modeling and optimization of synchronous behavior for ... solution for the synchronous behavior of a...

Modeling and Optimization of SynchronousBehavior for Packaging Machines

Sathyamyla Kanthabhabhajeya, Bengt Lennartson

Automation Research Group, Department of Signals and Systems,Chalmers University of Technology, SE-41296 Gothenburg, Sweden

(e-mail: [email protected])

Abstract: This paper proposes a new modeling solution for the synchronous behavior ofpackaging machines, and a strategy for maximizing the production rate based on a formal model.A common modeling platform is recommended to handle information exchange and to developa collaborative workflow, in this paper involving mechanical design and software development.The modeling solution for the synchronous behavior is developed in SysML (Systems ModelingLanguage), being the common platform. Then a formal modeling language called SequencePlanner Language (SPL) is interfaced with SysML, to overcome some limitations of SysML.The synchronous behavior of the packaging machine is also developed in SPL, from whichthe optimization problem is defined. The result of the optimization shows that it is possibleto improve the efficiency of packaging machines with new configurations compared to moreconventional design. The proposed strategy is evaluated for a filling machine at Tetra Pak.

Keywords: SysML, Formal Modeling, Optimization, Synchronous behavior, Workflow

1. INTRODUCTION

The complexity in manufacturing industry has increaseddue to introduction of partial automation and enormousinformation exchange. Though technological developmentsare intended to provide a simpler manufacturing environ-ment, it complicates the design and control of manufac-turing systems. This complex design and control increasesthe design cost, time and maintenance. Design of complexmanufacturing systems is often based on a virtual modelof the system. A high-level abstract model of the system isthen developed during the design stages. Abstract model-ing, based on a high-level architecture, gives an overviewof the manufacturing system. However, a methodology isrequired to use this model during different stages of thedesign. This model of the manufacturing system also needsto be accessed by different domains in the industry.

A workflow of any manufacturing industry therefore in-cludes different domains working in a collaborative way.One example of such a collaborative workflow is illustratedin Figure 1, where mechanical design and software de-velopment are integrated, sharing common information.A more specific example, also illustrated in Figure 1, iscontrol design and implementation in a PLC controllerthat need to be integrated with the physical system design,involving both plant dynamics, actuators, and sensors. InKanthabhabhajeya et al. (2012), this collaborative work-flow is related to more detailed development & informationmodels, such as the V-model, the Waterfall model andProduct Lifecycle Management.

The need to handle information efficiently, and to reducethe commissioning time, lead to the requirement of a com-mon modeling platform, as described in the collaborativeworkflow. Automation in manufacturing industry uses dif-

ferent software applications for different domains. This ne-cessitates manual intervention for exchange of information.Different domains in the manufacturing industry includeprocess design, mechanical design, software engineering,electrical system design, environmental demands, produc-tion, sales and marketing, etc. The information from thesedomains is dependent on each other. The information isstored in different formats and in different software appli-cations, thereby complicating the information exchange.

Therefore, Systems Modeling Language (SysML) (Frieden-thal et al. (2012)) is proposed as a common modelingplatform. Kanthabhabhajeya et al. (2012) explain howSysML fits well as such a platform in a collaborative

Fig. 1. Collaborative workflow including integrated me-chanical design and software development.

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workflow involving mechanical design and software devel-opment. SysML is also preferable as an interface betweendifferent applications, which helps to improve exchangeof information between different domains. Furthermore,it is mentioned in Qamar et al. (2011) that SysML isa common modeling language between other modelinglanguages, because it supports strong relations betweendomain-specific models and generic system models.

SysML, being a graphical modeling language also has thepossibility to model structural and behavioral constructsof a manufacturing system. The architecture of SysMLincludes, ”structures to domain concept, mapping of do-main concepts to language concepts, and instantiation andrepresentation” as described in Friedenthal et al. (2012).Nine diagrams in SysML intend to satisfy the require-ments of System Engineers and facilitate the construc-tion of a graphical model of a manufacturing system, seeOMGSpecification (2010). SysML has also been used as amodeling framework to describe the integration of a newexecution system with an existing one, see Pietrac et al.(2011).

In this paper, the modeling platform based on SysMLis used for integrated mechanical and software design,focussing on the packaging industry. To obtain a commonmodel, it is required to understand the complexity of thepackaging industry. Industrial automation in the last twodecades has replaced the mechanical shafts, cams andmotors, with electric drives and servo motors controlledby Programmable Logic Controllers (PLCs) within thisindustry, see Bassi et al. (2011). However, this transitionstill imitates the former mechanical behavior, by replacingthe mechanical parts with mechatronic devices.

Mathematical models of motion profiles are defined tocontrol the servo motors in master-slave relations. Themotion profiles are defined by choosing an accelerationprofile fitted to the position points of the servo motorsagainst a shaft angle (0−360◦). The motion profile definesvelocity curves for the slave motors and hence generatesa synchronized motion between different behaviors. Bothmechanical and software design need a common model torepresent this synchronous behavior. A modeling solutionrepresenting this synchronous behavior is therefore devel-oped in this paper based on SysML.

Though SysML acts as a common modeling platformin the workflow, it is only a semi-formal language. Itsstructure is not suited for formal verification, as arguedby Bassi et al. (2011). Hence, a related but more formalmodeling language, called Sequence Planner Language(SPL), is interfaced with SysML for verification of themodel developed in SysML. The framework of SPL isbased on sequences of operations and also includes a formalrelation between products and processes, see Lennartsonet al. (2010) (where SPL is referred as SOP - Sequencesof Operations). Kanthabhabhajeya et al. (2012) classifythe advantages of SPL over SysML and the need for thisinterface.

The behavioral functions of the machine are formally de-fined using SPL. This formal mathematical model alsoincludes necessary information for optimization. Further-more, SPL adds to the value by providing visualization ofdifferent projections of the same model such as product

view, resource view, operator view, etc. An interface be-tween SPL and SysML is therefore implemented, and theresults are presented in Kanthabhabhajeya et al. (2013).

The main contributions of this paper are as follows: Amodeling solution for the synchronous behavior of a pack-aging machine using SysML is proposed. This modeling so-lution is analyzed in a case study of a filling module of theTR/28 machine, from Tetra Pak, a global company deliv-ering packaging solutions. In addition, this paper developsan SPL model of the complete TR/28 filling machine. Anoptimization problem, to maximize the production rate, isthen formulated by the SPL model and solved using exist-ing solvers. The result of this optimization shows that itis possible to improve the efficiency of the TR/28 machinecompared to the current configuration of the machine.

2. SYSTEMS MODELING LANGUAGE

SysML, as described in Section 1, is a general purposemodeling language, extended from UML and has nine dia-grams to represent the model of a system. These diagramsare shown in the SysML taxonomy in Figure 2, which alsodifferentiates between the diagrams taken directly fromUML and those partly or completely added as new ones.In a broader perspective, Structural diagrams are used torepresent a system composed by its parts, interconnec-tions, properties and constraints. Behavioral diagrams areused to describe the flow of parts, relations between userand model, and also description of functions with statetransitions. In this section, a few of the diagrams used inthe case study model (Section 4), are described in detail,c.f. Friedenthal et al. (2012).

Fig. 2. SysML Taxonomy.

2.1 Structure Diagrams

Among the structure diagrams in SysML, the Block Def-inition Diagram (BDD) is used to represent the system’shierarchy by defining composition and/or classificationof modules as well as parts of the system. The BDDincludes blocks, to which the connections are exhibitedwith composite association, reference association or gen-eralization path. A block defines the modular unit of astructure, with uniquely identifiable instances. A block ina BDD has compartments to add different properties likeParts, References and Values. As the name suggests, theParts compartment includes the parts that compose therespective block. Reference property of a block is used todescribe whether the current block has any reference toanother block. The Values compartment includes the value

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properties of a block, and hence relates to the physicalproperties of the real system.

With the overall description of a system in a BDD, thedetails of parts, item flows, interconnections, allocations,etc, are defined in an Internal Block Diagram (IBD).Avoiding the details on IBD, the Parametric Diagram(PD) in SysML relates the model with the real system andsupports engineering analysis. This diagram coordinatesthe constraint and value properties of the blocks defined inBDD. A constraint property is added either as a separateconstraint block or in the compartment of the respectiveblock in BDD.

PD defines the details of binding connections between theadded constraints and their parameters, along with thevalues of the block. This feature used in the modeling ofthe synchronous behavior of filling machines in Section 6.Time dependent constraints need a time property, whichcan be expressed explicitly as a reference clock propertywith its unit and quantity defined. This is also applied inthe synchronous modeling in Section 6.

Finally, we observe that the Package diagram of SysMLhelps to define the hierarchy of the model of the system.

2.2 Behavior Diagrams

Among the behavior diagrams in SysML, the ActivityDiagram (AD) involves actions to represent a particularbehavioral function of the system. The actions are inter-connected according to the flow of items and flow of controlin the real system. The AD of SysML is influenced by PetriNets, see Reisig (1992), which involve tokens generationand consumption to represent the flow of control throughan executable action. An action in an AD needs at leastone token to be consumed at the input to execute, and gen-erates new token(s) at the output. The relation betweenactions is expressed by fork-join, decision-merge nodes.

An action can be described in detail with a State-MachineDiagram (STM) including states, transitions and events.This diagram is similar to any classic representation of be-havioral modeling with states and transitions. As observedin SysML taxonomy, there is no hierarchical structurebetween behavioral diagrams, but in the actual usabilityof the STM diagram, it is typically initiated by an actionin an AD.

The Sequence Diagram in SysML describes the interactionbetween the system and the user, while the Use CaseDiagram describes the functionality of a system withrespect to different users’ goals of a system. These twodiagrams represent users as actors who interact with thesystem. The latter define in detail the outcome that theactor needs to achieve.

Finally, the Requirement Diagram in SysML lists thespecification of the system that needs to be modeled.This diagram includes text, tables and keywords to addmeaning to the requirement list. The case study in thispaper involves the BDD, PD, AD and STM of SysML togenerate a model of the system, which is later analyticallyexecuted.

3. SEQUENCE PLANNER LANGUAGE

The Sequence Planner Language (SPL) is a graphicalmodeling language that models hierarchical operationsand sequences of operations, formally defined by automataextended with variables, see Lennartson et al. (2010). Byintroducing this type of formalism and reusable informa-tion, there exists a potential to obtain automated design,optimization and correct implementation of embeddedcontrol functions. The SPL, its graphical structure andproperties are now explained by an illustrative example,presented in Figure 3.

Fig. 3. Illustrative example of an SPL.

Three-state operation model An SPL operation is athree-state model, represented as an automaton with vari-ables, as shown in Figure 4. The three state model defineswhether the operation is currently in its intial, executedor final state. An operation Ok moves from its initialstate Oi

k to its execution state Oek when the precondition

C↑k is satisfied and the event O↑k occurs, and it moves

from its execution state Oek to its final state Of

k when the

postcondition C↓k is satisfied and the event O↓k occurs.

Fig. 4. Three state model of an operation.

Self-contained operations Though this formal model hasa graphical structure similar to Sequential Function Chartand Grafcet, as can be seen in Figure 3, every operationis self-contained, since it holds all necessary informationto determine its own state but also, together with otheroperations, to determine their relation to each other. Therelation between a number of operations is often a straightsequence, but may also include other relations, see below.

For example, OP24 in Figure 3, contains information onits pre-condition that OP6 has to be finished, but also


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from the graphical relations that OP20 must be completedbefore OP24 can be executed. This allows the operationsto be grouped and viewed automatically from differentperspectives, see more below on visualization.

Resources & Operations Some of the operations includeallocation of necessary resources. SPL uses simple variablenotations to book and unbook the resources. In Figure3, OP12 books the resource R29 in its pre-condition(R+

29) and unbook it (R−29) after executing the operationOP31. Similarly, OP23 also requires the same resourceR29, as OP12. This implies that operations OP12 andOP23 cannot be executed at the same time, providedthat the availability of the resource R29 has capacityone. This expresses the mutual exclusion between the twooperations, due to the shared resource R29.

Fig. 5. Resource view for resource R29 based on the SPLin Figure 3.

Relations The identified relations between different op-erations, which can be expressed graphically in SPL,can be divided into five categories. Sequence, Parallel,Alternative, Hierarchy and Arbitrary order are the re-lations between operations that define the flow of pro-cesses/products in an SPL model. An operation that canonly be started after another operation is finished exhibitsa sequence relation between the two operations. OP8 andOP9 in Figure 3 are alternative operations, where onlyone of them is executed, provided the corresponding pre-condition is satisfied. The parallel relation between OP11and OP12 represents that both operations need to beexecuted and be in their final state, before the followingoperation OP31 begins. A highest hierarchy is representedby operation OP19 in Figure 3 with OP20 being the initialoperation of the sequence within OP19. The operationOP19 is considered to be completed first when OP27 hasreached its final state. The arbitrary order combines theparallel operation and mutual exclusion, where operationsare executed in parallel but not at the same time andin arbitary order. A detailed description of the relationsbetween operations in SPL is available in Lennartson et al.(2010), Bengtsson (2012).

Visualization SPL allows the sequences of operations tobe projected into different views with respect to resource,product or other perspectives such as safety, involvementof operator, etc. The example presented in this section,uses different resources for executing some of the oper-ations. The product view of this sequence of operationsis shown in Figure 3. SPL has also the facility to viewthe sequences of operations with respect to a particularresource as shown in Figure 5. The operations related toresource R29 are OP12, OP8, OP31 and OP23. Theseoperations include their relations to each other, but also

to other operations in their pre-conditions. Such differ-ent views can be automatically generated, see Bengtsson(2012), based on the self-contained operation informationmentioned above.

SysML - SPL Interface For SysML, being a commonmodeling platform, but semi-formal, the behavioral partof the model is interfaced with SPL. The required infor-mation from the behavioral part of an SysML model ismapped across SPL, using built-in methods and additionalalgorithms. The purpose of this interface is to make use ofthe benefits of SPL over SysML, c.f. Kanthabhabhajeyaet al. (2013)

4. FILLING MODULE OF PACKAGING MACHINE

The filling module of a packaging machine (Tetra RexTR/28) is modeled in SysML and SPL in Kanthabhab-hajeya et al. (2012). This filling module of the TR/28machine uses a Lift and a Pump to perform the oper-ation of filling a carton. The SysML model of this fillingmodule is now extended with the motion profile along withsynchronous behavior of the machine. The filling moduleis divided into two sections: One section includes the liftand the servomotor for the lift, while the second sectionincludes the pump and valves for filling the liquid in thecarton. The cartons are fed to the filling module throughan indexing conveyor. The Lifts move the cartons up.When lowering the cartons, the Pumps fill the liquid. Themovements of the Lifts and Pumps are synchronized suchthat the filling process begins as soon as the lift along withthe carton starts to move down. The filling module withthe lift moving down and the pump filling the liquid areshown in Figures 6 and 7.

Fig. 6. Filling module of packaging machine, see TetraPak-Engineers (2007).

On a more detailed level the lift is defined with an UP andDOWN movement. The lift needs to move UP 250mmin 100ms, while it takes 400ms to move DOWN. Theacceleration stays negative (i.e, below 9.81m/s2) while thelift is moving DOWN. This negative acceleration makessure that the carton follows the lift. The cyclic behavior ofthis machine is considered to have a fixed machine cycletime of 1000ms.


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The pump filling stroke is required to move 150mm in400ms to fill the required product in the carton, whilethe lift is reaching the bottom level. The pump profile isrelative to sustain the dip level (as shown in Figure 6)constant. The return stroke for the pump is at the desiredposition before the next cycle begins, as shown in Figure 7.This filling module has a batch size of two cartons, i.e, twocartons are filled at the same time. These cartons are filledwith two lifts and two filling pumps following the exactmotion profiles, respectively.

Fig. 7. Lift-fill profiles of filling module, see TetraPakEngi-neers (2007).

An Indexing Conveyor transports the cartons to differentmodules through the machine. The machine cycle deter-mines the indexing and halting time of the conveyor. Asseen in Figure 7, Indexing (moving the conveyor) occursduring the beginning and end of the filling module. Thiscycle is repeated with the next two empty cartons. Thecartons are filled when the conveyor is halted. The dura-tion of indexing the conveyor depends on the batch size ofthe filling module. The halting duration of the conveyorwill not change, with the assumption that the number ofresources (Lift, Pump, etc) proportionally increase withrespect to the batch size. Based on the SPL model of thefilling module, this model is extended by including theother modules of TR/28 like Folder, Bottom Sealing andTop Sealing.

5. MOTION PROFILE PRINCIPLES

Earlier generations of packaging machines were composedof mechanical shafts, cam wheels and indexing gearboxes,as shown in Figure 8. Motion control of these machineswere managed by controlling the motion of the mainshaft with respect to the design of the cam wheels andgearboxes. The human interface to these machines, innormal operation procedure, was only used to start/stopthe main motor, while the position of the shaft and camwheels were read by the encoders and fed as inputs to aPLC. The necessary input/output events were triggeredby the PLC with respect to the position of the shaft. Itwas the cam wheel that delivered the necessary positionand velocity of the respective moving parts in the machine.

In modern packaging machines, the principle of the oldmechanical system is duplicated with a single master andmany slaves designed by servo motors. The main shaftwith different cam wheel profiles is introduced as mathe-matical models in virtual environment. In motion control

Fig. 8. Packaging machine with mechanical solution, seeTetraPakEngineers (2007).

systems, controllers in closed loops are used to control thevelocity and position of machines in order to generatedesired motions, see Nguyen et al. (2008). Polynomialequations representing the cam wheel profiles are used forcontrol purposes. Different slaves from multiple axes arecontrolled with respect to their particular profiles. Thereis no feedback control in normal operation, hence the openloop motion control is expected to perform in a correctway. Error handling is taken care of by the controller thatperforms an exception event when a fault is induced.

Motion control is a key concept in many manufacturingapplications, where the precision of position and velocityof moving parts is critical. Nguyen et al. (2008) states thats-curve velocity profiles have the tendency to reduce vibra-tion and achieve better precision. A pulse and sinusoid arecombined to form the acceleration profile for Tetra Pak.Desired position points, depending on the machine, deter-mine the velocity profile, considering the specified accel-eration profile. These defined curves have their respectivepolynomial equations to be used for motion control of theslaves.

A mathematical model of the profiles of Lift and Pump (asshown in Figure 7) is determined and used for extendingthe model of TR/28 in SysML. Although the behaviorsof the Lift and the Pump is controlled individually, thesynchronized behavior of both parts yield the requiredoutcome. The velocity profile is utilized for controllingthe respective moving parts of the machine. The modelingof this synchronous behavior in SysML is explained inSection 6.

Motion Profiles - Optimization For the Indexing Con-veyor, simplified motion profiles are determined with re-spect to the Batch Size (S) and Machine Cycle time (mc).The position curve decides the duration of the displace-ment of the conveyor and halting time of the conveyor.This duration is directly proportional to the number ofcartons in the respective batch and the width of eachcarton. A trapezoidal velocity profile generates a linear anda constant slope. A proportion of time called formfactor(ff) that falls as the constant velocity is determined byexperience at Tetra Pak. This can also be considered as an


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optimization problem, which we consider for future work.In this paper, the optimization problem, maximizes theProduction Rate (PR) with constraints on the Acceleration(a). Replacing the trapezoidal velocity profile with moreexact velocity profiles in the optimization of the indexingconveyor will also be considered for future work.

6. MODELING SYNCHRONOUS BEHAVIOR INSYSML

The SysML model for the filling machine in Kanthabhab-hajeya et al. (2012) includes block diagrams of the fillingmodule along with the flow of items between differentparts. An activity diagram describes the sequence of flowof actions that are necessarily performed by the blocks ofthe filling module. In this paper, the synchronous behavioramong the elements of the module, is also taken intoaccount. The model of the filling module is also dividedinto two sections as upper and lower sections, similar tothe actual machine (as described in Section 4). The mainfilling module, along with the pump, the supply unit withvalves together with the tank assembly, form the uppersection, while the lower section includes the carton lifterwith lift, gripper and cleaning module.

Fig. 9. BDD of filling module, including constraint prop-erties of ServoMotor.

Constraint properties The motion profiles of the Lift andthe Pump in the filling module, as given in Section 5, arerepresented by a 3rd order polynomial equation as shownin Figure 9. In the lower section of the filling modulemodel, a constraint block is added to include the constraintproperty of the Lift profile as described in Section 2.This constraint block describes the 3rd order polynomialequation of the respective motion profile. This constraintproperty is composed to the ServoMotor, which is a partof the block CartonLifter. This ServoMotor is responsiblefor the control of the Lift’s speed and/or position withrespect to the pre-defined motion profile. The necessaryparameters along with the value types, of the constraintproperty are listed in the ServoMotor. The parameterssuch as time and liftPosition are supplemented to theServoMotor for the lift profile. These two parameters aredefined as vectors of size varying from 1 to n. The definedvectors store the respective values of liftPosition at itsrespective times. The unit millisecond (ms) and millimeter(mm) are used to denote time and liftPosition. In the same

way, the profile for Pump is modeled with a constraintproperty, which defines its polynomial equation and therespective parameters.

Fig. 10. PD of filling module, including LiftProfile, Pump-Profile and ClockGenerator for synchronization.

Synchronization of Lift and Pump profiles As describedin Section 2, the constraint property is a mechanism forengineering analysis and these constraint properties need aParametric Diagram (PD), where the binding connectorsconnect the properties and their respective parameters.The PD for the filling module, with the Lift and the Pumpprofile constraint properties, is shown in Figure 10. Thisdiagram defines the connection between the constraintproperties, cp1:LiftProfile, cp2:PumpProfile and the con-straint for the clock generation. The value typed parame-ters required for these constraints are denoted along withthe binding connectors, connecting the parameters to re-spective constraint properties. The constraint property forthe clock generation model uses the default cMathemat-ica property of constraint block from SysML. The clockgenerates ticks that are fed to both cp1 & cp2 profilessynchronously. This mechanism in PD is the key in thesynchronization of the Lift and Pump profiles.

7. SPL MODEL OF TR/28

The complete TR/28 packaging machine from a behavioralconstruct is modeled in SPL. The modules of the machinesuch as Bottom Sealing, Filling and Top Sealing aremodeled as operations on the highest hierarchical level.The complete SPL model of the machine is given inFigure 11.

Module operations The operations of each module aremodeled within their respective module hierarchy. Cartonsare the products of the TR/28 machine, represented asvariables in the SPL model. The products flow one afterthe other, through the operations of the model. The Fillingmodule handles two products with redundant resourcesworking at the same time. A buffer variable, waiting fortwo products at the Filling module is defined in the SPLmodel. The Bottom Sealing module includes operationsrelated to the sealing process of carton sheets. A five armMandrel is the resource, carrying one folded carton ineach arm and performing the operations Heating, Folding,Squeezing one after the other for each sheet. Each sheetfills the position of the empty arm of the Mandrel andexecutes the sequence of operations as mentioned before.


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The respective operations of the Filling and the TopSealing modules are also defined in the SPL model. TheFilling module includes operations Charge Stroke, LiftUp, Lift Down and Fill Stroke; where Lift Down & FillStroke are synchronized by parallel operations in the SPLmodel. The Lift and Pump are booked as resources forrespective operations in the Filling module. With thehelp of Indexing Conveyor, cartons are transported to theFilling module by every two steps. The operations of theIndexing Conveyor are synchronized with other modules ofthe machine as mentioned in Section 5. The motion profilesof Lift, Pump & Conveyor are modeled by adding therelevant execution time of each operations which use theseresources. The fact that operations such as Filling and TopSealing are executed only when the conveyor is halted istaken care of by considering the conveyor motion profile.Hence, this SPL model includes the conveyor operationsto be performed in parallel to other operations.

Fig. 11. SPL model of TR/28 packaging machine.

Resource View The SPL model of the TR/28 machineincludes Lift, Pump and Conveyor as resources. Theseresources are booked and unbooked by correspondingoperations. Projecting the sequences of operations froma resource point of view is visualized in SPL, as discussedin Section 3. Visualizing the sequences of operations withrespect to the Pump is shown in Figure 12. The operations,ChargeStroke and FillStroke along with LiftUp followed byLiftDown are identified as relevant sequences of operationswith respect to the resource Pump.

Fig. 12. Resource view of pump in SPL.

Optimization The three state SPL operation modelholds a formal definition which is directly translated toan optimization model. A mathematical programming op-timization model is developed with respect to the start andfinish time of each operation in the case study. The relationbetween the operations is defined by including the minimalduration time of each operation. Summation of start timeand minimal duration time of the previous operation gives

the earliest possible start time of the current operation.This type of model can represent relations such as se-quence, parallel, hierarchy, etc. Sundstrom et al. (2012)explain in detail the relation between an SPL model andan optimization model.

The optimization problem considered in this paper is tomaximize the production rate (PR) of TR/28 with theconstraint that the acceleration of the conveyor being lessthan 7m/s2. In the current case study, the cartons arebeing processed in batches of two as described in Section 4.In order to identify the optimial solution, the BatchSizeand the Machine Cycle are varied from 1 to 10 and 0.6 to1.3 s, respectively.

Objective Function:

maxPRs.t. a ≤ 7m/s2

where

PR =3600

mc∗N ∗ S

N is number of Index Lines = 2,S is BatchSize = 1 to 10,mc is machineCycle = 0.6 to 1.3 s,a is acceleration,PR is Production Rate

The optimization model is developed in AMPL (A Mod-eling Language for Mathematical Programming) platformand the Bonmin solver is used to find the optimal solution.AMPL, is a powerful algebraic tool for linear and nonlinearoptimization problems by utilizing different solvers, c.f.AMPL (2013). The nonlinearity in the optimization modelis handled by Bonmin. By including the constraint for theacceleration, the optimal solution with production rate of16600 cartons per hour is obtained at a BatchSize of 3 andMachine Cycle 1.3 s. The production rate of the currentmachine with BatchSize 2 and Machine Cycle 1 s is 12000cartons per hour.

8. DISCUSSION & CONCLUSION

The need for modeling synchronous behavior raises fromthe built-in nature of packaging machines. Single mastersending commands to a number of slaves, and the motionsbetween slaves being synchronized are the traditions thatthe packaging industry still follows. The necessity for acommon model to be shared between different domainscreates a gap for synchronous behavior modeling. In thispaper, a modeling solution for the synchronous behaviorsusing SysML is given and implemented with the casestudy of Tetra Pak TR/28 machine’s filling module. Themotion profiles are added as constraints to the respectiveresources. The resulting model is validated analyticallyand the results are documented in Kanthabhabhajeya(2013).

The entire TR/28 machine is also modeled in SPL, tomake use of the advantage of the formal sequence planninglanguage. The model is also projected with respect to oneof the resources. An optimization model with objectivefunction to maximize the production rate is developed withthe support of the SPL model. The resulting optimal so-lution gets a maximum production rate, 16600 with batchsize of 3 and machine cycle 1.3 s. This simple optimization


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of the TR/28 machine shows that minor modification ofan existing packaging machine may generate significantimprovements. The optimization model will be extendedto include more detailed motion profiles, as well as mutualexclusion between shared resources.

ACKNOWLEDGEMENTS

This work was carried out in collaboration with and sup-port from Tetra Pak as well as the Wingquist LaboratoryVINN Excellence Center within the Area of Advance,Production at Chalmers, supported by the Swedish Gov-ernmental Agency for Innovation Systems (VINNOVA).The support is gratefully acknowledged.

REFERENCES

AMPL (2013). A Modeling Language for MathematicalProgramming. http://www.ampl.com/.

Bassi, L., Secchi, C., and Bonfe, M. (2011). A sysml-basedmethodology for manufacturing machinery modelingand design. IEEE/ASME Trans. Mechatronics, 16,1049–1062.

Bengtsson, K. (2012). Flexible Design of Operation Be-havior using Modeling and Visualization. Ph.D. thesis,Chalmers University of Technology, Sweden.

Friedenthal, S., Moore, A., and Steiner, R. (2012). APractical Guide to SysML - The Systems ModelingLanguage. Morgon Kauffman OMG Press, 2nd edition.

Kanthabhabhajeya, S. (2013). Analytical and Simulationvalidation of the synchronous model using sysml plugins.Report, to be published.

Kanthabhabhajeya, S., Berglund, J., Falkman, P., andLennartson, B. (2013). Interface between sysml andsequence planner language for formal verification. Pro-ceedings of 23rd Annual INCOSE International Sysm-posium.

Kanthabhabhajeya, S., Falkman, P., and Lennartson, B.(2012). System modeling specification in sysml andsequence planner language - comparison study. Proceed-ings of 14th IFAC Symposium on Information ControlProblems in Manufacturing Information Control Prob-lems in Manufacturing.

Lennartson, B., Bengtsson, K., Yuan, C., Andresson, K.,Fabian, M., Falkman, P., and Akesson, K. (2010). Se-quence planning for integrated product, process andautomation design. IEEE Transactions on AutomationScience and Engineering, 7, 791–802.

Nguyen, K.D., Ng, T., and Chen, I. (2008). On algorithmsfor planning s-curve motion profiles. InternationalJournal of Advanced Robotic Systems, 5, 99–106.

OMGSpecification (2010). OMG Systems Modeling Lan-guage (OMG SysML). Technical report, Object Man-agement Group SysML. URL http://www.omg.org/spec/SysML/1.2/.

Pietrac, L., Leleve, A., and Henry, S. (2011). On theuse of sysml for manufacturing execution system design.Proceedings of IEEE ETFA.

Qamar, A., Wikander, J., and During, C. (2011). Modelingcontinuous system dynamics in sysml. Proceedings ofIEEE International Conference on Mechatronics.

Reisig, W. (1992). A Primer in Petri Net Design.Springer-Verlag, New York, 1st edition.

Sundstrom, N., Wigstrom, O., Falkman, P., and Lennart-son, B. (2012). Optimization of operation sequencesusing constraint programming. Proceedings of 14thIFAC Symposium on Information Control Problems inManufacturing Information Control Problems in Manu-facturing.

TetraPakEngineers (2007). OM operation manual, TetraRex TR/28 XH. Technical report, Tetra Pak, Lund,Sweden.


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