Polymer Processing Laboratory University of Maryland Physics Based Modeling and Control of Extrusion...

Polymer Processing Laboratory University of Maryland

Physics Based Modeling and Control of Extrusion

Paul Elkouss

David Bigio


Motivation• Control extrudate quality – anything that can be

measured online• Use a physically based model• Closed loop control using kinematic and additional

plant models to regulate the product qualities• Example vis-breaking of polypropylene:

– Vis-breaking = cutting of polymer chain– MWD influences product properties – Control product properties: Viscosity, Yield strength, etc.– Peroxide has very high control influence


Experimental Approach

Polymer

Optical Analysis S

D

Mixing Section

Probe DAQ/PC

ch

gap

cl

ap


Experimental System


Research Diagram


Background – Summary• Simple and Complex models of extruder behavior• Different models of peroxide degradation, but most are

based on work by Tzoganakis• FEM has been used to model degradation in the extruder

(computationally intensive), but none have used lamellar modeling yet.

• Most open loop model structures have been determined statistically (arbitrary), but Walsh et. al. are first to use model based on kinematics.


3rd Order Plant Model

3

3

)()(

aseasG

std

•Like 3 CSTR’s with transport delay

•Model fits for each probe

•Deconvolve signals to get fits for individual probes


RTD’s and Model Fits


Mean Residence Measures

N

QBAQtm

BQ

NANtm

• Mean Residence Volume

• Mean Residence Revolution


RTDs at Different Operating Conditions


Model Validation


Other Kinematic Representations

• RRD - Residence Rotation Distribution– The same specific throughput (Q/N) gives the

same curve.

• RVD – Residence Volume Distribution– The curves w/o volume delay collapse to one

curve– One set of shape parameters describes all

conditions


RRD


Model fits in Volume Domain (RVD)

3

ˆ3

)ˆ()ˆ(

ˆ

cs

ecsG

Qtv

Qac

Qss

sv

dd

d


3rd Order with Different Poles

))()(()(

321

)(321

123

321

asasas

eaaasG

sttt ddd

•Like 3 CSTR’s of different volumes with transport delay


• An important question: What frequency disturbances can be damped by mixing process given the screw geometry?

Disturbance Rejection

filledcritical V

2

3

3

)()(

Cs

eCKsG

svC

d

2/13/2 )1(

2

filledVC


Lamellar Model• One dimensional model of material transfer (Ottino et.

al.)

• Useful for studying laminar mixing, diffusion and reaction

• Three dimensional flows one dimension.

• Example - simplified calculations.– Relate to operating conditions– Calculate diffusion and inter-material area growth– No need to calculate reaction, or geometry


Background – Lamellar Model(x)= Vx=-x

iii RNt

c

*2

2

iR

t

tc

t

tc

r

ci

d

ci

2

12ln ctt

tesx 0


System ID

• For determining open-loop kinematic model of plant

• Determine volume delay, and shape factor for sensor

dttatta

ttad

tt

aaaaa

e

aaaaa

eaaaaaaaa

e

aaa

tt

tcdd

d

))(())((

)(1

0

)(

13121

)(

12232

)(

233132213

)(

321 12

3


Closed Loop Control Issues

• Modeling the Plant

• Online property measurement– What to measure– Measurement delay

• Control Scheme– Simple, smith predictor– Advanced control: Robust, Adaptive control– Online parameter correction


What is currently being done

• Warp time model– Compare to steady state results– Relate to operating conditions to predict the DC

Gain

• Control Scheme– Apply adaptive control to the plant– Verify with Experiments


Conclusions

• Kinematic model is main model for the extruder

• The model is applicable to many different measurable quantities

• Additional models can be added to provide better control

Polymer Processing Laboratory University of Maryland Physics Based Modeling and Control of Extrusion...

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