Twin-Screw Food Extrusion: Control Case Study Joel Schlosburg May - - PowerPoint PPT Presentation

Twin-Screw Food Extrusion: Control Case Study

Joel Schlosburg May 12th,2005

HOWARD P. ISERMANN DEPARTMENT OF CHEMICAL & BIOLOGICAL ENGINEERING RENSSELAER POLYTECHNIC INSTITUTE TROY, NY 12180

Contents

• Motivation & Past Study
• Model Development
• SISO Control
• RGA: MVSISO Pairing
• SVD: MVSISO Performance
• Disturbance Rejection
• Possibilities for Modification

Motivation

• To produce a control problem based on a

real-life experimental and industrial

• peration.
• Provide system parameters that can be

modeled and controlled, while challenging the student on concepts of control stability and design choices.

Examined Possible Systems for Case-Study Project

• Anesthetic Drug Infusion – Straightforward

biomedical application, but with 0’s in transfer function matrix. May be a interesting module, but RGA would be too simple for case-study project.

• Mechanical Ventilator – Complex

biomechanical application that is based on sinusoidal inputs and split-second time-frames.

• Desalination Plant – A common chemical

engineering operation, though large system needs to be reduced from a 6x6 system.

Twin-Screw Cooking Food Extruder

• Common food processing

unit, mostly in baking industry.

• Fast-speed bioreactor

with heating, cooling, compressing, mixing, evaporating, cutting, and aerating in one unit.

• Twin-screw is now

becoming more common, as it is easier to manipulate a number of parameters.

Previous Control Work

• Work involving the twin-screw extruder include:

–

• Dr. Rosana Moreira at Texas A&M (Schonauer 1995, 1996, & 1997)

– University of Newcastle in Australia (Wang 2001, 2004) –

• Dr. Steven Mulvaney at Cornell University (Lu 1993, Singh 1994, and Haley

2000)

• Control primarily MPC and GPC, with the exception of

PID control by Singh and Mulvaney (1994), for which this study is based.

• Previous control inputs and outputs on this system

include:

– Inputs: screw speed, motor torque, specific mechanical energy, liquid injection rate, moisture content, individual zone and overall jacket temperature, die pressure, and product temperature. – Outputs: “color of extrudate, bulk density, expansion (diameter, lineal, ratio), texture (breaking strength), water solubility index, water absorption index, gelatinization, dextrinization, sensory attributes, dimensional (diameter and length), and surface texture”, motor torque, screw speed, and product or outlet temperature.

Plant Transfer Functions

⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + + + − + + + − + + + − + + − − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ BT MC SS ) 1 s 1 . 127 )( 1 s 6 . 149 ( 47 . 1 s 5 . 83 4 . 2 ) 1 s 4 . 13 )( 1 s 6 . 29 ( 12 . 1 s 5 . 121 12 . ) 1 s 9 . 26 )( 1 s 4 . 79 ( ) 1 s 2 . 123 ( 87 . ) 1 s 45 . 17 ( ) 1 s 6 . 14 ( 32 . PT MT

2

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = 0.007813 0.006732

• 0.01455
• 0.00823
• 0.01198
• 0.03125

0.01495

• 0.0497
• 0.0625

0.04034

• 0.1084
• 125

. 0.02627

• 0.1146
• A

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = 0.05062 0.2295

• 0.03873

0.0316

• 0.105
• 0.4042
• 0.03363
• 0.06137

C .0625 0.03125 25 . 5 . 0625 . 125 . B ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = D

Model Development

Model Transfer Functions (SS Step)

Model Development

• SS-MT loop has inverse response and second
• rder dynamics that require modeling using

figures 3-9, 3-11 to determine τn and τp. Must first assume ζ=1.

• SS-PT loop is simple first order.
• MC-MT loop has positive numerator dynamics,

but modeled as first order plus time delay.

• MC-PT loop is first order plus time delay.

Model Transfer Functions (MC Step)

Final Empirical Models ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

+ − + + − + + − −

− −

MC SS PT MT

1 s 84 e 4 . 2 1 s 62 . 44 12 . 1 s 55 . 11 e 87 . ) 1 s 2 . 14 ( ) 1 s 15 ( 32 .

s 39 s 39 2

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + − + + + + + − + + − − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− −

MC SS 1 s 5 . 83 e 4 . 2 ) 1 s 4 . 13 )( 1 s 6 . 29 ( 12 . ) 1 s 9 . 26 )( 1 s 4 . 79 ( e ) 1 s 2 . 123 ( 87 . ) 1 s 45 . 17 ( ) 1 s 6 . 14 ( 32 . PT MT

s 39 s 39 2

Model Plant

SISO Tuning Parameters

15 + 107.5

• λ

λ 17 . 455

19.5 + 54.474

• λ

20.5 + 43.54

• λ

30-40 sec 16.48 104.5

MC-PT

100-110 sec 7.25 31.05

MC-MT

25-35 sec 54.62

SS-PT

30-40 sec 8.55 34.4

SS-MT

Optimal Experimental λ Range τD (s) τI (s) kc Loop name (input-output)

SS-MT SISO

SS-PT SISO

MC-MT SISO

MC-PT SISO

Relative Gain Analysis

Gain array=

• λ11 & λ22 are closer to one, and therefore are the better control loop pairings.
• Being closer to one allows the closed-loop performance to better match the
• pen-loop performance.
• This means the two control loops are:

– SS controlling MT – MC controlling PT

• Since 0<λ<1, our closed loop may be too aggressive in their control action.
• To prevent instability and overshoot, kc was detuned by the λ value.

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ λ λ λ λ = Λ

− − − − − −

88 . 12 . 12 . 88 .

21 12 22 11 22 11 21 12 22 11 21 12 21 12 22 11 21 12 21 12 22 11 22 11

k k k k k k k k k k k k k k k k k k k k k k k k 22 21 12 11

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 4 . 2 12 . 87 . 32 . k k k k

22 21 12 11

Optimal RGA Control System

SVD Analysis

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⋅ ⋅ =

−

960 . 960 . 267 . 963 . 1 5 100 4 . 2 12 . 87 . 32 . 5 . 12 / 1 3 . 16 / 1 S G S * G

1 i

• T

T

9946 . 1034 . 1034 . 9946 . 9754 . 1948 . 2 8771 . 4803 . 4803 . 8771 . V U G ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡− = Σ =

• SVD based on scaled gain matrix G*
• SVD matrices calculated in Matlab.
• Strongest step directions are MT decrease and PT increase.

25 . 2

min max

= σ σ

SVD Simultaneous Step Changes

⎥ ⎦ ⎤ ⎢ ⎣ ⎡− = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡− ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⋅ ⋅ =

−

75 . 2 50 . 1 95 . 1 60 . 3 8771 . 4803 . 4803 . 8771 . 5 . 12 3 . 16 * 25 . U S 25 . * Y

1

SVD Simultaneous Step Changes

⎥ ⎦ ⎤ ⎢ ⎣ ⎡− = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡− ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⋅ ⋅ =

−

75 . 2 50 . 1 95 . 1 60 . 3 8771 . 4803 . 4803 . 8771 . 5 . 12 3 . 16 * 25 . U S 25 . * Y

1

RGA Validation

⎥ ⎦ ⎤ ⎢ ⎣ ⎡− = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡− ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⋅ ⋅ =

−

75 . 2 50 . 1 95 . 1 60 . 3 8771 . 4803 . 4803 . 8771 . 5 . 12 3 . 16 * 25 . U S 25 . * Y

1

Disturbance Rejection

• Barrel jacket temperature is disturbance

rejection.

• Increase is barrel temperature obviously

should have a direct impact on product temperature.

• Barrel temperature was originally a

manipulated input in Singh (1994), but that choice was designed for minimal loop

• interaction. This diminishes the choice

necessary in the RGA, and not the best case- study choice.

Disturbance Rejection (Cont’d.)

Conclusions and Suggestions

• Stable and flexible bidirectional control of both

motor torque and product temperature.

• Consistent issues of slight overshoot, but not
• utside of reasonable percentage.
• More complicated modeling of the positive

numerator dynamics could improve control, but may be beyond ability of students beyond guess-and-check.

• However, simplified modeling of loop shows the

sacrifices necessary with plant-model mismatch, while still able to achieve stable control.

References

1. Bequette BW. 2003. Process Control: Modeling, Design, and Simulation. Prentice Hall: Upper Saddle River, NJ. 2. Haley TA, and Mulvaney SJ. 2000. On-line system identification and control design

• f an extrusion cooking process: Part I – System Identification. Food Control. 11:

103-120. 3. Haley TA, and Mulvaney SJ. 2000. . On-line system identification and control design of an extrusion cooking process: Part II – Model predictive and inferential control design. Food Control. 11: 121-129. 4. Lu Q, Mulvaney SJ, Hsieh F, and Huff HE. 19993. Model and strategies for computer control of a twin-screw extruder. Food Control. 4: 25-33. 5. Schonauer S, and Moreira RG. 1995. Development of a fixed-GPC controller for a food extruder based on PQA- Part I: System identification. Transactions of the Institute of Chemical Engineers. 73(c):189-199. 6. Schonauer S, and Moreira RG. 1996. A variable restrictive valve as an extra independent control variable for food extrusion process. Food Science and Technology International. 2: 241-248. 7. Schonauer S, and Moreira RG. 1997. Dynamics analysis of on-line product quality attributes for automation of food extruders. Food Science and Technology

• International. 12: 1210-1220.

8. Singh B, and Mulvaney SJ. 1994. Modeling and process control of twin-screw cooking food extruders. Journal of Food Engineering. 23: 403-428. 9. Wang L, Gawthrop P, Chessari C, Podsiadly T, and Giles A. 2004. Indirect approach to continuous time system identification of food extruder. Journal of Process Control. 14: 603-615.

• 10. Wang L, Chessari C, and Karpiel E. 2001. Inferential control of product quality

attributes – application to food cooking extrusion process. Journal of Process

• Control. 11: 621-636.