# Model-Based Predictive Control of a Solar Hybrid Thermochemical Reactor for High-Temperature Steam Gasification of Biomass

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## Abstract

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## 1. Introduction

## 2. Horizon 2020 Project SFERA III

- networking activities to improve the cooperation between the research infrastructures, the scientific community, industries and other stakeholders;
- transnational access activities aiming at providing access to all European researchers from both academia and industry to singular scientific and technological solar research infrastructures;
- joint research activities to improve the infrastructure’s integrated services.

## 3. Modeling of the Solar Reactor

#### 3.1. Description of the Model

- When no oxygen is injected—DNI is higher than 800 Wm${}^{-2}$—only the endothermic gasification of biomass occurs, with an enthalpy change $\Delta {H}_{r}^{o}=143\phantom{\rule{3.33333pt}{0ex}}$kJ mol${}^{-1}$. This reaction is as follows:$$\begin{array}{c}\hfill {\mathrm{CH}}_{1.66}{\mathrm{O}}_{0.69}+0.31{\mathrm{H}}_{2}\mathrm{O}\to \mathrm{CO}+1.14{\mathrm{H}}_{2}\end{array}$$
- When oxygen is injected—DNI is lower than 800 $\mathrm{W}{\mathrm{m}}^{-2}$—combustion occurs in the cavity along with gasification, with an enthalpy change $\Delta {H}_{r}^{o}=-452$ kJ mol${}^{-1}$. Combustion of the biomass resource—the reaction is exothermic—can be described as follows:$$\begin{array}{c}\hfill {\mathrm{CH}}_{1.66}{\mathrm{O}}_{0.69}+1.07{\mathrm{O}}_{2}\to {\mathrm{CO}}_{2}+0.83{\mathrm{H}}_{2}\end{array}$$

_{2}O injection rates. However, it should be mentioned that incomplete conversion may still occur at temperatures lower than 800 ${}^{\circ}$C, whatever the quantity of injected steam [27]. The gas phase is modeled as a mixture of H

_{2}, CO, CO

_{2}, CH

_{4}, H

_{2}O, O

_{2}and Ar, whose properties are given by the NASA GRI-MECH 3.0 database [28]. The elemental chemical composition of the mixture is determined by the wood input flow rate, its moisture fraction (8.9% in weight), and its molecular composition (CH

_{1.66}O

_{0.69}, on a dry basis). The high heating value (HHV) of the reference wood sample, measured by calorimetry, is also provided to compute the corresponding standard enthalpy of formation, enabling the calculation of the inlet flow enthalpy. The outlet flow enthalpy at the reactor’s temperature is directly given by the Cantera function. All these heat transfers are applied to the reactor wall and determine the impact of both DNI variations and chemical inputs on the reactor’s temperature. Thus, the reactor’s temperature can be modeled through the following first-order non-linear ordinary differential which represents the heat balance of the reactor:

#### 3.2. Simulation of the Model

#### 3.2.1. Without Oxygen Injection

#### 3.2.2. With Oxygen Injection

## 4. Control of the Solar Reactor

#### 4.1. Reference (PID/RB) Controller

#### 4.1.1. Adaptive PID Controller for the Oxygen Flow Rate

- ${K}_{p}$ is the proportional gain, helping the controller reach the setpoint faster, with the risk of overshooting; a small value will result in an important steady-state error;
- ${K}_{i}$ is the integral gain, helping to eliminate the steady-state error; a large value can result in a longer settling time and higher oscillations;
- ${K}_{d}$ is the derivative gain, generating a fast response and a stabilizing effect in dynamic regime.

- $\mathrm{DNI}<150\mathrm{W}{\mathrm{m}}^{-2}$: The reactor’s aperture is closed (${A}_{aperture}=0$) to limit radiative losses, which affects the thermal equilibrium of the system. The PID controller manages the system by injecting a minimum of 0.88 th${}^{-1}$ of oxygen.
- $150\mathrm{W}{\mathrm{m}}^{-2}\u2a7d\mathrm{DNI}\u2a7d800\mathrm{W}{\mathrm{m}}^{-2}$: The reactor’s aperture is open, and the amount of DNI received is not sufficient to maintain the reactor’s temperature without oxygen injection. The PID controller determines the oxygen flow rate allowing to minimize the error between the setpoint and the measured temperature.
- $\mathrm{DNI}>800\mathrm{W}{\mathrm{m}}^{-2}$: The excess of DNI forces the PID controller to recommend a minimal oxygen flow rate allowing the reactor to cool down and play on defocusing if the reactor’s temperature is higher than the setpoint.

#### 4.1.2. Rule-Based Controller for the Defocusing Factor

- if $\mathrm{DNI}\left(k\right)>800\mathrm{W}{\mathrm{m}}^{-2}$ and $T\left(k\right)>1473$ K, $D\left(k\right)=800\mathrm{DNI}\left(k\right)$;
- if $\mathrm{DNI}\left(k\right)\u2a7d$ 800 Wm${}^{-2}$ and $T\left(k\right)<1473$ K, $D\left(k\right)=1$.

#### 4.2. MPC Controller

#### 4.3. DNI Forecasting

#### 4.3.1. Database

#### 4.3.2. Smart Persistence Forecasts

#### 4.3.3. Image-Based Forecasts

- An HDR image is processed to detect clouds using a segmentation model and estimate their motion with the aim of localizing the part of the image that will interact with the Sun at time $k+h$. This region is called the region of interest (ROI) in the sequel.
- The cloud fraction (CF) in the ROI (${\mathrm{CF}}_{{\mathrm{ROI}}_{h}}$) is calculated. ${\mathrm{CF}}_{{\mathrm{ROI}}_{h}}$ is defined as the ratio of the number of cloud pixels to the number of clear-sky pixels in the ROI.
- The model decides if a ramp will occur by analyzing the variation of ${\mathrm{CF}}_{{\mathrm{ROI}}_{h}}$ between two consecutive time steps. If this variation is greater than 3% of the maximum value of ${\mathrm{CF}}_{{\mathrm{ROI}}_{H}}$, then a ramp is expected. This value is chosen to avoid ramp detection due to noise in the ${\mathrm{CF}}_{{\mathrm{ROI}}_{H}}$ signal. This approach also determines the ramp’s direction, since an increase in ${\mathrm{CF}}_{{\mathrm{ROI}}_{H}}$ indicates a possible decrease in DNI and vice versa.
- The DNI forecast at time $k+h$ is obtained by a persistence (if no ramp is expected) or a persistence to which the ramp magnitude RM is added (if a ramp is expected):$$\begin{array}{c}\widehat{\mathrm{DNI}}(k+h)=\mathrm{DNI}\left(k\right)+\delta \left(k\right)\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\widehat{\mathrm{RM}}\left(k\right)\end{array}$$$$\delta \left(k\right)=\{\begin{array}{cc}1,\hfill & \mathrm{if}\phantom{\rule{4.pt}{0ex}}\Delta {\mathrm{CF}}_{{\mathrm{ROI}}_{H}}\left(k\right)<-7.65\hfill \\ -1,\hfill & \mathrm{if}\phantom{\rule{4.pt}{0ex}}\Delta {\mathrm{CF}}_{{\mathrm{ROI}}_{H}}\left(k\right)>7.65\hfill \\ 0,\hfill & \mathrm{else}\hfill \end{array}$$

#### 4.3.4. Performance Criteria

- The root mean squared error (RMSE) is calculated as follows:$$\begin{array}{c}\mathrm{RMSE}=\sqrt{\frac{1}{{n}_{obs}}\sum _{k=1}^{{n}_{obs}}{\left(\mathrm{DNI}\left(k\right)-\widehat{\mathrm{DNI}}\left(k\right)\right)}^{2}}\end{array}$$
- The skill factor (SF) is employed to evaluate the models’ performance versus the smart persistence model (a positive skill factor means that the proposed model outperforms the smart persistence model). It is defined as follows:$$\mathrm{SF}=100\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\left(1-\frac{{\mathrm{RMSE}}_{\mathrm{M}}}{{\mathrm{RMSE}}_{\mathrm{SPM}}}\right)$$
- The mean average error (MAE) is calculated as follows:$$\begin{array}{c}\mathrm{MAE}=\frac{1}{{n}_{obs}}\sum _{k=1}^{{n}_{obs}}\left(\mathrm{DNI}\left(k\right)-\widehat{\mathrm{DNI}}\left(k\right)\right)\end{array}$$
- Finally, a criteria called ramp detection index (RDI) is used [45]. It is designed to evaluate the ability of the model to predict ramps, which have an important impact on CSP plants: predicting them can thus be helpful in the control process. First, the ramp magnitude (RM) is calculated as:$$\mathrm{RM}\left(k\right)=\frac{\left|\mathrm{DNI}\left(k\right)-\mathrm{DNI}(k+h)\right|}{{\widehat{\mathrm{DNI}}}_{\mathrm{CS}}\left(k\right)}$$Usually, high-magnitude DNI ramps are defined by $\mathrm{RM}\left(k\right)>0.5$ and moderate DNI ramps are defined by $0.3<\mathrm{RM}\left(k\right)<0.5$. A ramp detection (also called a hit) is achieved if the two following conditions are satisfied:$$\begin{array}{cc}\hfill \mathrm{RM}\left(k\right)& >0.15\hfill \end{array}$$$$\begin{array}{cc}\hfill sign(\mathrm{DNI}\left(k\right)-\widehat{\mathrm{DNI}}(k+h))& =sign\left(\mathrm{DNI}\right(k)-\mathrm{DNI}(k+h\left)\right)\hfill \end{array}$$The chosen $\mathrm{RM}$ value represents ramps with high occurrence probability, thus increasing the challenge of scoring a high RDI by increasing the number of considered ramps in the RDI calculation. The ramp is not detected (a miss) if Equation (20) is met while Equation () is not. Finally, the ramp detection index is calculated as follows:$$\mathrm{RDI}=\frac{{N}_{hit}}{{N}_{hit}+{N}_{miss}}$$

#### 4.3.5. Forecasting Results

## 5. Control Results

#### 5.1. Performance Criteria

#### 5.2. Comparative Study

- $D(k+i)=1\phantom{\rule{0.277778em}{0ex}}\forall i\in \u27e61;n\u27e7$. This initialization is chosen so that the optimal input found is near 1, which means solar energy is used at its best;
- ${f}_{oxygen}^{in}(k+i)=0.5\phantom{\rule{0.277778em}{0ex}}\forall i\in \u27e61;n\u27e7$. This initialization is chosen so that the optimizer converges fast to the optimal solution, which is around $0.5$$\mathrm{t}$${\mathrm{h}}^{-1}$. Other initialization values resulted in an increase in computation time and some performance degradation.

#### 5.3. Case Study

## 6. Computationally-Tractable MPC Controller

#### 6.1. Model Simplification

- for a given reactor’s temperature, ${Q}_{reaction}$ is mainly a linear function of the oxygen flow rate (0 th${}^{-1}$$\u2a7d{f}_{oxygen}^{in}\u2a7d1.8$ th${}^{-1}$);
- for a given oxygen flow rate, ${Q}_{reaction}$ is a linear function of the reactor’s temperature ($1453\mathrm{K}\u2a7dT\u2a7d1493\mathrm{K}$).

#### 6.2. MPC Controller with Simplified Reactor Model vs. MPC Controller with Original Reactor Model

#### 6.3. MPC Controller with Simplified Reactor Model vs. Reference Controller

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Evolution of the reactor’s temperature in response to various DNI steps (the biomass flow rate is set to ${f}_{biomass}^{in}$ = 1.465 th${}^{-1}$ and the initial temperature is 1073 K).

**Figure 3.**Power balance corresponding to the steady state of the DNI steps in Figure 2.

**Figure 4.**Reactor’s temperature in response to sudden DNI variations with nominal design values (T = 1473 K, $\mathrm{DNI}=800\mathrm{W}{\mathrm{m}}^{2}$ and ${f}_{biomass}^{in}=1.465\mathrm{t}{\mathrm{h}}^{-1}$).

**Figure 5.**Evolution of the reactor’s temperature for various biomass flow rates when DNI is equal to $900\mathrm{W}{\mathrm{m}}^{2}$ and corresponding syngas production (dashed line: H

_{2}; solid line: H

_{2}+ CO).

**Figure 7.**Evolution of the reactor’s temperature for various oxygen flow rates and DNI levels (${f}_{biomass}^{in}=1.465$ th${}^{-1}$ and the initial temperature is 1073 K).

**Figure 8.**Evolution of the reactor’s temperature in case of a closed aperture and an oxygen flow rate ${f}_{oxygen}^{in}=0.88$ th${}^{-1}$ (${f}_{biomass}^{in}=1.465$ th${}^{-1}$, and the initial temperature is 1073 K).

**Figure 9.**The reference controller, defined as a combination of an adaptive PID controller with optimized gains (for the oxygen flow rate ${f}_{oxygen}^{in}$) and a rule-based controller (for the defocusing factor D).

**Figure 10.**The MPC controller. The optimizer used is the trust-region constrained algorithm [32].

**Figure 11.**

**Left**: The sky imager installed at the PROMES-CNRS laboratory in Odeillo (France).

**Right**: A high-dynamic-range (HDR) sky image, without correction of the distortion.

**Figure 12.**High-dynamic-range (HDR) sky images and associated sky situations: clear sky, overcast and mixed. Days with mixed situations can be partially clear sky or partially overcast.

**Figure 13.**Global architecture of the proposed forecast model, showing two main blocks: image processing and DNI forecasting. ${\mathrm{CF}}_{{\mathrm{ROI}}_{H}}$ is the cloud fraction in the ROI. The interested reader is referred to [24] for details about the image processing block.

**Figure 14.**Image-based model results: RMSE, SF, MAE, and RDI as a function of the forecast horizon H (test phase).

**Figure 16.**Case study results: MPC controller with perfect DNI forecasts (${MPC}_{\mathrm{PF}}$). The prediction horizon of the controller is 1 min.

**Figure 17.**Case study results: MPC controller with smart persistence DNI forecasts (${MPC}_{\mathrm{SF}}$). The prediction horizon of the controller is $1.5$ min.

**Figure 18.**Case study results: MPC controller with image-based DNI forecasts (${MPC}_{\mathrm{IF}}$). The prediction horizon of the controller is 2 min.

**Figure 19.**Power resulting from the gasification reaction as a function of oxygen flow rate variations (

**left**) and reactor’s temperature variations (

**right**).

**Figure 20.**The computationally tractable MPC controller. The orignial reactor model $\mathcal{M}$ is replaced with the simplified model to solve the optimization problem. The original model $\mathcal{M}$ is still used to perform the simulation.

**Table 1.**First-order dynamic model corresponding to the temperature curves shown in Figure 2.

DNI [Wm${}^{-2}$] | Static Gain [-] | $\mathit{\tau}$ [min] | ${\mathit{T}}_{\mathit{r}}$ [min] |
---|---|---|---|

700 | 0.3 | 31.5 | 69.3 |

800 | 0.5 | 26.3 | 58 |

900 | 0.6 | 23 | 50.6 |

DNI < 150 Wm${}^{-2}$ | 150 Wm${}^{-2}$ ⩽ DNI ⩽ 800 Wm${}^{-2}$ | DNI > 800 Wm${}^{-2}$ | |
---|---|---|---|

${K}_{p}$ | 1.6 × 10${}^{-2}$ | 3.4 × 10${}^{-2}$ | 1.5 × 10${}^{-3}$ |

${K}_{i}$ | 0 | 9.0 × 10${}^{-4}$ | 1.5 × 10${}^{-4}$ |

${K}_{d}$ | 1.2 × 10${}^{-2}$ | 2.5 × 10${}^{-2}$ | 1.0 × 10${}^{-5}$ |

H [min] | Time Support (Observations) | LSTM Layers (Units) | Fully Connected Layers (Units) | |||||
---|---|---|---|---|---|---|---|---|

1st | 2nd | 3rd | 4th | 1st | 2nd | 3rd | ||

0.5 | 8 | 179 | 229 | 204 | 104 | 20 | 5 | 5 |

1 | 8 | 254 | 204 | 219 | 229 | 20 | 5 | ⌀ |

1.5 | 8 | 229 | 54 | 204 | 179 | 5 | 20 | 20 |

2 | 8 | 254 | 104 | 79 | 229 | 5 | 20 | 20 |

2.5 | 8 | 154 | 179 | 104 | 4 | 5 | 5 | ⌀ |

**Table 4.**MPC evaluation, for the three types of DNI forecasts (7-day simulation). RMSE is the root mean squared error. ${m}_{{\mathrm{O}}_{2}}$ is the amount of oxygen injected in the reactor. ATV is the average temperature variation. ${f}_{obj}$ is the objective function value. ${\tau}_{opt}$ is the mean optimization time per time step. Reference performance (PID/RB controller): RMSE = 4.88 K, ${m}_{{\mathrm{O}}_{2}}$ = 31,933 kg and ATV = 2.27 K.

Controller | Performance Criterion | Prediction Horizon of the MPC Controller [min] | ||||
---|---|---|---|---|---|---|

0.5 | 1 | 1.5 | 2 | 2.5 | ||

${MPC}_{\mathrm{PF}}$ | RMSE [K] | 0.451 | 0.073 | 0.075 | 0.078 | 0.078 |

${m}_{{\mathrm{O}}_{2}}$ [kg] | 31,945.55 | 31,968.33 | 31,964.17 | 31,988.02 | 31,959.63 | |

$\mathrm{ATV}$ [K] | 0.018 | 0.031 | 0.032 | 0.034 | 0.036 | |

${f}_{obj}$ | −42,139.13 | −48,657.01 | −48,653.24 | −48,549.71 | −48,559.12 | |

${\tau}_{opt}$ [s] | 1.5 | 5.0 | 10.0 | 15.0 | 30.0 | |

${MPC}_{\mathrm{SF}}$ | RMSE [K] | 1.92 | 1.79 | 1.71 | 1.72 | 1.71 |

${m}_{{\mathrm{O}}_{2}}$ [kg] | 32,080.55 | 32,074.03 | 32,089.23 | 32,075.459 | 32,090 | |

$\mathrm{ATV}$ [K] | 1.50 | 1.47 | 1.542 | 1.58 | 1.47 | |

${f}_{obj}$ | 74,260.74 | 56,858.36 | 48,620.45 | 49,702.90 | 48,638.47 | |

${\tau}_{opt}$ [s] | 1.0 | 4.6 | 9.7 | 14.5 | 29.0 | |

${MPC}_{\mathrm{IF}}$ | RMSE [K] | 1.88 | 1.72 | 1.64 | 1.60 | 1.61 |

${m}_{{\mathrm{O}}_{2}}$ [kg] | 32,142 | 32,058.87 | 32,063.25 | 32,091.25 | 32,143.56 | |

$\mathrm{ATV}$ [K] | 3.0 | 1.45 | 1.46 | 1.54 | 1.47 | |

${f}_{obj}$ | 68,903 | 49,334.44 | 40,786.92 | 36,446.05 | 37,996.54 | |

${\tau}_{opt}$ [s] | 1.5 | 5.0 | 10.0 | 15.0 | 30.0 |

**Table 5.**MPC evaluation: simplified reactor model vs. original reactor model $\mathcal{M}$ for the three types of DNI forecasts (7-day simulation). RMSE is the root mean squared error. ${m}_{{\mathrm{O}}_{2}}$ is the amount of oxygen injected in the reactor. ATV is the average temperature variation. ${f}_{obj}$ is the objective function value. ${\tau}_{opt}$ is the mean optimization time per time step.

Controller | Performance Criterion | Prediction Horizon of the MPC Controller (min) | ||||
---|---|---|---|---|---|---|

0.5 | 1 | 1.5 | 2 | 2.5 | ||

${MPC}_{\mathrm{PF}}$ with simplified reactor model | RMSE (K) | 0.49 | 0.10 | 0.10 | 0.11 | 0.11 |

${m}_{{\mathrm{O}}_{2}}$ (kg) | 31,956 | 31,961 | 31,965 | 31,972 | 31,979 | |

$\mathrm{ATV}$ (K) | 0.04 | 0.05 | 0.05 | 0.05 | 0.05 | |

${f}_{obj}$ | −40,831.19 | −48,508.93 | −48,500.45 | −48,493.56 | −48,487.42 | |

${\tau}_{opt}$ (s) | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | |

${MPC}_{\mathrm{PF}}$ with original reactor model $\mathcal{M}$ | RMSE (K) | 0.451 | 0.073 | 0.075 | 0.078 | 0.078 |

${m}_{{\mathrm{O}}_{2}}$ (kg) | 31,945.55 | 31,968.33 | 31,964.17 | 31,988.02 | 31,959.63 | |

$\mathrm{ATV}$ (K) | 0.018 | 0.031 | 0.032 | 0.034 | 0.036 | |

${f}_{obj}$ | −42,139.13 | −48,657.01 | −48,653.24 | −48,549.71 | −48,559.12 | |

${\tau}_{opt}$ (s) | 1.5 | 5 | 10 | 15 | 30 | |

${MPC}_{\mathrm{SF}}$ with simplified reactor model | RMSE (K) | 2.01 | 1.97 | 1.74 | 1.73 | 1.74 |

${m}_{{\mathrm{O}}_{2}}$ (kg) | 32,043 | 32,093 | 32,137 | 32,152 | 32,106 | |

$\mathrm{ATV}$ (K) | 1.60 | 1.50 | 1.50 | 1.49 | 1.50 | |

${f}_{obj}$ | 85,065.71 | 80,101 | 51,807 | 51,350 | 51,652.50 | |

${\tau}_{opt}$ (s) | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | |

${MPC}_{\mathrm{SF}}$ with original reactor model $\mathcal{M}$ | RMSE (K) | 1.92 | 1.79 | 1.71 | 1.72 | 1.71 |

${m}_{{\mathrm{O}}_{2}}$ (kg) | 32,080.55 | 32,074.03 | 32,089.23 | 32,075.459 | 32,090 | |

$\mathrm{ATV}$ (K) | 1.50 | 1.47 | 1.542 | 1.58 | 1.47 | |

${f}_{obj}$ | 74,260.74 | 56,858.36 | 48,620.45 | 49,702.90 | 48,638.47 | |

${\tau}_{opt}$ (s) | 1 | 4.6 | 9.7 | 14.5 | 29 | |

${MPC}_{\mathrm{IF}}$ with simplified reactor model | RMSE (K) | 1.97 | 1.89 | 1.64 | 1.62 | 1.63 |

${m}_{{\mathrm{O}}_{2}}$ (kg) | 32,102 | 32,081 | 32,114 | 32,126 | 32,146 | |

$\mathrm{ATV}$ (K) | 3.10 | 1.47 | 1.47 | 1.47 | 1.47 | |

${f}_{obj}$ | 80,943 | 69,440 | 41,032.92 | 38,072 | 40,028 | |

${\tau}_{opt}$ (s) | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | |

${MPC}_{\mathrm{IF}}$ with original reactor model $\mathcal{M}$ | RMSE (K) | 1.88 | 1.72 | 1.64 | 1.60 | 1.61 |

${m}_{{\mathrm{O}}_{2}}$ (kg) | 32,142 | 32,058.87 | 32,063.25 | 32,091.25 | 32,143.56 | |

$\mathrm{ATV}$ (K) | 3.00 | 1.45 | 1.46 | 1.47 | 1.47 | |

${f}_{obj}$ | 68,903 | 49,334.44 | 40,786.92 | 36,446.05 | 37,996.54 | |

${\tau}_{opt}$ (s) | 1.5 | 5 | 10 | 15 | 30 |

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## Share and Cite

**MDPI and ACS Style**

Karout, Y.; Curcio, A.; Eynard, J.; Thil, S.; Rodat, S.; Abanades, S.; Vuillerme, V.; Grieu, S. Model-Based Predictive Control of a Solar Hybrid Thermochemical Reactor for High-Temperature Steam Gasification of Biomass. *Clean Technol.* **2023**, *5*, 329-351.
https://doi.org/10.3390/cleantechnol5010018

**AMA Style**

Karout Y, Curcio A, Eynard J, Thil S, Rodat S, Abanades S, Vuillerme V, Grieu S. Model-Based Predictive Control of a Solar Hybrid Thermochemical Reactor for High-Temperature Steam Gasification of Biomass. *Clean Technologies*. 2023; 5(1):329-351.
https://doi.org/10.3390/cleantechnol5010018

**Chicago/Turabian Style**

Karout, Youssef, Axel Curcio, Julien Eynard, Stéphane Thil, Sylvain Rodat, Stéphane Abanades, Valéry Vuillerme, and Stéphane Grieu. 2023. "Model-Based Predictive Control of a Solar Hybrid Thermochemical Reactor for High-Temperature Steam Gasification of Biomass" *Clean Technologies* 5, no. 1: 329-351.
https://doi.org/10.3390/cleantechnol5010018