Self-learning Rotator Control: Control of the orientation process of a bulk to tray line - Zelflerende Rotator regelaar: Regelaar voor orientatie proces in een bulk to tray line

Delft University of Technology

FACULTY MECHANICAL, MARITIME AND MATERIALS ENGINEERING

Department Maritime and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

This report consists of ## pages and # appendices. It may only be reproduced literally and as a whole. For commercial purposes only with written authorization of Delft University of Technology. Requests for consult are only taken into consideration under the condition that the applicant denies all legal rights on liabilities concerning the contents of the advice.

Specialization: Transport Engineering and Logistics

Report number: 2016.TEL8086

Title:

Self-learning Rotator Control:

Control of the orientation process

of a bulk to tray line.

Author:

B.A.M. Zeeuw van der Laan

Title (in Dutch) Zelflerende Rotator regelaar: Regelaar voor orientatie proces in een bulk to tray line.

Assignment: Masters thesis

Confidential: yes (until Month dd, yyyy) Initiator (university): prof.dr.ir. G. Lodewijks

Initiator (company): ir. S.A.M. Coenen (Vanderlande, Veghel) Supervisor: dr. ir. Y. Pang

Delft University of Technology

FACULTY OF MECHANICAL, MARITIME AND MATERIALS ENGINEERING

Department of Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

Student: B.A.M. Zeeuw van der

Laan Assignment type: Master project

Supervisor (TUD): Dr.ir. Y. Pang Creditpoints (EC): 35 Supervisor (Company): Ir. S.A.M. Coenen Specialization: TEL

Report number: 20xx.TL.xxxx Confidential: Yes / no

until: Month dd, yyyy

Subject: Self-learning Rotator Control: Control for the orientation process in a bulk to tray line.

Introduction

Vanderlande is the global market leader in baggage handling systems for airports, and sorting systems for parcel and postal services. The company is also a leading supplier of warehouse automation solutions. In the business area distribution Vanderlande is offering a new level of automation to the market: Automated Case Picking (ACP).

Vanderlande’s ACP systems provide the tools to outperform traditional order fulfillment methods. Such a system automates the typical process of a food retailer’s warehouse; storing pallets with a single type of supermarket products and next picking of an order containing a mix of different types of supermarket products.

In ACP the cases of an incoming pallet with a single type of product are stored with 1 or more cases in a tray. An incoming pallet typically has a layer pattern where its cases are not all oriented the same way. To load the tray as efficiently as possible, all cases of the pallet need to be in a preferred

orientation. Thereto, the case rotator function rotates cases if necessary to this preferred orientation. The rotation of a case is performed in transport on a conveyor belt with a velocity of v b = 1 m/s. The function, displayed in the figure, consist of four phases:

Alignment of cases to left side of the conveyor.

Pre-rotation of cases, for which the orientation needs to be changed, to a specified angle α pre by pushing away the tail of a case.

Rotation of cases to β exit =90˚ by running it against a block that sticks out at a specified length l rot. Alignment of cases to the left of the conveyor and correcting any under- or over rotation.

In the current implementation, the settings for the pre-rotator and rotation have been determined empirically by performing numerous tests with a select number (150) of products, and classifying these products (now 20 classes), where every class of products has its specific settings. However, the customers involved have 1000 to 10000 different products that may require pre/rotation. To limit test effort, a rigid body model has been developed. This model can predict the settings of the pre-rotator and rotator with limited accuracy (±10˚) such that the cases rotate to the desired β exit =90˚.

Assignment description – Problem and goal

The problem in this research is the need for a better control strategy for the orientation porcess system. The cases classes can’t possibly take all the variables concerned into account and therefore aren’t optimal. In order to improve performance better settings for cases are preferred. However, this would require a lot of test effort. Suppliers can also change their cases and new types can go in and out the assortment.

The goal of this research is to determine a control strategy for the system that allows the system to find the settings for operation of different products during operation.

The professor,

SUMMARY

Distribution Centres (DC) in the (food)-retail market see a lot of advantages in Automatic Case Picking (ACP). These ACP systems could lead to an improved fill rate of pallets. The ergonomically unsafe picking activities are taken over by machines. The pallets that are supplied to the DC are filled with one case type. The pallets or roll containers leaving the DC for the supermarkets is stacked with various case types in the correct order for the supermarkets.

The ACP system has a temporary storage of cases in the system in trays. In this way, the system has a buffer of cases from all the different Stock Keeping Units SKUs. When a case is demanded for loading it can be quickly supplied by the system. To refill the trays with cases a process called the Bulk to Tray line is used. During this process, full pallets are loaded of layer by layer. For optimal use of the storage on a pallet cases are orientated in different ways. To optimize the storage in the trays of the system the cases need to be in the same orientation. This process is called the orientation phase. This research concerns the orientation phase.

In the orientation phase. The layers are separated into single rows of cases and these are then spaced out on separate belt conveyors called the Singulator. The cases are then aligned to the side of the system by the Skewed Rollers and Vertibelt. Then a so called Pre-Rotator and Rotator will rotate the cases by non-prehensile manipulation while they are moving a long on a conveyor belt. This process makes use of stick slip behaviour from the friction between the case the belt and the Rotator. After the Rotator the cases are transported on a second set of Skewed Rollers and Vertibelt to further rotate the cases to the desired 90 degrees and to align them to the side of the belt again.

Currently the settings of this process have been empirically found by testing a limited number of SKUs. From these experiments 20 different types of settings were determined.

The goal of this research is to come up with a control strategy that could learn the settings for the orientation process during online operation in a robust way. The cases should rotate to 90 degrees and the gap between the cases at the end of the process should be at least 100mm.

For the conceptual design phase there is made use of a methodical design approach. Based on an analysis of the system different control options are proposed. These options are combined to strategies. Since performing tests on the real system requires a lot of time a simulation model based on a model from a prior research was used. The strategies were simulated with a representative dataset from a large retailer. The results of the simulations combined with a simplified feasibility and simplicity measurement were compared on determined weight factors in a Multiple Criteria Analysis. The best strategy was selected and tested on the real system. On the simulation the strategy is able to learn optimized settings for operation after iterative runs.

With the limited amount of experiments on the real test setup the strategy has shown to work for some SKUs. The proposed strategy shows the possiblity to learn the optimal settings for the process during online operation. The optimized settings show a higher throughput then when the current settings are used. Tests with a SKU with large variances have shown that the strategy doesn’t work on every SKU. In order to verify if the strategy would be applicable more tests with different SKUs needs to be done.

PREFACE

This report contains my master’s thesis. This master thesis concerns a research within Vanderlande. It is part of the Automatic Case Picking (ACP) project.

I want to thank my supervisor from the university; Y. Pang for his guidance and helpful advice. My gratitude goes as well to the professor, G. Lodewijks, for his keen feedback during presentations. I would like to thank Vanderlande for the opportunity to perform my research. My special appreciation goes to S.A.M. Coenen and B. van Dartel who gave me this position, helped me during the project and supervised me every week by discussing the progress.

Furthermore, I would like to thank M. Godjevac for his willingness to take part in my exam committee. Finally, I want to thank my fellow students at the university and the ones who also graduated at Vanderlande, for their input and moral support during my graduation project.

Page 1 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

LIST OF SYMBOLS

𝑎 Acceleration [𝑚/𝑠!_]

𝑎! Acceleration of centre [𝑚/𝑠!]

𝛽 Angle for case rotator [°] 𝑐𝑣 Coefficient of variation

𝛾 Initiation ratio Pre-rotator stroke 𝐹! Frictional force [N] 𝐹!"# Net force [N] 𝐹! Normal force [N] 𝑔𝑎𝑝_!" Incoming gap [m] 𝑔𝑎𝑝!"# Outcoming gap [m] 𝐼 Inertia

𝐾_!"#$%& Ratio of weight divided by leading edge [kg/m]

𝑘 Run of case

L Length case [m]

LL Length leading

𝑙!"# Length Pre-rotator [m]

𝑙_! Length Rotator [m]

𝑙!"!#$% Length of Pre-rotator and Rotator system [m]

𝑙!"#$#%&'((#&! Length of first skewed roller [m]

𝑙!"#$%&$'$&% Length of belt at Pre-rotator and Rotator [m]

𝑀 Mass [kg]

𝜃 Angle of case [°]

𝜙 Angle of diagonal case [°]

𝑟! Radius of perpendicular force [m]

𝑟𝑟 Radius centre case to point of contact rotator [m] 𝑟 Radius centre case to corner of case [m]

𝑠 Length initiation Pre-rotator stroke [m]

𝜎 Standard deviation

𝑇!"# Net torque [𝑁 ∗ 𝑚]

𝑇𝑎 Time of acceleration Pre-rotator [s] 𝑇!"# Time of stroke Pre-rotator [s]

𝜏 Torque [𝑛 ∗ 𝑚]

𝑢 Control action

𝜇 Coefficient of friction

𝑣! Belt speed [𝑚/𝑠]

𝑣_! Velocity in x-direction of centre of case [𝑚/𝑠] 𝑣_! Velocity in y-direction of centre of case [𝑚/𝑠] 𝑣_!"##$!% Speed of skewed rollers [𝑚/𝑠]

𝑣_𝑣𝑏 Velocity Vertibelt [𝑚/𝑠]

W Width case [m]

WL Width leading

𝜔 Angular velocity [𝑟𝑎𝑑/𝑠]

𝑥 State

𝑥_! Displacement of centre case in the x-direction [m] 𝑦! Displacement of centre case in the y-direction [m]

𝑦 Measurement

SUMMARY ... 6

PREFACE ... 8

LIST OF SYMBOLS ... 1

1.

INTRODUCTION ... 3

1.1.

1.2.

1.3.

1.4.

1.5.

1.6.

2.

ANALYSIS ... 10

2.5.

2.6.

2.7.

2.8.

2.9.

2.10.

2.11.

3.

REQUIREMENTS OF CONTROL SOLUTION ... 35

3.1.

3.1.1.

3.2.

3.3.

3.4.

3.5.

3.6.

3.7.

3.8.

3.9.

4.

CONCEPTS ... 45

4.1.

4.2.

Page 1 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

4.4.

4.5.

4.6.

4.7.

4.8.

5.

SIMULATION ... 53

5.1.

5.2.

5.3.

6.

MULTIPLE CRITERIA ANALYSES ... 61

6.2.

7.

VERIFICATION OF PROPOSED STRATEGY ... 66

7.1.

7.2.

7.3.

8.

CONCLUSION AND RECOMMENDATIONS ... 75

8.2.

8.3.

APPENDIX A: TEST RESULTS ... 79

APPENDIX B MEASUREMENT OPTIONS ... 83

8.4.

8.5.

8.6.

8.7.

8.8.

APPENDIX C: SKU FLOW ... 88

Page 3 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

1. INTRODUCTION

1.1. The ACP project

Vanderlande’s Automated Case Picking (ACP) systems provide the tools to outperform traditional order fulfilment methods. These improvements not only benefit distribution centres, but also the efficiency of the processes at work in stores. Vanderlande’s ACP design is setup to allow modular growth and ensures availability by utilizing parallel activities.

The service levels of a supermarket are highly dependent on the quality and velocity of its replenishment systems. When the store orders a shipment from the distribution centre, it is essential that the pallets are selected in the same sequence of product groups as the store’s layout. Before the pallets are stacked, the load forming logic software defines an optimal stacking pattern, with this product group sequence in mind.

The software also defines how to form stable pallets that are filled with maximum efficiency, so that the transport volume is minimized. The finished pallets will be wrapped and transported to stores, where there will be no need for extra sortation and they can be used immediately to fill the shelves.

Figure 1: ACP black box process

1.2. The system

The complete ACP system has an input of pallets of a single type of case from the suppliers on the incoming side. On the output side of the process sorted carts or pallets ordered by the supermarkets, with the demanded cases in the right order. The system can roughly be divided into three sub processes. The first sub process is to put the cases of incoming pallets from suppliers in a tray. The pallets are loaded off and the cases are transported on a conveyor, orientated and put into trays for temporary storage. The storage is the second sub process. Every tray contains one or more cases of the same type. These trays are then stored in racks until a case is demanded for loading. In the third sub process, the loading takes place. Cases are taken out of their trays and are loaded onto a pallet or roll container by a robotic arm.

• Bulk to tray • Storage • Pallet loading

This assignment focuses on the orientation part. The orientation part in the bulk to tray area consists of different sub-systems. These are the:

• Singulator • Pre-Rotator • Rotator

1.2.1. Orientation on incoming pallet

To optimally use the available space on a pallet and for stability reasons, pallets can be loaded with cases in different orientations see Figuur 2: Palet layout. The cases are loaded off from the pallets by a complete layer at a time. These are then placed on a conveyor. The layers are then separated to single rows and later the rows to cases with spacing in between.

However, the orientation of the cases is still the same as on the pallet. For the cases to go into the trays in the correct orientation. Some of the cases need to be rotated by 90 degrees. Once the cases are on the conveyor the edge which is traveling perpendicular to the direction of travel of the belt, is called the leading edge.

Figuur 3: Leading edges 1.2.2. Tray orientation

The reason the cases need to be in the same orientation is because they are put into the storing trays in a certain pattern for optimal use of the space. Depending on the dimension a different

Page 5 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

pattern for the filling of the tray is chosen. Depending on the chosen pattern cases need to be rotated from length leading to width leading or the other way around.

Figuur 4: Tray patterns

1.2.3. Length leading to width leading

The turn from length leading to width leading, LL to WL, means the cases coming in which are length leading need to be rotated.

1.2.4. Width leading to length leading

The turn from width leading to length leading, WL to LL, means the cases coming in which are width leading need to be rotated.

Figuur 6: WL to LL

1.3. Components

Figuur 7: Rotator system

1.3.1. Singulator

The products will first be singled into different rows. Then the products are spaced out by what is called the Singulator. The Singulator consists of different shorter conveyor belts that can

alternate their velocity. The Singulator can introduce a gap between the cases going onto the belt of the pre-rotator and rotator.

1.3.2. Pre-rotator

The pre-rotator initiates the rotation of cases. The pre-rotator is an actuator in the form of a rod placed at an angle of 45 degrees to the direction of belt travel. It can move out in a controlled way.

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1.3.3. Rotator

The rotator further rotates the cases. The rotator is an actuated rod which can be set to a certain length. The rotator has two possibilities of noses to be used. The first has a 90-degree angle and the second rotator nose is skewed under an angle of 45 degrees. In this research, only the 90-degree nose is considered.

1.3.4. Skewed rollers and Vertibelt

The Skewed rollers and Vertibelt correct the rotation and aligns the cases after the rotation phase

1.4. Stock keeping units

One of the difficulties with the use of the system is that it is used for the cases for supermarkets. The companies have a large number of different stock keeping units, SKU’s. Every one of them having slightly different characteristics. Due to different characteristics, different settings for the system need to be used. A typical food retailer has 2000-10000 different SKU’s that need to be transported over an ACP system.

1.5. Boundary conditions and requirements

Looking at the system as a black box the orientation process can be seen as a box with cases as input and cases as an output.

Figuur 8: Orientation area black box

The requirements for the operation of the orientation process are: • Cases should be rotated to 90 degrees

• The outcoming gap between cases should be 100mm • Cases should not collide during operation

• The system should learn the settings itself during on-line operation

1.6. Problem description

The orientation process in the bulk to tray line is required to rotate the cases which aren’t orientated in the correct orientation. In order to orientate the cases, the pre-rotator and rotator are used. In the current implementation, the settings for these sub-systems have been

empirically determined.

These have been empirically determined by numerous tests on a select number, around 150, of cases. The cases were classified into 20 different classes. Every class has its specific settings. However, the customers of the ACP systems can have between 2000-10000 different cases.

The cases classes can’t possibly take all the variables concerned into account and therefore aren’t optimal. In order to improve performance better settings for cases are preferred. However, this would require a lot of test effort. Suppliers can also change their cases and new types can go in and out the assortment.

Therefore, the system could benefit by being able to find the control settings itself for a new type of case. The ‘optimal’ settings could be determined a lot more exact. In order to do this control of the system is preferred to find ‘optimal’ settings.

1.6.1. Assignment and goal

The goal is to determine control strategies for the system that allows the system to find the settings for operation on-line. By comparing the strategies, a preferred strategy will come forward. This strategy will be validated for possible use.

1.7. Project approach

This project is to come up with a strategy. Methodical design is used to come to a conceptual design. There are different possible techniques, for example Kroonenberg & Siers, VDI,

Roosenberg&Eekels (Cross & Roozenburg, 1992). All methodical design methods show almost the same steps. This master thesis concerns the conceptual phase and some initial testing to verify the proposed strategy.

All the methodical design methods show approximately the same steps. In Figure 9: Methodical design chart the steps can be seen. The mechanical system itself is already realised and in operation. However, as an addition the control strategy designed in this project could be added. For this strategy, a conceptual design has to be made. In Figure 9: Methodical design chart this phase is coloured yellow.

Before the conceptual phase comes the initiation phase. The initiation phase describes the need for the project. This is described in section: 1.6.

For the conceptual design phase first a problem analysis is done. This analysis is done in section: 2. After this analysis, the system definition phase concerns the requirements for the solution. These can be found in chapter 3. In chapter 4 the system synthesis is addressed. In this chapter multiple strategies for the control are proposed. The different strategies will then be tested in a simulation model. This phase is called the simulation phase and can be found in chapter 5. During this phase the design criteria will be quantified. In order to make a decision for a concept a multi criteria analysis is done. This is part of the evaluation and selection phase. The proposed strategy is then tested to verify it on the real life setup.

Page 9 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

2. ANALYSIS

In the previous chapter the position of the process inside the total ACP process is shown. This chapter is an analysis of the system and shows the current solution. The goal of the analysis is to get a better understanding of the mechanical aspects of the process. An analysis of the effects of certain variables on the process is made. In previous research a model for the outcoming angles of the process was made, this model and the assumptions will also be discussed in this chapter.

2.1. Analysis of system

Figuur 10: Schematic drawing of system

The process can first be divided in four separate stages.

Figuur 11: Sub-processes

2.2. Mechanical analysis

The rotation of the cases works by a stick and slip process. Cases are transported on a conveyor and by impact they get turned. The pre-rotator and rotator both operate on the same conveyor belt. To simplify the model, the case is assumed a rigid body.

Figuur 12: Pre-Rotator and Rotator process

To describe the processes of the pre-rotator and rotator they are divided into four different stages:

Page 11 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

2. After Pre-rotator phase 3. Rotator phase

4. After rotator phase

2.2.1. Nonprehensile manipulation

The process of manipulating a case without a form or closed grasp is called Nonprehensile manipulation. Without the grasp the case is free to roll, slide or break contact with the

manipulators. The process is usually unilateral, meaning the manipulators can only push not pull. The manipulators work by contact forces on the cases. There are no kinematic equality

constraints on the manipulators connection to the case at all times. (Lynch & Murphey, 2002) and (Mason, 1986) have done research to the control of non-prehensile manipulation. The manipulation could occur with a robotic hand which could move in the whole plane. A case is in stable orientation ones it has contact with two separate pivot points. Stable

orientations for a case are ones a side is parallel to the side. (Mason, 1986) In this process the

2.2.2. Friction coefficient

The process of turning the cases on the conveyor works by friction. Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. The type of friction between a case and the conveyor is called dry friction. The dry friction can be subdivided into static and dynamic friction.

Static friction - is the friction between two non-moving surfaces. Dynamic friction - is the kinetic friction between two moving surfaces.

Friction is not a fundamental force itself, but is a result of inter surface adhesion, surface roughness and deformation. The determination of the amount of friction is very complex and therefore the empirically found coefficient of friction is often used.

The coefficient of friction, 𝜇, is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together.

(Heslot, Baumberger, Perrin, Caroli, & Caroli, 1994)

The friction results in a force perpendicular to the normal force. The frictional force 𝐹_! can be calculated by the product of the normal force 𝐹! acting on the surfaces and the coefficient of

friction 𝜇.

𝐹_! = 𝜇 ∗ 𝐹_!

2.2.3. Rigid body model

By assuming that the case is a rigid body, we can apply the Newton-Euler equations. The Newton-Euler equations state that the net force acting on the centre of mass on a rigid body is equal to the product of the mass of the case and the acceleration of the centre of the mass.

𝐹_!"#= 𝑀 ∗ 𝑎_!

The net moment of the moments around the centre of mass should also equal the product of the moment of inertia and the angular acceleration of the body.

• T - torque • I – inertia

• 𝛼 − angular acceleration • 𝜔 – angular velocity

The 𝜔 is the angular velocity of the case around the centre of mass. 𝜔 is given by the change of angular displacement of the rotation angle 𝜃. The moment of inertia 𝐼 can be defined as the mass of property of a rigid body that determines the torque needed for an angular rotation around an axis of rotation. 𝐼 depends on the shape of the case and may be different at different axes of rotation.

2.2.4. Momentum equation

When the case rotates around a certain point the friction with the belt will lead to reactional forces. These reactional forces will cause a momentum around the rotating point. In Figure 13: Momentum equation we see a case having contact with the rotator. The momentum force is defined as the cross product of the vector by which the force's application point is offset relative to the rotating point in the y direction. All of the area below the dotted line will therefore contribute to moment force in the

required rotational direction. All of the area above the dotted line, shown with a negative sign, will have a negative effect on the momentum for rotation. 𝑇_!"# is the net sum of al the moment forces acting on the case around the rotating point.

𝜏 = 𝑟!∗ 𝐹

Figure 13: Momentum equation 2.2.5. Pre-rotator phase

The case which is aligned to the upper wall passes by the pre-rotator. The pre-rotator is angled under 45 degrees and its movement can be controlled. The pre-rotator is activated when 85% of its length has passed the pre-rotator. Then the pre-rotator is activated. It’s controlled in such a way that the point of contact of the pre-rotator to the case stays constant. The case will rotate around its front corner, which has contact with the side wall. The length the pre-rotator moves outward is calculated in a way that it stops when the cases has reached the desired ‘pre-rotator angle’, theta. The maximum length of the pre-rotator is denoted as 𝑙!"#. At the moment the

pre-Page 13 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

rotator reaches the length 𝑙!"# the case reaches its maximum velocity. The pre-rotator stops to

enlengthen and the case will lose contact with the pre-rotator.

The distance 𝛾 is measured from the front corner making contact to the side wall, named O. The length of 𝛾 is 85% of the length of the side of the case L. With a given pre-rotator angle 𝛼!"# and

the length 𝐿 the length of the pre-rotator 𝑙!"# can be calculated.

𝛾 ∗ 𝐿 ∗ sin 𝛼!"# = 𝑙!"#∗ cos (

𝜋 4) 𝑙!"#= 𝛾 ∗ 𝐿 ∗ sin 𝛼!"# /cos (!_!)

The pre-rotator is limited in its acceleration and length, leading to the pre-rotator not always being able to reach the desired length for the given angle. The maximal velocity is 𝑎 = 2 𝑚/𝑠. 𝐿𝑝𝑟𝑒 > 𝑚𝑎𝑥 𝑙𝑒𝑛𝑔𝑡ℎ: Desired length is longer than the maximum length

If the desired length is longer than the maximum length the Pre-rotator can reach. If 𝑙!"#≥!_!∗ 𝑎 ∗ 𝑇!! then

𝑙_!"#=1

2𝑎 ∗ 𝑇!!+ 𝑎 ∗ 𝑇! ∗ 𝑇!"#− 𝑇!

𝑙_!"#< 𝑚𝑎𝑥 𝑙𝑒𝑛𝑔𝑡ℎ: Desired length is shorter than the maximum length

The length of the pre-rotator is reached before the maximum velocity has been reached.

𝑙_!"#=1 2𝑎 ∗ 𝑇!"#!

The final velocity will then be smaller than the maximum velocity and will be 𝑣 = 𝑎 ∗ 𝑇!"#.

Figuur 14: Mechanical analysis Pre-rotator

Depending on the characteristics it’s possible that the case will absorb some of the movement of the pre-rotator. Cases whom have more flexible sides for example will behave differently than cases with a very rigid side. This affects the outcome of the Pre-rotator angle. For this research the cases will be assumed rigid.

2.2.6. After pre-rotator phase

After the pre-rotator stops moving the case will lose contact with the pre-rotator. The case will have a velocity in both the forward and downward direction. It will also have a rotational velocity. Therefore, before the case comes to a halt compared to the moving belt, it will move in forward and downward direction and rotate further.

2.2.7. Rotator phase

The rotator will move outwards till a certain length. The case will hit the rotator with its side wall. If the centre of the case is outside of the point of contact with the rotator, the case will be able to turn. The velocity of the product will result in a reactional force around the point of contact initiating the movement. The area of contact of the case outside of the contact point will lead to a force resulting in further rotation of the case. When the frictional force resulting from the reactional force at the point of contact decreases below the force of the side movement the case will leave the rotator.

Figuur 15: Mechanical process Rotator The process at the rotator can be split up in three phases:

Impact

The case approaches the rotator at a certain angle 𝜃 and a position on the belt. The leading edge of the side wall will make contact with the corner of the rotator. The point of contact on the leading edge is a function of the position of the case on the belt, the dimension, the angle 𝜃 and the length of the rotator 𝑙!. The point of contact 𝑑𝑐 is expressed from the corner of the case

closest to the side. 𝑑𝑐 = 𝑓(𝐿, 𝐴, 𝜃, 𝑙!). The incoming case is traveling in x direction with the belt

Page 15 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

momentum of the movement will initiate the turn. The kinetic energy of the case will result in a torque force around the contact point.

This initial rotational velocity 𝜔 around the contact corner is calculated as follows:

𝜔 = 𝑣!∗cos 2 ∗ 𝜋 − 𝜋2 + 𝛽 + 𝜃_𝑟𝑟 /2

Figuur 16: Mechanical process Rotator initial rotation

Rotation

After the impact leading to the initial velocity around the corner point of the rotator, the case will stick to the edge of the rotator and rotate further. This will be as long as the frictional force at the rotator is larger than the force opposing this direction. Once this happens the case will slip away from the corner. The moving belt under the case will create a frictional force on the case. This force is depending on the type of surface and the pressure distribution and the relative velocity compared to the belt. For the model it is assumed that the friction coefficient is constant over the whole bottom and that the weight is also distributed evenly. The forces will lead to a momentum force around the rotator nose. The moment will lead to an acceleration of the rotational velocity.

Release

At the moment the frictional force at the rotator 𝐹! becomes smaller then the force moving

opposite to that direction the case will slip away from the rotator nose.

2.2.8. After rotator phase

After the case leaves the rotator its velocity will be slower than the belt and will still have some inertial movement in rotation. The after-rotator phase ends when the case doesn’t move anymore compared to the belt. The case will keep on turning and moving until the force caused by the deceleration of the inertial force becomes smaller than the frictional force with the belt.

2.2.9. Vertibelt and skewed rollers

The Vertibelt exists of skewed rollers under an angle of 10 degrees rolling towards the side edge. The rollers will cause the case to be moved towards the upper side of the system. Here a vertical belt is placed. This belt can be moved with a different velocity compared to the movement in x direction of the skewed rollers themselves. This can help to correct the angle of the cases. The Vertibelt process can be divided into four phases:

Page 17 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

Figure 18 Skewed roller and Vertibelt process

2.2.10. Case not making contact with the Vertibelt

The belt of the rotator system will lead the cases to the skewed rollers of the Vertibelt and skewed rollers. The skewed rollers are angled under a 10-degree angle. The case coming on the skewed rollers will have a velocity in the x-direction. The skewed rollers will roll at a velocity 𝑣!"##$!% so that the velocity in x-direction is equal to that of the belt at the rotator and Pre-rotator.

𝑣!"##$!% = 𝑣! / cosd 10

The skewed rollers will start applying a frictional force to the case in the y-direction. This will cause the case to accelerate in the y direction. The velocity in the y direction of the skewed rollers is:

𝑣!"#$$%"&= 𝑣!"##$!%∗ 𝑡𝑎𝑛𝑑(10)

2.2.11. Impact of case to Vertibelt

There are three possible situations when the case makes contact with the Vertibelt. The case could be already rotated to exactly 90 degrees. In this situation, no further rotation occurs during impact. The other two situations are a case that has rotated short of 90 degrees or more than 90 degrees. In both these two situations the impact to the Vertibelt will be with on the corner of the case. Once the corner hits the Vertibelt the inertia of the case will cause the case to rotate. The rotation will be around the corner contacting the belt. Depending on the ratio of the dimensions and the angle of the case the case will rotate clockwise or counter clockwise. The initial velocity of rotations is calculated as follows.

𝜔 = 𝑣!∗ sin (𝜃 + 𝜙 −

𝜋 2)

2.2.12. Case in contact with Vertibelt but not aligned

While the case has contact with the vertibelt but is not jet aligned with the side, two processes can be going on. The first is the skewed rollers pushing the case to the side causing the case to align. The second is the effect of the vertibelt if it has a relative velocity to the x-direction of the

skewed rollers. The belt will then assert a force on the corner of the case causing a momentum to rotate the case.

Effect of skewed rollers

The skewed rollers push the case into the vertibelt. This will create a momentum force around the corner having contact with the vertibelt. This will increase the rotational velocity around the corner point.

Effect of vertibelt

The vertibelt can have a relative velocity to the x-direction of the skewed rollers. In this case due to friction a force will be exerted on the corner of the case having contact with the belt. This will increase the rotational velocity. The force the corner is applying on the corner is a function of: 𝐹! - the normal force between the case and the vertibelt

𝜇 - the dynamical friction coeffiecient between the corner and the belt 𝐹!= 𝐹!∗ 𝜇

Figuur 19: Vertibelt effect 2.2.13. Case aligned with Vertibelt.

Once the side of the case is aligned to the side, the skewed rollers will keep on pushing the case to the vertibelt. The case will continue traveling on the skewed rollers until the end.

2.2.14. Analysis of Vertibelt and skewed rollers

Whether the vertibelt and skewed rollers are able to further rotate the case to the desired 90 degrees depends on multiple factors. The main factor is the L/W ratio compared to the incoming angle at the vertibelt. When the centre of the case is in front of a perpendicular line with the belt the sum of the moment forces will cause the case to move in the correct direction. This is due to the net sum of the moment forces, see paragraph: 2.2.4. We define the angle between a perpendicular trough the contact point and line from the contact point trough the centre of the case as the correction margin 𝜓. The correction margin is the value for 𝜓. This is the smallest 𝜓 which will lead to a 90 degree rotated case at the end of the vertibelt.

𝜓 = 𝜃 + 𝜙 − 90

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Figuur 20: Correction margin Skewed rollers and Vertibelt

2.2.15. Slip and displacement

The process to rotate the case is by non-prehensile manipulation. The rotator itself doesn’t move. The force comes from the moving conveyor which the cases travel up on. This process leads to slip. With slip the amount of negative displacement in the x-direction is meant. This displacement is measured from the relative position of the cases centre in the x-direction to the belt at the beginning of the process.

Figuur 21: Displacement axis of case

2.2.16. Gap

The gap is a function of the amount of slip of the two consecutive cases, the dimensions of the cases, the initial orientation and their out coming orientation.

There are four situations possible where the first case rotates and is followed by another case. These four situations can be seen in Figure 22: Case sequences In the case a case doesn’t rotate there is assumed to be no slip.

Figure 22: Case sequences

2.2.17. LL à WL followed by WL

In this case the first case rotates and the second remains in the same orientation. The function for the out coming gap is:

𝑔𝑎𝑝_!"#= 𝑔𝑎𝑝_!"− 𝑠𝑙𝑖𝑝_!!"− 1/2(𝐿 − 𝑊)

Figuur 23: Gap LL followed by WL 2.2.18. LL à WL followed by LLà WL

In this case both cases rotate from LL to WL The function for the out coming gap is:

Page 21 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

Figuur 24: Gap LL followed by LL 2.2.19. WL à LL followed by LL

In this case the first case rotates from WL to LL. The function for the out coming gap is:

𝑔𝑎𝑝_!"#= 𝑔𝑎𝑝_!"− 𝑠𝑙𝑖𝑝_!!"+1

2(𝐿 − 𝑊)

Figuur 25: Gap WL followed by LL 2.2.20. WLà LL followed by WL à LL

In this case both case rotate from WL to LL. The function for the out coming gap is:

𝑔𝑎𝑝!"#= 𝑔𝑎𝑝!"− 𝑠𝑙𝑖𝑝!!"− 𝑠𝑙𝑖𝑝!!" + (𝐿 − 𝑊)

In this situation, it’s possible for the gap to increase. If the difference in slip of the first compared to the second case is smaller than the difference in length between length and width of the cases. Since the slip of the two cases will be approximately equal, this will result in an out coming gap which is larger than the incoming gap.

Figuur 26: Gap WL followed by WL

2.3. Existing model

A model of the process of the Pre-rotator and Rotator process has allready been made. (Niyitegeka, Liu, & Qiao, 2015) The model is a rigid body model that simplifies the process and takes certain assumptions. The model has been verified and validated on tests performed on the system. The model is validated and verified for the turn from WL to LL. The model is able to predict the outcoming angle with an accuracy of ±10%. The inputs of the model are the dimensions of the case, the belt velocity, Pre-rotator length, Rotator ratio and the dynamic friction coefficient. The model gives the angle after the pre-rotator process and after the rotator process as an output. As well as the amount of time spent at the different processes.

2.3.1. Assumptions for model

Since the model is a simplified version of the reality some assumptions were made for the realisation of the model.

• Cases are rigid bodies • Cases have straight edges • Weight is uniformly distributed

• Bottom surface is equally distributed on belt

2.3.2. Inputs of model

The model has the following inputs: • Length

• Width

• Dynamical coeficient of fricition • Belt speed

• Length Pre-rotator • Rotator ratio

2.3.3. Outputs of model

The model has the following outputs: • Angle after Pre-rotator • Angle after Rotator • Times spent at phases

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2.4. Dimensions

The system is already designed and in current use. In Figuur 27: Dimensions of Rotator system the dimensions of the belts and the Pre-rotator and Rotator is shown.

Figuur 27: Dimensions of Rotator system

Name Length [mm]

Total length 𝑙_!"!#$% 6375

Skewed Roller 1 𝑙_{!"#$#%&'((#&!} 1950

Rotator Belt 𝑙!"#$%&$'$&% 1950

length rotator 𝑙! 100 (max)

Skewed roller 2 𝑙!"#$#%&'((#&!! 2475

Vertibelt 2 𝑙_!"#$%&"'$! 2690

2.5. Requirements for operation

During operation cases shouldn’t collide. This could cause cases to not be able to rotate correctly and cause the system to block.

2.5.2. Throughput

The throughput is the number of cases that can go through the system. The throughput is a function of the velocity of the belt 𝑣! and the gap between the cases. The throughput is

calculated in the number of cases that can go through the system in one hour. 𝑡ℎ𝑟𝑜𝑢𝑔ℎ𝑝𝑢𝑡 = 𝑣!

𝑔𝑎𝑝!"∗ 3600 [

𝑐𝑎𝑠𝑒𝑠 ℎ𝑟 ]

2.5.3. Out coming angle

The goal of the process is to rotate cases to the desired output. At the end of the process the out coming angle 𝜃 should be 90 degrees.

2.6. Control variables

The Singulator works by different belts in series alternating velocity. Therefore, being able to create a gap between the cases before they enter the first skewed rollers. Due to limitations of this system it is not possible to create any desired gap. The possible gaps aren’t a continuous function but are in discrete steps. The possible incoming gap will always be chosen larger than the desired gap. For this research the Singulator is assumed to be able to introduce the cases at the desired gap.

The gap between cases is created by the principle of different conveyors running at different velocities. Assuming the weight of the case is uniformly distributed around the product, a prediction of the introduced gap between two conveyors can be made. Simplified it can be assumed that a case will start moving with the velocity of the next conveyor when half of its area is on the next belt. The fact that the case will start moving at the speed of the second conveyor instantly when half of its area is on the second conveyor is also an assumption. The gap between two succeeding cases is a function of the velocity between the two belts and the orientations of the cases. 𝐺𝑎𝑝 =! !∗ !!! !_!!− 1 ∗ (𝑁𝑜𝑛𝑙𝑒𝑎𝑑𝑖𝑛𝑔 𝑒𝑑𝑔𝑒 1𝑠𝑡 + 𝑁𝑜𝑛𝑙𝑒𝑎𝑑𝑖𝑛𝑔 𝑒𝑑𝑔𝑒 2𝑛𝑑)

In the example below 𝑣!!= 2 ∗ 𝑣!!. The outcoming gap for two WL cases is then 2 times the

length. For two LL cases the gap is equal to the width. For two cases with different orientation the gap is half the length plus half the width.

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2.6.2. Pre-rotator

Length pre-rotator

The length of the pre-rotator can be varied to acquire the desired angle for the pre-rotator process.

Point of initiation

The point of initiation is the point at which the pre-rotator pushes the case. The company has decided this to be at 85% of the case length. This variable will not be changed.

Belt velocity

The Belt velocity can be varied. However due to limitations on the control of the motors for the belts the velocity can be set to certain discrete values. The belt operating at the pre-rotator and the rotator is the same and therefore the velocities should be the same.

2.6.3. Rotator

Type of Rotator

The rotator has two possible noses. One at a 45-degree angle and one at a 90-degree angle.

Length of Rotator

The length of the rotator can be set. The maximum length of the rotator is 100mm. The length of the Rotator can also be expressed as the Rotator ratio. The Rotator ratio is a function of the length of the leading edge before rotation and the length of the rotator 𝑙!.

𝑅𝑜𝑡𝑎𝑡𝑜𝑟 𝑟𝑎𝑡𝑖𝑜 = 𝑙!

𝑙𝑒𝑛𝑔𝑡ℎ 𝑙𝑒𝑎𝑑𝑖𝑛𝑔 𝑒𝑑𝑔𝑒

Belt velocity

The Belt velocity can be varied. However due to limitations on the control of the motors for the belts the velocity can be set to certain discrete values. The belt operating at the pre-rotator and the rotator is the same and therefore the velocities should be the same.

2.6.4. Skewed rollers 2 + Vertibelt

Velocity rollers

The velocity of the rollers can be set.

Relative velocity of Vertibelt

The relative velocity of the vertibelt can be varied. It can either go faster, equal to, or slower than the belt velocity.

2.7. Variables

Cases have different types of shapes, sizes and other characteristics influencing the process. Before products are introduced into the system some characteristics are known others are unknown.

2.7.1. Known characteristics • Weight

• LXBXH • Shape 2.7.2. Unknown characteristics • Mu static • Mu dynamic • Dynamical behaviour • Weight distribution of cases 2.7.3. Variations within same SKU

Within the same SKU none of the cases are exactly the same. For example, the weight

distribution or the shape of the bottom of the cases will probably influence the process. However, these may differ slightly per case.

2.8. Current solution

The system is already in operation. The current settings for different types of cases have been empirically found. Depending on the characteristics cases are divided into different categories. For the operation from WL to LL 20 different categories have been determined. The categories lead to a certain type of settings.

Categories are decided from characteristics that have imperially been found to have effect on the rotation process.

2.8.1. K-Factor

The K-factor is a function of the weight and the length of the leading side. 𝐾𝑓𝑎𝑐𝑡𝑜𝑟 = 𝑤𝑒𝑖𝑔ℎ𝑡

𝑙𝑒𝑛𝑔𝑡ℎ 𝑙𝑒𝑎𝑑𝑖𝑛𝑔 𝑠𝑖𝑑𝑒

2.8.2. Length

The length of the case. When the length of the cases exceeds the 400mm different settings are chosen.

2.8.3. Length width ratio

This is a function of the length and the width. 𝐿

𝑊 𝑟𝑎𝑡𝑖𝑜 = 𝑙𝑒𝑛𝑔𝑡ℎ/𝑤𝑖𝑑𝑡ℎ 2.8.4. Damage risk

Page 27 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

Figuur 29: Settings for WL to LL rotation

2.8.5. Settings

For these categories different settings have been found empirically. The different settings can be seen in Fout! Verwijzingsbron niet gevonden.. The settings vary in the Pre-rotator angle 𝛼, the type of rotator nose, rotator stroke length 𝑙_! and the velocity of the vertibelt 𝑣_!".

2.8.6. Incoming gap

The settings for the incoming gap are also empirically found. For this setting a formula is created depending on the dimensions of the case. The incoming gap is calculated as a function of the length and the width of the case.

𝐼𝑛𝑐𝑜𝑚𝑖𝑛𝑔𝐺𝑎𝑝 = 0.2 + 0.5 ∗ 𝐿 − 0.4 ∗ 𝑊 `

The incoming gap is measured as the distance between two cases.

2.8.7. Disadvantages current solution

There are a lot of variables influencing the optimal settings. The number of different categories already shows this. Within the categories, it is probably possible to improve even further. The number of categories is already complex so doing this by adding extra categories is undesirable. The amount of gap introduced between two cases is now chosen so that a correct end gap is achieved for every case with the given dimension. The formula is therefore chosen to introduce a gap large enough that the cases with the most amount of slip have a correct result. Therefore, the gap is unnecessarily big for SKUs which have less slip.

2.9. Effect analysis

To get a better understanding of what the effects of certain variables are an anaylis is made in this section. The goal is to get a better understanding of what the effect of certain variables is. This can later be used to determine what is the effect when the settings are changed. The effect of the coefficient of friction is also varied. This variable isn’t controllable but it varies for the SKU’s. The model is used to study the different outcomes for certain settings. This is done to determine the effect of certain variables. The model is used to simulate the outcome when one of the variables is varied.

A case with a length of 0,4 m and a width of 0,2 m is used for the simulation. The other settings are:

Mu = 0,4

Rotator ratio = 0,25

Pre-rotator angle = 10 degree Belt velocity = 1 m/s

The outcomes show the amount of slip occurring at the rotator in meters, the total out coming angle and the amount of rotation the rotator was accountable for. The total angle is the angle after the complete process. The rotator angle is the total angle minus the angle after the pre-rotator process.

2.9.1. Belt velocity

The belt velocity is varied between 0.5 and 1.5 and the results are shown in Figure 30: Variable belt velocity. The amount of slip and oncoming angle seem to be pretty constant between 0.5 m/s and 1 m/s. Ones the velocity is increased further the amount of slip rapidly decreases and the total angle increases. This is probably due to increasing effects of rotation due to kinetic impacts. This is an unwanted situation. With an increasing velocity the impact on cases also increases, this could lead to damaged cases.

Page 29 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

The current operating velocities of the company at 0.75 m/s and 1 m/s seem therefore to be well chosen.

Figure 30: Variable belt velocity 2.9.2. Pre-rotator angle

The pre-rotator angle is varied between 0 and 25 degrees the results are shown in Figure 31: Variable pre-rotator angle. With an increasing pre-rotator angle the amount of slip decreases rapidly. This is due to the fact that less rotation occurs at the rotator where slip happens. The total out coming angle however also decreases. There is a lesser amount of rotation at the rotator.

2.9.3. Rotator Ratio

The rotator ratio is varied between 5% and 50%. The results can be seen in Figure 32: Variable rotator ratio. As can be seen in the graph the out coming angle is fairly low for a rotator ratio smaller than 15%. This is probably due to the fact that the case bounces of the rotator. The fact that no slip occurs means there is no sustained contact. The case makes contact leading to some rotation due to kinetic effects. But the contact time is almost zero. Therefore, no rotation takes place during real contact. When the rotator ratio increases the amount of rotation at the rotator also increases. The amount of rotation at the rotator increases asymptotically. The amount of slip increases almost linear. This means that to increase the rotation by the rotator further at a certain point will result in relatively more slip.

Figure 32: Variable rotator ratio 2.9.4. Mu

The value for the coefficient of friction is varied between 0.2 and 0.7. The results can be seen in Figure 33:Variable mu. The approximate mu is around 0,4. As can be seen in the results the amount of slip increases with a higher mu. The total angle decreases, but reaches a steadier turn by the rotator.

Page 31 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

Figure 33:Variable mu 2.9.5. Weight

Tests performed at Vanderlande (Niyitegeka et al., 2015) have shown that the out coming angle were the same with the weight varied. Changing the weight in the model will also lead to similar results. The extra mass requires a larger force to accelerate 𝐹 = 𝑀 ∗ 𝑎. However, the reactional forces with the belt increase with the same ratio. 𝐹!= 𝜇 ∗ 𝐹!. Where 𝐹!= 𝑚𝑎𝑠𝑠 ∗ 9,81.

2.10. System analysis

The system has cases coming in and being processed at discrete intervals 𝑘. Case go through four different sub-processes. Depending on the actions 𝑢 taken the state 𝑥 of the case changes. Measurements 𝑦 of the state of the case can be taken. During the processes disturbances 𝑑 can occur. Disturbances on the measurements are denoted by 𝑛.

2.11. Stock keeping unit analysis

One of the difficulties with the use of the system is that it is used for the cases of large retailers. The companies have a high number of different stock keeping units, SKU’s. All having slightly different characteristics. Due to different characteristics, different settings for the system need to be used.

The goal of this Stock keeping analysis is to get a representative set of cases that can be used for the simulation. When all the different cases would be used, the simulation would become too long. Since the representation covers the cases dimensions the simulation is expected to be done with a realistic set of SKUs.

The analysis of the SKU’s comes from data of SKU of a large retailer and represents a full flow dataset. The data of the most common SKU’s of a large retailer can be found in Appendix C: SKu Flow. The analysis is done for the cases that will make a turn from WL to LL. The dimensions of the cases are taken into account. To get a representative outcome of the throughput the flow of the different SKU’s is taken into account. This is done because there will be differences in the

throughput performances for the different SKU’s. To get a realistic number for the effective throughput of the system the flow per SKU is used. The flows of the different cases are given as a percentage of the total flow. To limit the total simulation times, the SKU’s are divided into different categories representing the different case geometries. The categories are divided by taking the four percentiles of the Length and the four percentiles of the ratio of the width and the length and combining them to make 4 ∗ 4 = 16 diferent categories.

The selection has been made with the criteria for cases making a WL to LL turn. The minimum and maximum dimensions are taken into account. Due to the width of the trays the maximum length of a case to rotate to width leading is 407mm. The minimum dimensions for cases to be handled by the orientation process is 200 x 120mm. Smaller cases wouldn’t be able to be handled by the skewed rollers very well. Therefore these minimal dimensions have been chosen.

[mm]

Minimum Length 200

Minimum Width 120

Maximum Length 407

Page 33 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

Figuur 35: Box plot of Width/Length ratio cases

2.11.1. Flow of SKU’s

Some SKU’s will have a larger flow then others. The flow per category can be seen in Table 2: Flow per category.

Category Flow Length Width

1 1% 241 113 2 12% 241 157 3 7% 241 171 4 5% 241 211 5 2% 306 143 6 9% 306 199 7 6% 306 218 8 3% 306 268 9 7% 361 169 10 2% 361 235 11 4% 361 257 12 3% 361 316 13 6% 400 187 14 6% 400 260 15 3% 400 284 16 10% 400 350

Table 2: Flow per category

2.11.2. Pallet analysis

Cases are introduced to the system on pallets. The pallets are build up out of layers. Depending on the size of the SKU more or less cases will fit in one layer. The pallets consist of multiple layers. The number of layers depends on the height of the SKU and the height of the pallet. On average the number of layers per pallet is 8 and the number of cases per layers is 10. The average amount of cases on a pallet is then 80. (Velraeds, 2010). This amount will differ of course due to the dimensions of the SKU.

Amount Average number of cases per layer 10

Average number of layers 8

Page 35 of 132 M.Sc Thesis B.A.M. Zeeuw van der Laan

3. REQUIREMENTS OF CONTROL SOLUTION

The current process is open loop. Input parameters are set feedforward based on some of the characteristics of the cases. With open loop, it is meant that for the control settings of the process no feedback is taken into account. Whatever the outcome of the process is, the settings are determined based on the incoming case.

3.1. Goal of the control

Find the ‘optimal’ setting for different cases that leads to a 90-degree rotation, an out coming gap of at least 100mm and no collisions during operation while getting the highest throughput possible.

• Not to work with category settings

• Find the ‘optimal’ settings for individual SKU’s • Limited information of variables

• Stable control is required without overshoot • On-line process control

• Throughput should be optimized • End gap should be at least 100mm • Outcoming angle should be 90 degrees

3.1.1. On-line process control

Control of a process during operation of the system. (Sachs, Ingolfsson, & Hu, 1995) The ‘optimal’ settings for the different SKU’s should be found during normal operation.

3.1.2. Closed loop

Since there are many factors that have effect on the outcoming result, the result is hardly to predict exactly by the provided model. The dimensions are known during the beginning of the process but other variables like the coefficient of friction or the amount of absorption are unknown. Since the model is not able to predict the outcomes of the process and to be able to cope with disturbances in the process closed loop control is considered. Closed loop control is control with feedback. The outcome of a process is taken into account for new settings.

3.2. Control Steps

Due to the nature of the processes it’s difficult to control the case during the different sub-processes during a run of the case itself. The Rotator can be set to a fixed length for the run, but it can’t be controlled during the run. Therefore, the control is limited to the iteration of a run of the process. The outcomes after the separate processes could be measured. The outcomes can be used as feedback for the control. This is called output-feedback control. For each case new settings could be used, depending on the outcomes of the previous runs adjustments to the controls can be made. (Del Castillo & Hurwitz, 1997)

• Receive the measurements 𝑦 𝑘

• Determine the state x(k) from the measurements • Determine the new control actions 𝑢 𝑘 + 1 • Return the control action u(k) to the system • 𝑘 is a run of a case

𝑢 𝑘 + 1 = 𝑓(𝑦 𝑘 + 𝑢 𝑘 )

3.2.1. Self-learning control

Since the system has no information on the outcomes of the process and the effects of the settings are unkown it is not possible to make an accurate transfer function for the system. Therefore the control should iteratively find the settings. The system will learn the settings from multiple runs. By starting at a safe initial point a correct outcome is guaranteed. However these settings are not optimized. By then iteratively changing the settings untill the outcomes are optimized the system will learn the optimal settings.(Wang, Gao, & Doyle, 2009)

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3.2.2. Variations between SKU’s

Some of the variables that have impact on the rotation process are known. Others are not. With the given variables, it’s not possible to predict the optimal settings. Therefore, new settings have to be found for each different SKU.

When a new SKU is introduced the system should find the ‘optimal’ settings by a learning process.

Figuur 37: New SKU

3.3. Optimize settings

The eventual goal for the settings of a SKU is to find the ‘optimal’ setting for different cases that leads to a 90-degree rotation, an out coming gap of at least 100mm and no collisions during operation while getting the highest throughput possible.

The throughput was a function of the gap between the cases. The necessary gap depends on the amount of slip during the process. The amount of slip is dependent on the necessary angle for a correct rotation.

Basically, the dependency and order for optimization is therefore as shown in Figure 38: Optimization order.

Figure 38: Optimization order

3.3.1. Out coming angle

As seen in the analyses the out coming angle is depended on the pre-rotator angle, the rotator length and the skewed rollers and vertibelt. Slip occurs at the Rotator phase. It’s not possible to achieve the desired angle without the use of the rotator. So there will be some slip during the process in order to achieve the desired angle.

3.3.2. Incoming gap

The goal is to get the highest throughput possible. However, this should happen without collisions, a minimal end gap and the correct rotation.

The loss for the throughput is the amount of gap that’s introduced between cases. As found in section 2.2.15 the out coming gap is a function of the incoming gap, and the slip occurring of the relative cases during the process. The out coming gap of a rotation from WL to LL.

𝑔𝑎𝑝!"#= 𝑔𝑎𝑝!"− 𝑠𝑙𝑖𝑝!!"+

1

2(𝐿 − 𝑊)

To determine the minimum 𝑔𝑎𝑝!" to acquire the minimal out coming gap of 100mm the formula

can be rewritten to:

𝑔𝑎𝑝_!" ≥ 𝑔𝑎𝑝_!"#+ 𝑠𝑙𝑖𝑝_!!"+1

2(𝑊 − 𝐿)

It can be seen that the incoming gap is limited to the dimensions of the case and the out coming gap. The length and width of the case are given. The minimal value for the out coming gap is 100mm. The amount of slip is the variable determining the minimum incoming gap.

3.3.3. Slip

The amount of slip is depended on multiple variables. Most of them which aren’t controllable. The two controllable variables that have effect on the amount of slip are the length of the pre-rotator and the length of the rotator. These two variables also have effect on the out coming angle after the rotator phase.

Length Pre-Rotator

Increasing the length of the pre-rotator will lead to a decrease in slip. However, there are limitations to the amount of pre-rotator angle used. This is due to the fact that cases will also be possibly damaged and will have a large displacement in the y direction.

Length rotator

The length of the rotator effects the amount of slip and the out coming angle. As can be seen in section 2.6.3 there is a positive non-linear correlation between the two. The requirement is to get an output of 90 degrees at the end of the skewed rollers and vertibelt. In order to achieve this the case needs to have rotated to a certain angle after the rotator process. The skewed rollers and vertibelt will then be able to further rotate the case to the desired angle.

In section 2.2.14 an analysis was made depending on the correctable angle for the skewed rollers and vertibelt. The minimal 𝜃 required to get a correct angle is simplified to a function of the geometry of the case 𝜙 and a correction factor 𝜓.

𝜓 = 𝜃 + 𝜙 − 90 𝜃 ≥ 90 − 𝜙 + 𝜓

Optimization

If a case is rotated far beyond the minimal 𝜃 required to achieve a proper rotation this will only lead to unnecessary slip at the rotator. In order to optimize the incoming gap, the amount of slip needs to be optimized. This can be done optimizing the rotator ratio. The out coming angle after the rotator should however not decrease below the minimal 𝜃 required for a correct rotation.