improving the consistency of injection molding products by

Research ArticleImproving the Consistency of Injection Molding Products byIntelligent Temperature Compensation Control

Yufei Ruan Huang Gao and Dequn Li

State Key Laboratory of Material Processing and Die amp Mould Technology Huazhong University of Science and TechnologyWuhan 430074 China

Correspondence should be addressed to Huang Gao gaohuanghusteducn

Received 10 April 2019 Revised 24 May 2019 Accepted 10 June 2019 Published 1 July 2019

Guest Editor Srikanth Pilla

Copyright copy 2019 Yufei Ruan et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Temperature stability is critical to the consistency of product quality in the injection molding process and it is very necessaryto improve the temperature control accuracy under dynamic conditions However due to the large time delay strong couplingand the dynamic characteristics existing in the system it is not an easy task to achieve precise temperature control in the injectionmolding process In this paper a new intelligent temperature compensation control strategy for the injectionmolding process underdynamic conditions is proposed in order to solve two key problems in the compensation control strategy the compensation timeand compensation quantity A data-based feedforward iterative learning control (ILC) algorithm is designed to learn the optimalcompensation timeOnce the optimal compensation time is learned a deepQ-learning algorithmwhich combinedQ-learning withan artificial neural network (ANN) is proposed to learn the optimal compensation quantity An experimental platform is designedto validate the superiority of the proposed method Experimental results show that the proposed method can effectively improvetemperature control accuracy under dynamic conditions Meanwhile the product consistency has also been improved

1 Introduction

Polymer injection molding is one of the most widely usedprocessing methods for producing polymer products [1] Asa typical batch production process product consistency iscritical in the injection molding process [2] Temperatureis one of the two dominant factors that affect productconsistency (the other one is pressure) And in the workreported by Gim et al [3] temperature shows a strongercorrelation Therefore improving the stability of tempera-ture control is very important to improve product qualityconsistency In general in addition to the effects of machinedesign and materials the stability of temperature is mainlydetermined by the following processing parameters barreltemperature screw rotation speed back pressure dwell timeand injection stroke Limited by the processing technologyand production efficiency except for the barrel temperaturethe other parameters are not controllable variables in theproduction process Therefore precise barrel temperaturecontrol is critical to improve the stability of melt temperatureand product consistency

However it is challenging to achieve precise control ofbarrel temperature due to the two major particular charac-teristics namely large time delays and strong coupling [4]Usually the barrel is heated by using electrical resistanceheating The heaters are wrapped around the outside surfaceof the barrel Therefore heat is concentrated on the outsidesurface of the barrel and heating the material inside the barrelby means of heat conduction Due to the thick barrel wallit usually takes dozens of seconds or more until the heat istransferred to the internal part of the barrel Thus there is ahuge time delay in the system On the other hand owing tothe intermittent disturbances caused by (1) the ease of heatconduction (2) the fresh raw materials entering (3) changesin the environment and (4) the shear heat generated duringthe operation these make it a strong coupling system

In most of the existing injection molding processes thetemperature is usually controlled by a proportional integraldifferential (PID) algorithm [5] The PID algorithm hasbeen widely applied in temperature control [6 7] It iseasy to implement and can provide good robustness understatic conditions But the polymer injection molding process

HindawiAdvances in Polymer TechnologyVolume 2019 Article ID 1591204 13 pageshttpsdoiorg10115520191591204

2 Advances in Polymer Technology

Mold

Zone 1 Zone 2 Zone 3 Zone 4

Heater

Nozzle

Insulation

Runner

CavityRotating

Hopper

Screw Barrel

Material

Melt

Figure 1 Structure diagram of an injection molding machine injection unit

contains several iterative and repeated operations Eachoperation is performed intermittently Therefore the barrel isin dynamic conditions during the injection molding processHence the PID algorithm cannot provide a satisfactory barreltemperature control performance for the whole operationprocess In the past decades in order to solve the barrel tem-perature control problem many advanced control methodshave been proposed such as adaptive decoupling control [8]model predictive synchronous control [9] multivariable self-tuning predictive control [10] self-optimizing model pre-dictive control [11] adaptive generalized predictive control[12] and response identification and internal model control[13]These methods can effectively solve the problem of largetime delay However most of these existing methods arebased on feedback control strategies and cannot deal with theintermittent disturbances On the other hand these methodsdo not take into account the dynamic characteristics of theinjection molding process

Considering the repeated operation characteristics of thepolymer injection molding process it is feasible to use afeedforward compensation strategy to eliminate the effects ofintermittent disturbances For example Yao et al proposeda barrel temperature control method using the combinationof a generalized predictive control with an iterative learningfeedforward control [14] The experimental results show thatusing a feedforward compensation strategy can effectivelyprevent large temperature variations caused by intermittentdisturbances There are two key points that must be con-firmed when using a feedforward compensation strategy forthe barrel temperature control (1) the compensation timeand (2) the compensation quantity However it is not an easytask to get the accurate compensation time and compensationquantity for the barrel temperature control They are affectedby many complex factors such as raw materials environ-ment injection molds and process parameters Thereforeit is difficult to obtain the accurate compensation time andcompensation quantity through model-based methods

According to the previous analysis it is crucial to obtainthe accurate compensation time and compensation quantitywhen using a feedforward compensation control strategy forthe injection molding temperature control Considering therepeated behavior of the system iterative learning control

(ILC) is recognized as an effective control method for thesystems with repeated characteristics [15 16] ILC is a kindof data-based learning control method [17] ILC generatesfeedforward control signals that apply to the next batch byusing information from previous batches that have beenstored As a data-based control method ILC does not requirean accurate system model so it can be easily adapted toa variety of complex conditions Thus it is feasible to useILC to obtain the accurate compensation time However asa feedforward control strategy ILC cannot achieve accuratecompensation quantity control As a typical batch productionprocess it is feasible to adopt a reinforcement learning (RL)algorithm to the control system [18]

In this paper a new intelligent barrel temperature controlmethod which fully considers the dynamic characteristicsof the injection molding process is proposed The proposedcontrol method adopts a feedforward compensation strat-egy to improve the stability of temperature control underdynamic conditions The proposed method first learns theoptimal compensation time in each batch using a feedforwardILC algorithm Subsequently a deep Q-learning algorithmcombiningQ-learningwithANN is adopted to learn the opti-mal compensation quantity for each compensation periodWith this innovation control strategy the stability of tem-perature control can be effectively improved and the productconsistency can be significantly improved

The rest of this paper is organized as follows In Section 2the system description is presented Section 3 develops thefeedforward compensation temperature control strategy InSection 4 temperature control experiments with differentconditions are performed In Section 5 the product consis-tency experiments are given to verify the effectiveness of thedeveloped control strategy in improving product consistencyFinally conclusions are drawn in Section 6

2 System Description

The typical structure diagram of an injection moldingmachine injection unit is shown in Figure 1 It mainly consistsof a screw a barrel a nozzle and a heating system In generalthe heating system has multiple heating zones For eachheating zone there is a heater and a temperature sensor

Advances in Polymer Technology 3

MemoryLearningFunctionMemory Feedforward

Controller

TemperatureError Conversion

ILC

System

+

-

+ +

uk(t)

yk(t) ek(t)

yr(t)

ek(T)

Figure 2 Schematic representation of the ILC-based compensation time control algorithm

In most cases the temperature set for each heating zonevaries according to the requirements of the process In orderto save energy the heating system is covered with a layerof thermal insulation materials The system has no coolersystem Therefore the cooling rate of the system is very slow

During the injection molding process the raw materialsenter the barrel from the hopperThe rawmaterials are heatedto molten state in the barrel Then the screw rotates andretreats thereby mixing the melt evenly and squeezing themelt to the front of the barrel Finally the screw movesforward to inject the melt into the mold During this processthe temperature is affected by multiple factors

(1) The heating coil around the outside of the barrel is thedominant factor under static conditions

(2) The shear heat which is generated between the screwand the melt is the other major factor affecting thetemperature

(3) The thermal coupling is caused by the differenttemperature conditions of different heating zones andthe excellent thermal conductivity of metal

(4) There are also the process parameters setting (screwrotation speed back pressure etc) materials moldssurrounding environment and so on

Therefore for such a complicated system it is a greatchallenge to achieve precise temperature control Previousstudies have shown that it is impossible to solve this problemusing a modeling approach [12]

3 Methodology

31 Feedforward ILC for Compensation Time Control ILC is adata-based control method compared to traditional model-based control methods it does not require an accurate systemmodel and only needs a small amount of historical datafrom previous batches The objective of ILC is to generatea feedforward control signal by utilizing information fromprevious batches and reduce tracking error by iteration Inthis paper a feedforward ILC-based controller is designed toobtain the temperature compensation time

The schematic representation of the ILC-based compen-sation time control algorithm is shown in Figure 2 119896 =1 2 represents the number of iteration 119905 = 0 1 119879 minus1 represents the sample time and 119879 is the total numberof samples in each batch In batch 119896 119910119896(119905) denotes thesystem output at step 119905 119906119896(119905) denotes the input at step 119905119910119903(119905) denotes the control target at step t 119890119896(119905) denotes thetemperature error at step 119905 and 119890119896(119879) denotes the time errorThe control algorithm includedmainly consists of three parts(1) a feedforward controller (2) a learning function and (3)temperature error conversion The feedforward controller isused to handle the relationship between the previous batchinput and the next batch input The learning function is usedto calculate input changes for the next batchThe temperatureerror is converted into compensation time error according tothe temperature error conversion

The purpose of the compensation time control algorithmis to obtain the optimal compensation time In the practicalcontrol process the temperature sensor returns the tempera-ture of each sampling period The data of each cycle in each


System

Action Selection ANNs

Agent

Action Reward

Learningrate

State

Actionvalue

Discountfactor

Σ

at rt

st

Qt(st at)

Qtminus1

Figure 3 Schematic diagram of the RL-based compensation quantity control method

batch are saved in the memory At the end of a batch thetemperature error curve of the whole batch is obtained bycomparing with the reference value The time error 119890119896(119879)is obtained by analyzing the temperature error curve Thesystem input is given by

119906119896 (119905) = 119876 (119906119896minus1 (119905)) + Δ119906119896 (119905) (1)

where119876 is a filter 119906119896minus1(119905) is the control input of the previousbatch and Δ119906119896(119905) is the change in control input of the nextbatch which is obtained by the learning function It can becalculated as follows

min 119869119896 =119879minus1sum119905=0

[119890119896 (119905)]119879119860 (119905) [119890119896 (119905)]

+ 119879minus1sum119905=0

[Δ119906119896 (119905)]119879 119861 (119905) [Δ119906119896 (119905)](2)

12

120597119869119896120597119906119896 = minus119866119879119860 (119905) 119890119896 + 119861 (119905) Δ119906119896 (119905) = 0 (3)

Δ119906119896 (119905) = 119861 (119905)minus1 119866119879119860 (119905) 119890119896 (119905) (4)

119860(119905) and 119861(119905) represent the weighting matrices and 119866 isa Toeplitz matrix In the learning process a time constant119890(1198790) is selected as the maximum permissible error Thelearning process ends until the time error 119890119896(119879) le 119890(1198790)

32 Reinforcement Learning for Compensation Quantity Con-trol In the problem of RL an agent is able to improve itsperformance from its own experience by interacting withthe environment [19] A typical agent mainly consists of thefollowing three parts state 119904 action119886 and reward 119903The targetof the agent is to learn the optimal action policy to maximizethe total rewards it will receive in the future In a time step119905 the agent selects an action 119886119905 based on the current state 119904119905the system performs the selected action and returns a reward119903119905 and then goes to the next state 119904119905+1 Meanwhile the state-action values (119904119905 119886119905)119896 are recorded In this paper Q-learningis adopted to learn the optimal temperature compensationquantity Q-learning is a form of model-free off-policy RLalgorithm [20] As a kind of widely used RL algorithm Q-learning finds the optimal policy by learning the optimalaction value function 119876119905(119904119905 119886119905) in each state

The action value function 119876119905(119904119905 119886119905) is updated as follows

119876119905 (119904119905 119886119905)larr997888 119876119905minus1 (119904119905 119886119905)

+ 120572 [119903119905 + 120582max119886isin119860

119876119905minus1 (119904119905+1 119886) minus 119876119905minus1 (119904119905 119886119905)] (5)

where 0 le 120582 lt 1 is the discount factor 0 lt 120572 le 1 is thelearning rate and 119860 is the action space

The schematic representation of the RL-based temper-ature compensation quantity control method is shown inFigure 3 The sampling temperature 119910119905 temperature error 119890119905


and control input 119906119905 constitute the state space 119878119905 it can beexpressed by

119878119905 = (119910119905 119890119905 119906119905) (6)

The action space is expressed as

119860 119905 = +Δ119906119905 0 minusΔ119906119905 (7)

Δ119906119905 is the minimum control voltage value and Δ119906119905 = 01VThree actions are available increase input (+Δ119906119905) decreaseinput (minusΔ119906119905) and 0 means no modification is made thesystem performs the previous temperature control signal

In order to prevent the algorithm from falling into thelocal optimal solution the 120576-greedy algorithm is adopted tochoose the action The algorithm chooses an action 119886119894 in astate 119904119905 with a probability 119901(119904119905 119886119894) It can be described as

119901 (119904119905 119886119894) = 1 minus 120576 119886119894 = max

1198861015840119876(119904119905 1198861015840)

120576 otherwise (8)

120576 is a small positive constant During the control process thealgorithm will choose a greedy action with a probability 1 minus 120576or randomly select an action with a probability 120576

The system will perform the selected action and return areward 119903119905 and then goes to the next state 119904119905+1 The agent willreceive a positive reward (+1) if the temperature error 119910119890119905 isless than the maximum permissible error If the temperatureerror is greater than the maximum permissible error butless than the previous temperature error 119910119890119905minus1 the agent willreceive a small positive reward (+01) In other cases the agentwill receive a reward (-1) In summary the reward functioncan be defined as follows

119903119905+1 =

+1 if 10038161003816100381610038161199101198901199051003816100381610038161003816 le 119910119890011990501 if 10038161003816100381610038161199101198901199051003816100381610038161003816 gt 1199101198900119905 and 10038161003816100381610038161199101198901199051003816100381610038161003816 le 1003816100381610038161003816119910119890119905minus11003816100381610038161003816minus1 otherwise

(9)

Conventionally the Q-learning method requires a lookuptable to store the value of each state-action pair Howeverit is impossible to build a lookup table for actual controlproblems The state space of the temperature control processis very large It may lead to a series of problems when using alookup table For example it may cause high computationalcost or the algorithm cannot converge In order to dealwith the problem of a large number of state-action pairs inthe temperature control in this paper neural networks areapplied to approximate the optimal action value function Ineach step 119905 the action value can be expressed as follows

119876119905 =119899sum119894=1

119908(2)119905119894 119889119905119894 (10)

where

119889119905119894 = 11 + 119890minusℎ119905119894 (11)

ℎ119905119894 =119898sum119895=1

119908(1)119905119894119895119909119905119895 (12)

119899 is the number of hidden nodes of the neural network 119898 isthe number of neural network inputs ℎ119905119894 and 119889119905119894 representthe input and output of the 119894th hidden nodes 119908(1)119905119894119895 and119908(2)119905119894 (119894 = 1 2 119899 119895 = 1 2 119898) are the connectionweights and 119909119905119895 isin 119878119905 (119895 = 1 2 119898) is the 119895th element ofthe state 119878119905

According to (5) the weight matrix 119882119905 of the ANN isupdated as follows

Δ119882119905= 120572 [119903119905+1 + 120574max

1198861015840isin119860119876119905 (119904119905+1 1198861015840) minus 119876119905 (119904119905 119886119905)] nabla119908119876119905 (13)

119882119905 represents the connection weight matrix 119882(1)119905 or 119882(2)119905 and nabla119908119876119905 = 120597119876119905120597119882119905 is a vector of the gradient and it iscalculated as follows

120597119876119905120597119908(2)119905119894 = 119889119905119894 (14)

120597119876119905120597119908(1)119905119894119895 = 119908(2)119905119894 119889119905119894 (1 minus 119889119905119894) 119909119905119895 (15)

Using neural networks to approximate the action valuefunctions will solve some existing problems However somenew problems will arise when RL is combined with neu-ral networks Firstly there are the correlations betweenthe state-action pairs [21] In an actual control problemthe current state is usually very similar to the adjacentsampling period so the correlation between the samplesis very strong Secondly the target value is affected bynetwork weight The update of network weight in the cur-rent step will affect the target value of the other stepsTherefore if network weights are updated in every stepthis will lead to a very long time to converge or even todiverge

In this paper a mechanism called ldquoexperience replayrdquois adopted to solve the problems caused by using neuralnetworks [22] During the learning process the state-actionpair of every sampling period is first storedThenyou can ran-domly select data from the memory to update the networkthereby eliminating correlations between the state-actionpairs Furthermore different from the traditional onlineneural network update strategy the connection weights ofthe neural network are updated offline The connectionweights will be updated after the end of a batch Withthis offline update strategy the impact of weight updatein the traditional online update strategy can be effectivelyeliminated These innovations not only effectively reduce thecomputation time but also make the proposed method morefeasible

4 Temperature Control Experiments

41 Experiment Setups An experimental platform is de-signed to validate the proposedmethod as shown in Figure 4In order tomeet the experimental needs amodified injectionmolding machine is used for experiments A new set of


IO

Barrel

Hopper

RelayPowerSupply

IPC

MCP

AD-DA

2 134

Figure 4 Experiment platform

injection molding machine control system as shown inFigure 4 is established on the original injection moldingmachine The parameters of the injection molding machinerelated to the experiments are listed in Table 1 There arefive heating zones including one-nozzle zone the remainingfour zones are numbered 1-4 from the hopper to nozzleThe materials used for the experiments are polypropylene(PP) and polystyrene (PS) The thermophysical properties ofPP and PS are shown in Table 2 The parameters of the Q-learning algorithm are listed in Table 3

42 Single Zone Temperature Control with Open Loop ControlTo show the large time delays and strong coupling of theheating system an open loop control strategy is applied tozone 3 The target temperature is set at 180∘C and all zonesare heated from room temperature In addition to zone 3the other zones have no input The temperature results ofzone 3 zone 2 and zone 4 are shown in Figure 5(a) Thecontrol voltage is shown in Figure 5(b) 10 V means heatingwith the maximum power of the coil The temperature ofzone 3 reaches the target temperature after 1023 seconds thenstop heating It can be seen that after stopping heating thetemperature of zone 3 continues to rise until the maximumtemperature (1842∘C) is reached at 1085 seconds After thatthe temperature of zone 3 gradually drops During thisprocess the temperature of zone 2 and zone 4 will also riseowing to heat conduction It can be observed that even if thetemperature of zone 3 begins to decrease the temperature ofzone 2 and zone 4will still rise as long as there are temperaturedifferencesTherefore the heating system is a large time delayand strong coupling system

43 Temperature Control with Dynamic Conditions Asmen-tioned before during the injection molding process the

heating system is in a dynamic condition In order tovalidate the proposed temperature control strategy underdynamic conditions several sets of comparative experimentsare conducted The proposed temperature control strategyis compared with the generalized predictive control (GPC)method and the PID method The PID algorithm is the mostwidely used control algorithm in the field of temperaturecontrol the discrete PID model can be expressed as follows

Δ119906 (119905) = 1199020119890 (119905) + 1199021119890 (119905 minus 1) + 1199022119890 (119905 minus 2) (16)

where

1199020 = 119870119901 (1 + 119879119879119894 +

119879119889119879 )

1199021 = minus119870119901 (1 + 2119879119889119879 )1199022 = 119870119901119879119889119879

(17)

119905 = 2 3 4 represents the sample timeΔ119906(119905) representsthe change in control input 119890(119905) 119890(119905 minus 1) and 119890(119905 minus 2) areerrors in different sampling periods 119879 is the control cycle119870119901 is the proportional gain 119879119894 is the integral time and 119879119889is the derivative time The GPC algorithm has been widelyused in the field of temperature control in recent years andhas achieved excellent performance It can be expressed asfollows

119906 (119905) = 119906 (119905 minus 1) + 119867119873119888 (119866119879119866 + 120582119868119873119888)minus1119866119879 (119877 minus 119865) (18)

where

119867119873119888 = [1 0 0 0]1times119873119888


119866 =

[[[[[[[[[[[[[[

1198921 0 sdot sdot sdot 01198922 1198921 sdot sdot sdot 0 d

119892119873119888 119892119873119888minus1 sdot sdot sdot 1198921

1198921198732 1198921198732minus1 sdot sdot sdot 1198921198732minus119873119888+1

]]]]]]]]]]]]]]1198732times119873119888

119877 =[[[[[[[

119903 (119905 + 1)119903 (119905 + 1)

119903 (119905 + 1198732)

]]]]]]]

119865 =[[[[[[[[

Δ119906 (119905) [1198661 (119902minus1) minus 11989210] + 1198651 (119902minus1) 119910 (119905)Δ119906 (119905) 119902 [1198662 (119902minus1) minus (11989221 minus 11989220) 119902minus1] + 1198652 (119902minus1) 119910 (119905)

Δ119906 (119905) 1199021198732minus1 [1198661198732 (119902minus1) minus (1198921198732 1198732minus1 minus 11989211987321198732minus2 minus sdot sdot sdot minus 1198921198732 0) 119902minus(1198732minus1)] + 1198651198732 (119902minus1) 119910 (119905)

]]]]]]]]

(19)

119905 = 0 1 2 represents the sample time 119906(119905) represents thecontrol input 120582 gt 0 is the weighting factor and119873119888 is the stepsize of control time domain

With material PS a set of experiments are carried out Allexperiments start from the static conditionsThe temperatureresults of zone 3 are shown in Figure 6(a)The set temperatureis 220∘C It can be observed that all the three controlmethods can obtain excellent control performance understatic conditions The temperature variations are very smallat first Then the system switches to dynamic conditionsFirstly the screw moves forward to inject the melt Duringthis process the rawmaterial will flow into the barrel Usuallythe raw material is at the room temperature Therefore itwill cause a temperature drop As shown in Figure 6(a)there is a large temperature drop when using the GPC andPID control method Particularly with the PID methodthe temperature dropped by about 25∘C However whenusing the proposed control method the temperature has onlydropped by about 04∘C At the same time as shown inFigure 6(b) the control voltage will increase But due to thetime delay the temperature will not rise immediately Afterthe injection is completed the system enters the plasticationprocessThe screwwill rotate and retreat and the screw speedis shown in Figure 6(c) During this process the temperaturewill rise caused by the shear heat and the increased inputAfter the plastication process is finished the system returnsto static conditions again Due to the influence of thermalinertia the temperaturewill continue to rise for awhileThenthe temperature will slowly drop Finally the temperaturewill stabilize at the set value Throughout this processtemperature overshoot will occur It can be observed that the

maximum temperature overshoot is only 05∘C when usingthe proposedmethodHowever when using the PIDmethodthe maximum temperature overshoot is about 45∘C Largetemperature overshoots will affect the quality of productsor even lead to material decomposition The GPC methodcan effectively reduce temperature overshoot The maxi-mum temperature overshoot is about 13∘C under the GPCmethod

44 Temperature Control with Different Materials The ther-mophysical properties of different polymer materials varygreatly The change of material will significantly affect thetemperature control performance In order to check theperformance of the proposed method after changing thematerial another experiment is conducted In this exper-iment the polymer material PS is replaced by PP Thescrew periodically performs the action to simulate theactual production process The other conditions remain thesame

The results are shown in Figure 7 It is observed that thetemperature variations are very large at the beginning themaximum temperature variation is larger than 25∘C This ismainly caused by the difference in heat capacity As shown inTable 2 the heat capacity of PP is much larger than PS Afterchanging materials the feedforward compensation strategyhas not been updated At this time the learning process willbe executed to learning the new compensation strategy Afterabout 1500 seconds the maximum temperature variation isreduced to 05∘C This indicates that the system has alreadylearned the new compensation strategy for PP After that


Maximumtemperature

Continuerising

Stop heating

(180)

(1085)

(1023)

(1842)200

160

120

80

40

0

Tem

pera

ture

(∘C)

0 300 600 900 1200 1500

Time (s)

(a)

(b)

zone 2zone 3

zone 4

0 300 600 900 1200 1500

Time (s)

12

10

8

6

4

2

0

Con

trol V

olta

ge (V

)

zone 2zone 3

zone 4

Figure 5 (a) Temperature (b) control voltage with open loop control

Table 1 The parameters of the injection molding machine

Machine parameters ValuesHeating zones 5 (including one nozzle)Maximum heating power (w) 1260 (nozzle 500)Maximum screw speed (rpm) 196Maximum injection pressure (MPa) 185Maximum shot weight (g) 321

the learning process will temporarily stop and the newcompensation strategy will be stored When the maximumtemperature variation is larger than the set value the learningprocess will be reactivated to obtain the new compensationstrategy

5 Products Consistency Experiments

Asmentioned before the barrel temperature control is criticalto product consistency And the purpose of this paper isto improve the consistency of injection molding productsby improving the stability of the temperature Thus in thissection products consistency experiments are performedto further verify the validity of the proposed method bycomparing with the GPC method and the PID methodIn this paper the product consistency is reflected by theproduct weight There are multiple definitions of the qualityof injection molding products such as weight warpagesurface properties mechanical properties optical propertiesand crystallization [23] And warpage is an important factorreflecting product quality Temperature unevenness is animportant factor leading to warpage But many other factors


Table 2 Thermophysical properties of PP and PS

Material Heat capacity (kj(kglowast∘C)) Density (kgm3) Thermal conductivity (w(mlowast∘C))PP 1926 900 0138PS 1340 1050 0126

StaticDynamicStatic226

224

222

220

218

216

Tem

pera

ture

(∘C)

0 60 120 180 240 300

Time (s)

Proposed MethodPID MethodGPC Method

5

4

3

2

1

0Con

trol V

olta

ge (V

)

100

80

60

40

20

0Rota

tion

Spee

d (r

pm)

0 60 120 180 240 300

Time (s)

(c)

(b)

(a)

0 60 120 180 240 300

Time (s)



Figure 6 Comparison of the proposed method PID and GPC

Table 3 The parameters of the Q-learning algorithm

Parameters Description Values120572 Learning rate 06120582 Discount factor 098120576 Action selection policy 01

can also cause warpage such as cooling time ejectionmechanism and injection pressureThepurpose of this paper

Learning process225

223

221

219

217

215

Tem

pera

ture

(∘C)

0 600 1200 1800 2400 3000 3600

Time (s)

0 600 1200 1800 2400 3000 3600

Time (s)

100

80

60

40

20

0

Rota

tion

Spee

d (r

pm)

Figure 7 Temperature control performance with the proposedmethod after change of material

is to improve the stability of the process through tempera-ture compensation control to improve product consistencyProduct weight can reflect process stability and productconsistency very well For example in the work reported byZhou et al [24] they claimed that the product weight has aclose relationship to other quality properties and the productweight can be a good indicator of process stability On theother hand the weight of the product can be very convenientto measure and quantify Therefore it is feasible to use theweight of the product to reflect the consistency of the product

51 Experiment Setups The experiments are conducted onthe aforementioned experiment platform A strip product isused for the experiments The product is produced using adouble cavity mold The CAD model of the molded productis shown in Figure 8(a) The picture of the actual moldedproduct is shown in Figure 8(b) The polymer material usedin the experiments is PP The settings of correspondingprocess parameters are listed in Table 4 In addition to theseparameters that directly affect the melt temperature in thebarrel injection velocity is also an important factor thataffects the temperature of the melt entering the cavity And inorder to eliminate the effects of different injection velocitiesthe injection velocities are set to the same for all experimentsThe cooled products are weighted by a METTLER TOLEDOanalytical balance LE204Ewith aminimum resolution 00001g Furthermore in order to reduce the impact of machinefluctuations on product weight a total of 80 cycles producing


Runner

Product 1

Product 2

Gate 1

Gate 2

(a)

Product 1

Product 2

(b)

Figure 8 Experimental injection product (a) CAD model (b) actual molded product

337

333

329

321

325

317

313

Prod

uct1

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(a)

337

333

329

321

325

317

313

Prod

uct2

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(b)

Figure 9 Comparison of the product weight equipped with the proposed GPC and PID control methods (a) product 1 (b) product 2

Table 4 The settings of process parameters

Process parameters Value

Temperature (∘C)

Zone 1 150Zone 2 215Zone 3 220Zone 4 225Nozzle 220

Screw rotation speed (rpm) 90Back pressure (MPa) 2

will be conducted in each set of experiments The first 30cycles will be abandoned only the remaining 50 cycles willbe used for measurement

52 Product Consistency under Different Temperature ControlMethods The results of the product weight are shown inFigure 9 It can be observed that under the proposedtemperature control method both products have very smallweight variations Themaximumweight variation is less than04 gThis indicates that excellent product consistency can beachieved when using the proposed control method However

when using the PID method the product weight consistencydeteriorated significantly The maximum weight variation isabout 12 g Further the difference in weight between productone and product two is sometimes very large even in thesame batch This indicates that there is a filling imbalancedue to temperature variation The weight consistency withthe GPC method is better than the PID control method butthe product weight variations are still relatively large whencompared with the proposed method

Additionally several statistical methods are used to ana-lyze and compare the data As shown in Table 5 the meanabsolute deviation is used to describe the degree of datadispersion The weight repeatability is calculated as follows

120575 = radic(1 (119899 minus 1)) sum119899minus1119894=1 (119898119894 minus 119898)2119898 times 100 (20)

where 119894 = 1 2 119899 denotes the sample number 119899 is the totalnumber of samples 119898 is the average weight and 119898119894 is theweight of sample The smaller the value of 120575 the better theweight repeatability The statistical analysis of results showsthat under the proposed control method the mean absolutedeviation and the repeatability of product weight are muchbetter than the PID and GPCmethod On the other hand the


Table 5 Statistical analysis of results under different control methods

Method Sample Average weight (g) Mean absolute deviation Repeatability

ProposedProduct 1 324882 00739 02883Product 2 324856 00636 02572

Sum 324869 00687 02718

PIDProduct 1 323956 03109 10855Product 2 323532 02577 09396

Sum 323744 02864 10123

GPCProduct 1 325868 02071 07253Product 2 325814 01857 06744

Sum 325841 01965 06968

difference between different cavities is also very small whichimplies that excellent consistency can be achieved in differentbatches and different cavities

53 Product Consistency with Different Process ParametersIn addition to the effect of barrel temperature the melttemperature in the barrel is also affected by the followingprocess parameters screw rotation speed back pressuredwell time and injection stroke The effect of these processparameters on melt temperature consistency is shown inTable 6 It can be seen that reducing the screw rotation speedthe heat generated by shearing will reduce and the melttemperature difference due to the screw rotation speed willalso reduceTherefore reducing the screw rotation speed canincrease the consistency of the melt temperature to a certainextent On the other hand as the back pressure increasesduring the plastication process the speed at which the screwretreats decreases Thus the melt stays longer in the barreland the material in the barrel is denser Therefore increasingthe back pressure can increase the consistency of the melttemperature and melt temperature Increasing the dwell timeallows the melt in the barrel to be warmed up for a longerperiod of time and the heat conduction is more fully carriedout thereby improving the melt temperature consistencyHowever it will increase the cycle time which is unacceptablefor a batch production process In the actual productionprocess in order to increase production efficiency the dwelltime is usually set as small as possible Therefore in thispaper the dwell time is not selected Decreasing the injectionstroke can improve the melt temperature consistency But theinjection stroke is limited by themold and cannot be adjustedat will during the production process In summary due toprocess conditions or production efficiency limitations thescrew rotation speed and back pressure are selected to justifythe effectiveness of the proposed method

In this set of experiments the back pressure and screwrotation speed are selected as the variable The other processparameters remain unchanged during the experiment Theexperimental designs are listed in Table 7

As shown in Figure 10(a) the back pressure changesfrom 2 MPa to 3 MPa after 20 cycles Due to the change inback pressure the shear heat generated during operation willchange and the temperature will also change Therefore theproduct consistency will be affected resulting in a sudden

Table 6 Effects of relevant process parameters onmelt temperatureconsistency

Processparameters

Change ofparameters

Melttemperatureconsistency

Screw rotationspeed Decrease Improved

Back pressure Increase ImprovedDwell time Increase ImprovedInjection stroke Decrease Improved

Table 7 Experimental designs with different process parameters

Experiment 1 Experiment 2Process parameters Back pressure Screw rotation speedVariable value 2 MPa 3 MPa 90 rpm 60 rpmCycles 20 30 20 30

change in product weight Subsequently as the temperaturereturns to stability the product weight gradually returnsto the original range When using the proposed methodthe product weight can return to the original range inabout 5 cycles However when using the PID method andGPC method it will take more than 10 cycles until theproduct weight returns to stability Analogously as shown inFigure 10(b) when the screw rotation speed changes from 90rpm to 60 rpm there is also a sudden change in the productweight Different from back pressure changes reducing thescrew rotation speed will lower the temperature leading to anincrease in the product weight With the proposed methodthe product weight can quickly return to the original rangedue to the fast recovery of temperature This indicates thatthe proposed method can effectively eliminate temperaturechanges due to process parameters change thus improvingproduct consistency

The statistical analysis of results with process parameterschange is listed in Table 8 It can be observed that as theprocess parameters change the mean absolute deviation andrepeatability will deteriorate However compared with thePID and GPCmethod the proposed method can still achieveexcellent results On the other hand it can be seen that afterreducing the screw rotation speed the product consistency


Back pressure2 MPa 3 MPa

0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)

Screw rotation speed90 rpm 60 rpm

0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)

Figure 10 Product weight with variations in (a) back pressure (b) screw rotation speed

Table 8 Statistical analysis of results in the case of changes in process parameters

Method Variable Average weight (g) Mean absolute deviation Repeatability

Proposed Back pressure 324148 01475 08625Rotation speed 325564 01185 07220

PID Back pressure 321168 05036 20190Rotation speed 325394 02781 11851

GPC Back pressure 324822 02921 13028Rotation speed 327690 02504 11501

will improve This implies that reducing the screw speed willmake the temperature distribution more uniform and leadsto an increase in product consistency

6 Conclusions

In this paper a new intelligent temperature compensationcontrol strategy which fully considers the dynamic charac-teristics of the injection molding process is proposed Basedon the presented experimental results the conclusions can bedrawn as follows

(1) The proposed barrel temperature control method sig-nificantly reduced the temperature variations underdynamic conditions The experimental results indi-cated that the maximum temperature variation isabout plusmn05∘C under the proposed method comparedwith GPC (plusmn25∘C) and PID (plusmn45∘C)

(2) The proposed method can effectively improve theconsistency of injection molding products in differentbatches and different cavities Statistical analysis ofresults showed that the repeatability is less than 03when using the proposed method which is muchbetter than the PID method (about 1) and GPCmethod (about 07)

(3) The proposed strategy is a kind of data-based learningcontrol method It does not require an accuratesystemmodel and the system can improve its perfor-mance by learning from its historical data Therefore

it can be easily applied to different machines materi-als and process conditions

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the National Natural Science Foun-dation of China (Grant Numbers 51635006 51675199) andthe Fundamental Research Funds for the Central Universities(Grant Numbers 2016YXZD059 2015ZDTD028)

References

[1] P Zhao H Zhou Y Li and D Li ldquoProcess parametersoptimization of injection molding using a fast strip analysisas a surrogate modelrdquo The International Journal of AdvancedManufacturing Technology vol 49 no 9-12 pp 949ndash959 2010

[2] R Zhang R Lu A Xue and F Gao ldquoPredictive functionalcontrol for linear systems under partial actuator faults andapplication on an injection molding batch processrdquo Industrial


amp Engineering Chemistry Research vol 53 no 2 pp 723ndash7312014

[3] J Gim J Tae J Jeon J Choi and B Rhee ldquoDetectionmethod offilling imbalance in a multi-cavity mold for small lensrdquo Interna-tional Journal of Precision Engineering and Manufacturing vol16 no 3 pp 531ndash535 2015

[4] K Yao and F Gao ldquoOptimal start-up control of injectionmolding barrel temperaturerdquo Polymer Engineering amp Sciencevol 47 no 3 pp 254ndash261 2007

[5] C Abeykoon ldquoSingle screw extrusion control a comprehensivereview and directions for improvementsrdquo Control EngineeringPractice vol 51 pp 69ndash80 2016

[6] Y Wang Q Jin and R Zhang ldquoImproved fuzzy PID controllerdesign using predictive functional control structurerdquo ISATrans-actions vol 71 pp 354ndash363 2017

[7] N Pachauri A Rani and V Singh ldquoBioreactor temperaturecontrol using modified fractional order IMC-PID for ethanolproductionrdquo Chemical Engineering Research and Design vol122 pp 97ndash112 2017

[8] C-H Lu and C-C Tsai ldquoAdaptive decoupling predictivetemperature control for an extrusion barrel in a plastic injectionmolding processrdquo IEEE Transactions on Industrial Electronicsvol 48 no 5 pp 968ndash975 2001

[9] Y Peng W Wei and J Wang ldquoModel predictive synchronouscontrol of barrel temperature for injection molding machinebased on diagonal recurrent neural networksrdquo Materials andManufacturing Processes vol 28 no 1 pp 24ndash30 2012

[10] C-C Tsai and C-H Lu ldquoMultivariable self-tuning temperaturecontrol for plastic injection molding processrdquo IEEE Transac-tions on Industry Applications vol 34 no 2 pp 310ndash318 1998

[11] R Dubay ldquoSelf-optimizing MPC of melt temperature in injec-tionmouldingrdquo ISATransactions vol 41 no 1 pp 81ndash94 2002

[12] S Huang K Tan and T Lee ldquoAdaptive GPC control of melttemperature in injection mouldingrdquo ISA Transactions vol 38no 4 pp 361ndash373 1999

[13] T Liu K Yao and F Gao ldquoIdentification and autotuningof temperature-control system with application to injectionmoldingrdquo IEEETransactions onControl SystemsTechnology vol17 no 6 pp 1282ndash1294 2009

[14] K Yao F Gao and F Allgower ldquoBarrel temperature controlduring operation transition in injection moldingrdquo ControlEngineering Practice vol 16 no 11 pp 1259ndash1264 2008

[15] L Wang F Liu J Yu P Li R Zhang and F Gao ldquoIterativelearning fault-tolerant control for injection molding processesagainst actuator faultsrdquo Journal of Process Control vol 59 pp59ndash72 2017

[16] K Liu Y Chen T Zhang S Tian and X Zhang ldquoA survey ofrun-to-run control for batch processesrdquo ISA transactions vol83 pp 107ndash125 2018

[17] R Chi X Liu R Zhang Z Hou and B Huang ldquoConstraineddata-driven optimal iterative learning controlrdquo Journal of Pro-cess Control vol 55 pp 10ndash29 2017

[18] K Arulkumaran M P Deisenroth M Brundage and A ABharath ldquoDeep reinforcement learning a brief surveyrdquo IEEESignal Processing Magazine vol 34 no 6 pp 26ndash38 2017

[19] R S Sutton and A G Barto Reinforcement Learning AnIntroduction MIT Press Cambridge England 1998

[20] B Luo D Liu T Huang and D Wang ldquoModel-free optimaltracking control via critic-only Q-learningrdquo IEEE Transactionson Neural Networks and Learning Systems vol 27 no 10 pp2134ndash2144 2016

[21] V Mnih K Kavukcuoglu D Silver et al ldquoHuman-level controlthrough deep reinforcement learningrdquo Nature vol 518 no7540 pp 529ndash533 2015

[22] Y Ruan Y Zhang T Mao X Zhou D Li and H ZhouldquoTrajectory optimization and positioning control for batchprocess using learning controlrdquo Control Engineering Practicevol 85 pp 1ndash10 2019

[23] P Zhao Y PengWYang J Fu andL-S Turng ldquoCrystallizationmeasurements via ultrasonic velocity study of poly (lactic acid)partsrdquo Journal of Polymer Science Part B Polymer Physics vol53 no 10 pp 700ndash708 2015

[24] X D Zhou Y Zhang T Mao and H M Zhou ldquoMonitoringand dynamic control of quality stability for injection moldingprocessrdquo Journal ofMaterials Processing Technology vol 249 pp358ndash366 2017

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018


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Chemistry

Analytical ChemistryInternational Journal of


ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of



Advances in Condensed Matter Physics


International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of


NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of


High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in



ChemistryAdvances in


Advances inPhysical Chemistry


BioMed Research InternationalMaterials

Journal of


Na

nom

ate

ria

ls


Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom


Mold

Zone 1 Zone 2 Zone 3 Zone 4

Heater

Nozzle

Insulation

Runner

CavityRotating

Hopper

Screw Barrel

Material

Melt

Figure 1 Structure diagram of an injection molding machine injection unit

contains several iterative and repeated operations Eachoperation is performed intermittently Therefore the barrel isin dynamic conditions during the injection molding processHence the PID algorithm cannot provide a satisfactory barreltemperature control performance for the whole operationprocess In the past decades in order to solve the barrel tem-perature control problem many advanced control methodshave been proposed such as adaptive decoupling control [8]model predictive synchronous control [9] multivariable self-tuning predictive control [10] self-optimizing model pre-dictive control [11] adaptive generalized predictive control[12] and response identification and internal model control[13]These methods can effectively solve the problem of largetime delay However most of these existing methods arebased on feedback control strategies and cannot deal with theintermittent disturbances On the other hand these methodsdo not take into account the dynamic characteristics of theinjection molding process

Considering the repeated operation characteristics of thepolymer injection molding process it is feasible to use afeedforward compensation strategy to eliminate the effects ofintermittent disturbances For example Yao et al proposeda barrel temperature control method using the combinationof a generalized predictive control with an iterative learningfeedforward control [14] The experimental results show thatusing a feedforward compensation strategy can effectivelyprevent large temperature variations caused by intermittentdisturbances There are two key points that must be con-firmed when using a feedforward compensation strategy forthe barrel temperature control (1) the compensation timeand (2) the compensation quantity However it is not an easytask to get the accurate compensation time and compensationquantity for the barrel temperature control They are affectedby many complex factors such as raw materials environ-ment injection molds and process parameters Thereforeit is difficult to obtain the accurate compensation time andcompensation quantity through model-based methods

According to the previous analysis it is crucial to obtainthe accurate compensation time and compensation quantitywhen using a feedforward compensation control strategy forthe injection molding temperature control Considering therepeated behavior of the system iterative learning control

(ILC) is recognized as an effective control method for thesystems with repeated characteristics [15 16] ILC is a kindof data-based learning control method [17] ILC generatesfeedforward control signals that apply to the next batch byusing information from previous batches that have beenstored As a data-based control method ILC does not requirean accurate system model so it can be easily adapted toa variety of complex conditions Thus it is feasible to useILC to obtain the accurate compensation time However asa feedforward control strategy ILC cannot achieve accuratecompensation quantity control As a typical batch productionprocess it is feasible to adopt a reinforcement learning (RL)algorithm to the control system [18]

In this paper a new intelligent barrel temperature controlmethod which fully considers the dynamic characteristicsof the injection molding process is proposed The proposedcontrol method adopts a feedforward compensation strat-egy to improve the stability of temperature control underdynamic conditions The proposed method first learns theoptimal compensation time in each batch using a feedforwardILC algorithm Subsequently a deep Q-learning algorithmcombiningQ-learningwithANN is adopted to learn the opti-mal compensation quantity for each compensation periodWith this innovation control strategy the stability of tem-perature control can be effectively improved and the productconsistency can be significantly improved

The rest of this paper is organized as follows In Section 2the system description is presented Section 3 develops thefeedforward compensation temperature control strategy InSection 4 temperature control experiments with differentconditions are performed In Section 5 the product consis-tency experiments are given to verify the effectiveness of thedeveloped control strategy in improving product consistencyFinally conclusions are drawn in Section 6

2 System Description

The typical structure diagram of an injection moldingmachine injection unit is shown in Figure 1 It mainly consistsof a screw a barrel a nozzle and a heating system In generalthe heating system has multiple heating zones For eachheating zone there is a heater and a temperature sensor



Controller


ILC

System

+

-

+ +

uk(t)

yk(t) ek(t)

yr(t)

ek(T)









3 Methodology





System


Agent

Action Reward

Learningrate

State

Actionvalue

Discountfactor

Σ

at rt

st

Qt(st at)

Qtminus1



119906119896 (119905) = 119876 (119906119896minus1 (119905)) + Δ119906119896 (119905) (1)


min 119869119896 =119879minus1sum119905=0

[119890119896 (119905)]119879119860 (119905) [119890119896 (119905)]

+ 119879minus1sum119905=0

[Δ119906119896 (119905)]119879 119861 (119905) [Δ119906119896 (119905)](2)

12

120597119869119896120597119906119896 = minus119866119879119860 (119905) 119890119896 + 119861 (119905) Δ119906119896 (119905) = 0 (3)

Δ119906119896 (119905) = 119861 (119905)minus1 119866119879119860 (119905) 119890119896 (119905) (4)




119876119905 (119904119905 119886119905)larr997888 119876119905minus1 (119904119905 119886119905)

+ 120572 [119903119905 + 120582max119886isin119860






119878119905 = (119910119905 119890119905 119906119905) (6)


119860 119905 = +Δ119906119905 0 minusΔ119906119905 (7)



119901 (119904119905 119886119894) = 1 minus 120576 119886119894 = max

1198861015840119876(119904119905 1198861015840)




119903119905+1 =


(9)


119876119905 =119899sum119894=1

119908(2)119905119894 119889119905119894 (10)

where

119889119905119894 = 11 + 119890minusℎ119905119894 (11)

ℎ119905119894 =119898sum119895=1

119908(1)119905119894119895119909119905119895 (12)



Δ119882119905= 120572 [119903119905+1 + 120574max

1198861015840isin119860119876119905 (119904119905+1 1198861015840) minus 119876119905 (119904119905 119886119905)] nabla119908119876119905 (13)


120597119876119905120597119908(2)119905119894 = 119889119905119894 (14)

120597119876119905120597119908(1)119905119894119895 = 119908(2)119905119894 119889119905119894 (1 minus 119889119905119894) 119909119905119895 (15)






IO

Barrel

Hopper

RelayPowerSupply

IPC

MCP

AD-DA

2 134






Δ119906 (119905) = 1199020119890 (119905) + 1199021119890 (119905 minus 1) + 1199022119890 (119905 minus 2) (16)

where

1199020 = 119870119901 (1 + 119879119879119894 +

119879119889119879 )

1199021 = minus119870119901 (1 + 2119879119889119879 )1199022 = 119870119901119879119889119879

(17)



where

119867119873119888 = [1 0 0 0]1times119873119888


119866 =

[[[[[[[[[[[[[[




]]]]]]]]]]]]]]1198732times119873119888

119877 =[[[[[[[

119903 (119905 + 1)119903 (119905 + 1)

119903 (119905 + 1198732)

]]]]]]]

119865 =[[[[[[[[



]]]]]]]]

(19)







Maximumtemperature

Continuerising

Stop heating

(180)

(1085)

(1023)

(1842)200

160

120

80

40

0

Tem

pera

ture

(∘C)

0 300 600 900 1200 1500

Time (s)

(a)

(b)

zone 2zone 3

zone 4

0 300 600 900 1200 1500

Time (s)

12

10

8

6

4

2

0

Con

trol V

olta

ge (V

)

zone 2zone 3

zone 4











224

222

220

218

216

Tem

pera

ture

(∘C)

0 60 120 180 240 300

Time (s)


5

4

3

2

1

0Con

trol V

olta

ge (V

)

100

80

60

40

20

0Rota

tion

Spee

d (r

pm)

0 60 120 180 240 300

Time (s)

(c)

(b)

(a)

0 60 120 180 240 300

Time (s)







Learning process225

223

221

219

217

215

Tem

pera

ture

(∘C)

0 600 1200 1800 2400 3000 3600

Time (s)

0 600 1200 1800 2400 3000 3600

Time (s)

100

80

60

40

20

0

Rota

tion

Spee

d (r

pm)





Runner

Product 1

Product 2

Gate 1

Gate 2

(a)

Product 1

Product 2

(b)


337

333

329

321

325

317

313

Prod

uct1

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(a)

337

333

329

321

325

317

313

Prod

uct2

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(b)




Temperature (∘C)













Sum 324869 00687 02718


Sum 323744 02864 10123


Sum 325841 01965 06968






Processparameters

Change ofparameters










0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)


0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)








6 Conclusions






Data Availability




Acknowledgments


References





























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Controller


ILC

System

+

-

+ +

uk(t)

yk(t) ek(t)

yr(t)

ek(T)









3 Methodology





System


Agent

Action Reward

Learningrate

State

Actionvalue

Discountfactor

Σ

at rt

st

Qt(st at)

Qtminus1



119906119896 (119905) = 119876 (119906119896minus1 (119905)) + Δ119906119896 (119905) (1)


min 119869119896 =119879minus1sum119905=0

[119890119896 (119905)]119879119860 (119905) [119890119896 (119905)]

+ 119879minus1sum119905=0

[Δ119906119896 (119905)]119879 119861 (119905) [Δ119906119896 (119905)](2)

12

120597119869119896120597119906119896 = minus119866119879119860 (119905) 119890119896 + 119861 (119905) Δ119906119896 (119905) = 0 (3)

Δ119906119896 (119905) = 119861 (119905)minus1 119866119879119860 (119905) 119890119896 (119905) (4)




119876119905 (119904119905 119886119905)larr997888 119876119905minus1 (119904119905 119886119905)

+ 120572 [119903119905 + 120582max119886isin119860






119878119905 = (119910119905 119890119905 119906119905) (6)


119860 119905 = +Δ119906119905 0 minusΔ119906119905 (7)



119901 (119904119905 119886119894) = 1 minus 120576 119886119894 = max

1198861015840119876(119904119905 1198861015840)




119903119905+1 =


(9)


119876119905 =119899sum119894=1

119908(2)119905119894 119889119905119894 (10)

where

119889119905119894 = 11 + 119890minusℎ119905119894 (11)

ℎ119905119894 =119898sum119895=1

119908(1)119905119894119895119909119905119895 (12)



Δ119882119905= 120572 [119903119905+1 + 120574max

1198861015840isin119860119876119905 (119904119905+1 1198861015840) minus 119876119905 (119904119905 119886119905)] nabla119908119876119905 (13)


120597119876119905120597119908(2)119905119894 = 119889119905119894 (14)

120597119876119905120597119908(1)119905119894119895 = 119908(2)119905119894 119889119905119894 (1 minus 119889119905119894) 119909119905119895 (15)






IO

Barrel

Hopper

RelayPowerSupply

IPC

MCP

AD-DA

2 134






Δ119906 (119905) = 1199020119890 (119905) + 1199021119890 (119905 minus 1) + 1199022119890 (119905 minus 2) (16)

where

1199020 = 119870119901 (1 + 119879119879119894 +

119879119889119879 )

1199021 = minus119870119901 (1 + 2119879119889119879 )1199022 = 119870119901119879119889119879

(17)



where

119867119873119888 = [1 0 0 0]1times119873119888


119866 =

[[[[[[[[[[[[[[




]]]]]]]]]]]]]]1198732times119873119888

119877 =[[[[[[[

119903 (119905 + 1)119903 (119905 + 1)

119903 (119905 + 1198732)

]]]]]]]

119865 =[[[[[[[[



]]]]]]]]

(19)







Maximumtemperature

Continuerising

Stop heating

(180)

(1085)

(1023)

(1842)200

160

120

80

40

0

Tem

pera

ture

(∘C)

0 300 600 900 1200 1500

Time (s)

(a)

(b)

zone 2zone 3

zone 4

0 300 600 900 1200 1500

Time (s)

12

10

8

6

4

2

0

Con

trol V

olta

ge (V

)

zone 2zone 3

zone 4











224

222

220

218

216

Tem

pera

ture

(∘C)

0 60 120 180 240 300

Time (s)


5

4

3

2

1

0Con

trol V

olta

ge (V

)

100

80

60

40

20

0Rota

tion

Spee

d (r

pm)

0 60 120 180 240 300

Time (s)

(c)

(b)

(a)

0 60 120 180 240 300

Time (s)







Learning process225

223

221

219

217

215

Tem

pera

ture

(∘C)

0 600 1200 1800 2400 3000 3600

Time (s)

0 600 1200 1800 2400 3000 3600

Time (s)

100

80

60

40

20

0

Rota

tion

Spee

d (r

pm)





Runner

Product 1

Product 2

Gate 1

Gate 2

(a)

Product 1

Product 2

(b)


337

333

329

321

325

317

313

Prod

uct1

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(a)

337

333

329

321

325

317

313

Prod

uct2

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(b)




Temperature (∘C)













Sum 324869 00687 02718


Sum 323744 02864 10123


Sum 325841 01965 06968






Processparameters

Change ofparameters










0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)


0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)








6 Conclusions






Data Availability




Acknowledgments


References





























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





System


Agent

Action Reward

Learningrate

State

Actionvalue

Discountfactor

Σ

at rt

st

Qt(st at)

Qtminus1



119906119896 (119905) = 119876 (119906119896minus1 (119905)) + Δ119906119896 (119905) (1)


min 119869119896 =119879minus1sum119905=0

[119890119896 (119905)]119879119860 (119905) [119890119896 (119905)]

+ 119879minus1sum119905=0

[Δ119906119896 (119905)]119879 119861 (119905) [Δ119906119896 (119905)](2)

12

120597119869119896120597119906119896 = minus119866119879119860 (119905) 119890119896 + 119861 (119905) Δ119906119896 (119905) = 0 (3)

Δ119906119896 (119905) = 119861 (119905)minus1 119866119879119860 (119905) 119890119896 (119905) (4)




119876119905 (119904119905 119886119905)larr997888 119876119905minus1 (119904119905 119886119905)

+ 120572 [119903119905 + 120582max119886isin119860






119878119905 = (119910119905 119890119905 119906119905) (6)


119860 119905 = +Δ119906119905 0 minusΔ119906119905 (7)



119901 (119904119905 119886119894) = 1 minus 120576 119886119894 = max

1198861015840119876(119904119905 1198861015840)




119903119905+1 =


(9)


119876119905 =119899sum119894=1

119908(2)119905119894 119889119905119894 (10)

where

119889119905119894 = 11 + 119890minusℎ119905119894 (11)

ℎ119905119894 =119898sum119895=1

119908(1)119905119894119895119909119905119895 (12)



Δ119882119905= 120572 [119903119905+1 + 120574max

1198861015840isin119860119876119905 (119904119905+1 1198861015840) minus 119876119905 (119904119905 119886119905)] nabla119908119876119905 (13)


120597119876119905120597119908(2)119905119894 = 119889119905119894 (14)

120597119876119905120597119908(1)119905119894119895 = 119908(2)119905119894 119889119905119894 (1 minus 119889119905119894) 119909119905119895 (15)






IO

Barrel

Hopper

RelayPowerSupply

IPC

MCP

AD-DA

2 134






Δ119906 (119905) = 1199020119890 (119905) + 1199021119890 (119905 minus 1) + 1199022119890 (119905 minus 2) (16)

where

1199020 = 119870119901 (1 + 119879119879119894 +

119879119889119879 )

1199021 = minus119870119901 (1 + 2119879119889119879 )1199022 = 119870119901119879119889119879

(17)



where

119867119873119888 = [1 0 0 0]1times119873119888


119866 =

[[[[[[[[[[[[[[




]]]]]]]]]]]]]]1198732times119873119888

119877 =[[[[[[[

119903 (119905 + 1)119903 (119905 + 1)

119903 (119905 + 1198732)

]]]]]]]

119865 =[[[[[[[[



]]]]]]]]

(19)







Maximumtemperature

Continuerising

Stop heating

(180)

(1085)

(1023)

(1842)200

160

120

80

40

0

Tem

pera

ture

(∘C)

0 300 600 900 1200 1500

Time (s)

(a)

(b)

zone 2zone 3

zone 4

0 300 600 900 1200 1500

Time (s)

12

10

8

6

4

2

0

Con

trol V

olta

ge (V

)

zone 2zone 3

zone 4











224

222

220

218

216

Tem

pera

ture

(∘C)

0 60 120 180 240 300

Time (s)


5

4

3

2

1

0Con

trol V

olta

ge (V

)

100

80

60

40

20

0Rota

tion

Spee

d (r

pm)

0 60 120 180 240 300

Time (s)

(c)

(b)

(a)

0 60 120 180 240 300

Time (s)







Learning process225

223

221

219

217

215

Tem

pera

ture

(∘C)

0 600 1200 1800 2400 3000 3600

Time (s)

0 600 1200 1800 2400 3000 3600

Time (s)

100

80

60

40

20

0

Rota

tion

Spee

d (r

pm)





Runner

Product 1

Product 2

Gate 1

Gate 2

(a)

Product 1

Product 2

(b)


337

333

329

321

325

317

313

Prod

uct1

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(a)

337

333

329

321

325

317

313

Prod

uct2

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(b)




Temperature (∘C)













Sum 324869 00687 02718


Sum 323744 02864 10123


Sum 325841 01965 06968






Processparameters

Change ofparameters










0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)


0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)








6 Conclusions






Data Availability




Acknowledgments


References





























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






119878119905 = (119910119905 119890119905 119906119905) (6)


119860 119905 = +Δ119906119905 0 minusΔ119906119905 (7)



119901 (119904119905 119886119894) = 1 minus 120576 119886119894 = max

1198861015840119876(119904119905 1198861015840)




119903119905+1 =


(9)


119876119905 =119899sum119894=1

119908(2)119905119894 119889119905119894 (10)

where

119889119905119894 = 11 + 119890minusℎ119905119894 (11)

ℎ119905119894 =119898sum119895=1

119908(1)119905119894119895119909119905119895 (12)



Δ119882119905= 120572 [119903119905+1 + 120574max

1198861015840isin119860119876119905 (119904119905+1 1198861015840) minus 119876119905 (119904119905 119886119905)] nabla119908119876119905 (13)


120597119876119905120597119908(2)119905119894 = 119889119905119894 (14)

120597119876119905120597119908(1)119905119894119895 = 119908(2)119905119894 119889119905119894 (1 minus 119889119905119894) 119909119905119895 (15)






IO

Barrel

Hopper

RelayPowerSupply

IPC

MCP

AD-DA

2 134






Δ119906 (119905) = 1199020119890 (119905) + 1199021119890 (119905 minus 1) + 1199022119890 (119905 minus 2) (16)

where

1199020 = 119870119901 (1 + 119879119879119894 +

119879119889119879 )

1199021 = minus119870119901 (1 + 2119879119889119879 )1199022 = 119870119901119879119889119879

(17)



where

119867119873119888 = [1 0 0 0]1times119873119888


119866 =

[[[[[[[[[[[[[[




]]]]]]]]]]]]]]1198732times119873119888

119877 =[[[[[[[

119903 (119905 + 1)119903 (119905 + 1)

119903 (119905 + 1198732)

]]]]]]]

119865 =[[[[[[[[



]]]]]]]]

(19)







Maximumtemperature

Continuerising

Stop heating

(180)

(1085)

(1023)

(1842)200

160

120

80

40

0

Tem

pera

ture

(∘C)

0 300 600 900 1200 1500

Time (s)

(a)

(b)

zone 2zone 3

zone 4

0 300 600 900 1200 1500

Time (s)

12

10

8

6

4

2

0

Con

trol V

olta

ge (V

)

zone 2zone 3

zone 4











224

222

220

218

216

Tem

pera

ture

(∘C)

0 60 120 180 240 300

Time (s)


5

4

3

2

1

0Con

trol V

olta

ge (V

)

100

80

60

40

20

0Rota

tion

Spee

d (r

pm)

0 60 120 180 240 300

Time (s)

(c)

(b)

(a)

0 60 120 180 240 300

Time (s)







Learning process225

223

221

219

217

215

Tem

pera

ture

(∘C)

0 600 1200 1800 2400 3000 3600

Time (s)

0 600 1200 1800 2400 3000 3600

Time (s)

100

80

60

40

20

0

Rota

tion

Spee

d (r

pm)





Runner

Product 1

Product 2

Gate 1

Gate 2

(a)

Product 1

Product 2

(b)


337

333

329

321

325

317

313

Prod

uct1

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(a)

337

333

329

321

325

317

313

Prod

uct2

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(b)




Temperature (∘C)













Sum 324869 00687 02718


Sum 323744 02864 10123


Sum 325841 01965 06968






Processparameters

Change ofparameters










0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)


0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)








6 Conclusions






Data Availability




Acknowledgments


References





























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





IO

Barrel

Hopper

RelayPowerSupply

IPC

MCP

AD-DA

2 134






Δ119906 (119905) = 1199020119890 (119905) + 1199021119890 (119905 minus 1) + 1199022119890 (119905 minus 2) (16)

where

1199020 = 119870119901 (1 + 119879119879119894 +

119879119889119879 )

1199021 = minus119870119901 (1 + 2119879119889119879 )1199022 = 119870119901119879119889119879

(17)



where

119867119873119888 = [1 0 0 0]1times119873119888


119866 =

[[[[[[[[[[[[[[




]]]]]]]]]]]]]]1198732times119873119888

119877 =[[[[[[[

119903 (119905 + 1)119903 (119905 + 1)

119903 (119905 + 1198732)

]]]]]]]

119865 =[[[[[[[[



]]]]]]]]

(19)







Maximumtemperature

Continuerising

Stop heating

(180)

(1085)

(1023)

(1842)200

160

120

80

40

0

Tem

pera

ture

(∘C)

0 300 600 900 1200 1500

Time (s)

(a)

(b)

zone 2zone 3

zone 4

0 300 600 900 1200 1500

Time (s)

12

10

8

6

4

2

0

Con

trol V

olta

ge (V

)

zone 2zone 3

zone 4











224

222

220

218

216

Tem

pera

ture

(∘C)

0 60 120 180 240 300

Time (s)


5

4

3

2

1

0Con

trol V

olta

ge (V

)

100

80

60

40

20

0Rota

tion

Spee

d (r

pm)

0 60 120 180 240 300

Time (s)

(c)

(b)

(a)

0 60 120 180 240 300

Time (s)







Learning process225

223

221

219

217

215

Tem

pera

ture

(∘C)

0 600 1200 1800 2400 3000 3600

Time (s)

0 600 1200 1800 2400 3000 3600

Time (s)

100

80

60

40

20

0

Rota

tion

Spee

d (r

pm)





Runner

Product 1

Product 2

Gate 1

Gate 2

(a)

Product 1

Product 2

(b)


337

333

329

321

325

317

313

Prod

uct1

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(a)

337

333

329

321

325

317

313

Prod

uct2

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(b)




Temperature (∘C)













Sum 324869 00687 02718


Sum 323744 02864 10123


Sum 325841 01965 06968






Processparameters

Change ofparameters










0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)


0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)








6 Conclusions






Data Availability




Acknowledgments


References





























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





119866 =

[[[[[[[[[[[[[[




]]]]]]]]]]]]]]1198732times119873119888

119877 =[[[[[[[

119903 (119905 + 1)119903 (119905 + 1)

119903 (119905 + 1198732)

]]]]]]]

119865 =[[[[[[[[



]]]]]]]]

(19)







Maximumtemperature

Continuerising

Stop heating

(180)

(1085)

(1023)

(1842)200

160

120

80

40

0

Tem

pera

ture

(∘C)

0 300 600 900 1200 1500

Time (s)

(a)

(b)

zone 2zone 3

zone 4

0 300 600 900 1200 1500

Time (s)

12

10

8

6

4

2

0

Con

trol V

olta

ge (V

)

zone 2zone 3

zone 4











224

222

220

218

216

Tem

pera

ture

(∘C)

0 60 120 180 240 300

Time (s)


5

4

3

2

1

0Con

trol V

olta

ge (V

)

100

80

60

40

20

0Rota

tion

Spee

d (r

pm)

0 60 120 180 240 300

Time (s)

(c)

(b)

(a)

0 60 120 180 240 300

Time (s)







Learning process225

223

221

219

217

215

Tem

pera

ture

(∘C)

0 600 1200 1800 2400 3000 3600

Time (s)

0 600 1200 1800 2400 3000 3600

Time (s)

100

80

60

40

20

0

Rota

tion

Spee

d (r

pm)





Runner

Product 1

Product 2

Gate 1

Gate 2

(a)

Product 1

Product 2

(b)


337

333

329

321

325

317

313

Prod

uct1

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(a)

337

333

329

321

325

317

313

Prod

uct2

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(b)




Temperature (∘C)













Sum 324869 00687 02718


Sum 323744 02864 10123


Sum 325841 01965 06968






Processparameters

Change ofparameters










0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)


0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)








6 Conclusions






Data Availability




Acknowledgments


References





























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





Maximumtemperature

Continuerising

Stop heating

(180)

(1085)

(1023)

(1842)200

160

120

80

40

0

Tem

pera

ture

(∘C)

0 300 600 900 1200 1500

Time (s)

(a)

(b)

zone 2zone 3

zone 4

0 300 600 900 1200 1500

Time (s)

12

10

8

6

4

2

0

Con

trol V

olta

ge (V

)

zone 2zone 3

zone 4











224

222

220

218

216

Tem

pera

ture

(∘C)

0 60 120 180 240 300

Time (s)


5

4

3

2

1

0Con

trol V

olta

ge (V

)

100

80

60

40

20

0Rota

tion

Spee

d (r

pm)

0 60 120 180 240 300

Time (s)

(c)

(b)

(a)

0 60 120 180 240 300

Time (s)







Learning process225

223

221

219

217

215

Tem

pera

ture

(∘C)

0 600 1200 1800 2400 3000 3600

Time (s)

0 600 1200 1800 2400 3000 3600

Time (s)

100

80

60

40

20

0

Rota

tion

Spee

d (r

pm)





Runner

Product 1

Product 2

Gate 1

Gate 2

(a)

Product 1

Product 2

(b)


337

333

329

321

325

317

313

Prod

uct1

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(a)

337

333

329

321

325

317

313

Prod

uct2

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(b)




Temperature (∘C)













Sum 324869 00687 02718


Sum 323744 02864 10123


Sum 325841 01965 06968






Processparameters

Change ofparameters










0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)


0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)








6 Conclusions






Data Availability




Acknowledgments


References





























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








224

222

220

218

216

Tem

pera

ture

(∘C)

0 60 120 180 240 300

Time (s)


5

4

3

2

1

0Con

trol V

olta

ge (V

)

100

80

60

40

20

0Rota

tion

Spee

d (r

pm)

0 60 120 180 240 300

Time (s)

(c)

(b)

(a)

0 60 120 180 240 300

Time (s)







Learning process225

223

221

219

217

215

Tem

pera

ture

(∘C)

0 600 1200 1800 2400 3000 3600

Time (s)

0 600 1200 1800 2400 3000 3600

Time (s)

100

80

60

40

20

0

Rota

tion

Spee

d (r

pm)





Runner

Product 1

Product 2

Gate 1

Gate 2

(a)

Product 1

Product 2

(b)


337

333

329

321

325

317

313

Prod

uct1

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(a)

337

333

329

321

325

317

313

Prod

uct2

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(b)




Temperature (∘C)













Sum 324869 00687 02718


Sum 323744 02864 10123


Sum 325841 01965 06968






Processparameters

Change ofparameters










0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)


0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)








6 Conclusions






Data Availability




Acknowledgments


References





























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





Runner

Product 1

Product 2

Gate 1

Gate 2

(a)

Product 1

Product 2

(b)


337

333

329

321

325

317

313

Prod

uct1

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(a)

337

333

329

321

325

317

313

Prod

uct2

Wei

ght (

g)

0 10 20 30 40 50

Cycle Number (N)


(b)




Temperature (∘C)













Sum 324869 00687 02718


Sum 323744 02864 10123


Sum 325841 01965 06968






Processparameters

Change ofparameters










0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)


0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)








6 Conclusions






Data Availability




Acknowledgments


References





























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








Sum 324869 00687 02718


Sum 323744 02864 10123


Sum 325841 01965 06968






Processparameters

Change ofparameters










0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)


0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)








6 Conclusions






Data Availability




Acknowledgments


References





























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






0 10 20 30 40 50

Product Number (N)


34

332

324

316

308

30

Prod

uct W

eigh

t (g)

(a)


0 10 20 30 40 50

Product Number (N)


Prod

uct W

eigh

t (g)

35

342

334

326

318

31

(b)








6 Conclusions






Data Availability




Acknowledgments


References





























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




improving the consistency of injection molding products by

Documents