Gain-Scheduling Model Predictive Control of a Fresnel Collector Field

This is a repository copy of. “Gain-scheduling model predictive control of a Fresnel collector field” in the Depósito de Investigación de la Universidad de Sevilla Version: Author Accepted Version Citation: Antonio J. Gallego, Gonzalo M. Merello, Manuel Berenguel & Eduardo F. Camacho. “Gain-scheduling model predictive control of a Fresnel collector field”. Control Engineering Practice – ISSN 0967-0661. Vol.:82, pp. 1-13. Enero 2019. 10.1016/j.conengprac.2018.09.022 To cite this publication, please use the final published version (if applicable). Please check the document version above. Copyright: Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy: Please contact us ([email protected]) and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim Gain-Scheduling Model Predictive Control of a Fresnel Collector Field Antonio J. Gallegoa, Gonzalo M. Merelloa, Manuel Berenguelb, Eduardo F. Camachoa aDepartamento de Ingenier´ ıa de Sistemas y Autom´ atica, Universidad de Sevilla, Camino de los Descubrimientos s/n., 41092 Sevilla, Spain bCentro Mixto CIESOL, ceiA3, Departamento de Inform´ atica, Universidad de Almer´ ıa. Ctra. Sacramento s/n, 04120, Almer´ ıa, Spain Abstract Model predictive control strategies have been applied successfully when controlling solar plants. If the control algorithm uses a linear model associated only to an operating point, when the plant is working far from the design conditions, the performance of the controller may deteriorate. In this paper, a gain scheduling model predictive control strategy is designed for the Fresnel collector field located at the Escuela Superior de Ingenieros de Sevilla. Simulation results are provided comparing the proposed strategy with another linear MPC controller showing a better performance. Furthermore, two real tests are presented showing the effectiveness of the proposed strategy. Keywords: Solar energy, Fresnel collector, Gain Scheduling, Model Predictive Control 1. Introduction Interest in renewable energy sources such as solar energy experienced a great impulse after the Big Oil Crisis in the 70s. Driven mainly by economic factors, this interest decreased when oil prices fell. Nowadays, there is a renewed interest in renewable energies spurred by the need to reduce the environmental impact produced by the use of fossil energy systems (Goswami et al. (2000); Camacho and Berenguel (2012)). Solar energy is, by far, the most abundant source of renewable energy. In fact, wind and most of the hydraulic energies come from solar energy (Camacho and Gallego (2013)). Many solar energy plants have been commissioned in the last 15 years. The three 50 MW Solnova and the two 50 MW Helioenery parabolic trough plants of Abengoa in Spain can be mentioned as examples, as well as the SOLANA and Mojave Solar parabolic trough plants constructed in Arizona and California, each of 280 MW power production (Yield (2017)). Examples of solar tower plants are plants PS10 and PS20 in Southern Spain of 10 MW and 20 MW respectively. In 2016, the 50 MW solar tower plant Khi Solar One operated by Abengoa Solar was commissioned in South Africa (Abengoa (2017)). Email addresses: [email protected] (Antonio J. Gallego), [email protected] (Gonzalo M. Merello), [email protected] (Manuel Berenguel), [email protected] (Eduardo F. Camacho) 1phone/fax number: +34 954487347 One of the main applications of solar energy is the production of electricity. For example, in parabolic trough plants the solar radiation coming from the sun is focused onto a metal tube where a fluid is circulating. The fluid is heated up and then used in a steam generator to produce electricity (Camacho et al. (1997);Camacho et al. (2011)). Another application of solar energy is the supply of air conditioning in buildings. The interest in solar cooling systems has been increasing for several decades, driven by the fact that the need for air conditioning is usually well correlated to solar radiation (Sonntag et al. (2008);Kima and Infante-Ferreira (2008)). This paper deals with the control of a Fresnel collector field which belongs to the solar cooling plant located on the roof of the Engineering School (ESI) of Seville (Bermejo et al. (2010)). The plant was commissioned in 2008, consisting of a Fresnel collector field, a double effect LiBr+ water absorption chiller and a storage tank. The Fresnel collector delivers pressurized water at 140-170 °C to the absorption machine for producing air conditioning. If solar radiation is not high enough for heating the water up to the required temperature, the storage tank may be used. If neither the solar field nor the storage tank are able to heat up the water to the operation temperature, the absorption machine must resort to burning natural gas. In (Witheephanich et al. (2013);Witheephanich. et al. (2014)) possible control approaches for this kind of plant are discussed, showing simulation results of the Preprint submitted to Control Engineering Practice September 20, 2018 application of an explicit model predictive control. Similar facilities have been deployed in other places (D¨ oll et al. (2014);Zhou et al. (2017)). Regarding similar applications for buildings, in (Berger et al. (2012)) a prototype of a linear Fresnel collector providing the driving heat at temperatures up to 200 °C for two cascading ammonia water absorption chillers is presented, including some experimental tests defocusing collectors. In (H¨ aberle et al. (2007)), a linear concentrating Fresnel collector is used to drive an NH3-H20 absorption chiller, without including control issues. Fresnel collectors are also used to feed an Organic Rankine Cycle with storage in Rodat et al. (2014). The solar plant is simulated using both oil and water/steam as heat transfer fluid. Simulations with Dymola using Modelica code are provided. Operating experiences are included in Rodat et al. (2015) using cascade PI control and a reference governor. An interesting application of building integration of Fresnel concentrators for solar cooling applications can be found in Chemisana et al. (2013). The control objective in this kind of plant is to maintain the outlet temperature of the solar field around a desired set-point (Berenguel et al. (2005)). Many works related to the control of solar plants have been developed and published since 1980. Most of them were tested in the parabolic trough ACUREX solar collector field. This trough plant consisted of a field of solar collectors, a heat storage system and an electrical conversion unit (0.5 MW Stal Laval turbine) (Carmona (1985)). In (Camacho et al. (2007);Camacho et al. (2007b);Rubio et al. (2006)) a review of different control strategies applied to the ACUREX plant is presented. Moreover, the books by Camacho and coworkers (Camacho et al. (2012)) and Lemos and coworkers (Lemos et al. (2014)) overview different approaches related to predictive and adaptive control of this kind of system. Since a solar collector field is affected by multiple disturbance sources and its dynamics change strongly with the operating conditions (Pin et al. (2007)), conventional linear control strategies do not perform well throughout the entire range of operation, thus requiring the application of nonlinear control strategies many of them treated in Camacho et al. (2012) and Lemos et al. (2014). In this paper a gain scheduling generalized model predictive control (henceforth GS-GPC) for a Fresnel plant is developed. Gain scheduling is a control technique where process dynamics can be associated to the value of some process variables related, in this case, to the operating point, so that the controller parameters can be computed from these variables. In Camacho et al. (2007b), there is a section devoted to gain scheduling summarizing the main approaches already used in the field, mainly using the actual oil flow as scheduling variable. Regarding MPC, different control approaches have also been applied in this scope and summarized in Camacho et al. (2007b), Camacho et al. (2012) and Lemos et al. (2014). As recent examples, with applications to the ACUREX field, in Limon et al. (2008) a robust MPC for tracking was designed, while in Gallego et al. (2013), an observer based MPC was developed and tested. Andrade et al. (2013) developed a practical nonlinear MPC. More recently, in Khoukhi et al. (2015) a nonlinear continuous time generalized predictive control (GPC) is developed and tested only in simulation. The main contribution of this paper is the development of a gain scheduling model predictive control for a Fresnel collector field. The approach is similar to that proposed in Camacho et al. (1994) for a parabolic trough solar field. However there are some significant differences which are listed below: 1. The model developed is different because the controller is applied to a different type of plant. This plant is based on a Fresnel collector and not on a parabolic trough and uses water as heat transfer fluid instead of oil. 2. In the approach developed in Camacho et al. (1994), the unconstrained GPC problem was solved for 4 values of the flow. The controller gains were obtained for these four points and the control scheme interpolated the controller gains. In the MPC controller developed in this paper, the interpolation is done for the parameters of the linear model not for the solution of the GPC problem. Furthermore, the approach proposed in Camacho et al. (1994) does not solve a constrained GPC problem, as in this case. The main drawback of using the interpolation between the controller parameters is that it provides an approximation to the global solution of the optimization problem, but for the unconstrained case. It uses the explicit solution of the GPC problem for the four considered points and interpolates among them. The approach used here, interpolating between the linear model parameters allows constraints in the GPC optimization problem to be taken into account in an easy way, and to be solved using a QP algorithm. A simulation to compare the performance of the two approaches (for the unconstrained case) has been included. The one proposed here performs 2 Table 1: List of Abbreviations GPC Generalized Model Predictive Control GS-GPC Gain-Scheduling Model Predictive Control HTF Heat Transfer Fluid ISE Integral of the Square Error ITAE Integral of Time multiplied by Absolute Error MF-GPC Medium-Flow Generalized Model Predictive Controller MPC Model Predictive Control PCM Phase Change Material PDE Partial Differential Equation PRBS Pseudo random binary sequence slightly better as is shown in section 5. 3. Additionally, the unconstrained GPC problem has been solved for several water flow levels considering the actual linear model associated to every point (obtained by a least square identification method). The evolution of some of the optimal controller parameters is compared to the evolution obtained by the approach presented here and the one proposed in Camacho et al. (1994). The approach proposed here is closer to the optimal evolution, especially at low flow levels. 4. Moreover, in this paper an estimation of the efficiency loss produced by the miscalibrated mirrors is carried out for the real tests. This estimation is useful for the feedforward controller which uses a better optical efficiency estimation. The GS-GPC control strategy developed in this paper is tested using a nonlinear distributed parameter model and compared to a GPC designed for medium flow conditions (MF-GPC), showing its advantages. Two real tests carried out at the actual plant are also shown and discussed. The paper is organized as follows: section 2 briefly describes the solar cooling plant. Section 3 presents the mathematical model of the Fresnel collector field used in this paper. Section 4 describes the design process of the proposed control strategy. Section 5 presents the simulation results and the real tests performed at the actual plant. Finally, section 6 draws to a close with concluding remarks. 2. Brief plant description The solar cooling plant was commissioned in 2008 and consists of three subsystems: the double-effect LiBr+ water absorption chiller of 174 kW nominal cooling capacity. The solar Fresnel collector field which heats up the pressurized water and delivers it to the water absorption chiller. The PCM storage tank which helps to supply energy to the water to reach the required operation temperature whenever the solar field is not able to reach it. Figure 1 shows the scheme of the whole plant. Figure 1: Plant general scheme Water absorption chiller: this is a double-effect cycle LiBr+ absorption machine with 174 kW and a theoretical COP of 1.34, which transforms the thermal energy (hot water at 140-170 °C) coming from the Fresnel solar field or the PCM storage tank, into cold water to be used by the ESI of Seville Bermejo et al. (2010). Apart from the hot water, a cooling fluid for the condenser is needed in the absorption machine. This is obtained from the water catchment of the Guadalquivir river. Solar Field: the solar field consists of a set of Fresnel solar collectors (see Figure 2) which concentrate solar radiation onto a line where a 64 m long absorption tube is located. The energy is transferred to a heat transfer fluid (in this case, pressurized water). PCM storage tank: the PCM storage is a 18 metre long shell-tube heat exchanger with a 1.31 metre diameter (Figure 3). It consists of a series of tubes containing a heat transfer fluid and PCM fills in the space between the tubes and the shell. The storage tank uses a hydroquinone as a PCM because the melting temperature is about 170 °C, which is suitable for the water absorption chiller operational range (145-170 °C). 3. Mathematical modeling of the Fresnel collector field In this section, the mathematical model of the solar collector field is presented. The equations governing the 3 Figure 2: Fresnel collector field Figure 3: PCM storage tank system dynamics are similar to those used in the case of the parabolic trough fields (Carmona (1985)). The difference relies on the computation of the geometrical efficiency and the shade factor. In (Pino et al. (2013)), the experimental validation of an optical and thermal model of the Fresnel collector was carried out in steady state. There are two ways of modeling this kind of system: the concentrated parameter model and the distributed parameter model (Berenguel (1996)). In this paper, the distributed parameter model is used for simulation purposes and the concentrated parameter model is used for obtaining a feedforward controller. It is worth pointing out that the equations used for this plant are the same as those used for modeling the parabolic trough solar plant. The difference depends on the way in which the model parameters are computed: the fluid characteristics (density, specific heat, Symbol description Units t Time s x Space m ρ(t)Density kgm−3 C(t) Specific heat capacity JK−1kg−1 ACross sectional area m2 T(x,t)Temperature K,°C q(t)water flow rate m3s−1 I(t)Solar radiation Wm−2 no(t)geometric efficiency Unitless Kopt Optical efficiency Unitless GCollector aperture m Ta(t)Ambient temperature K,°C Hl(t)Global coefficient of thermal loss Wm−2°C−1 Hv(t)Temperature-dependent part of the heat transmission coefficient Wm−5s°C−1 Ht(t)Coefficient of heat transmission metal-fluid Wm−2°C−1 LLength of pipe line m Table 2: Parameters description metal-fluid heat transmission coefficient...), the thermal loss coefficient, the geometric properties of the solar field and the computation of the geometric efficiency which is more complicated than the case of the parabolic trough plant, as explained in Robledo et al. (2010). 3.1. Distributed parameter model As described in section 2, the Fresnel solar collector field consists of a set of Fresnel solar collectors which concentrate solar radiation onto a line where a 64 m long absorption tube is located. The model is described by the following system of partial differential equations (PDE) describing the energy balance (Spoladore et al. (2011)): ρmCmAm ∂Tm ∂t=IKopt noG−HlG(Tm−Ta)−LHt(Tm−Tf) ρfCfAf ∂Tf ∂t+ρfCfq∂Tf ∂x=LHt(Tm−Tf)(1) where msubindex refers to metal and fsubindex refers to a fluid. In Table 2, parameters and their units are shown. The PDE system is solved by dividing the metal and fluid into 64 1m long segments. The integration step is 4 chosen to be 0.5 seconds. The computation of the geometric efficiency, which takes into account the effect of the cosine of the incidence angle of the solar beam and the shade factor, involves complex trigonometric formulas. These are well explained in Robledo et al. (2010). Some parameters have been better adjusted than those presented in (Spoladore et al. (2011)). In particular, the density, specific heat and coefficient of heat transmission have been obtained as polynomial functions of the segment temperature and water flow using thermodynamical data of pressurized water. The coefficient of thermal losses has been obtained using real data from the Fresnel solar field. Their expression are as follows: ρf=−0.0025 T2 f−0.203 Tf+1003.91 (2) C f =5.16e−7T4 f−1.56e−4T3 f+0.0277 T2 f −1.627 Tf+4207.403 (3) Hv=1.34e−4T4 f−7.78e−2T3 f+18.73 T2 f −2.57e3Tf+4.11e5 Ht=Hvq0.8(4) The thermal loss coefficient can be calculated using equation (5): Hl= (0.00122)(Tm−Ta)+0.001763 (5) In order to adjust the model parameters, a set of 10 days covering different operating conditions has been used. The following two days have not been used for identification but for validation of the model behavior. Figure 4 corresponds to a typical summer day. The oscillations in the inlet temperature are produced by the temperature returning from the chiller. Figure 5 shows the evolution of the error between the distributed parameter model and the real data. A maximum error of 2.5 °C (1.6 %) can be observed. Figure 6 corresponds to a day when the solar collector field is working in recirculation mode. This operation mode is used to heat up the solar field. Figure 7 shows the evolution of the error between the distributed parameter model and the real data throughout the day. At 14.6 h, a part of the solar field (70 %) is defocused. A maximum error of 1.6 °C (about 2 %) can be observed. Figure 4: Solar field evolution Model vs Real: 29/06/2009 Figure 5: Errors between distributed parameter model and real data: 29/06/2009 5 Figure 6: Solar field evolution Model vs Real: 31/07/2017 Figure 7: Errors between distributed parameter model and real data: 31/07/2017 3.2. Concentrated parameter model The concentrated parameter model provides a lumped description of the whole field. The variation in the internal energy of the fluid can be described by the equation (Robledo et al. (2010)): CdTout dt =Kopt noSI −qPcp(Tout −Tin)−HlS(¯ T−Ta) (6) where qis the water flow, Tout and Tin are the outlet and inlet oil temperatures, respectively, ¯ Tis the mean value between inlet and outlet temperatures and Tais the ambient temperature. Cis the thermal capacity of the solar field, Kopt is the optical efficiency (which incorporates the effects of mirror reflectivity, tube absorptance, interception factor), Iis the solar irradiance and Sis the total reflective surface measuring 352 m2. The geometric efficiency no is a function of the cosine of the incidence angle between the mirrors’ normal vector and the solar beam and the shade factor, Pcptakes into account some geometrical and thermal properties of the loop and Hlis the coefficient of thermal losses. Figure 8 shows a comparison between the evolution of the distributed parameter model, the concentrated parameter model and the real data. Although the evolution of the concentrated parameter model is close to the real one, the distributed parameter model achieves a more accurate response as expected. Figure 9 depicts the evolution of the error for the two considered models. Figure 8: Solar field evolution Distributed Model vs Real vs Concentrated Model: 31/07/2017 6 Figure 9: Error Comparison: 31/07/2017 In this paper, the concentrated parameter model is used to implement a feedforward controller. 4. Gain Scheduling Generalized Model Predictive Control Strategy In this section, the proposed model predictive control strategy is presented. 4.1. MPC control scheme Since the dynamics of the solar collector field is highly nonlinear a feedforward in series with the plant is used. The feedforward controller has a twofold objective: on one hand, the feedforward controller has demonstrated to be very useful in rejecting the multiple disturbance sources which affect a solar collector field (Camacho et al. (1992)). On the other hand, a series feedforward linearizes approximately the highly nonlinear response of the solar field as explained in Camacho et al. (1997). In fact, this approach is simple and provides results comparable to the use of feedback linearization (Cirre et al. (2007)), with lower complexity. The linear model to be used in the control strategy corresponds to the set feedforward+plant. The control strategy works as follows: The model predictive control receives the desired outlet temperature set-point and the current outlet temperature of the solar field. It computes a virtual reference temperature Tre fvir given to the feedforward controller. The feedforward controller, using the data from the solar field, computes the water flow to reach the desired set-point. For the MPC controller, the set feedforward+plant behaves as a linear model with an approximate unitary gain. Figure 10: Control Scheme The feedforward is computed using the concentrated parameter model as follows: q=(Kopt noSI −HlS(¯ T−Ta)) qPcp(Tre fvir −Tin)(7) It is worth noting that, if the model is perfect, Tre fvir will be equal to Tre f in steady state. However, because the model is, in general, not perfect, these two values will not be equal. The GS-GPC controller computes Tre fvir so that the outlet temperature of the solar field tracks the desired reference. Another point to be considered is that, although a series feedforward compensation is used, the plant dynamics change substantially with the water flow level. In particular, this kind of system is difficult to control at low flow level. If the control strategy uses only a particular linear model associated to a flow level to predict the system evolution, when the plant works at a different flow level, the dynamics will change and the performance of the controller may be deteriorated. In order to deal with this problem, a gain scheduling approach is used in this paper. 4.2. MPC problem formulation MPC control algorithms consist of the following 3 steps (Camacho and Bordons (2004), Rawlings and Mayne (2009)): 7 (i) Use a model to predict the process evolution at future time instants (horizon), depending on a control sequence. (ii) Compute the control sequence which minimizes a certain objective function. (iii) Apply only the first element of the control sequence, then recalculate the sequence shifting the horizon one step in the future (receding horizon). The model used to predict the process evolution can be either linear or nonlinear. The model used to predict the future evolution of the plant is considered to be a discrete-time transfer function. The model predictive control strategy, in this case, is called generalized predictive controller (GPC) (Clarke et al. (1987a); Clarke et al. (1987b);Beschi et al. (2013)). In general, the mathematical expression of the MPC problem can be posed as follows: min ∆uJ= Np ∑ t=1yk+t|k−yre f k+t|yk+t|k−yre f k+t +λ Nc−1 ∑ t=0 ∆u| k+t|k∆uk+t|k s.t. yk+t|k=f(∆u,yk+t−1,yk+t−2,...) uk+t=uk+t−1+∆uk+t umin ≤uk+t≤umax t=0,...,Np−1 where Npand Ncstand for the prediction and the control horizons respectively. The parameter λpenalizes the control effort. ∆uis the vector of future control moves (∆u= [∆uk,∆uk+1···∆uk+Nc−1]). For the Fresnel solar collector field, the variable yk+t|kis the prediction of the system temperature at instant k+tbased on the available information at instant kand using the linear model (see subsection 4.3). The variable yre f is the desired reference temperature for the outlet temperature. The control signal ukis the virtual temperature reference Tre fvir provided to the feedforward by the GPC algorithm. In this case, only the following constraints in the amplitude of the signal uare considered: Tin ≤uk+t|k≤225 (8) This range is chosen because the solar field cannot work above 225 °C and working in a temperature below the inlet temperature is not of interest. To ensure that the water flow is confined to the desired values, it is saturated. 4.3. Gain Scheduling approach A gain scheduling controller is an easy way to cope with the changing dynamics of a nonlinear system. Since a linear controller is tuned to a particular working point, when the plant evolves far from the design conditions, the linear controller performance may deteriorate. A simple solution would be to design a set of controllers covering the different operating conditions and switching smoothly among them (Leith and Leithead (2000)). In this case, the parameters of the linear model used to predict the future evolution of the plant change with respect to the water flow. This approach is similar to that proposed in Camacho et al. (1994): four water flow levels are considered covering the entire range of operation (3.8-9.1 m3/h). In Camacho et al. (1994), the unconstrained GPC problem is solved for four flow levels and four gains are obtained. The controller gain is interpolated between the intermediate values. In the approach used here, the linear model parameters are interpolated for intermediate flow values and, then, the GPC problem is solved. The discrete-time transfer functions have been chosen as indicated in equation (9): G(z−1) = bo+b1z−1+b2z−2+b3z−3+b4z−4 1+aoz−1+a1z−2(9) The high order of the numerator aims at modeling high frequency dynamics (Pickhardt (2000)). The sampling time for the MPC control strategy has been chosen as 20 seconds. This choice is suitable for grasping the fundamental dynamics of the plant (time constants between 140 and 350 seconds) and, at the same time, for keeping the real part of the poles of the discretized system reasonably smaller than 1 (Astr¨ om and Wittenmark (1997)). The time constants are estimated for different flow conditions using a step in the input of the extended plant (feedforward and plant). That is, a step in the temperature reference Tre fvir to the series feedforward in steady state. To identify the linear model parameters, a PRBS signal is applied to the distributed parameter model in series with the feedforward and then, using a least square identification method to obtain those parameters. Figure 11 shows the step response for the discrete transfer functions associated to four water flow conditions. As can be seen, the system response becomes substantially slower at low flow levels. Table 4.3 shows the parameter of linear models for the considered water flow conditions. Let Ai(z−1)=[1aoz−1a1z−2]and Bi(z−1) = [bob1z−1b2z−2b3z−3b4z−4b5z−5], the parameters for 8 state-of-the-art review. International Journal of Refrigeration 31, 3–15. Leith, D. J., Leithead, W. E., 2000. Survey of gain-scheduling analysis and design. International Journal of Control 73 (11), 1001–1025. Lemos, J. M., Neves-Silva, R., Igreja, J. M., 2014. Adaptive Control of Solar Energy Collector Systems. Springer-Verlag. Limon, D., Alvarado, I., Alamo, T., Ru´ ız, M., Camacho, E. F., 2008. Robust control of the distributed solar collector field Acurex using MPC for tracking. Proceedings of the 17th World Congress The International Federation of Automatic Control, 958–963. Normey-Rico, J., Bordons, C., Berenguel, M., Camacho, E. F., 1998. A robust adaptive dead-time compensator with application to a solar collector field. In: Proceedings of the IFAC Linear Time Delay Systems Workshop. Grenoble (France). Pickhardt, R., 2000. Adaptive control of a solar power plant using a multi-model control. IEEE Proceedings Theory and Applications 147 (5), 493–500. Pin, G., Falchetta, M., Fenu, G., 2007. Adaptative time-warped control of molten salt distributed collector solar fields. Control Engineering Practice 16, 813–823. Pino, F. J., Caro, R., Rosa, F., Guerra, J., 2013. Experimental validation of an optical and thermal model of a linear fresnel collector system. Applied Thermal Engineering 50, 1463–1471. Rawlings, J., Mayne, D., 2009. Model Predictive Control: Theory and Design. Nob Hill Publishing, LLC. Robledo, M., Escano, J. M., N´ unez, A., Bordons, C., Camacho, E. F., 2010. Development and experimental validation of a dynamic model for a fresnel solar collector. In: 18th IFAC World Congress. Milan (Italy). Rodat, S., Bruch, A., Dupassieux., N., El-Mourchid, N., 2015. Unique fresnel demonstrator including ORC and thermocline direct thermal storage: operating experience. Energy Procedia 69, 1667– 1675. Rodat, S., Souza, J. V. D., Thebault, S., Vuillerme, V., Dupassieux, N., 2014. Dynamic simulations of fresnel solar power plants. Energy Procedia 49, 1501–1510. Rubio, F., Camacho, E. F., Carmona, R., 2006. Control de campos de colectores solares. RIAI Revista Iberoamericana de Automatica e Informatica Industrial 3, 26–45. Sonntag, C., Ding, H., Engell, S., 2008. Supervisory control of a solar air conditioning plant with hybrid dynamics. European Journal of Control 6, 451–463. Spoladore, M., Camacho, E. F., Valcher, M. E., 2011. Distributed parameters dynamic model of a solar fresnel collector field. In: Proceedings of the IFAC 18th World Congress. IFAC World Congress (18). No. 18. pp. 14784–14790. Witheephanich., K., Escano, J. M., Bord´ ons, C., 2014. Control strategies of a solar cooling plant with fresnel collector: a case study. In: International Electrical Engineering Congress IEEECON. Chonburi (Thailand). Witheephanich, K., Escano, J. M., Gallego, A. J., Camacho, E. F., 2013. Pressurized water temperature of a fresnel collector field type cooling system using explicit model predictive control. In: Proceedings of the IASTED conference. Thailand. Yield, A., 2017. URL http://www.atlanticayield.com/ Zhou, L., Li, X., Zhao, Y., Dai, Y., 2017. Performance assessment of a single/double hybrid effect absorption cooling system driven by linear fresnel solar collectors with latent thermal storage. Solar Energy 151, 82–94. 15