DOUBLE-PENDULUM CRANE OPERATOR PERFORMANCE …people.ucalgary.ca/~ajeya.karajgikar/...Finalpaper.pdf · DOUBLE-PENDULUM CRANE OPERATOR PERFORMANCE COMPARING PD-FEEDBACK CONTROL AND

Advances in Computational Multibody DynamicsMULTIBODY DYNAMICS 2011,ECCOMAS Thematic ConferenceBrussels, Belgium, 4-7 July 2011

DOUBLE-PENDULUM CRANE OPERATOR PERFORMANCECOMPARING PD-FEEDBACK CONTROL AND INPUT SHAPING

Ajeya Karajgikar †, Joshua Vaughan † and William Singhose†

†Woodruff School of Mechanical EngineeringGeorgia Institute of Technology,

Atlanta, GA 30332e-mail: [email protected],[email protected],[email protected]

Keywords: Double Pendulum, Input Shaping, PD-Feedback Control, Operator Performance

Abstract. A primary limitation on crane operations is the difficulty of controlling payloadoscillations. Given the significance of cranes, it is not surprising that a large amount of re-search has been dedicated to eliminating crane payload oscillation. Numerous feedback-based control methods have been proposed. Command-shaping is another method thathas received significant attention. This paper compares the two methods for double-pendulum crane control. Using feedback control on double-pendulum cranes can bequite challenging because sensing the payload and hook motion is difficult. The paperpresents a study of ten novice crane operators using representative two-mode input shap-ing and feedback-control methods. In this study, both feedback control and input shapingreduced average task completion time from the manually controlled case; however, inputshaping provided the lowest average completion time. Input shaping also allowed theoperators to move the trolley over a shorter total path length to complete the tasks, sug-gesting that input shaping may save energy compared to feedback and manual controlmethods. Implementing input shaping also resulted in zero obstacle collisions during thetests thereby improving safety.

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[email protected], [email protected], [email protected]

Ajeya Karajgikar, Joshua Vaughan and William Singhose

1 INTRODUCTION

Cranes have a wide range of applications in manufacturing, construction, and shipping port ac-tivities. Thus, improving crane efficiency and safety can have a great impact on a wide varietyof industries. All cranes share the same problem of inefficiency caused by payload oscilla-tions. Payload swing makes it difficult to manipulate payloads quickly, accurately and safely.The problem is further compounded when the payload creates a double-pendulum effect. Thispaper compares the control of a double-pendulum crane payload with input shaping and PD-feedback control. The results of crane operator studies comparing these two control methodsare also presented.

To illustrate this problem, consider the double-pendulum crane model in Fig. 1. In this planarmodel, the hook is connected to the crane trolley via an inflexible cable of length l1 and thepayload is attached to the hook with a massless, inflexible rigging of length l2. The mass ofthe hook and payload are mh and mp, respectively.

Example trolley and payload responses for a simple, point-to-point move are shown in Fig. 2.The payload oscillates around the trolley position during and after the move. This oscillationmakes it difficult to accurately position the payload and increases task completion time, whiledecreasing safety. The frequencies and the associated amplitudes depend heavily on the pay-load configuration [1–4].

Many researchers have suggested feedback methods to control payload oscillation. A thoroughreview of these techniques developed during the 20th century is presented in [5]. However, toachieve reliable feedback control, critical challenges in crane operation must be overcome. Thefirst problem is that most researchers assume that the crane payload is well known and its statesare easily sensed. This is typically not the case. Crane payloads continually change, leading tovarying dynamic effects, especially when the crane payload and hook create double-pendulumeffects. These changing dynamics are especially difficult for feedback control systems; un-known and/or greatly varying high-modes are difficult to control and can lead to instability.

In addition to the lack of knowledge about payload characteristics, payload states are also verydifficult to sense. Several payload sensing systems have been proposed, but they are eitherimpractical in real working conditions or very expensive, which limits their use to a smallfraction of expensive cranes.

γ

φ

Trolley

Hook, mh

Payload, mp

l2

l1

u(t)

Figure 1: Double Pendulum Crane Model

00.10.20.30.40.50.60.70.8

0 2 4 6 8 10

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Posi

tion

(m)

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Figure 2: Example Trolley and Payload Responses

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Another major factor of crane operation that should be considered during control design andimplementation is the fact that nearly all cranes are controlled by human operators. This hasseveral important implications. The first of these is that the crane control system needs tobe compatible with human operators. Systems that create non-intuitive crane behavior can beunsettling to the crane operator and, as a result, ultimately detrimental to crane performance.The second factor is that the human operator is a feedback controller. It is well known thatcompeting feedback controllers can degrade performance. This is especially true given thatthe human feedback control properties can vary widely from task-to-task and from operator-to-operator. The changing human feedback control properties can make it difficult to tunecomputerized feedback control systems for compatibility.

Input shaping is a control method that reduces payload oscillation by filtering the human-operator commands [6, 7]. This approach has several advantages over feedback-based con-trollers. One main advantage is that no computerized feedback is used, leaving the humanoperator as the sole feedback controller. As such, it is compatible with human operators, assupported by the results from numerous crane-operator studies [3, 4, 8, 9].

All that is needed to implement input shaping are estimates of the natural frequencies anddamping ratios (which are near zero for most cranes). A major advantage compared to feed-back control is that, for input shaping design, these estimates need not be calculated in realtime. The input shaper can also be made robust to changes in these frequencies and dampingratios with little penalty [7, 10, 11].

In the next section, the challenges of using feedback for crane control are discussed in de-tail. Then, in Section 3, the input-shaping method is reviewed. The advantages and disadvan-tages of each method are discussed throughout the text. The implementation of a PD-feedbackcontroller and an input-shaping controller on a 10-ton industrial bridge crane is discussed inSection 4. A study of ten novice crane operators is then presented in Section 5.

2 USING FEEDBACK CONTROL ON CRANES

One major challenge of implementing feedback control systems on crane is the difficulty inaccurately and robustly sensing the crane payload. Another major challenge is human-operatorcompatibility. This section will discuss these two challenges in more detail.

2.1 Sensing Crane Payloads

In order to successfully implement a feedback control system, there must be some way to ac-curately and reliably sense the system motion. Many researchers proposing feedback methodsfor crane control assume that either the payload or hook can be easily sensed. In practice, thisassumption proves false.

However, there are a few methods that have been used with some success: machine vision,gyroscopes and simple, angle sensors are examples. Some researchers have proposed visionsystems mounted throughout the crane workspace and have shown them to work well in labo-ratory conditions [12, 13]. Cranes at Georgia Tech [14] and Logan Aluminum [15] have beenequipped with trolley-mounted vision systems to track the crane hook. However, machine vi-sion has several potential drawbacks. The systems mentioned above were all located in fairly

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Figure 3: Tower Crane in Seattle, WA

Figure 4: Image from Trolley-Mounted Vision Sys-tem

controlled environments, where lighting conditions were fairly constant and background clut-ter was minimal. Many cranes operate in conditions that are significantly less ideal. Visionsystems will have additional difficulties in the crowded, harsh, and changing environments inwhich many cranes operate. For example, a vision system on a tower crane like the one shownin Fig. 3 would have to be able to separate the hook and payload from the background clutterof the surrounding buildings and streets. It would also have to do this over a very large rangeof suspension cable lengths.

Even under ideal conditions, sensing the crane payload is not trivial. One obvious location tomount a machine vision system is overhead, attached to the crane trolley. This provides thebest opportunity to keep the crane hook and payload in the camera field-of-view. In this con-figuration, tracking the crane hook is the most straightforward, given the correct environmentalconditions (lighting, etc.). However, the crane hook and suspension cables obscure the cam-era’s view of the payload. For example, the image in Fig. 4 was taken by a trolley-mountedcamera. The hook and suspension cables fill a significant portion of the image, blocking thepayload below.

Other researchers have used gyroscope-based sensing solutions with some success [16–18].In this work, the gyroscopic measurements are often coupled with secondary means of sens-ing, such as potentiometers measuring cable deflection, and observers are used to smooth theresulting signals. The design and implementation of such observers introduces an additionallayer of complexity to the system.

In addition to the difficulties associated with sensing the location of the payload, most cranefeedback controllers also require accurate knowledge of higher-order states, such as the ve-locity of the payload. With constantly varying payload sizes, shapes, material, etc., measuringhigher-order states can be much more challenging than sensing payload location. With eachadditional sensor necessary to measure the states of the payload, additional complexity, design

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time, failure modes, and cost is added to the controller.

2.2 Conflict Between Feedback and Human Operators

Another major challenge of implementing feedback control is conflict with human operators.For pre-designated motions, feedback control of cranes, ignoring the difficulties mentionedabove, can work well. However, most cranes are not operated via a computer or driven throughpre-defined trajectories. Rather, they are controlled in real time by human operators. Hereinlies the challenge. The human operator provides not only the initial reference command tothe crane, but also introduce adjustments and additional feedback as necessary to maneuverthe crane through the desired trajectory. Any additional input from a computerized feedbackcontroller can adversely conflict with the input from the human operator. For example, craneoperators at the Port of Savannah in Georgia intentionally disable the anti-sway feedback sys-tems because they interfere with their "expert" methods of manually eliminating swing.

3 INPUT SHAPING

Input shaping is a command shaping method that has been successfully used to limit cranepayload oscillations [2–4, 8, 9, 19]. Another related method uses Infinite Impulse Response(IIR) filters [20]. Figure 5 demonstrates the input-shaping process. A series of impulses isconvolved in real-time with the original reference command to create a shaped command.In Fig. 5, the original velocity pulse command is transformed into a staircase command thatmoves the system without oscillation.

The amplitudes and time locations of the impulses that compose an input shaper are designedusing estimates of the natural frequencies and damping ratios. There are always errors in theseestimates, so input shapers can be made robust to changes in these parameters [7,10,11]. Thisis a much different requirement than knowing the states of the system in real-time, as is neededwith feedback control. To design an input shaper, these estimates can be determined, and thedesign can be completed offline. Once the shaper is designed, no further knowledge of thecrane states is needed. In addition, shapers can be designed to account for system nonlinearities[21, 22] and to eliminate multiple modes of vibration [2, 23–25].

In addition to eliminating the need for payload sensors, the command-shaping nature of thecontrol system is compatible with human operators. This fact is supported by numerous studiesof crane operators [3, 4, 8, 9]. The primary disadvantage of input shaping is that it is unable toreduce oscillation caused by disturbances to the hook or payload, due to its open-loop nature.

0 Δ

*

Figure 5: The Input-Shaping Process

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Figure 6: 10-ton Industrial Bridge Crane

GpPD

Humanyd y

eq +

++

-

Figure 7: PD-Feedback Controller

GpInput ShaperHumanyd

y

Figure 8: Input-Shaping Controller

4 CONTROL OF A 10-TON INDUSTRIAL BRIDGE CRANE

Both feedback and input-shaping control methods were implemented on the 10-ton industrialbridge crane in Fig. 6. It has a workspace that is 6 meters high, 5 meters wide, and 42 meterslong. Signals generated by the human operator travel from the push-button control pendent tothe hoist controls and bridge-and-trolley control box. A Siemens PLC performs the control al-gorithms. The crane is also equipped with a Siemens vision system to track the hook response.This vision system is also the primary sensor when the feedback control system is used on thecrane.

The block diagram in Fig. 7 is a conceptual representation of the feedback system implementedon the bridge crane. The machine vision system is used to feed back the hook deflection, θ, to aProportional-Derivative (PD) feedback controller. The human operator acts as a feedback con-troller on position, issuing velocity commands based upon the current and desired positions ofthe crane, y and yd, respectively. The commands created by the human operator are combinedwith those from the PD-controller on payload oscillation and issued to the crane.

It should be noted that the operating conditions of the crane tested here are favorable forthe machine-vision-based feedback system. The area below the crane is generally clear ofobstacles and other items that could make distinguishing the hook from the image backgrounddifficult. In addition, the lighting in the crane workspace is fairly constant, further reducingthe necessary complexity of the vision system. On many industrial cranes, such favorable

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Figure 9: "Manual" Control Point-to-point Move

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Figure 10: PD-Feedback Control Point-to-pointMove

conditions would not exist.

A block diagram of the input-shaping control system is shown in Fig. 8. Because input shapingdoes not require feedback, the control system structure is much simpler. The human operatorstill acts to position the crane. However, his/her commands are modified by the input shaperbefore they are issued to the crane so that they do not excite significant oscillation.

4.1 Example Point-to-Point Moves

To compare the effectiveness of the proposed control methods, straight line 3 m point-to-pointmoves were conducted on the crane in Fig. 6. For these trials, a 22.7 kg (50 lb) payload wasattached to the 50 kg (110 lb) crane hook via a 1.8 m rigging. The resulting frequencies fromthis double-pendulum payload configuration were 0.26 Hz and 1.61 Hz. The PD-control gainsand two-mode ZV input shaper [25] parameters were selected for this system configuration.

A response from a 3 m point-to-point move of the 10-ton bridge crane using “manual” control(no feedback or input shaping) is shown in Fig. 9. The hook oscillates around the locationof the trolley both during the move and after it is completed. The low damping of the cranemeans that this oscillation continues for a significant amount of time, unless stopped manually.A similar move using the PD-feedback control system is shown in Fig. 10. The feedback con-troller greatly reduces the hook oscillation. The two-mode ZV shaper is able to reduce payloadoscillation to nearly zero for this move, as shown in Fig. 11. The input-shaped response alsoexhibits lower oscillation during the move than the PD-feedback control system. This can beseen in Fig. 12, which shows the hook deflection for the three control cases. Both the peakamplitude of transient vibration and the residual amplitude of oscillation are lower with in-put shaping than with PD control. Both controllers provide significant improvements over themanually controlled case.

4.2 Example Point-to-Point Moves – Controllers Designed for Single Mode

As previously mentioned, sensing crane payloads is difficult. One control design option is todesign the controller to eliminate only the low, pendulum mode and ignore higher modes. Formany applications, this is a valid control strategy, as this lower mode dominates the oscillatoryresponse. This section will examine the effect of ignoring the second mode of oscillation on

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Figure 11: Two-Mode ZV Shaped Point-to-pointMove

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ManualPD-Feedback ControlTwo-mode ZV-Shaped

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Figure 12: Hook Angle for Point-to-point Moves

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Figure 13: PD-Feedback Control (One-ModeGains) Point-to-point Move

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Figure 14: Single-Mode ZV Shaped Point-to-pointMove

the crane with parameters identical to those tested in Sec. 4.1.

A PD-feedback control system that was designed to control the movement of a single-pendulum payload was implemented on the double-pendulum payload configuration [26]. Theresponse of the crane for a point-to-point move with this controller is shown in Fig. 13. Asingle-mode Zero Vibration (ZV) input shaper [7] was also designed for the low mode of thecrane and used to move the payload of a crane. Figure 14 shows the implementation of thisone-mode ZV input shaper on the double-pendulum crane. Using a single-mode ZV shaperresulted in less oscillation of the payload than both the unshaped and PD-feedback controllerdesigned for a single-mode, as shown by the hook-deflection plots in Fig. 15. Figure 16 showsall of the hook angle deviations for the five different control methods described above. Thisprovides a clear comparison between the responses when the double-pendulum mode is con-sidered during design and when it is not. It is clearly advantageous to account for the secondaryoscillatory mode.

4.3 Double-Pendulum Controller Robustness

In order to test the robustness of the PD-feedback controller and the two-mode ZV shaperto changes in payload configuration, different masses were attached, but gains and shaperparameters left were left unchanged. The payload was first changed from 22.7 kg (50 lb) to11.35 kg (25 lb). The result of the point-to-point move under PD-feedback control is shown

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0.0 5.0 10 15 20 25 30 35 40A

ngle

(deg

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Figure 15: Hook Angle for Point-to-point Moves(Controllers Designed for One Mode only)

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ManualPD Feedback (Single-Pend. Gains)PD Feedback (Double-Pend. Gains)One-Mode ZV ShaperTwo-Mode ZV Shaper

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le (d

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Figure 16: Overview of Hook Angle for Point-to-point Moves

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Figure 17: PD-Feedback Control Point-to-pointMove for 11.35 kg (25 lb) Payload

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Figure 18: Two-Mode ZV-Shaped Point-to-pointMove for 11.35 kg (25 lb) Payload

in Fig. 17. The result of the point-to-point move is shown in Fig. 18. The ZV-shaped responseexhibits much lower oscillation than the PD controlled response, indicating it is more robustto the change in payload than the feedback controller.

The same PD gains and two-mode ZV shaper were used to move the crane with a 34 kg (75lb) payload over a 3 m point-to-point move. The response under PD-feedback control is shownin Fig. 19. The result of the point-to-point move using the two-mode ZV shaper is shown inFig. 20. It can be seen that using the ZV shaper reduces the residual oscillations even if thereis a change in the payload mass. However, the PD-feedback controller exhibits significantlymore payload oscillation than at the configuration for which it was designed.

5 STUDIES OF HUMAN CRANE OPERATORS

The effects of input shaping on human crane operator performance have been well studied[3, 4, 8, 9]. Fewer studies have been conducted with feedback control methods. This sectionwill present a study that compares operator performance with “manual” control to that withfeedback control and with input shaping.

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Figure 19: PD-Feedback Control Point-to-pointMove for 34 kg (75 lb) Payload

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Figure 20: Two-Mode ZV-Shaped Point-to-pointMove for 34 kg (75 lb) Payload

Nominal Path

Start End

1.50 m

3.00 m

1.75 m

1.00 m

0.25 m

Obstacles

0.50 m

Figure 21: Obstacle Course Used for Operator Study

5.1 Operator Study Protocol

Ten novice operators were asked to complete a series of tasks using the industrial bridge crane.The crane operators completed trials on the obstacle course shown in Fig. 21. The task assignedto the operators was to move the crane payload from the 0.25 m diameter start circle, througha set of obstacles, to the 0.5 m diameter target as quickly and safely as possible.

The crane suspension cable length was set to approximately 3.5 m, and a rigging of 1.8 m wasused to attach a 22.7 kg (50 lb) payload. Operators did not raise or lower the crane payloadduring any trial. Each operator completed the task with three different control methods: manualcontrol (no feedback or input shaping), two-mode Zero Vibration (ZV) input shaping [25], andPD-feedback control. Prior to beginning the study, every operator completed the course witheach control method to familiarize themselves with the control of the crane. Following thispractice session, the trials began with the task order randomized to help mitigate operator-learning effects.

For each trial, the task completion time was recorded. Task completion time was measuredfrom when the operator first moved the crane until the payload settled within the end zone. Inaddition, the total distance traveled by the trolley during each trial was calculated. The totaltravel distance gives an approximation of energy use; longer travel distances use more energy.

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End

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Figure 22: Example Trial with Manual Control

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Figure 23: Example Trial with PD-Control

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Figure 24: Example Trial with ZV-shaped Control

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Figure 25: Task Completion Times

5.2 Operator Study Results

An example trial with manual control is shown in Fig. 22. The trolley tracks a safe path throughthe obstacle course and is easily positioned over the target location. However, the hook un-dergoes significant oscillation, making final positioning difficult. For this trial, the operatorrequired 238 s to position the payload within the target region.

The same operator’s attempt to complete the task with the PD-feedback control system isshown in Fig. 23. The hook exhibited much less oscillation than during the manual controlledcase, making positioning within the target region much easier. The trial was completed in 60 s,representing a 75% reduction from this operator’s completion time with the manual controller.

An example trial with the input-shaping controller from the same operator is shown in Fig. 24.Like the PD controller, input shaping drastically reduced the hook oscillation from the manualcontrol case. The operator again was quickly able to position the payload in the target region;the trial was completed in only 35 s.

The task completion times for all ten operators are shown in Fig. 25. The PD controller andinput shaping allowed every operator to complete the task more quickly than the manual con-troller. The average task completion time for each controller is shown in Fig. 26. The error barsindicate one standard deviation above and below the mean. The average completion time withPD-control was 66% less than manual control (55 s vs. 161 s). Input shaping further reducedthe average completion time to 38 s, representing a 31% reduction from PD control and a

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0

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Figure 26: Average Task Completion Times

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ravele

d (

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Figure 27: Average Distance Traveled by the CraneTrolley

76% reduction from manual control. In addition, the standard deviation with the input shapingcontroller was less than with PD control, indicating that the performance varied less betweenoperators. A one-way analysis of variation (ANOVA) test verified that the differences in com-pletion time between methods were statistically significant, F (2, 27) = 24.91, p � 0.001.A paired t-test indicated that differences in completion time between PD-control and inputshaping were less statistically significant, t(18) = 1.99, p = 0.06.

The average total distance the trolley traveled using each control method is shown in Fig.27. The average distance the trolley traversed under manual control was 9.52 m. This is ap-proximately 3 m more than the nominal path through the obstacle course. With PD control,the average travel distance was reduced to 9.07 m, a 5% reduction from manual control andcloser to the distance required for the nominal path. The average distance traveled using theinput-shaping controller was slightly less, 7.88 m. The shorter total travel distance afforded byinput shaping provides evidence that is is more energy efficient than either manual control orPD control. However, a one-way ANOVA indicated that the differences in travel distance ob-served between control methods were not statistically significant, F (2, 27) = 1.61, p = 0.22.However, the differences seen in travel distance suggest that energy use between methodsshould be a goal of future investigations.

The number of collisions that took place when each of the operators moved the crane from thestarting point to the end point is shown in Fig. 28. Each collision was defined to be the topplingover of the obstacle when the payload hit it. The total number of collisions in the unshapedcase was 18 whereas in the PD-feedback case was only 2. The ZV shaped case resulted in nocollisions throughout the study. The mean and standard deviation of the three cases is given inFig. 29. A one-way ANOVA confirmed that the differences in number of collisions observedbetween control methods were statistically significant, F (2, 27) = 15.28, p� 0.001.

6 CONCLUSIONS

This paper discussed the use of feedback controllers and input-shaping controllers on cranes.The difficulties of implementing feedback controllers on cranes were outlined, including dif-ficulty sensing the payload and human operator compatibility problems. Implementation of arepresentative feedback controller and input shaper on a 10-ton industrial bridge crane wasalso presented. Both the feedback control system and input shaping reduced oscillation of this

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Figure 28: Number of Collisions per Operator

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Figure 29: Average Number of Collisions

crane. A study of ten, novice crane operators demonstrated that the reduction in oscillation al-lowed the operators to more quickly complete crane positioning tasks. Of the control methodstested, input shaping produced the lowest average task completion times and shortest averagetrolley travel distance, while being the safest in terms of collision avoidance.

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