gantry crane system

8/19/2019 Gantry Crane System

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Gantry Crane System

A gantry crane is a popular process for educational purposes in the eld of controlengineering. Most important is that the system is suitable for the demonstration of awide range of control algorithms. With the ongoing improvement of tooling thetesting and implementation trajectory of control algorithms has become more

ecient and therefore faster.

Figure 1 shows a typical gantry crane system. Such a crane is used in harbors forthe loading and unloading of containers to and from ships. The crane M! is movedby a transport belt which is connected to a motor controlled by a fre"uencyconverter. #uring the movement the load m! will oscillate relative to the crane.$ormally the operator of the crane will control the motor in such a way that thismovement will be limited. This oscillating can cause that the load or the truc% isdamaged during the loading process. &n the laboratory scale model the load andthe length of the cable between the load and the crane is 'ed. Also the joints andthe cable between the load and the crane are 'ed. The goal of the controller is to

move the load m! to a new position '! with a minimal overshoot as fast aspossible. The components used for the gantry crane scale model are listed in Table1. To be able to model the gantry crane system a decomposition in four parts can bedone. A model for the motor( the transport belt( the mass M! and the load m!.


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).). *u++y ,ontroller

The actions performed by a fu++y controller are dependant of a rule base. -ased onthe angle of the rod( the deviation in the position and the rule base the controller

decides which voltage is being sent to the motor. *igure is the bloc% diagram of this controller. *irst step when creating a fu++y controller is the denition of themembership functions. *igure /. shows the membership function for the positiondeviation. $e't step is the creation of the membership function for the voltage tothe motor. *igure 0 shows the membership function for the voltage of the motor.1ast step for the creation of the fu++y controller is the rulebase which determineshow the input membership functions are related to the output membershipfunctions Table 2. displays the used rule base. The rulebase can be read as follow.2f the load angle deviation is left and the position deviation is center the motor ,3will be right. Figure 7 gives a graphical representation of the behaviour of the fu++ycontroller. To ma%e the system more 4e'ible gains are connected to the fu++y

controller inputs and outputs 5 rod( 5 pos and 5cv!. With these gains thenormali+ed membership functions can be stretched or compressed withoutchanging the membership functions.


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Figure 1 is being used as a base for the calculations regarding the position of theload. The force in ' direction

Substitute to v

Then the tor"ue is being balanced

*or the simulation and the modelling the approachmentcos6!789sin6!76 is usedand substitution to v is done

With a mathematical tool such as Maple formula 80!and formula 8:! can be usedto create the transfer function for the speed of the load

This is also done for the angle of the load 6;u!


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5.3. Validation of Fuzzy Controller

$e't the fu++y controller was validated. Table 13 shows the parameter list withcontroller settings.

Figure 17 shows the result when a step of


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=2#

*igure 8 shows a schematic diagram of a gantry crane system that is considered inthis wor%. The

parameters of m8( m?( l( x, , T and F are payload mass( trolley mass( cable length(hori+ontal position

of trolley( swing angle( tor"ue and driving force respectively. $onlinear model of thegantry crane

system is modeled based on @). Some assumptions have been made to minimi+ethe diculties of

modeling such as cable of trolley and hanged load are assumed to be rigid andmassless. The system

parameters are shown in Table 8.


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Figure 1. Schematic diagram of a Bantry ,rane System

odeling of a Gantry Crane System

Several methods can be used to model the gantry crane system. *rom theinvestigations( it is found

that the 1agrangeCs e"uation is more suitable to derive the mathematicale'pression for modeling the

system. The B,S has two independent generali+ed coordinates namely trolleydisplacement( x and

payload oscillation( . The standard form for 1agrangeCs e"uation is given asD

8!

where L, Qi and qi represent 1agragian function( nonconservative generali+ed forcesand independent

generali+ed coordinate. The 1agragian function can be written asD

?!

with T and P are respectively %inetic and potential energies. This relationshipinvolved in calculating

on how it is related to be more 4e'ible coordinates. 5inetic and potential energiescan be derived asD


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)!

Solving for equation (1) yields nonlinear differential equations as:

!

/!

Since the dynamic #, motor is included in this gantry crane model( diEerentiale"uations with their

eEects is derived. -y considering the dynamic of #, motor( a complete nonlinear

diEerential e"uation

of the gantry crane can be obtained as e"uation 0! and F! where V is an inputvoltage.

0!

F!

Thus, PID and PD controllers are implemented for this nonlinear gantry crane as shown in figure 3.

Priority-based Fitness Binary Particle Swarm Optimization (PFBPSO)

The basic PSO is developed by Kennedy and Eberhart in 1995. It based on behaviors of fish

schooling and bird flocking in order to search and move to the food with certain speed and position. It

has been applied successfully and applied easily to solve various function optimization problems

especially for nonlinear models. In 1997, Binary PSO (BPSO) has been introduced to solve discrete

optimization problem. Applications of BPSO can be seen in many engineering problems, such as

routing in VLSI, computational biology, job scheduling and agriculture.


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In this research, a new method of Priority-based Fitness Binary Particle Swarm Optimization

(PFBPSO) is proposed for tuning of PID and PD parameters. In this work, settling time (Ts) is set as

highest priority, followed by steady state error (SSE) and overshoot (OS). Figure 2 illustrated the

PFBPSO process where the P BEST and G BEST are updated according to the priority. The particles find for

the local best, P BEST and subsequently global best, G BEST for each iteration in order to search for optimal

solution. Each particle is assessed by fitness function. Thus, all particles try to replicate their historical

success and in the same time try to follow the success of the best agent. It means that the P BEST and

G BEST are updated if the particle has a minimum fitness value compared to the current P BEST and G BEST

value. Nevertheless, only particles that within the range of the system's constraint is accepted. The new

velocity can be calculated and as in equation (8).

:!

Where r1 and r2 represent random function values [0,1] while c1 is cognitive component and c2 is social

component. Next, new particles are updated using equation (9) based on the sigmoid concept which is

probability of the normal distribution. The all five parameters are obtained based on binary numbers

(either 0 or 1) and then converted into decimal number that represents KP, KI, KD, KPS and KDS.

G!


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Figure 2. The 4ow chart of =*-=S& in determining gantry crane system parameters

(a) =rocess of =*-=S& algorithm b! Hpdated rules for PBEST and GBEST

!m"lementation# $esults and %is&ussion

2n this wor%( a control structure that combines =2# and =# controllers as shown ingure ) is proposed. *or this structure( =2# controller is used for the positioningcontrol meanwhile the =#controller is used for adjusting the payload oscillation.

Therefore( =*-=S& algorithm is designed to tune and nd all of these ve optimalparameters of controllers.


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With an input voltage( two system responses namely trolley displacement andpayload oscillation are e'amined. 2n this study( ?< particles are considered with 8


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Subsequently, it is desirable to examine the controller’s performance under various desired

positions. Figure 5 shows the system responses with desired positions at 1.0 m, 0.8 m and 0.2 m. It is

shown that the system response successfully track desired positions. In the PFBPSO algorithm,

overshoot, settling times and payload oscillation are affected with various desired positions. Therefore,

SSE is achieved for all conditions. Table 4 summarizes simulation results with various desired

positions.


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7. $eferen&es


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@8 S. I. $ordfjord and J. =Klsson( L1>B&,rane ,ontroller

using N,O and Nobo1abP. httpD;;fu++y.iau.dtu.d%;

download;legoG;legoG.pdf

@? M. A. Ahmad and A. $. 5. $asir( LJybrid 2nput Shaping

and 1QN control schemes of a Bantry ,rane System(P

Proceedings of te )rd !nternational "onference on

#ecatronics( !"$#R. Salami( L,ontrol

Strategy for Automatic Bantry ,rane SystemsD A

=ractical and 2ntelligent Approach(P !nternational ornal

of &d*anced +ootic S'stems( 3ol. ( $o. ( ?

gantry crane system

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