# Nonlinear Model-Based Inferential Control of Moisture Content of Spray Dried Coconut Milk

^{1}

^{2}

^{3}

^{*}

## 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}), $\Delta {E}_{v}$ is the apparent activation energy, ${R}_{G}$ is gas constant (J/mol·K), and ${T}_{s}$ is the droplet interface temperature. ${\rho}_{v,s}$ and ${\rho}_{v,b}$ are the water vapor concentration at droplet interface and in drying air (kg/m

^{3}), respectively. Calculation of apparent activation energy is done based on rearrangement of Equation (1). The derivative $dX/dt$ is determined from the drying curve, i.e., moisture content over time.

^{2}/s), $Re$ is Reynolds number, and $Sc$ is Schmidt number [35]. Activation energy can be linked to the moisture content of the sample as formulated in Equation (3):

^{2}value was used throughout this paper to determine the fitness of the time-series model for the given data set. Equation (5) is used to calculate the R

^{2}:

#### 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

^{−1}), flowrate of air (kgs

^{−1}), droplet temperature (K), and hot air temperature (K), respectively. $Y$ is absolute humidity of air (kg water kg dry air

^{−1}), $\lambda $ is the latent heat of water vaporization (Jkg

^{−1}), ${h}_{h}$ is the heat transfer coefficient (Js

^{−1}m

^{−2}K

^{−1}), $\theta $ is number of particle size and ${A}_{p}$ is the area of the droplet (m

^{2}). ${C}_{p,water}$, ${C}_{p,solid},$ and ${C}_{p,b}$ are the specific heat of water, dried particle, and air (Jkg

^{−1}K

^{−1}), respectively.

^{−2}K

^{−1}), D is diameter of chamber (m), L is length of chamber (m), and ${T}_{amb}$ is ambient temperature (K). Other related equations are listed in Appendix A.

^{®}environment with built-in ODE45 Runge-Kutta method. Variables and properties used in the model are listed in Table 1. Data and values are obtained from experimental work, assumption, and previous studies. The heat capacity of solid is obtained from the differential scanning calorimetry (DSC) analysis of the coconut milk powder.

#### 2.3. Formulation of Empirical Models

#### 2.3.1. NARX Model Development

#### 2.3.2. Neural Network (NN) Estimator Development

^{®}by using Neural Network Toolbox. Neural network with one input layer, one hidden layer, and one output layer was used as network architecture, and inlet temperature, and outlet temperature were selected as the input variables. The output layer consisted of one neuron that is the moisture content of the powder.

#### 2.4. Inferential Controller Design

_{cu}and ultimate period, P

_{u}from trial-and-error of proportional-only controller. The controller performance is evaluated based on percent overshoot, setting time, and rise time.

#### 2.5. Controller Performance

## 3. Results

#### 3.1. Drying Kinetic Model of Coconut Milk Droplet

^{−5}m

^{2}, respectively. Large surface area of droplet and high droplet temperature allow water to evaporate faster as more area is exposed to hot air and water has more energy to escape from the droplet. Normalized relative activation energy, $\left(\Delta {E}_{v}/\Delta {E}_{v,b}\right)$ is calculated and plotted against difference between moisture content to equilibrium moisture content $\left(X-{X}_{b}\right),$ as shown in Figure 4. It can be seen from the graph that minimum energy is required when the droplet has high moisture content. Energy required to remove the water increases as less water is present in the droplet. The relative activation energy correlating to moisture content represented by 4th order polynomial equation (Equation (17)) with REA model fitted with the experimental data with R

^{2}value of 0.9786. R

^{2}> 0.8 indicates good fit of regression equation to observed data [47].

^{2}value of 0.882. The developed kinetic model can be integrated to the one-dimensional model of the spray drying process.

#### 3.2. One-Dimensional Model

^{2}of 1.00. This result is in good agreement with the relation of inlet and outlet temperature of co-current spray dryer studied by George et al. [9]. Slightly nonlinear relation is observed between inlet temperature and moisture content as the data perfectly fit the second order polynomial regression with R

^{2}= 1.00. A similar trend is observed for moisture content obtained from experimental work.

#### 3.3. NARX Model

_{in}) of hot air to outlet temperature of hot air (T

_{out}), while NLARX2 relates inlet temperature of hot air (T

_{in}) to moisture content of powder (MC). The wavelet network was used as nonlinearity estimator. In NARX model development, number of regressors, i.e., the number of past observations samples, play the most important role in capturing the nonlinearity of the system. It was found out that the NARX with one input and output regressor is the most accurate model to represent the process. A similar finding was obtained by Ramesh et al. [51] in NARX model development of distillation column, where one output regressor is sufficient to capture the nonlinearity of the process as its provide linear relation with process nonlinearity. In this study, higher number of regressor is not discussed as it leads to increase in complexity of the model, which consequently reduces the model accuracy. Meanwhile, the input regressor is crucial to be considered as it provides direction to the output.

_{out}(t) = f(T

_{out}(t − 1),T

_{in}(t − 1))

_{in}(t − 1))

#### 3.4. Neural Network Estimator

^{−9}for training and validation phases. It is found out that neural network approach is able to provide high accuracy in predicting the dynamic nonlinear of the spray drying process regardless of network architecture used. This high accuracy is crucial to minimize the error between the estimated moisture content with its actual value as this error became the main contributor to static control offset in inferential control system [52]. It is also found out that NN-NARX models are more accurate compared to NN-N models in predicting the moisture content of the powder with MSE value lower than 4.0 × 10

^{−9}for training and validation phases. It proves that previous output value provides useful insight of the system, therefore it provides better prediction of the model. A similar finding was obtained by Osman and Ramasamy [53] and Singh, et al. [54], where the NARX architecture outperformed other network architectures in soft sensor development using time-series data.

_{out}(t − 1), T

_{in}(t − 1))

#### 3.5. Inferential Control of Moisture Content

_{I}, which leads to fast controller response and fast integral action, respectively.

^{−4}kg/kg. Static offset was observed by Kalbani and Zhang [52] during inferential composition control in distillation column and they found out that this offset can only be eliminated if true value of the variable is known.

#### 3.6. Set Point Tracking

^{−4}kg/kg. Meanwhile, the offset of responses at low set point is less than 3 × 10

^{−4}kg/kg. These results are tabulated in Table 7. This indicates the NN-NARX estimator has high accuracy to predict the moisture content of powder. TL-PI inferential controller outperforms other controller settings by producing a stable response with minimum overshoot at all set points. This is in agreement with error analysis, i.e., ITAE and IAE presented in Table 7. Based on these results, TL-PI inferential controller has the smallest error compared to other tuning rules at all set points with ITAE values less than 6.1 and IAE values less than 0.27. This indicates the good performance of the TL-PI inferential controller in controlling the moisture content of powder. It is also found that all responses create minimal offset with value less than 3 × 10

^{−4}kg/kg.

#### 3.7. Disturbance Rejection

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

#### Correlations Used in REA Model and One-Dimensional Model Development

^{2}/s), which is calculated from Equation (A.4). Reynolds number, $Re$, Schmidt number, $Sc,$ and Prandtl number, $Pr$ is calculated based on Equations (A5)–(A7), respectively [22].

^{3}), ${C}_{p,b}$ is specific heat of air (J/(kg.K)).

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**Figure 4.**Reaction engineering approach (REA) approach fitted to normalized relative activation energy versus moisture content curve.

**Figure 8.**Comparison of experimental data of moisture content (MC) and outlet temperature (Temp) with simulation data.

**Figure 9.**Simulated dynamic profile of outlet temperature (Outlet Temp) and moisture content (MC) of coconut milk powder subjected to multiple step change in the inlet temperature (Inlet Temp).

**Figure 10.**Response of inferential control system for Ziegler Nichols (ZN), Tyreus-Luyben (TL) and Relaxed-Ziegler Nichols (R-ZN) tuning rules. (

**a**) Moisture content, (

**b**) controller output.

**Figure 11.**Response of inferential control system at various set points. (

**a**) Moisture content, (

**b**) controller output.

**Figure 12.**Response of inferential control system for disturbance rejection. (

**a**) Positive deviation and (

**b**) negative deviation.

Variable/Property | Value | Reference |
---|---|---|

${C}_{p,water}$ | 4185 J/kg·K | [39] |

${C}_{p,solid}$ | 1389 J/kg·K | Measured |

${C}_{p,v}$ | 1800 J/kg·K | [39] |

${C}_{p,b}$ | 1000 J/kg·K | [39] |

${d}_{s\text{}}$ | 200 μm | [24] |

${v}_{p}$ | 5 m/s | [40] |

${v}_{a}$ | 100 m/s | [40] |

${R}_{G}$ | 8.314 J/mol·K | [39] |

$\lambda $ | 2501 $\times $ 10^{3} J kg^{−}^{1} | [39] |

${T}_{amb}$ | 300 K | Measured |

${U}_{p}$ | 22.8 W/m^{2}·K | Calculated |

$L$ | 0.5 m | Measured |

$D$ | 0.22 m | Measured |

Variable | Value |
---|---|

Droplet: | |

Moisture content | 2.67 kg/kg |

Temperature | 27 °C |

Flowrate | 9.8 $\times $ 10^{−4} kg/s |

Hot air: | |

Humidity | 0.021 kg/kg |

Temperature | 160 °C |

Flowrate | 0.011 kg/s |

Tuning Rules | $\mathbf{Controller}\text{}\mathbf{Gain},\text{}\mathit{Kc}$ | $\mathbf{Integral}\text{}\mathbf{Time},\text{}{\mathit{\tau}}_{\mathit{i}}$ |
---|---|---|

Zigler-Nichols (ZN) | 0.45 K_{cu} | P_{u} /1.2 |

Tyreus-Luyben (TL) | 0.32 K_{cu} | P_{u} |

Relaxed-Ziegler Nichols (R-ZN) | 0.31 K_{cu} | 2.2 P_{u} |

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, K_{c} | Integral Time (s), τ_{I} |
---|---|---|

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 |

**Table 7.**Integral absolute error (IAE), integral time absolute error (ITAE) and static control offset of inferential controllers for set point tracking.

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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## Share and Cite

**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Abdullah, 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