research article an iterative learning control technique

Research ArticleAn Iterative Learning Control Technique for Point-to-PointManeuvers Applied on an Overhead Crane

Khaled A. Alhazza,1 Abdullah M. Hasan,1 Khaled A. Alghanim,1 and Ziyad N. Masoud2

1 Department of Mechanical Engineering, Kuwait University, P.O. Box 5969, Safat, 13060 Kuwait City, Kuwait2 Department of Mechatronics Engineering, The German-Jordanian University, Amman 11180, Jordan

Correspondence should be addressed to Khaled A. Alhazza; [email protected]

Received 14 March 2014; Accepted 28 April 2014; Published 12 May 2014

Academic Editor: Mohammad Elahinia

Copyright © 2014 Khaled A. Alhazza et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

An iterative learning control (ILC) strategy is proposed, and implemented on simple pendulum and double pendulummodels of anoverhead crane undergoing simultaneous traveling andhoistingmaneuvers.The approach is based on generating shaped commandsusing the full nonlinear equations ofmotion combinedwith the iterative learning control, to use as acceleration commands to the jibof the crane. These acceleration commands are tuned to eliminate residual oscillations in rest-to-rest maneuvers. The performanceof the proposed strategy is tested using an experimental scaled model of an overhead crane with hoisting. The shaped commandis derived analytically and validated experimentally. Results obtained showed that the proposed ILC control strategy is capable ofeliminating travel and residual oscillations in simple and double pendulummodels with hoisting. It is also shown, in all cases, thatthe proposed approach has a low sensitivity to the initial cable lengths.

1. Introduction

One of the major problems in industries that involve craneoperations is payload oscillations in point-to-point cranemaneuvers. Many control techniques have been developedin the past few decades to reduce these residual oscillations.Point-to-point maneuvers of cranes pose a major challengeto crane controller designers. A large bulk of research havebeen devoted to dynamics and control of cranes [1]. Themain objective of such research is to eliminate the travel andresidual oscillations and/or reduce maneuvers time.

Massive payloads are generally transferred using cranes.Inefficient crane operations can cause substantial productiondelays, devastating property damage, and even loss of lives. Tomaintain fast and safe crane operations, many feedback andfeedforward control techniques were proposed. Researchershave successfully used feedback for oscillation control ofcranes [2–7]. Although feedback controllers can effectivelyreduce residual oscillations, these controllers may requireinstallation of additional hardware on the crane or in somecases alteration to the existing system. These changes may becostly or impractical.

To overcome such disadvantages of feedback controllers,open-loop techniques are becoming more popular especiallyin point-to-point maneuvers. Input-shaping crane controlstrategy is considered one of the most commonly used open-loop techniques and it can be defined as amethod of reducingresidual oscillations by convolving a sequence of impulseswith a baseline reference command [8–10]. If the baselinecommand is constant, then the produced command is aninput-shaped step function.

Several input-shaping techniques were derived in the pastfour decades. Early step shapers were designed to eliminatethe residual oscillations of crane payloads at themodeled nat-ural frequency and damping ratio. These shapers are knownas zero vibration (ZV) input shaper. Many command shapershave been developed later on to increase the robustness ofthe ZV shaper. Vaughan et al. [10] compromised betweenrapidity of motion and shaper robustness for several input-shaping methods. They showed that robust shapers typicallyhave longer durations that slow the system response. Usingsimulation and experiments, Terashima et al. [11] developeda three-dimensional open-loop control strategy for sway-free,point-to-point maneuvers of a rotary crane. They showed

Hindawi Publishing CorporationShock and VibrationVolume 2014, Article ID 261509, 11 pageshttp://dx.doi.org/10.1155/2014/261509

2 Shock and Vibration

that the proposed control method is effective in eliminatingresidual oscillations and centrifugal force influence. Starr[12] used a symmetric double-step acceleration profile totransport a suspended object with minimal oscillations. Alinear approximation of the oscillation period was used tocalculate the switching times and to generate an analyticalexpression for the acceleration profile. This work was laterextended by employing a nonlinear approximation of thepayload frequency to generate single-step and double-stepsymmetric acceleration profiles [13].

Kress et al. [14] proved analytically that input shapingis equivalent to a notch filter applied to a general inputsignal and centered around the natural frequency of thepayload oscillations. They applied a second-order robustnotch filter to shape the acceleration input of a gantrycrane. Numerical simulation and experimental verification ofthis strategy implemented on an actual bidirectional crane,moving at arbitrary step acceleration and changing cablelength at a slow constant speed, showed that the strategywas able to efficiently suppress residual payload oscillation.Their work was later extended by developing an input-shaping notch filter to reduce payload oscillation of rotarycranes excited by operator commands. It was reported that,in general, there was no guarantee that applying such filterto the operator’s speed commands would result in excitationterms having the desired frequency content and that it onlyworks for low speed and acceleration commands [15]. Parkeret al. [16] experimentally verified their numerical simulationresults.

Other types of command shapers were used in theliterature. A new single stage variable acceleration profile wasintroduced by Alhazza and Masoud [17]. They successfullyeliminated travel and residual payload oscillations of anoverhead crane. Their approach resulted in an accelerationprofile which was smoother compared to the double-stepacceleration profile.Their work was later extended to includethe effect of damping [18]. Numerical simulations and exper-iments proved that the proposed profiles were capable ofeliminating residual oscillations for different damping ratios[19].

A significant part of the research on crane control wasfocused on simple pendulum models of a crane with aconstant cable length, to avoid the complexity of analyses thatinclude hoisting. It is well known that hoisting introducestime varying parameters in the equations of motion. Theseparameters make solving such equations very challenging.Following this line of research, many researchers introducednew shapers and techniques. Singhose et al. [20] studied fourdifferent input-shaping controllers considering the effect ofhoisting. In their work, they reported that the best input-shaper produced a reduction of 73% in transient oscillationsover the time-optimal rigid-body commands. They alsoshowed that input-shaping technique using constant lengthcan reduce residual vibrations to acceptable levels with-out eliminating them. Masoud and Daqaq [21] successfullyextended the double-step shaped-commands to accommo-date large hoisting maneuvers. Performance was validated ona scaled experimental model of a container crane performinglarge simultaneous hoisting and traversing maneuvers.

New line of research has emerged recently on commandshaping for double pendulum models of cranes. The interestin such research is due to the fact that the mass of the hookused, in heavy lift cranes, can be so large that the payloadand the hoisting mechanismmay exhibit a double pendulumbehavior [22, 23]. In such application, designing a controlsystem using a simple pendulum model suffers a majordrawback due to the uncontrolled second mode oscillations.Such control systems may even induce larger second modeoscillation amplitude.

In multidegrees of freedom systems, command shapersdesigned for the first mode may eliminate higher modes ofoscillations provided that their frequencies are odd integermultiples of the first mode frequency. Using this fact,Masoudet al. [24] and Masoud and Alhazza [25] used model-based feedback to develop command shapers for a doublependulum model of an overhead crane.

A rest-to-rest maneuver is a repeated process that exe-cutes the same task with the same initial conditions.This factmade the iterative learning control (ILC) technique a perfectcandidate for such application. There are many learningcontrol techniques, such as adaptive control, neural network,and repetitive control (RC). Iterative learning controlmethodis a cyclical process that modifies the input commandsat each cycle or repetition. Research using this techniquefaces many challenges, especially because of jerks in thecommand profiles and slow system rise time. Wang et al.[26] reviewed and compared three different control methods:iterative learning control (ILC), repetitive control (RC), andrun-to-run control (R2R). In their work, they approximatelycategorized 400 papers related to learning-type control. Inaddition, a flowchart based on the unique features of thedifferent methods is presented as a guideline for choosingan appropriate learning-type control for different problems.Scardua et al. [27] studied the use of reinforcement learning(RL) for developing a time-optimal antiswing control of aship unloader. They used double-step functions to optimizethe output. In real world, there are many industrial systemsthat perform repeated processes. ILC has been used success-fully in many applications [28–42].

In the present work, iterative learning control techniqueis proposed and implemented experimentally on a model ofan overhead crane to reduce residual oscillations of simpleand double pendulum systems with hoisting. The approachis based on generating a discrete time shaped accelera-tion command profile using the full nonlinear equationsof motion, complemented with iterative learning controltechnique. The number of discrete time points is chosenbased on the level of accuracy required or in accordancewith the actual experimental crane minimum time steps.The proposed approach modifies input commands at eachrepetition of a cyclical process. As the learning processmakes more progress in identifying the system’s output,the predicted next repetition output comes closer to theactual output, and, consequently, the learning method yieldsimproved results. The controller parameters, such as time,maximum acceleration, maximum velocity, and accelerationjumps or jerks, are tuned to eliminate residual oscillationsin rest-to-rest maneuvers. The controller performance is

Shock and Vibration 3

Payload

Hook

Moving cart (crane jib)

Hoisting cable l1

uy

x

𝜃

m1

𝜙

m2

Connecting cable l2

Figure 1: Overhead crane with a massive hook model.

determined analytically and validated experimentally on ascaled model of an overhead crane. Results obtained showedthat the proposed control technique is capable of eliminatingresidual oscillations in both simple and double pendulumcases.

2. Mathematical Model

Most of the research on crane control simplifies the cranedynamics as a simple pendulum system. Although thisassumption is valid for some cases and can result in signif-icant performance improvement, large payloads or massivehooks may give rise to significant second mode oscillations.In such cases, single mode controller would produce subop-timal performance. To solve this problem, double pendulummodels are used to represent cranes with large payloads.

In this work, an overhead crane with a large hook ismodeled as a double pendulum. The length of the hoistingcable, 𝑙

1, is considered variable; see Figure 1. The length 𝑙

2of

the cable connecting the payload to the hook of the crane isassumed to be constant.The position vectors to the hook,𝑚

1,

and the payload of the crane,𝑚2, are

p1= [𝑢 − 𝑙

1sin (𝜃) , −𝑙

1cos (𝜃)] ,

p2= [𝑢 − 𝑙

1sin (𝜃) − 𝑙

2sin (𝜙) ,

−𝑙1cos (𝜃) − 𝑙

2cos (𝜙)] .

(1)

Using (1), the kinetic and potential energies are

𝑇 =1

2𝑚1p1⋅ p1+1

2𝑚2p2⋅ p2,

𝑉 = 𝑚1𝑔𝑝1𝑦

+ 𝑚2𝑔𝑝2𝑦.

(2)

Applying Lagrange’s formulation, the nonlinear equationsof motion of the double pendulum model in terms of thegeneralized coordinates 𝜃 and 𝜙 are

(𝑚1+ 𝑚2) [𝑙2

1

𝜃 + 𝑙1𝑔 sin (𝜃) + 2𝑙

1𝑙1𝜃]

+ 𝑚2𝑙1𝑙2[ 𝜙 cos (𝜃 − 𝜙) + 𝜙

2 sin (𝜃 − 𝜙)]

= (𝑚1+ 𝑚2) 𝑙1cos (𝜃) ��,

𝑚2𝑙2

2𝜙 + 𝑚2𝑙2𝑙1sin (𝜃 − 𝜙)

− 𝑚2𝑙2𝑙1[ 𝜃2 sin (𝜃 − 𝜙) − 𝜃 cos (𝜃 − 𝜙)]

+ 2𝑚2𝑙2𝑙1𝜃 cos (𝜃 − 𝜙) + 𝑚

2𝑔𝑙2sin (𝜙)

= 𝑚2𝑙2cos (𝜙) ��.

(3)

3. Learning Control

Learning control method is a cyclical process that, in general,modifies the input commands in repeated cycles. Each cyclestarts with, typically, the same initial conditions. Identifyingeffect of the system’s input on the system’s output directly,without taking into consideration the dynamics of the system,is the key behind learning control process. The followingderivation clarifies the concept of learning control technique.Consider a cyclic system of piecewise step inputs at fixed timesteps; the system output at any repetition can be expressed as

𝑌𝑖= 𝐵𝑖𝑈𝑖+ er𝑖, (4)

where

𝑌𝑖= [ 𝑦𝑖 (Δ𝑡) 𝑦

𝑖(2Δ𝑡) 𝑦

𝑖(3Δ𝑡) ⋅ ⋅ ⋅

𝑦𝑖((𝑝 − 1) Δ𝑡) 𝑦

𝑖(𝑝Δ𝑡) ]

𝑇

𝑈𝑖= [ 𝑢𝑖 (0) 𝑢

𝑖(Δ𝑡) 𝑢

𝑖(2Δ𝑡) ⋅ ⋅ ⋅

𝑢𝑖((𝑝 − 2) Δ𝑡) 𝑢

𝑖((𝑝 − 1) Δ𝑡) ]

𝑇

.

(5)

𝑌𝑖is the system output vector of length 𝑝, 𝐵

𝑖is the 𝑝 ×

𝑝 system parameter matrix, 𝑈𝑖is the system input vector of

length𝑝, and er𝑖is the estimated error vector of length𝑝, with

all being at the 𝑖th repetition.The system parameter matrix 𝐵 can be initiated arbi-

trarily; however, the initial estimation of this matrix has aconsiderable effect on the progression of the identificationprocess. Since the exact parameter matrix is unpredictable,it is suggested to start with the identity matrix as an initialestimation of 𝐵. By assuming a very small error er

𝑖in (4), the

next repetition output is expressed as

𝑌𝑖+1

= 𝐵𝑖+1

𝑈𝑖+1

. (6)

Since 𝐵𝑖+1

cannot be predicted without knowing 𝑌𝑖+1

,therefore, assuming a small change in the matrix 𝐵 betweeneach two consecutive iterations,𝐵

𝑖will be used instead of𝐵

𝑖+1.

Therefore, (6) can be written as

𝑌𝑖+1

≈ 𝐵𝑖𝑈𝑖+1

= 𝐵𝑖(𝑈𝑖+ 𝛿𝑈𝑖+1

) = 𝑌𝑖+ 𝐵𝑖𝛿𝑈𝑖+1 (7)


and the difference between the actual output and desiredoutput is given by

𝑒𝑖+1

= 𝑌∗− 𝑌𝑖+1

= 𝑌∗− 𝑌𝑖− 𝐵𝑖𝛿𝑈𝑖+1

, (8)

where 𝑒𝑖is the variation between the actual and desired

output at the 𝑖th repetition and 𝑌∗ is the desired output.

As more information pertaining to the system is acquired,the estimated output that comes from matrices calculationsbecomes closer to the system’s actual output. In sequence, thevariation and error term decrease and 𝑌

𝑖+1becomes closer to

𝑌∗.For explaining the optimizing process, consider a fitness

function 𝐽 that needs to be minimized as follows:

𝐽 =1

2𝑒𝑇

𝑖+1𝑄𝑒𝑖+1

+1

2𝛿𝑈𝑇

𝑖+1𝑆𝛿𝑈𝑖+1

, (9)

where𝑄 and 𝑆 are weighingmatrices. In fact, matrix𝑄worksto put more effort in minimizing the variation, while 𝑆 triesto minimize the input differences among repetitions.

Substituting 𝑌𝑖+1

from (7) into (9), the resulted equationis differentiated with respect to 𝛿𝑈

𝑖+1, which gives

𝜕𝐽

𝜕𝛿𝑈𝑖+1

= −𝐵𝑇

𝑖𝑄 (𝑌∗− 𝑌𝑖) + 𝛿𝑈

𝑇

𝑖+1𝐵𝑇

𝑖𝑄𝐵𝑖+ 𝛿𝑈𝑇

𝑖+1𝑆. (10)

To solve for the optimal input, we set (10) to zero and solvefor 𝛿𝑈

𝑖+1, which leads to

𝛿𝑈𝑖+1

= (𝐵𝑇

𝑖𝑄𝐵𝑖+ 𝑆)−1

𝐵𝑇

𝑖𝑄 (𝑌∗− 𝑌𝑖) , (11)

where

𝑈𝑖+1

= 𝑈𝑖+ 𝛿𝑈𝑖+1

. (12)

In order to reduce jumps between input points or jerks,the differences between input values at the same repetitionshould be minimized; therefore, a smoothing matrix 𝐾 isintroduced as

𝐾 =

{{

{{

{

1, 𝑖 = 𝑗,

−1, 𝑗 = 𝑖 + 1,

0, 𝑖 = 𝑗, 𝑗 = 𝑖 + 1

(13)

and the term1

2(𝐾𝛿𝑖)𝑇

𝑊(𝐾𝛿𝑖) (14)

is added to (9). In result, (11) becomes

𝛿𝑈𝑖+1

= (𝐵𝑇

𝑖𝑄𝐵𝑖+ 𝑆 + 𝐾

𝑇𝑊𝐾)−1

× [𝐵𝑇

𝑖𝑄 (𝑌∗− 𝑌𝑖) − 𝐾𝑇𝑊𝐾𝑈

𝑖] ,

(15)

where 𝑊 is weighing identity matrix of smoothing term.Matrix 𝑊 works to put more effort in minimizing inputdifferences in the same repetition.

To keep the system parameter matrix applicable in esti-mating the next repetition output and to keep the learningprocess within its range, reducing changes among repetitionsin the system’s input is important. If the system’s inputvaries widely in two consecutive repetitions, the learningand identifying processes become unfeasible. So, it is vital tomaintain the differences in the input small enough.

Figure 2: Experimental model.

4. Numerical and Experimental Validation

To verify the performance of the proposed method, four testcases are presented. The first two cases are of a simple pen-dulum with a constant cable length and a simple pendulumwith hoisting. The other two cases are of a double pendulumwith a constant cable length and a double pendulum with avariable hoisting cable length.

A MATLAB code is used to calculate the optimizedacceleration of the jib of the crane.This acceleration is used tonumerically solve the equations ofmotion; see (3). Results arethen compared with results obtained using an experimentalmodel of the overhead crane (see Figure 2).

The experimental model of the overhead crane is a3D crane made by INTECO. The model is located in theAdvanced Vibration Lab at Kuwait University. The motionsof the jib and the bridge of the crane are controlled by twoidentical DC motors. Five optical encoders are used to mea-sure the state variables of the crane; two encodersmeasure thejib and bridge motions, two encoders measure the oscillationangles of the hoisting cable, and one encoder measures thelength of the hoisting cable. The resolution of the encoders is1024 pulses per rotation.The interface between a PC runningMATLAB’s real-time Simulink environment and the cranesetup is achieved using an RT-DAC/PCImultipurpose digitalI/O board. The jib of the crane has a maximum speed of0.3m/s and a maximum acceleration of 0.9m/s2. The cranehas a 0.6m usable jib and bridge tracks. Light weight cablesare used with two masses representing the crane hook andpayload.

In the following tests, the bridge of the crane is fixed andonly planar motion is considered. The incremental encoderinstalled on the jib of the crane, which measures the oscil-lation angle, 𝜃, of the hoisting cable, is used for monitoringpurposes only. It is important here to emphasize that theproposed control technique is an open-loop technique.

4.1. Simple Pendulum Crane with a Constant Cable Length.The length of the hoisting cable length is set to 0.4m.The mass of the payload is 0.21 kg. Using these parameters,the optimized acceleration profile is generated as shown inFigure 3(a). The velocity and the displacement of the jib arealso shown in Figure 3(a). The maximum velocity of the jib


0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

Time (s)

Jib m

otio

n

AccelerationVelocity

DisplacementTORB acceleration

−1

−0.8

−0.6

−0.4

−0.2

(a) TORB and ILC acceleration profiles

0 1 2 3 4

0

0.05

0.1

0.15

0.2

0.25

Time (s)

Experimental ILC Numerical ILC

TORB

−0.25

−0.2

−0.15

−0.1

−0.05

𝜃(r

ad)

(b) Oscillation angle of the hoisting cable

0.7 0.8 0.9 1 1.1 1.2 1.30

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

NumericalExperimental

Length ratio ls l1/

Ang

le𝜃

(rad

)

(c) Residual oscillation sensitivity

Figure 3: Simulations and experiments on a simple pendulum for𝑚 = 0.21 kg payload and 𝑙 = 0.4m hoisting cable.

and a displacement of 0.55m are used as constraints for theILC. It is clear that the proposed ILC technique is capable ofutilizing the full capability of the crane.

Without a reference to the payload oscillations, the fastestmaneuver is achieved using the time-optimal rigid-body(TORB) acceleration profile. Based on the jib maximumvelocity and acceleration, the time needed to complete aTORB maneuver is 2.2 seconds.

Experimental and simulated oscillation angle of thehoisting cable, as shown in Figure 3(b), demonstrate theeffectiveness of the ILC technique in eliminating residual

oscillations. A small discrepancy between the experimentaland simulated results is observed, which is attributed tomanyunmodeled nonlinearities, such as friction and mechanicalbacklash. Further examination of Figure 3(b) shows that themaximum transient oscillation angle using the ILC profileis 0.08 rad while it rises to 0.15 rad using the TORB profile.Furthermore, residual oscillations are reduced by approxi-mately 99%. The complete maneuver time of the ILC is 2.9seconds.Despite being longer than theTORBmaneuver time,the extra time is a small price to pay for the 99% reductionin the residual oscillation. The sensitivity of ILC to modeling


0 0.1 0.2 0.3 0.4 0.5 0.6Jib displacement

Cabl

e len

gth

−0.1

−0.56

−0.54

−0.52

−0.5

−0.48

−0.46

−0.44

(a) Maneuver profile

0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

Time (s)

Jib m

otio

n

−1

−0.8

−0.6

−0.4

−0.2



(b) ILC and TORB acceleration profiles

0 1 2 3 4

0

0.05

0.1

0.15

0.2

0.25

Time (s)

−0.25

−0.2

−0.15

−0.1

−0.05

𝜃(r

ad)


TORB

(c) Oscillation angle of the hoisting cable

0.7 0.8 0.9 1 1.1 1.2 1.30

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Ang

le𝜃

(rad

)

Length ratio ls l1/

NumericalExperimental

(d) Residual oscillation sensitivity

Figure 4: Simulations and experiments on a simple pendulum for𝑚 = 0.21 kg and variable hoisting cable length.

error in the hoisting cable length, and hence in the designfrequency, is shown in Figure 3(c). Further examination ofFigure 3(c) shows that 10% error in initial cable length resultsin approximately a 0.02-radian final residual angle. With thislarge initial error of 10%, the performance of the proposedtechnique sustains a reduction of almost 92% compared tothe TORB.

4.2. Simple Pendulum Crane with Hoisting. In this test, thecomplexity of the task increases due to the effect of hoisting

on the system dynamics. Simultaneous hoisting and jibmotion are performed. Hoisting is assumed to be linear as

𝑙 = 𝑙0+ 𝑅𝑡, (16)

where 𝑅 is the hoisting speed. The length of the hoistingcable is changed from 0.55m to 0.45m during the accel-eration phase and then increased from 0.45m to 0.5m inthe deceleration phase; see Figure 4(a). The accelerationprofiles in Figure 4(b) show a small time penalty on theILC profile compared to the TORB complete maneuver time.


0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

Time (s)

Jib m

otio

n

−1

−0.8

−0.6

−0.4

−0.2



(a) ILC and TORB acceleration profiles

0 1 2 3 4

0

0.05

0.1

0.15

0.2

Time (s)

−0.2

−0.15

−0.1

−0.05

𝜃(r

ad)


TORB

(b) Oscillation angle of the hoisting cable

0.7 0.8 0.9 1 1.1 1.2 1.30

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Ang

le𝜃

(rad

)

Length ratio ls l1/

Numerical 𝜃Numerical 𝜙

Experimental 𝜃

(c) Sensitivity of residual oscillations of 𝑙1

0.5 0.6 0.7 0.8 0.9 1 1.1 1.20

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Ang

le𝜃

(rad

)

Length ratio ls l2/


Experimental 𝜃

(d) Sensitivity of residual oscillations of 𝑙2

Figure 5: Simulations and experiments on a double pendulum with no hoisting.

The change in the hoisting cable length used is limited by the0.12m/s maximum hoisting speed of the experimental crane.Significant reduction in residual oscillations is achieved; seeFigure 4(c).The sensitivity of ILC tomodeling errors is shownin Figure 4(d). Comparing Figure 4(d) with Figure 3(c) showsthat underestimating the initial cable length results in anincrease in the final residual vibration while overestimatingthe initial length results in a decrease in the final residualangle. It is worth noting that the sensitivity curves are afunction of the initial length, velocity, hoisting speed, andacceleration. Changing any of these parameters results in a

small change in the sensitivity curve but keeps the generalshape.

4.3. Double Pendulum Crane with a Constant Hoisting CableLength. In this test, a double pendulum is attached to the jibof the crane with an upper mass of 0.105 kg representing thehook of the crane and a lower mass of 0.210 kg representingthe crane payload.The length of the hoisting cable is set to 𝑙

1=

0.40mwhile the length of the connecting length is arbitrarilyset to 𝑙

2= 0.17m (see Figure 1).


0 0.1 0.2 0.3 0.4 0.5 0.6Jib displacement

Cabl

e len

gth

−0.1−0.34

−0.33

−0.32

−0.31

−0.3

−0.29

−0.28

−0.27

−0.26

−0.25

−0.24

(a) Maneuver profile

0 1 2 3 4

00.20.40.60.8

1

Time (s)

Jib m

otio

n

−1

−0.8

−0.6

−0.4

−0.2



(b) TORB and ILC acceleration commands

Time (s)0 1 2 3 4

00.05

0.10.15

0.20.25

−0.25

−0.2

−0.15

−0.1

−0.05𝜃(r

ad)


TORB

(c) Oscillation angle of the hoisting cable

0.7 0.8 0.9 1 1.1 1.2 1.30

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Ang

le𝜃

(rad

)

Length ratio ls/l1


Experimental 𝜃

(d) Sensitivity of residual oscillations of 𝑙1

0.5 0.6 0.7 0.8 0.9 1 1.1 1.20

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Ang

le𝜃

(rad

)

Length ratio ls/l2


Experimental 𝜃

(e) Sensitivity of residual oscillations of 𝑙2

Figure 6: Simulations and experiments on a double pendulum with hoisting.


In the double pendulum test cases, only the oscillationangle of the hoisting cable is measured. Figure 5(a) showsthat the ILC profile satisfies the maximum velocity anddisplacement constraints.

Figure 5(b) shows some discrepancy between simulatedandmeasured oscillation angle due tomodeling uncertaintiesand neglected nonlinearities. Due to this discrepancy, mea-sured residual oscillations were reduced by 98% compared tothe complete elimination of these oscillations in simulatedresults. A small time penalty of approximately 0.6 secondswas the price of that 98% oscillation reduction.

The sensitivity of residual oscillations in the angles of thehoisting and connecting cables is shown in Figures 5(c) and5(d), respectively. Figure 5(c) shows that a 10% error in theinitial length results in a final residual vibration of only 0.01radian and 20% error results in an angle less than 0.02 radian.The same observation is noticed in Figure 5(d). An interestingobservation is obtained by further inspection of these figures,which shows that the ILC is less sensitive to modeling errorsin the case of a double pendulum model compared to thesimple pendulum model case. Again, changing any of thesystem parameters results in a small quantitative change inthe performance of the controller.

4.4. Double Pendulum Crane with Hoisting. In this test, thelength of the hoisting cable is changed linearly as in (16).Thischange in length is very challenging since both frequencies ofthe double pendulum change during maneuver. In this test,hoisting takes place during the acceleration and decelerationphases only.

The initial cable length was set to 0.3m. The cruisingcable length was 0.25m.The final hoisting cable length at theend of the maneuver was 0.33m; see Figure 6(a). ILC andTORB inputs are shown in Figure 6(b). It is clear that, evenwith such a complicated case, ILC successfully satisfies systemconstraints in terms of maximum velocity and displacement.Despite the complexity of the test, Figure 6(c) shows excellentperformance of the ILC both simulated and measured, andthe residual vibrations are reduced by almost 99%.

Sensitivity curves for both oscillation angles of the hoist-ing and the connecting cables are shown in Figures 6(d) and6(e), respectively. Figure 6(d) shows that a 10% change inthe initial length estimation results in a small residual angleof 0.015 radian. This result showed that, unlike the simplependulum, the effect of hoisting increased the sensitivity ofthe controller performance. On the other hand, Figure 6(e)shows that a 10% error in the initial estimation results inonly a 0.005-radian residual angle.This result showed that thehoisting reduces the sensitivity of the system to errors in theinitial mass estimation.

It is worth noting that the proposed technique success-fully handled numerically all the cases examined even withhigh hoisting speed, larger acceleration, small initial length,different number of points, and so forth. All parameters inthe demonstrated cases examined, such as the number ofpoints, maximum acceleration, distance, maximum speed,and hoisting speed, are chosen to be within the experimentalconstrains.

5. Conclusions

In the present work, an iterative learning control techniqueis proposed to generate acceleration profiles of overheadcrane maneuvers involving hoisting. The proposed ILC tech-nique is most useful for applications where repeated auto-mated maneuvers are involved. Simulations and experimentsdemonstrate the effectiveness of the proposed ILC techniquein eliminating residual oscillations in simple pendulumand double pendulum models of overhead cranes. Whilecompletely eliminated in simulations, experiments on rest-to-rest maneuvers using ILC result in a reduction of residualoscillations of approximately 98%. The ILC technique isshown to handle maneuvers involving hoisting as effectivelyas cases with no hoisting with small calculating efforts.The ILC demonstrated significant robustness and reducedsensitivity to modeling errors and uncertainties.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

References

[1] E. M. Abdel-Rahman, A. H. Nayfeh, and Z. N. Masoud,“Dynamics and control of cranes: a review,” Journal of Vibrationand Control, vol. 9, no. 7, pp. 863–908, 2003.

[2] Z. N. Masoud, A. H. Nayfeh, and D. T. Mook, “Cargo pendu-lation reduction of ship-mounted cranes,”Nonlinear Dynamics,vol. 35, no. 3, pp. 299–311, 2004.

[3] Z. N.Masoud, A. H. Nayfeh, andN. A. Nayfeh, “Sway reductionon quay-side container cranes using delayed feedback con-troller: simulations and experiments,” Journal of Vibration andControl, vol. 11, no. 8, pp. 1103–1122, 2005.

[4] H. Schaub, “Rate-based ship-mounted crane payload pendula-tion control system,” Control Engineering Practice, vol. 16, no. 1,pp. 132–145, 2008.

[5] S.-K. Cho and H.-H. Lee, “A fuzzy-logic antiswing controllerfor three-dimensional overhead cranes,” ISA Transactions, vol.41, no. 2, pp. 235–243, 2002.

[6] D. Liu, J. Yi, D. Zhao, and W. Wang, “Adaptive sliding modefuzzy control for a two-dimensional overhead crane,” Mecha-tronics, vol. 15, no. 5, pp. 505–522, 2005.

[7] H. M. Omar and A. H. Nayfeh, “Gantry cranes gain schedulingfeedback control with friction compensation,” Journal of Soundand Vibration, vol. 281, no. 1-2, pp. 1–20, 2005.

[8] W. Singhose, “Command shaping for flexible systems: a reviewof the first 50 years,” International Journal of Precision Engineer-ing and Manufacturing, vol. 10, no. 4, pp. 153–168, 2009.

[9] K. L. Sorensen, W. Singhose, and S. Dickerson, “A controllerenabling precise positioning and sway reduction in bridge andgantry cranes,” Control Engineering Practice, vol. 15, no. 7, pp.825–837, 2007.

[10] J. Vaughan, A. Yano, and W. Singhose, “Comparison of robustinput shapers,” Journal of Sound and Vibration, vol. 315, no. 4-5,pp. 797–815, 2008.

[11] K. Terashima, Y. Shen, and K. Yano, “Modeling and optimalcontrol of a rotary crane using the straight transfer transfor-mation method,” Control Engineering Practice, vol. 15, no. 9, pp.1179–1192, 2007.


[12] G. P. Starr, “Swing-free transport of suspended objects with apath-controlled robot manipulator,” Journal of Dynamic Sys-tems, Measurement and Control, vol. 107, no. 1, pp. 97–100, 1985.

[13] D. R. Strip, “Swing-free transport of suspended objects: a gen-eral treatment,” IEEE Transactions on Robotics and Automation,vol. 5, no. 2, pp. 234–236, 1989.

[14] R. L. Kress, J. F. Jansen, andM.W.Noakes, “Experimental imple-mentation of a robust damped-oscillation control algorithmon a full-sized, two-degree-of-freedom, AC induction motor-driven crane,” in Proceedings of the 5th International Symposiumon Robotics andManufacturing: Research, Education, and Appli-cations (ISRAM ’94), pp. 585–592, Maui, Hawaii, USA, 1994.

[15] G.G. Parker, K.Groom, J.Hurtado, R.D. Robinett, and F. Leban,“Command shaping boom crane control system with nonlinearinputs,” in Proceedings of the IEEE International Conference onControl Applications (CCA ’99), vol. 2, pp. 1774–1778, KohalaCoast, Hawaii, USA, August 1999.

[16] G. G. Parker, K. Groom, J. E. Hurtado, J. Feddema, R. D.Robinett, and F. Leban, “Experimental verification of a com-mand shaping boom crane control system,” in Proceedings of theAmerican Control Conference (ACC ’99), pp. 86–90, San Diego,Calif, USA, June 1999.

[17] K. A. Alhazza and Z. N. Masoud, “A novel wave-formcommand-shaping control with application on overheadcranes,” in Proceedings of the ASME Dynamic Systems andControl Conference (DSCC ’10), pp. 331–336, Cambridge, Mass,USA, September 2010, DSCC2010-4132.

[18] K. A. Alhazza, A. Al-Shehaima, and Z. N. Masoud, “A con-tinuous modulated wave-form command-shaping for dampedoverhead cranes,” in Proceedings of the ASME InternationalDesign Engineering Technical Conferences & Computers andInformation in Engineering Conference, Washington, DC, USA,August 2011, DETC2011-48336.

[19] K. A. Alhazza, “Experimental validation on a continuous mod-ulated wafe-form command shaping applied on damped sys-tems,” in Topics in Dynamics of Civil Structures, Volume 4, Pro-ceedings of the 31st IMACConference on Structural Dynamics,Proceedings of the Society for Experimental Mechanics Series39, Springer, Garden Grove, Calif, USA, 2013.

[20] W. E. Singhose, L. J. Porter, and W. P. Seering, “Input shapedcontrol of a planarGantry cranewith hoisting,” inProceedings ofthe JIn American Control Conference, pp. 97–100, Albuquerque,NM, USA, 1997.

[21] Z. N. Masoud andM. F. Daqaq, “A graphical approach to input-shaping control design for container cranes with hoist,” IEEETransactions on Control Systems Technology, vol. 14, no. 6, pp.1070–1077, 2006.

[22] M. Kenison and W. Singhose, “Input shaper design for double-pendulum planar gantry cranes,” in Proceedings of the IEEEInternational Conference on Control Applications (CCA ’99), pp.539–544, Kohala Coast, Hawaii, USA, August 1999.

[23] D. Kim and W. Singhose, “Reduction of double-pendulumbridge crane oscillations,” in Proceedings of the 8th InternationalConference on Motion and Vibration Control (MOVIC ’06), pp.300–305, Daejeon, Korea, 2006.

[24] Z. N. Masoud, K. A. Alhazza, M. A. Majeed, and E. A.Abu-Nada, “A hybrid command-shaping control system forhighly accelerated double-pendulumgantry cranes,” inProceed-ings of the ASME International Design Engineering TechnicalConferences (DETC ’09) and Computers and Information inEngineering Conference (CIE ’09), pp. 1809–1817, San Diego,Calif, USA, September 2009, Paper no. DETC2009-87501.

[25] Z. N. Masoud and K. A. Alhazza, “Command-shaping controlsystem for double-pendulum gantry cranes,” in Proceedings ofthe ASME International Design Engineering Technical Confer-ences & Computers and Information in Engineering Conference,Washington, DC, USA, August 2011, Paper no. DETC2011-48400.

[26] Y.Wang, F. Gao, and F. J. Doyle III, “Survey on iterative learningcontrol, repetitive control, and run-to-run control,” Journal ofProcess Control, vol. 19, no. 10, pp. 1589–1600, 2009.

[27] L. A. Scardua, J. J. da Cruz, andA.H. R. Costa, “Optimal controlof ship unloaders using reinforcement learning,” AdvancedEngineering Informatics, vol. 16, no. 3, pp. 217–227, 2002.

[28] S. Arimoto, S. Kawamura, and F.Miyazaki, “Bettering operationof robots by learning,” Journal of Robotic Systems, vol. 1, no. 2,pp. 123–140, 1984.

[29] D. A. Bristow and A. G. Alleyne, “A manufacturing system formicroscale robotic deposition,” in Proceedings of the AmericanControl Conference, pp. 2620–2625, June 2003.

[30] H. Elci, R. W. Longman, M. Phan, J.-N. Juang, and R. Ugoletti,“Discrete frequency based learning control for precisionmotioncontrol,” in Proceedings of the IEEE International Conference onSystems, Man and Cybernetics, pp. 2767–2773, October 1994.

[31] W. Messner, R. Horowitz, W.-W. Kao, and M. Boals, “A newadaptive learning rule,” IEEE Transactions on Automatic Con-trol, vol. 36, no. 2, pp. 188–197, 1991.

[32] M. Norrlof, “An adaptive iterative learning control algorithmwith experiments on an industrial robot,” IEEE Transactions onRobotics and Automation, vol. 18, no. 2, pp. 245–251, 2002.

[33] D. I. Kim and S. Kim, “An iterative learning control methodwith application for CNCmachine tools,” IEEE Transactions onIndustry Applications, vol. 32, no. 1, pp. 66–72, 1996.

[34] D. de Roover and O. H. Bosgra, “Synthesis of robust multivari-able iterative learning controllers with application to a waferstage motion system,” International Journal of Control, vol. 73,no. 10, pp. 968–979, 2000.

[35] H. Havlicsek and A. Alleyne, “Nonlinear control of an elec-trohydraulic injection molding machine via iterative adaptivelearning,” IEEE/ASME Transactions on Mechatronics, vol. 4, no.3, pp. 312–323, 1999.

[36] F. Gao, Y. Yang, and C. Shao, “Robust iterative learning controlwith applications to injection molding process,” Chemical Engi-neering Science, vol. 56, no. 24, pp. 7025–7034, 2001.

[37] M. Pandit and K.-H. Buchheit, “Optimizing iterative learningcontrol of cyclic production processes with application toextruders,” IEEE Transactions on Control Systems Technology,vol. 7, no. 3, pp. 382–390, 1999.

[38] S. S. Garimella and K. Srinivasan, “Application of iterativelearning control to coil-to-coil control in rolling,” in Proceedingsof the American Control Conference, vol. 2, pp. 1230–1234, AlcoaCenter, Pa, USA, June 1995.

[39] S. A. Saab, “A stochastic iterative learning control algorithmwith application to an induction motor,” International Journalof Control, vol. 77, no. 2, pp. 144–163, 2004.

[40] A. D. Barton, P. L. Lewin, and D. J. Brown, “Practical imple-mentation of a real-time iterative learning position controller,”International Journal of Control, vol. 73, no. 10, pp. 992–999,2000.

[41] W. Hoffmann, K. Peterson, and A. G. Stefanopoulou, “Iterativelearning control for soft landing of electromechanical valveactuator in camless engines,” IEEE Transactions on ControlSystems Technology, vol. 11, no. 2, pp. 174–184, 2003.


[42] Y. Q. Chen and K. L.Moore, “A practical iterative learning path-following control of an omni-directional vehicle,”Asian Journalof Control, vol. 4, no. 1, pp. 90–98, 2002.

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal ofEngineeringVolume 2014

Submit your manuscripts athttp://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


research article an iterative learning control technique

Documents