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Twin-Screw Food Extrusion: Control Case Study
Joel SchlosburgMay 12th,2005
HOWARD P. ISERMANN DEPARTMENT OF CHEMICAL & BIOLOGICAL ENGINEERING
RENSSELAER POLYTECHNIC INSTITUTETROY, 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 operation.
• 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
)1s1.127)(1s6.149(47.
1s5.834.2
)1s4.13)(1s6.29(12.
1s5.12112.
)1s9.26)(1s4.79()1s2.123(87.
)1s45.17(
)1s6.14(32.
PT
MT 2
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
=
00.00781300000000
0.006732-0.01455-00000000
000.00823-0000000
0000.01198-000000
000000.031250000
00000.01495-0.0497-0000
00000000.062500
0000000.04034-0.1084-00
000000000125.0
000000000.02627-0.1146-
A
⎥⎦
⎤⎢⎣
⎡=
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
=0.05062000.2295-000.03873000
000.0316-0 0.105-0.4042-000.03363- 0.06137C
000
.062500
0.0312500
025.0
000
05.0
000
000625.
000
00125.
B
⎥⎦
⎤⎢⎣
⎡=
000
000D
Model Development
Model Transfer Functions (SS Step)
Model Development
• SS-MT loop has inverse response and second order 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
1s84e4.2
1s62.4412.
1s55.11e87.
)1s2.14(
)1s15(32.
s39
s39
2
⎥⎦
⎤⎢⎣
⎡
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
+−
++
+++−
++−−
=⎥⎦
⎤⎢⎣
⎡−
−
MC
SS
1s5.83
e4.2
)1s4.13)(1s6.29(
12.)1s9.26)(1s4.79(
e)1s2.123(87.
)1s45.17(
)1s6.14(32.
PT
MTs39
s39
2
Model
Plant
SISO Tuning Parameters
15+107.5-λ
λ17.455
19.5+54.474-λ
20.5+43.54-
λ 30-40 sec16.48104.5MC-PT
100-110 sec7.2531.05MC-MT
25-35 sec054.62SS-PT
30-40 sec8.5534.4SS-MT
Optimal Experimental
λ RangeτD (s)τI (s)kc
Loop name(input-output)
SS-MT SISO
SS-PT SISO
MC-MT SISO
MC-PT SISO
Relative Gain AnalysisGain 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 open-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.
⎥⎦
⎤⎢⎣
⎡=
⎥⎥⎦
⎤
⎢⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡λλλλ
=Λ−−
−−
−−
88.12.
12.88.
21122211
2211
21122211
2112
21122211
2112
21122211
2211
kkkkkk
kkkkkk
kkkkkk
kkkkkk
2221
1211
⎥⎦
⎤⎢⎣
⎡−−−
=⎥⎦
⎤⎢⎣
⎡4.212.
87.32.
kk
kk
2221
1211
Optimal RGA Control System
SVD Analysis⎥⎦
⎤⎢⎣
⎡−−−
=⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡−−−
⎥⎦
⎤⎢⎣
⎡=⋅⋅= −
960.960.
267.963.1
50
0100
4.212.
87.32.
5.12/10
03.16/1SGS*G 1
io
TT
9946.1034.
1034.9946.
9754.0
01948.2
8771.4803.
4803.8771.VUG ⎥
⎦
⎤⎢⎣
⎡−−−
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡−=Σ=
•SVD based on scaled gain matrix G*
•SVD matrices calculated in Matlab.
•Strongest step directions are MT decrease and PT increase.
25.2min
max =σσ
SVD Simultaneous Step Changes⎥⎦
⎤⎢⎣
⎡−=⎥
⎦
⎤⎢⎣
⎡−⎥⎦
⎤⎢⎣
⎡=⋅⋅= −
75.250.1
95.160.3
8771.4803.
4803.8771.
5.120
03.16*25.US25.*Y 1
o
SVD Simultaneous Step Changes⎥⎦
⎤⎢⎣
⎡−=⎥
⎦
⎤⎢⎣
⎡−⎥⎦
⎤⎢⎣
⎡=⋅⋅= −
75.250.1
95.160.3
8771.4803.
4803.8771.
5.120
03.16*25.US25.*Y 1
o
RGA Validation⎥⎦
⎤⎢⎣
⎡−=⎥
⎦
⎤⎢⎣
⎡−⎥⎦
⎤⎢⎣
⎡=⋅⋅= −
75.250.1
95.160.3
8771.4803.
4803.8771.
5.120
03.16*25.US25.*Y 1
o
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
outside 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.
References1. 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
of 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.