under a wind disturbance condition Dynamic models of overhead crane drives and control were used for the development of computer programs to carry out laboratory over-head crane simulation dynamic tests with disturbance.A comparison of system dynamics can be made by switching on or off the compensa-tion system in the model,which makes it possible to check the in ?uence of the state simulator on the overhead crane working movement dy-namics.The duty cycle covers load transportation from the starting point P to the end point K along the straight line PK with a simultaneous

a) Compensation system switched off

b)

Dynamics of an overhead crane under a wind disturbance condition

Dynamics of an overhead crane under a wind disturbance condition

Compensation system switched on

Fig.11.Load oscillation damping:v w ,v sg ,ΔQ,ΔQS g and ΔS —as in Fig.6.

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J.Tomczyk et al./Automation in Construction 42(2014)100–111

motion of traveling and traversing mechanisms.Symbols x and y were assigned to represent the direction of the bridge movement and the di-rection of the carriage movement,respectively.The trajectory length PK was determined so as to carry out three phases of movement:starting,steady motion and braking.

The main purpose of the research was to determine the in ?uence of the control system with wind disturbance compensation on the over-head crane dynamics with a state simulator.Simulation tests including cases of the wind disturbance com-pensation system switched on or off were carried out for compari-son.In each case,load oscillation damping after the starting and braking phases was obtained for constant wind velocity v w =22m/s and constant wind direction perpendicular to the line PK,which is shown in Fig.7.The load position deviation ΔQ is high when the compensation system is off and reduced to zero when the system is on.

a) Compensation system switched off

b)

Dynamics of an overhead crane under a wind disturbance condition

Dynamics of an overhead crane under a wind disturbance condition

Compensation system switched on

Fig.12.Trajectories:S g the given load suspension point trajectory,S the real load suspension point trajectory,Q the real load trajectory.

108J.Tomczyk et al./Automation in Construction 42(2014)100–111

The load and its suspension point trajectory are important for the evaluation of the overhead crane operation with wind disturbance. They are shown in Fig.8for the same wind.

The real trajectory of the load Q in Fig.8a is displaced with regard to the determined trajectory PK.It is the result of wind action on the load with the compensation system switched off.The load does not move along the given trajectory in this case.When the compensation system is switched on,the load is moved along the given trajectory PK(Fig.8b) and the trajectory of the load suspension point S is displaced with refer-ence to the load trajectory,which compensates wind disturbance.

The results of research on wind velocity disturbance with a single impulse of wind velocity are shown in Figs.9and10.The wind velocity impulse has a shape of a half-sinusoid with an amplitude of22m/s and time of activity of2s with the wind direction perpendicular to the line PK.The impulse appears during steady motion.Load oscillations (Fig.9a)cannot be damped when the compensation system is switched off.The load oscillates after the braking phase as well(Fig.9a).

When switched on,the compensation system makes it possible to stop the working movement of the load at the determined point K. Load oscillations are damped as well(Fig.10b).

The compensation system works properly with a linear increase of wind velocity from0to22m/s during1s in a steady motion and at a wind direction perpendicular to the line PK(Figs.11and12).

The reaction of the compensation system against a disturbance is clearly visible in Fig.11b.The end of a duty cycle with the load posi-tioned in point K without oscillations is shown in Fig.12b.Load oscilla-tion damping is impossible when the compensation system is switched off(Fig.12a).

4.Experimental veri?cation

Experimental tests were carried out on a real overhead crane(Fig.13) characterized by the following parameters:

load Q=5[t]

bridge span L=10[m]

bridge track length L t=16[m]

nominal bridge speed v m=34[m/min]

nominal carriage speed v w=34[m/min]nominal hoisting speed v p=10[m/min]

hoisting height H=6.6[m].

Experimental tests of the compensation system for an overhead crane are conducted only in the motionless state of the crane.The load hanging on ropes is displaced in a horizontal direction by a force which simulates wind pressure.The compensation system is turned on and causes such a horizontal displacement of the rope suspension point(opposite to the direction of the load displacement)that the load is held in the previous position by de?ected ropes.

Time-based charts that show the movements of the bridge and car-riage driving mechanisms which compensate wind disturbances ap-plied to the load are presented in Figs.14–15.

The results of experimental tests of the compensation system co-operating with the traveling mechanism(in the direction of the bridge motion)are presented in Fig.14.The bridge moves in a direction oppo-site to the direction of the disturbance force,which allows the load to re-main at the start position.

In Fig.15,in a similar manner as for the bridge,experimental tests of the carriage are presented.In this case,the correct operation of the com-pensation system is evident and operational requirements are also met.

5.Conclusions

The conducted simulation tests con?rmed the correct operation of the presented control system.In conditions of wind action,the position of the rope suspension point was automatically changed to keep the load being under wind pressure in the given position.

In all tests,wind velocity was assumed to be perpendicular to the load trajectory,i.e.to be most unbene?cial.The maximum value of wind velocity was22m/s,which resulted in wind pressure at the level of300N/m2according to the terminal permissible conditions of crane operation.

Model research carried out for a constant wind direction and veloc-ity(Figs.7and8)showed that the load was moved along the assumed trajectory PK with high accuracy during working movement.

The simulation tests conducted for a sinusoidal wind impulse which appeared in a steady motion con?rmed the stability of the

Dynamics of an overhead crane under a wind disturbance condition

adjustment Fig.13.The experimental stand—an overhead crane.

109 J.Tomczyk et al./Automation in Construction42(2014)100–111

system (Figs.9and 10).Although the adjustment time was equal to about 10s,the oscillations of the load suspension point and load posi-tion decreased to zero (Fig.9b),also after the braking phase.The devia-tion of the load position in relation to the determined trajectory PK was low all the time (Fig.10b).The results of the simulation tests carried out for a wind ramp signal increasing with time (from zero to 22m/s)1s and appearing in a steady motion con ?rmed the stability of the adjustment system (Figs.11and 12).The oscillations faded (Fig.11b).The load was moved along the straight line PK with high accuracy (Fig.12b).

-150

-100-50050100150200250300350400450500550600650

Dynamics of an overhead crane under a wind disturbance condition

-300

-200-1000100200300

4005006007008009001000110012001300Fig.15.Corrective motions of a “stopped ”overhead crane carriage under disturbances acting on the load.W disturbance force acting on the load parallel to the bridge x wr corrective movement of the carriage,x Qw load position,

φQwr

vertical angle of load sway.

-150

-100-50050100150200250300350400450500550600650

Dynamics of an overhead crane under a wind disturbance condition

-300

-200-100

100

200300

400500600700

8009001000

110012001300Fig.14.Corrective motions of a “stopped ”overhead crane bridge under disturbances acting on the load.W disturbance force acting on the load perpendicularly to the bridge,x mr corrective movement of the bridge,x Qm load position,

φQmr

vertical angle of load sway.

110J.Tomczyk et al./Automation in Construction 42(2014)100–111

The good quality of the wind disturbance compensation system was con?rmed only on the grounds of simulation and simpli?ed experimental tests.The satisfactory effects of theoretical and simpli?ed experimental tests are the basis for wider experimental tests con?rming good operation of described system.The wider experimental tests of described overhead crane are presently carried.

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