Nonlinear Model-Based Inferential Control of Moisture Content of Spray Dried Coconut Milk
Abstract
:1. Introduction
2. Materials and Methods
2.1. Dynamic Model of the Spray Drying Process
2.1.1. Drying Kinetic Study
2.1.2. Experimental Setup of Drying Tunnel
2.1.3. Sessile Droplet Drying
2.1.4. Development of Drying Kinetic Model
2.1.5. Mathematical Formulation of Reaction Engineering Approach Model
2.2. Mathematical Formulation of One-Dimensional Spray Dryer Model
- The air behavior is close to that of an ideal gas, therefore the properties of air can be determined based on ideal gas law
- Hold-ups of dry air and solid powder are constant; therefore, the flowrate of dry powder is equal for stream entering and leaving the chamber
- The pressure in the dryer remained at atmospheric pressure
2.3. Formulation of Empirical Models
2.3.1. NARX Model Development
2.3.2. Neural Network (NN) Estimator Development
2.4. Inferential Controller Design
2.5. Controller Performance
3. Results
3.1. Drying Kinetic Model of Coconut Milk Droplet
3.2. One-Dimensional Model
3.3. NARX Model
3.4. Neural Network Estimator
3.5. Inferential Control of Moisture Content
3.6. Set Point Tracking
3.7. Disturbance Rejection
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
Correlations Used in REA Model and One-Dimensional Model Development
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Variable/Property | Value | Reference |
---|---|---|
4185 J/kg·K | [39] | |
1389 J/kg·K | Measured | |
1800 J/kg·K | [39] | |
1000 J/kg·K | [39] | |
200 μm | [24] | |
5 m/s | [40] | |
100 m/s | [40] | |
8.314 J/mol·K | [39] | |
2501 103 J kg−1 | [39] | |
300 K | Measured | |
22.8 W/m2·K | Calculated | |
0.5 m | Measured | |
0.22 m | Measured |
Variable | Value |
---|---|
Droplet: | |
Moisture content | 2.67 kg/kg |
Temperature | 27 °C |
Flowrate | 9.8 10−4 kg/s |
Hot air: | |
Humidity | 0.021 kg/kg |
Temperature | 160 °C |
Flowrate | 0.011 kg/s |
Tuning Rules | ||
---|---|---|
Zigler-Nichols (ZN) | 0.45 Kcu | Pu /1.2 |
Tyreus-Luyben (TL) | 0.32 Kcu | Pu |
Relaxed-Ziegler Nichols (R-ZN) | 0.31 Kcu | 2.2 Pu |
Model | Number of Delay, d | MSE | |
---|---|---|---|
Training | Validation | ||
NN-NARX | 1 | 3.960 × 10−9 | 8.678 × 10−10 |
2 | 1.482 × 10−9 | 1.583 × 10−9 | |
NN-N | 1 | 7.589 × 10−8 | 1.327 × 10−7 |
2 | 1.251 × 10−7 | 7.987 × 10−7 |
Tuning Rules | Controller Gain, Kc | Integral Time (s), τI |
---|---|---|
Ziegler Nichols (ZN) | −12.75 | 1.67 |
Tyreus-Luyben (TL) | −8.79 | 4.40 |
Relaxed-Ziegler Nichols (R-ZN) | −9.072 | 2.00 |
Tuning Rules | Overshoot (%) | Settling Time (s) | Rise Time (s) | Static Control Offset ×10−4 (kg/kg) |
---|---|---|---|---|
ZN | 3.8 | 208 | 2 | 2.04 |
TL | 0.4 | 126 | 11 | 2.18 |
R-ZN | 5.9 | 100 | 2.9 | 2.18 |
Set Point (kg/kg) | Tuning Rules | ITAE | IAE | Static Control Offset ×10−4 (kg/kg) |
---|---|---|---|---|
0.041 | ZN | 2.0683 | 0.0461 | 2.04 |
TL | 0.1917 | 0.0205 | 2.18 | |
R-ZN | 0.7400 | 0.0426 | 2.18 | |
0.056 | ZN | 5.7465 | 0.3226 | 0.85 |
TL | 3.4722 | 0.2625 | 0.85 | |
R-ZN | 5.7180 | 0.3260 | 0.85 | |
0.037 | ZN | 7.8142 | 0.2081 | 0.48 |
TL | 6.0877 | 0.1531 | 2.00 | |
R-ZN | 8.2237 | 0.2001 | 2.80 |
Tuning Rules | Positive Deviation | Negative Deviation | ||
---|---|---|---|---|
ITAE | IAE | ITAE | IAE | |
ZN | 0.237 | 0.008 | 0.761 | 0.023 |
TL | 0.370 | 0.018 | 6.277 | 0.112 |
R-ZN | 0.210 | 0.010 | 1.622 | 0.044 |
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Abdullah, Z.; Taip, F.S.; Kamal, S.M.M.; Rahman, R.Z.A. Nonlinear Model-Based Inferential Control of Moisture Content of Spray Dried Coconut Milk. Foods 2020, 9, 1177. https://doi.org/10.3390/foods9091177
Abdullah Z, Taip FS, Kamal SMM, Rahman RZA. Nonlinear Model-Based Inferential Control of Moisture Content of Spray Dried Coconut Milk. Foods. 2020; 9(9):1177. https://doi.org/10.3390/foods9091177
Chicago/Turabian StyleAbdullah, Zalizawati, Farah Saleena Taip, Siti Mazlina Mustapa Kamal, and Ribhan Zafira Abdul Rahman. 2020. "Nonlinear Model-Based Inferential Control of Moisture Content of Spray Dried Coconut Milk" Foods 9, no. 9: 1177. https://doi.org/10.3390/foods9091177