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

Twin-Screw Food Extrusion: Control Case Study Joel Schlosburg May 12 th ,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 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 − − + − + − ⎡ ⎤ . 32 ( 14 . 6 s 1 ) . 87 ( 123 . 2 s 1 ) . 12 ⎡ ⎤ SS ⎢ ⎥ ⎡ ⎤ + + + + ⎢ ⎥ MT 2 ( 79 . 4 s 1 )( 26 . 9 s 1 ) 121 . 5 s 1 ( 17 . 45 s 1 ) = ⎢ ⎥ ⎢ ⎥ MC ⎢ ⎥ − . 12 2 . 4 . 47 ⎣ ⎦ ⎢ ⎥ PT ⎢ ⎥ ⎣ ⎦ BT ⎢ ⎥ + + + + + ⎣ ⎦ ( 29 . 6 s 1 )( 13 . 4 s 1 ) 83 . 5 s 1 ( 149 . 6 s 1 )( 127 . 1 s 1 ) ⎡ ⎤ - 0.1146 - 0.02627 0 0 0 0 0 0 0 0 ⎢ ⎥ 0 . 125 0 0 0 0 0 0 0 0 0 ⎢ ⎥ ⎢ ⎥ 0 0 - 0.1084 - 0.04034 0 0 0 0 0 0 ⎢ ⎥ ⎢ 0 0 0.0625 0 0 0 0 0 0 0 ⎥ ⎢ ⎥ 0 0 0 0 - 0.0497 - 0.01495 0 0 0 0 = ⎢ ⎥ A ⎢ ⎥ 0 0 0 0 0.03125 0 0 0 0 0 ⎢ ⎥ 0 0 0 0 0 0 - 0.01198 0 0 0 ⎢ ⎥ ⎢ ⎥ 0 0 0 0 0 0 0 - 0.00823 0 0 ⎢ ⎥ 0 0 0 0 0 0 0 0 - 0.01455 - 0.006732 ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ 0 0 0 0 0 0 0 0 0.007813 0 ⎡ ⎤ . 125 0 0 ⎢ ⎥ 0 0 0 ⎢ ⎥ ⎢ ⎥ . 0625 0 0 ⎢ ⎥ ⎢ 0 0 0 ⎥ ⎢ ⎥ ⎡ ⎤ 0 . 5 0 0.06137 - 0.03363 0 0 - 0.4042 - 0.105 0 - 0.0316 0 0 = ⎢ ⎥ = B C ⎢ ⎥ ⎢ ⎥ 0 0 0 ⎣ 0 0 0 0.03873 0 0 - 0.2295 0 0 0.05062 ⎦ ⎢ ⎥ 0 . 25 0 ⎢ ⎥ ⎢ ⎥ 0 0 0.03125 ⎡ ⎤ ⎢ ⎥ 0 0 0 = D ⎢ ⎥ 0 0 .0625 ⎢ ⎥ ⎣ ⎦ 0 0 0 ⎢ ⎥ ⎣ ⎦ 0 0 0

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 τ n and τ p . 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 ⎡ ⎤ − − − + − + 39 s . 32 ( 14 . 6 s 1 ) . 87 ( 123 . 2 s 1 ) e ⎢ ⎥ ⎡ ⎤ ⎡ ⎤ + + + MT SS 2 ( 79 . 4 s 1 )( 26 . 9 s 1 ) ⎢ ( 17 . 45 s 1 ) ⎥ = ⎢ ⎥ ⎢ ⎥ − ⎢ − ⎥ 39 s ⎣ ⎦ ⎣ ⎦ PT MC . 12 2 . 4 e ⎢ ⎥ + + + ⎣ ⎦ ( 29 . 6 s 1 )( 13 . 4 s 1 ) 83 . 5 s 1 Plant ⎡ ⎤ − − − + − 39 s . 32 ( 15 s 1 ) . 87 e ⎡ ⎤ ⎡ ⎤ MT SS ⎢ ⎥ + = + 2 11 . 55 s 1 ( 14 . 2 s 1 ) ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ − − 39 s ⎣ ⎦ ⎣ ⎦ PT 2 . 4 e MC . 12 ⎣ ⎦ + + 44 . 62 s 1 84 s 1 Model

SISO Tuning Parameters Optimal Loop name τ I (s) τ D (s) Experimental k c (input-output) λ Range - 107.5 SS-MT 34.4 8.55 30-40 sec λ + 15 455 . 17 SS-PT 54.62 0 25-35 sec λ - 54.474 MC-MT 31.05 7.25 100-110 sec λ + 19.5 - 43.54 MC-PT 104.5 16.48 30-40 sec λ + 20.5

SS-MT SISO

SS-PT SISO

MC-MT SISO

MC-PT SISO

Relative Gain Analysis ⎡ ⎤ − − ⎡ ⎤ k k . 32 . 87 = 11 12 Gain array= ⎢ ⎥ ⎢ ⎥ − ⎣ ⎦ ⎣ ⎦ k k . 12 2 . 4 21 22 ⎡ − ⎤ k k k k λ λ ⎡ ⎤ ⎡ ⎤ 11 22 12 21 . 88 . 12 − − ⎢ ⎥ Λ = = = 11 12 k k k k k k k k ⎢ ⎥ ⎢ ⎥ 11 22 12 21 11 22 12 21 − λ λ ⎢ ⎥ k k k k ⎣ ⎦ ⎣ ⎦ . 12 . 88 12 21 11 22 ⎣ ⎦ 21 22 − − k k k k k k k k 11 22 12 21 11 22 12 21 • λ 11 & λ 22 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, k c was detuned by the λ value.

Optimal RGA Control System

SVD Analysis − − − − ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ 1 / 16 . 3 0 . 32 . 87 100 0 1 . 963 . 267 − = ⋅ ⋅ = = 1 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ G * S G S o i − − ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ 0 1 / 12 . 5 . 12 2 . 4 0 5 . 960 . 960 T ⎡− − ⎤ ⎡ ⎤ ⎡ ⎤ . 8771 . 4803 2 . 1948 0 . 9946 . 1034 = Σ = T ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ G U V − − ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ . 4803 . 8771 0 . 9754 . 1034 . 9946 σ = max 2 . 25 σ min •SVD based on scaled gain matrix G* •SVD matrices calculated in Matlab. •Strongest step directions are MT decrease and PT increase.

SVD Simultaneous Step Changes ⎡− ⎡− ⎡ ⎤ ⎤ ⎤ 16 . 3 0 . 8771 . 4803 3 . 60 1 . 95 − = ⋅ ⋅ = = 1 Y * . 25 S U . 25 * ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ o ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ 0 12 . 5 . 4803 . 8771 1 . 50 2 . 75

SVD Simultaneous Step Changes ⎡− ⎡− ⎡ ⎤ ⎤ ⎤ 16 . 3 0 . 8771 . 4803 3 . 60 1 . 95 − = ⋅ ⋅ = = 1 Y * . 25 S U . 25 * ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ o ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ 0 12 . 5 . 4803 . 8771 1 . 50 2 . 75

RGA Validation ⎡− ⎡− ⎡ ⎤ ⎤ ⎤ 16 . 3 0 . 8771 . 4803 3 . 60 1 . 95 − = ⋅ ⋅ = = 1 Y * . 25 S U . 25 * ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ o ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ 0 12 . 5 . 4803 . 8771 1 . 50 2 . 75

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.