USE OF CRANES IN SYSTEM DYNAMICSAND CONTROLS EDUCATION

William Singhose ∗ Joshua Vaughan ∗

Jonathan Danielson ∗ Jason Lawrence ∗

∗ Woodruff School of Mechanical Engineering,Georgia Institute of Technology

Atlanta, GA, USA

Abstract: Cranes provide an excellent platform for teaching system dynamicsand controls. Cranes have a simple pendulum-type oscillation that is useful fordemonstrating basic ideas. However, cranes also have additional dynamic effectssuch as motor dynamics, velocity limits, payload variations, and nonlinear slewingdynamics that make them well suited for advanced study. If the cranes are maderemotely operable, then students can also study tele-operation and control ofsystems with time delays. System dynamics and control courses taught at theGeorgia Institute of Technology utilize cranes in both the lecture and laboratoryexercises. The primary goal of using the cranes is to provide hands-on experiencesin system dynamics and implementation of controllers on real systems. This paperdescribes the cranes and the complementary curriculum.

Keywords: Crane Control, Oscillation, Vibration, Input Shaping, EngineeringEducation

1. INTRODUCTION

System dynamics and controls education is of-ten filled with extensive theoretical developmentand complicated mathematics such as differen-tial equations, Laplace transforms, and Nyquistplots. Therefore, students often lose sight of thepractical applications of the material. The use ofcomplementary laboratory exercises can alleviatethis problem. However, this introduces an addi-tional challenge to professors, who must developlab exercises that reinforce lecture material. Theymust also build and maintain experimental setups.

Cranes are excellent testbeds because crane pay-load oscillation is a problem that all students canimmediately see and understand. While there arenumerous types of cranes, all have an overheadsupport point that moves around a suspensioncable that lifts the payload. Moving the overheadsupport point, such as the trolley of a bridge

crane, is fairly straightforward; however, movingthe suspended payload in a controlled manneris quite challenging. Beyond the basic pendulummode, cranes also have additional dynamic effectssuch as motor time constants, velocity limits, andnonlinear payload dynamics that make them wellsuited for both introductory and advanced study.

Although cranes have many interesting dynamicproperties, the primary challenge is to control pay-load oscillation. Therefore, all crane-based cur-riculum has this as a primary component. Twomain control approaches can be used to reducepayload oscillation: feedback control and com-mand shaping. Feedback control is easily achievedfor the overhead support point, but it is difficult touse for payload control because accurate sensingof the payload oscillation is difficult to achieve.Command shaping does not require sensors. Itreduces oscillations by filtering out vibration-

Initial Command Input Shaper Shaped Command*

Figure 1. The Input Shaping Process.

StartCollisions

Goal

Obstacles

Typical Response

Input-Shaped Response

Figure 2. Typical Payload Responses.

Figure 3. 10-Ton Bridge Crane at Georgia Tech.inducing components from the command signal.This modification is accomplished by convolvingthe original command signal with a sequence ofimpulses (Smith, 1958; Singer and Seering, 1990).The result of the convolution is then used todrive the crane motors. This input-shaping pro-cess is demonstrated in Figure 1. Several varia-tions of this idea have been developed for cranecontrol (Starr, 1985; Singer et al., 1997; Parker etal., 1999; Khalid et al., 2004).

Figure 2 compares the responses of the crane pay-load of the 10-ton bridge crane at Geogia Tech,shown in Figure 3, for a typical maneuver understandard operation and when input shaping isenabled. The two responses are from the samehuman operator. The figure shows that undernormal operation the payload has large oscilla-tions. These oscillations are virtually eliminatedby input shaping. Such dramatic performanceimprovement motivates students to understandthe control system, especially when they are theones driving the crane. Input shaping also provesa worthwhile contrast to the feedback methodstaught in controls coursework and allows illustra-tive comparisons between open and closed-loopcontrol methods.

BridgeMotor 1

PLC Trolley MotorDrive

Bridge & Trolley Control Box

Bridge MotorDrive

Bridge

Trolley

ControlPendant

BridgeMotor 2

TrolleyMotor

Hoist Controls

To TrolleyMotor

To BridgeMotors

To HoistMotor

Figure 4. Crane Hardware and Control.

The next section describes four cranes that havebeen built at Georgia Tech for research and edu-cational purposes. Section 3 describes how crane-based homework, simulations, and laboratorieshave been integrated into the curriculum. In Sec-tion 3.5 presents the use of the cranes in interna-tional collaborations.

2. CRANE LABORATORY FACILITIES

2.1 10-Ton Industrial Bridge Crane.

The crane shown in Figure 3 has a workspace of6 meters high, 5 meters wide and 42 meters long.Figure 4 shows a schematic diagram of the craneand how it generates the input-shaped controlsignal. Signals generated by the human operatortravel from the control pendant to the hoist con-trols and to the bridge-and-trolley control box.A Siemens programmable logic controller (PLC)performs the input-shaping algorithm. The result-ing commands are then sent to the trolley and/orbridge motor drives. These drives use the incom-ing commands from the PLC as velocity set pointsfor the motors. To ensure accurate execution ofthe commands, the drives are Siemens Master-drives Series AC-AC inverters. This type of driveuses a pulse-width-modulated signal to accuratelycontrol the motors. Inverter duty capable motorswere selected to ensure good compatibility withthe drives. The crane is also equipped with aSiemens vision system to track payload response.

2.2 Portable Bridge Crane.

A small, transportable bridge crane is shown inFigure 5 (Lawrence and Singhose, 2005). Onepurpose of this crane is to provide a hands-onlearning tool for students outside Georgia Techthat cannot use the 10-ton crane. The crane wastransported to Georgia Tech Lorraine in Franceduring the fall of 2004. In the spring of 2006, itwas used in an Atlanta-area high school.

The portable bridge crane is approximately onecubic meter in volume. It is driven by Siemens ACsynchronous servomotors, which move the trolley

Figure 5. Portable Bridge Crane.

Figure 6. Bridge Crane Computer Interface.and bridge axes via two timing belts. A direct-drive DC motor is used for hoisting. A Siemensdigital camera is attached to the trolley and pointsdownward to measure the payload swing.

The control pendant for the crane has directionalbuttons to drive the crane and two buttons tochange the controller mode. The pendant signalis sent to a Siemens PLC that generates a seriesof velocity setpoints for the motors. The user alsohas the option to run a trajectory stored in asetpoint buffer.

The portable bridge crane has tele-operation ca-pabilities that allow it to be operated in real-time from anywhere in the world via the internet.To achieve tele-operation, the controlling PC wasequipped with UltraVNC. This program allowsusers with internet access to remotely control atarget PC. When operated remotely, the crane isdriven using the Graphical User Interface (GUI)shown in Figure 6. Local users also have the optionof using this interface to control the crane.

2.3 Portable Tower Crane.

A small, transportable tower crane, shown inFigure 7, has also been constructed (Lawrence etal., 2006b). The crane is approximately 2m tallwith a 1m jibarm. The crane has three degrees-of-freedom actuated by Siemens synchronous AC

Figure 7. Portable Tower Crane.

Figure 8. Tower Crane Computer Interface.

servomotors. The slewing axis is capable of 340◦

rotation. The trolley moves radially along the jibvia a lead screw, and a hoisting motor controls thesuspension cable length. A Siemens digital camerais mounted to the trolley and records the swingdeflection of the payload. This crane also hastele-operation capabilities similar to the portablebridge crane.

The PLC can receive velocity commands fromeither a control pendant or a PC. The PC con-trols the crane using the Graphical User Interface(GUI) shown in Figure 8. The upper left portionof the screen shows a real-time animation of thecrane from an overhead view using the camera andencoder data. The square is the trolley positionand the circle is the payload position. The currentconfiguration is also numerically displayed in thebottom center of the display (slew angle, trolleypos, etc.). The crane can be manually driven us-ing the directional arrows at the bottom left ofthe screen. In addition, velocity setpoints can bestored and then executed with the “Play” button.Other features include: input shaper selection,data recording, and a “Swing Reducer” that usesfeedback from the camera to automatically dampout payload sway. These features are common toall the portable cranes discussed in this paper.

Figure 9. Computer Model of Mobile Boom Crane.

2.4 Mobile Boom Crane

A small-scale, mobile boom crane, modeled inFigure 9, is currently under construction. Thecrane has a 2m boom capable of luffing from 10◦

to 90◦ and slewing 300◦. The crane is mountedon a rear-wheel drive mobile base with a front-wheel rack-and-pinion steering system. All fivedegrees-of-freedom are actuated by Siemens ACServomotors. Like the portable bridge and towercranes, the boom will be capable of being remotelycontrolled via the internet.

All of the electronics, including the power con-version, PLC, and motor drives are mounted onboard, allowing the crane to operate with only apower cable tethered to the ground. This allowsfor the crane to be easily tested on all types ofterrains outside of a laboratory setup. The oscil-lation of the payload is recorded by a Siemenscamera mounted at the tip of the boom. Theorientation of the camera is maintained by a four-bar mechanism.

The crane will be capable of being operated by twointerfaces. The first is a wireless joypad, capable ofactuating all degrees-of-freedom, as well as otherfunctions such as controller selection. The wirelesscapability will be useful when making use of thecrane’s mobile base. The second control interfaceis the GUI shown in Figure 10. The upper leftcorner of the interface is an overhead view craneand payload. This orientation is used to determinethe cranes slewing position as well as the payload’sswing. The bottom left corner shows a side viewof the crane, showing the luffing position of thecrane. The controls for the crane are in the topmiddle of the interface. Advanced options suchas input shaping control, data recording, andtrajectory playback can be edited in the bottomright of the interface.

Two network cameras used for observation of thecrane are also accessible on the interface. The firstis a camera attached to the base of the crane asto simulate the view from the “cockpit” of the

Figure 10. GUI of Mobile Boom Crane.

crane. The second is mounted as an overview ofthe entire crane workspace. This camera allowsusers a complete view of the crane at any time.

3. CRANE-BASED CURRICULUM

Since 2001, Georgia Tech has been developinga crane-based curriculum to improve system dy-namics and controls courses. Both the large andsmall-scale cranes have been used by students toconduct experiments. These learning tools supple-ment homework and lecture material with interac-tive and real-world examples of system dynamics,flexibility, and control techniques.

3.1 Homework Problems

A series of homework problems progressively in-creases the students’ understanding of crane dy-namics and control. These problems introducestudents to MATLAB’s simulation and plottingcapabilities, teach students how to combine me-chanical and electrical subsystems, and demon-strate how input shaping reduces vibration.

The first problem requires the students to derivethe dynamic model of a planar gantry crane. Stu-dents then use MATLAB to plot the responseof the crane to several inputs - step, pulse, andbang-bang functions. In the second homework as-signment, the students add a motor to the planargantry crane from the previous problem. The re-sult is that the motor dynamics delay the crane re-sponse. In the third homework problem, studentsanalyze the response of the original planar cranemodel to two different inputs. These inputs area bang-bang function and an input-shaped bang-bang function. The students are asked to com-ment on the responses. Most recognize that thevibration is cancelled in some way for the input-shaped command. Classroom instruction explainsthis concept, showing the students how inputs tothe system, timed appropriately according to thesystems natural frequency and damping ratio, cancancel vibration.

StartGoal

Obstacles

TrolleyPayload

Figure 11. Bridge Crane Simulation.3.2 Bridge Crane Simulation

After the preliminary homework assignments, thestudents are given a MATLAB simulation of agantry crane in a cluttered workspace. The oper-ators viewpoint is directly above the workspace,shown in Figure 11. The workspace contains astarting zone, goal region, obstacles, and the cranetrolley and payload. The crane’s trolley is con-trolled by using the numeric keypad on a comput-ers keyboard.

The objective is to get from the starting zone tothe goal region in the quickest and safest way pos-sible. Each student is given a score based on theircrane-driving performance. The score consists ofthe time-to-completion plus time penalties thatare added for collisions. Although scoring doesnot influence grades, giving the students a scoreensures some level of effort from the students.Each student drives the crane with and withoutinput shaping. This allows the students to seethe benefits of a vibration control scheme likeinput shaping. Even the relatively simple simula-tion proves a strong positive reinforcement of thematerial that students learn in lecture.

3.3 10-Ton Industrial Bridge Crane Labs

The primary use of the 10-ton Industrial BridgeCrane has been as a demonstration of crane dy-namics and advanced controls techniques, such asinput shaping. Students are able to operate thecrane and gain first-hand experience in the dif-ficultly in accurately positioning crane payloads.Students also operate the crane with input shap-ing enabled, demonstrating the effectiveness ofthis control technique.

Despite its effectiveness, the 10-ton IndustrialBridge Crane has one main disadvantage as an ed-ucational tool. The crane is in active use at Geor-gia Tech. This makes it challenging to schedule labtime for the students and limits the modificationsto the control architecture that the students cansafely make. This fact motivated the design and

construction of the smaller-scale, portable cranesdiscussed in Sections 2.2–2.4 and the developmentof the lab sequence discussed in the next section.

3.4 Portable Crane Labs

The laboratory sequence discussed in this sectioncan be applied to any of the portable cranesdiscussed previously. The progression also easilyscales to varying difficulty levels, making it suit-able for both undergraduate and graduate courses.The labs are divided into four main subdivisions:introductory labs, non-input shaping control labs,input shaping labs, and final group projects.3.4.1. Introductory Labs. The introductory labsin the progression serve to introduce the studentsto dynamic properties, as well as the operat-ing and programming procedures, of the portablecranes. The first introductory lab generally in-volves simple programming of the PLC and ob-servation of the response of the crane to varyingcommands. Students observe the compromise be-tween rapid system motion and payload oscilla-tion. During the second introductory lab session,more advanced programming is required and stu-dents begin to apply the control design techniquesthat they have learned in the lecture portion of thecourse. For example, students are asked to tunePI controller gains to achieve small trajectorytracking error of the trolley and small payloadoscillation. Student quickly realize that increasingthe PI gains will improve tracking error. Studentsalso realize that choosing lower PI gains reducespayload oscillation because it causes a sluggishtrolley response. The exercise reinforces one ofthe fundamental compromises in control design forflexible systems.

A third introductory lab exercise focuses on thedynamics of the portable cranes. Students areasked to vary operating parameters, such as sus-pension cable length, and observe the effect on thedynamics of the crane payload. The effects of theparameter variations are compared to theoreticalpredictions that the students develop, and theeffect on their previously developed controllers isexamined. This exercise demonstrates the neces-sity for robust control methods.3.4.2. Non-Input Shaping Labs. This subsec-tion of the lab progression is well suited to gradu-ate level courses as it provides practical experiencewith the implementation of advanced theoreticalconcepts. During it, students are asked to imple-ment one or more advanced controls technique,such as model reference control or zero phaseerror tracking (ZPET) control. The effectivenessof these controllers is compared to the simplermethods used in earlier labs. Students see thatthe reward for the increased complexity of the ad-vanced techniques is often very little improvementin system performance.

3.4.3. Input Shaping Labs. Given the successof Input Shaping as a crane control method(Starr, 1985; Singer et al., 1997; Parker et al.,1999; Khalid et al., 2004; Sorensen et al., 2007b),a large portion of the lab progression is devotedto it. Students are lead through input shapingtechniques over a series of three to five laboratorysessions. This progression begins with the designand implementation of an input shaper designedfor a single cable length. The students comparethe system response to commands generated us-ing the shaper to the unshaped responses theyobserved during the introductory lab exercises.

In subsequent labs, students examine the robust-ness of various input shapers to changes in systemparameters. During the examination of the inputshaper robustness, students are exposed to onefundamental compromise in input shaper design,increasing shaper robustness increases shaper du-ration and, as a result, system rise time. Studentsare also asked to design and implement an inputshaper to cancel two modes of vibration, whichoccur for certain crane payload configurations.

Another laboratory typically held during the in-put shaping portion of the progression is on track-ing control. The students are assigned the taskof navigating an obstacle field with two differentpayloads, one of which results in double-pendulumeffects. The students must use a single controllerfor both payloads. Students are not explicitly re-quired to use input shaping, but many do. This labfurther reinforces the necessity of robust controldesign techniques and helps push students towardthe integration of the control techniques coveredin the course. This lab has also been conductedunder the framework of a competition, where theteam with the fastest times for the two payloads,with penalties for obstacle collisions, is named thewinner.

3.4.4. Final Projects. In an effort to furtherpush students toward internalization of the con-trol techniques covered in the course, they areasked to complete a five-week final project. Thestudents are required to design and conduct novelcontrol experiments. This forces the students touse concepts outside of the bounds of what istaught in class. They must not only understandthe ideas, but synthesize new ones. For example,one group used the crane to dispense sand andwrite “GT”, as shown in Figure 12.

The implementation of a final project has been aparticularly successful endeavor. Three of the finalprojects from the fall 2005 session of a graduatelevel controls course were presented at interna-tional conferences (Huey et al., 2006; Blackburn etal., 2006; Bradley et al., 2006). Class projects fromthe fall of 2006 section of the course also resultedin quality research results that have resulted

Figure 12. Sample Student Project: Using Sand toSpell out “GT”.

in publications (Sorensen et al., 2007a; Enes etal., 2007).

3.5 International Cooperation

During the fall of 2005, two parallel, graduatelevel courses were taught at Georgia Tech andTokyo Tech. The Georgia Tech students primarilyused the bridge crane in Atlanta. The Tokyo Techstudents primarily used the tower crane in Japan.The Japan course taught command generationand feedforward control, with an emphasis on real-world complications. The students used the cranein three ways: to perform labs, to conduct andparticipate in a remote manipulation study, andto collect data for their final projects. Becausethe two courses were taught in parallel, the U.S.and Japanese students had the opportunity tocollaborate on the final projects.

The students were given the option of choosingone of three projects:

(1) Consider a crane where the trolley acceler-ates up to speed faster (or slower) than itcan brake. Test a new input shaper developedfor this system (Lawrence et al., 2006b) anddevelop an improved version of the shaper ifpossible.

(2) Both tower and bridge cranes are governedby nonlinear dynamics. Given the equationsof motion, verify these nonlinear dynamicsand develop controllers that compensate forthese nonlinearities.

(3) Explore remote operation of tower and bridgecranes. Perform studies that test the effec-tiveness of input shaping when used to re-motely control these cranes.

Because the final projects were performed near theend of the course, the students were well trainedon how to use both crane systems and collect data.In addition, since both cranes could be controlledremotely, the students in Japan or the U.S. coulduse either crane.

Due to the timing of the U.S. and Japan classes,the U.S. teams completed their final projects first.Then, the Japanese students were given the sameprojects along with the results from the U.S.

students. Their task was to further develop theprojects and improve the results from the U.S.students. In the final stage, the Japanese groupsand their U.S. counterparts came together to writeconference papers on their work (Blackburn etal., 2006; Bradley et al., 2006; Huey et al., 2006).

In addition to the Tokyo Tech collaboration,the portable cranes have been operated by re-searchers and students located throughout theUnited States, Japan, Korea, Switzerland, Spain,and Serbia.

3.6 Use of Cranes for Undergraduate ResearchThe cranes also provide an excellent opportunityfor undergraduates to get involved in research.In fact, numerous undergraduates have alreadyused the cranes to conduct research that hasresulted in technical publications (Khalid et al.,2004; Lawrence et al., 2006a; Hekman et al., 2006;Lawrence et al., 2006b; Khalid et al., 2006; Hueyet al., 2006; Kim and Singhose, 2006; Kim andSinghose, 2007; Vaughan et al., 2007).

4. CONCLUSIONSCranes provide an excellent platform for sys-tem dynamics and controls education. Theirpendulum-like oscillations are easily observableand make precise payload positioning difficult.The ability to address additional dynamic effectsmakes cranes an easily scalable educational tool.This paper reviewed the use of cranes in systemdynamics and controls courses at Georgia Tech. Itpresented the capabilities of the four cranes and acrane-based curriculum developed to utilize them.International collaborations utilizing the craneswere also presented.

ACKNOWLEDGMENTS

The authors would like to thank Siemens Energyand Automation, the Georgia Tech PURA, theNational Science Foundation, CAMotion, and the21st Century Center of Excellence in Robotics atthe Tokyo Institute of Technology for providingequipment and funding.

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