Experimental Performance of a Nonlinear Control Strategy to Regulate Temperature of a High-Temperature Solar Reactor

Solar fuels are energy carriers in which solar energy can be converted into a storable and transportable form. Utilizing concentrated solar energy allows for the production of solar fuel since the solar energy is stored by the reactants through thermochemical endothermic processes. A number of studies have been conducted to investigate various thermochemical energy storage candidates. However, the utilization of thermochemical energy storage system is constrained by the charging/discharging temperature range, volumetric energy, and the number of reuse cycles (lifetime) [1]. The charge/discharge temperature range in thermochemical energy storage systems depends on the chemical nature of the reactant used. For instance, the temperature range for the dehydration of metal hydroxides is 250–800 °C, whereas the temperature range is 100–950 °C for the decarboxylation of metal carbonates [2]. At higher temperatures, MgMn₂O₄ reacts between 1000 °C and 1500 °C [3].

Solar reactors are utilized for the thermochemical storage of solar energy, where concentrated solar energy is used to directly transfer heat to reactants through a window or indirectly transferred using a windowless reactor. The selection of a suitable solar reactor type is crucial in ensuring an effective chemical conversion process in a solar-driven high-temperature thermochemical reaction system. While window-type solar reactors are commonly used for low temperatures [4], a windowless plug-flow tubular solar reactor is preferred for high-temperature thermochemical reactions due to the melting point of reactor window components. In this type of reactor, the reactants are heated as a result of direct concentrated solar flux irradiation of the reactor tube wall, which is contained within a receiver cavity. In plug-flow tubular solar reactors, the chemical conversion process requires a flowing gas through the reactor tube and a steady-state activation temperature to ensure an efficient conversion process.

Maintaining a quasi-temperature within the reactor during on-sun operation is challenging due to the transitory nature of solar energy. Therefore, it is necessary to develop an effective control system to regulate the temperature consistently. To design an effective control system, it is essential to pre-evaluate the control system through a numerical model to reduce effort, time, and cost. The numerical analysis of a solar reactor, including flowing media and complex heat transfer modes, is not straightforward. However, a simplified numerical model is preferable for control purposes.

Indirectly heated packed-bed reactors are numerically analyzed using the finite volume method [5,6], while moving beds in tubular solar reactors are modeled as tubes exposed to an external heat flow with more complicated parameters [7]. The heat transfer interaction between granular flows was the basis for the thermal analysis of gravity-driven granular flow [8]. Recently, Huang et al. [9] developed a computational fluid dynamics (CFD) model to characterize the thermal properties of a 1D model plug-flow tubular reactor used for thermochemical energy storage system with counter-current flowing pellet-gas. The analysis of the 1D model was further extended to analyze 2D numerical model for the same system, where the numerical accuracy was enhanced compared to the 1D model [10]. In general, a thorough 2D or 3D CFD models are required to simulate two-phase flow problems to the acceptable level of accuracy.

The temperature inside the solar reactor can be controlled by adjusting the incoming direct normal irradiance (DNI) received by the reactor, or by adjusting the flowrates of gas/reactants. Using a variable size aperture to adjust the incoming DNI has proven to be an effective approach in cavity-type solar receivers [11]. Aiming the heliostats is another method to adjust the DNI by implementing a conventional proportional integral derivative (PID) controller, where the reactor temperature can be regulated [12]. Using model-based feedforward, the performance of the PID controller can be enhanced to control the temperature effectively in solar direct steam generation [13]. A simple form of proportional integral (PI) controller has also been implemented to regulate the temperature of a packed-bed tubular solar reactor [14].

Manipulating the gas flow is another approach to regulating the temperature in steam gasification of petcoke and carbothermal reduction [11]. Nevertheless, more advanced control methodologies, such as model predictive control (MPC) strategy, are preferred for systems with high nonlinearity, such as thermochemical reaction kinetics. This is because the production of solar fuel is a complicated dynamic process that involves multiple variables, including gas flow, solar fuel mass flowrate, and solar flux. Although the MPC controller has been shown to be a successful method for controlling the temperature of solar reactors, it involves more computational effort and optimization than a linear traditional PID controller [15].

In our previous works, we investigated the dynamics of a plug-flow tubular solar reactor used to produce MgMn₂O₄ solar fuel. Our earlier work [16] focused on developing a simplified physical model that was used to predict the temperature distribution along a horizontal tube solar reactor during the heating and cooling processes. The results from the numerical code demonstrated reasonable accuracy in the prediction of thermal performance for different operation conditions. The results from the low-order physical model were then used to design a PI control system to regulate the temperature inside a horizontal tube with packed bed [14]. The numerical analysis was extended to include a more complicated heat transfer model to study the dynamics of a high-temperature vertical tubular reactor with counter-current flowing pellet-gas. The system consists of a vertically oriented tubular reactor surrounded by heating elements at one segment, with the MgMn₂O₄ pellets fed from the top end through a funnel, and the gas was supplied from the bottom end. The sensible heat of the downward-moving pellets is recovered by a counter-current air flow, resulting in gas and pellets entering and leaving the reactor tube at temperatures close to room temperature. The inhouse code was tested under different operating conditions, including different particle/gas mass flowrates and heating levels. The numerical results showed excellent agreement between simulated and experimental data [17].

The low-order physical model was implemented to design a model-based combined PID controller, which was numerically tested to track different setpoints by simulating various weather conditions [15]. In our recent work [18], we used the inhouse code to evaluate another model-based control strategy, including an adaptive model predictive controller, to control the temperature inside a tubular plug-flow solar reactor. The results from the numerical code were used to improve the controller's performance by incorporating an updated algorithm to estimate controlling states via a system identification procedure. The performance of the proposed adaptive MPC was simulated to track different temperature setpoints and different operating conditions, including the chemical reaction at high temperatures.

In this work, the numerical control models presented in Refs. [17,18] were experimentally validated for the same vertical tubular reactor with different heating levels and particle/gas mass flowrates. The PID and MPC controllers were tested to track a steady-state setpoint of 1450 °C during the production of 5 kg of reduced solar fuel MgMn₂O₄ particles. The PID control system utilized a gain scheduling approach to model the system nonlinearity, while the MPC controller utilized a system identification process to estimate the measured temperature online by incorporating adaptive loop within the numerical code. The experimental methodology is presented in Sec. 2, the design of control systems is presented in Sec. 3, and the experimental results discussed in Sec. 4.

This research includes experimental testing to evaluate the performance of nonlinear control strategies used for regulating the temperature inside a solar reactor that features counter-current flowing gas and solid particles. The solar reactor is utilized in the production of a solid-state solar fuel MgMn₂O₄ by heating the reactor up to 1500 °C.

The thermal characteristics of the reactor were thoroughly studied in our previous works [14,16] by validating a simplified 1D heat transfer model under different operating conditions. The temperature inside the solar reactor can be controlled by adjusting the incoming solar power or the flowrate of the fluid/gas passing through the reactor. Numerical models of PID and MPC were successfully tested in our recent works [17,18]. The experimental setup consists of a reactor unit, control system, data acquisition (DAQ), and power supply unit. The reactor consists of a 152.4 cm in length alumina tube centered vertically through a 30.5 cm heating zone.

The reactor tube is heated circumferentially via a heat flux controlled by an adjustable power supply. The reactor tube receives MgMn₂O₄ particles of 3–3.66 mm in size from a funnel mounted at the top end of the tube. A gas-pulsation valve mechanism is installed at the bottom end of the reactor tube to control the particle's mass flowrate, and the discharged particles were collected inside a tank beneath the setup. The gas flowrate is controlled by a digital Alicat gas flow controller, with the gas flows in a counter-current orientation from bottom to top.

The counter-current flowing gas is utilized to recuperate the sensible heat of the downward flowing pellets using $(cpsm˙s=cpgm˙g)$⁠. A B-type thermocouple is installed at the center of the heating zone, and the measured temperature is received by DAQ USB-6343 from National Instruments to be analyzed by the control model deployed on labview software by NI^™. The output from the control system is fed to an silicon controlled rectifiers (SCR) power supply unit through the DAQ. The SCR power supply unit receives a signal of 4–20 mA whereas, the DAQ unit provides a voltage signal of 0–5 V. Therefore, a voltage-to-current converter module is used to link the DAQ output to a digital SCR input. Since the heat recuperation condition was considered, the amount of gas and particles mass flowrates are interrelated to maintain this condition. Hence, the signal provided from the DAQ to the flow controllers can be split via a proportional constant K, as shown in Fig. 1(a).

The control system consists of two controllers: A controller to regulate the input heat flux, whereas the other controller adjusts the particles mass flowrate, as shown in Fig. 2. To maintain the heat recuperation condition, mass flowrates of the gas and particles are interrelated, which technically requires one controller. The flow controller is an incremental controller with a fixed value of mass flow increment, and it is to be activated when the heat flux controller is saturated or fails to track the desired setpoint due to insufficient input power.

The experiment tests included the tuning processes and final testing of both PID and MPC controllers as follows:

First, the PID controller's parameters were tuned experimentally by heating the system with a packed bed from room temperature to 800 °C with a heating rate of 5.5 °C/min and a sampling time of 1 s. At the beginning of the heating process, the response temperature error fluctuated, and the tuning process was challenging due to the thermal inertia (transient) of the reactor block. However, the response tended to stabilize, and the controller accurately tracked the desired setpoint until the end of the test, as shown in Fig. 4(a). The controller parameters were obtained as K_P = 0.87, K_I = 0.0076, and K_D = 2.1 × 10⁻⁶. Although the temperature response was relatively smooth when the suitable controller parameters were specified (when T > 400 °C), the control input was relatively aggressive and severely fluctuated during the heating process, as depicted in Fig. 4(b). This was attributed to the limited response of the PID and the computational effort due to the value of the sampling time where the response of the SCR power supply alternates within high voltage range leading to significant fluctuates in power supply and hence temperature output fluctuates as well. One more test was performed to ensure the readiness of the PID controller and observe the possibility of using a smaller sampling time as shown in Fig. 5.

The controller was tested to track different setpoints including steady-state at 400 °C, heating up to 500 °C, and cooling down to 400 °C, as shown in Fig. 5, with a sampling time of 0.5 s. It can be noticed that the control system tracked the desired setpoints reasonably, and the input signal is less aggressive when compared to the process with a sampling time of 1 s (Fig. 4). Therefore, minimizing the sampling time is the key to obtaining a smoother response and less control effort.

It was noticed that the PID controller operates accurately with a slight change in the values of controller parameters depending on the operating condition. This is expected, as the reactor system involves inherent nonlinearities resulting from temperatures with higher order in addition to the nonlinearity from reaction kinetics, in addition to the strong nonlinearity associated with the thermochemical reaction of MgMn₂O₄. Therefore, it is practically suitable to implement gain scheduling technique with gain values close to the ones obtained from experimental tuning. With that said, the PID controller was challenged to regulate the temperature inside the reactor over a period of 3 h, including 90 min, which is enough to produce more than 5 kg of the solar fuel (charged particles).

Figure 6 illustrates the temperature response and corresponding input power during the production of solar fuel. The system was heated from room temperature to 1000 °C with a packed bed. Thereafter, the flow of gas/particles was initiated with a particle mass flowrate of 1.25 g/s and gas flowrate of 60 SLPM (Nitrogen). Meanwhile, the system was continuously heated up to 1450 °C with a heating rate of 4.5 °C/min and held steady for 80 min. The PID controller closely tracked the desired setpoint and handled the system nonlinearity in the presence of the thermochemical reaction, with small steady-state error and reasonable overshoot. Also, the large variations in the input power were significantly reduced by decreasing the sampling time to 50 ms, indicating a quick controller response.

The MPC controller was experimentally tuned and tested to track setpoints similar to those used in testing the PID controller. The MPC utilizes a system identification block coded within the MPC loop to estimate the system states online during the control process. Figure 7 illustrates a comparison between the experimentally measured temperature and the estimated temperature obtained by the system identification algorithm as shown in the magnified subplot. Despite the inconsistent and strongly fluctuating nature of the measured temperature, the numerically estimated temperature is very accurate and almost identical to the measured temperature, accurately simulating its behavior over time.

The final test of the MPC controller involved tuning the MPC parameters N_p, N_u, and ω to minimize the cost function in Eq. (11) and the results are illustrated in Fig. 8. The results showed that the optimal control action was achieved when N_p = 103, N_u = 100, and ω = 82. Similar to the PID controller, the MPC was challenged to regulate the temperature inside the reactor during the production of the solar fuel with a sampling time of 50 ms, and 0.75 g/s particle flowrate, and 36 SLPM gas flowrate. The controller tracked the desired setpoint (1450 °C) successfully and handled the system nonlinearity during the thermochemical reaction. Moreover, the overshoot in the measured temperature is 15% for the MPC, which is less than the overshoot observed in the PID controller (25%). The robustness of the MPC controller was also tested by suddenly increasing the particle's mass flowrate to 1 g/s during the steady-state, causing a sudden drop in temperature. The MPC increased the input power accordingly and brought the temperature back to the setpoint (1450 °C). The measured temperature for the MPC controller tends to show high oscillations in measured temperature due to the malfunction in the thermocouple connection during the process.

The last test was conducted to evaluate the performance of the flow controller by simulating the transient nature of solar power as shown in Fig. 9. The system was heated up to 1400 °C and held steady with a particle flowrate of 1.25 g/s and corresponding input power of around 1900 W. The input power is lowered to a constant value of 1800 W, and the flow controller was initiated to reduce the mass flowrate, heating up the reactor and bringing the temperature back to the setpoint until the mass flowrate converged to 0.92 g/s and the temperature was close to 1400 °C. To further test the flow controller, it was switched off, and the mass flowrate was increased to 2.5 g/s and maintained at that value for approximately 10 min until the temperature decreased by more than 30 °C. Once the flow controller was switched on, it began regulating the flowrate gradually until the temperature was brought back to the setpoint.

In this work, two control strategies were tested experimentally to regulate the temperature in a high-temperature tubular solar reactor that is used to produce solid-state solar fuel as a long-term thermal storage. The experimental setup consisted of a solar reactor unit housing a vertically oriented tubular reactor that is heated circumferentially via electric heaters. The inert particles are fed to the reactor tube from the top and the counter-current flowing gas is supplied to the tube from the bottom. The temperature of the reactor tube at the heating zone is measured and fed to the PC through a DAQ unit. The input signal is then analyzed numerically by control algorithms, and the control decision is fed to an SCR power supply unit to regulate the input power received by the electric heater or fed to the flow controller. First, a conventional PID controller was used with a gain scheduling method to regulate the temperature during the nonlinear process. Second, an MPC with a system identification block was used to estimate the system state online. Both control systems were tested to track ramping temperature and maintain steady-state temperature at 1450 °C to produce 5 kg of charged solar fuel. Both control strategies showed good tracking ability and quick response where the sampling time is 50 ms. The maximum steady-state error was <0.5% (6 °C) for all tests. Although both control strategies showed similar performance, the MPC had required less input power to achieve the desired output and better at handling the sudden disturbances compared to the PID. The flow controller was also tested by applying constant input power to simulate cloudy weather. The flow controller was able to regulate the temperature by adjusting the amount of particle/gas mass flowrates. The proposed control strategies showed very fast response with a small sampling time of 50 ms and can be successfully implemented in high-temperature solar applications.

This material is based upon work supported by the U.S. Department of Energy's Office of Energy Efficiency and Renewable Energy (EERE) under the Solar Energy Technology Office (SETO) Award Number DE–EE0008992. The authors would like to express great appreciation to Kelvin Randhir Michael Hayes and Philipp Schimmels for their support and collaboration in this work.

There are no conflicts of interest.

The authors attest that all data for this study are included in the paper.

c_p =

specific heat (J/kg/K)

D_i =

tube inner diameter (m)

D_o =

tube outside diameter (m)

N_p =

prediction horizon

N_u =

control horizon

Q_in =

input power at heating zone (W)

q″ =

heat flux (W/m²)

q⁻¹ =

backward shift operator

n_a, n_b =

polynomial orders for A and B

K_D, K_p =

coefficients of the PI controller

τ₁ =

coefficient of the PI controller