Event-based predictive control of pH in tubular photobioreactors

Computers and Chemical Engineering 65 (2014) 28–39

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Event-based predictive control of pH in tubular photobioreactors A. Pawlowski a,∗ , I. Fernández a , J.L. Guzmán a , M. Berenguel a , F.G. Acién b , J.E. Normey-Rico c a b c

Department of Informatics, University of Almería, ceiA3-CIESOL, 04120 Almería, Spain Department of Chemical Engineering, University of Almería, ceiA3, 04120 Almería, Spain Department of Systems and Automation, Federal University of Santa Catarina, Cx.P. 476, 88040-900 Florianópolis, SC, Brazil

a r t i c l e

i n f o

Article history: Received 17 July 2013 Received in revised form 21 February 2014 Accepted 4 March 2014 Available online 14 March 2014 Keywords: Event-based control Model Predictive Control Generalized Predictive Control pH control Microalgae

a b s t r a c t This work presents the application of an event-based model predictive control algorithm to regulate the pH in a microalgae production process. The control aim is to maintain the pH within specific limits and to minimize CO2 losses. The control scheme is based on a Generalized Predictive Control (GPC) algorithm with sensor deadband approach. In this algorithm, the controller execution frequency is adapted to the process dynamics. The event-based scheme works with low sampling frequency if controlled variable, pH in this case, is inside an established band. Otherwise, when the pH value is outside the band, the controller actuation frequency is increased to try to drive it quickly near the setpoint based on the selected tolerance. In such a way, the event-based control algorithm allows to establish a tradeoff between control performance and number of process update actions. This fact can be directly related with reduction of CO2 injection times, what is also reflected in CO2 losses. The control structure is first evaluated through simulations using a nonlinear model for microalgal production in tubular photobioreactors. Afterwards, real experiments are presented on an industrial photobioreactor in order to verify the results obtained through simulations. Additionally, the real tests on the industrial plant are used to verify the event-based control scheme in the case of plant-model mismatch, presence of measurement noise and disturbances. Moreover, the control results are compared with classical time-based solutions using well-known control performance indexes. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Microalgae have been proposed for the production of industrial commodities as biofertilizers and biofuels, in addition to CO2 abatement and wastewater treatment processes (Acién, Fernández, Magán, & Molina, 2012; Kokossis & Yang, 2010). They can contain more than 50% crude protein, with a 25-fold higher yield than soybeans, and their lipids productivity is several times larger than vegetable oils. Moreover, microalgae have been proposed as the only alternative for the sustainable production of biodiesel and bioethanol (Chisti, 2007). Nonetheless, to be competitive in the commodities market microalgal production must approximate crop prices, and become lower than 0.5 D /kg, much lower than actual production cost (Acién, González-López, Fernández, & Molina, 2012). Thus, in practice microalgae are used today in

∗ Corresponding author. Tel.: +34 950214532. E-mail addresses: [email protected] (A. Pawlowski), [email protected] (I. Fernández), [email protected] (J.L. Guzmán), [email protected] (M. Berenguel), [email protected] (F.G. Acién), [email protected] (J.E. Normey-Rico). http://dx.doi.org/10.1016/j.compchemeng.2014.03.001 0098-1354/© 2014 Elsevier Ltd. All rights reserved.

animal feed, in addition to human nutrition, cosmetics, and in the production of high-value ingredients such as polyunsaturated fatty acids and carotenoids (Spolaore, Joannis-Cassan, Duran, & Isambert, 2006). The worldwide production of microalgal biomass is 9000 t dry matter per year, its price ranging from 30 to 300 D /kg, and the size of these markets is growing considerably (Brennan & Owende, 2010; Charpentier, 2009). Although traditionally microalgae have been cultivated in open photobioreactors such as “open raceways” due to the simplicity and low cost, when high-value algal products from defined strains are required, it is necessary to use closed photobioreactors such as tubular photobioreactors (Taras & Woinaroschy, 2012). These photobioreactors allow to control the operating conditions and avoid contamination, being available to fulfill requirements for the production of biomass in food, feed, and additives (Wang, Lan, & Horsman, 2012). The main objective of the closed photobioreactor system is to obtain a high-quality biomass by adjusting the culture conditions to optimal values requested by microalgae strain used, especially pH. In tubular photobioreactors, pH control is performed by injection of pure carbon dioxide. The supply of pure carbon dioxide

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can constitute up to 30% of the overall microalgae production cost (Acién, Fernández, et al., 2012). Moreover, the carbon losses in tubular photobioreactors can be higher than 50% in extreme cases, but can be reduced below 30% through proper design and operation of the photobioreactor (Acién, García, & Chisti, 1999). To reduce this even further, it is necessary to design advanced control strategies that take into account the mixing and mass transfer phenomenon that occurs in the system (Cai, Wang, & Xu, 2013; García et al., 2003; Sierra et al., 2008). Thus, the main control problem for these processes will be to regulate the system pH by simultaneously minimizing the CO2 losses. The CO2 is used to control pH but also to supply inorganic carbon thus avoiding carbon limitation. Thus, excess of CO2 supply can reduce the pH in excess thus damaging the culture, whereas default of CO2 supply can reduce the inorganic carbon concentration below the minimum concentration that limits the growth (Beneman, Tillet, & Weissman, 1987; Berenguel, Rodríguez, Acién, & García, 2004). Although CO2 limitation can be easily avoided by supplying it in excess, the use of carbon dioxide represents a relevant operational cost of microalgae culture: then losses of CO2 in the exhaust gas need to be minimized (Beneman et al., 1987). In practice, ensuring sufficiency of carbon source in a long tubular photobioreactor and simultaneous minimization of losses should require multiple gas injection points along the length of the tube, this constituting a drawback due to the cost involved and the necessity of performing studies of how far apart the injection points have to be spaced. Thus, this tradeoff of pH regulation and minimization of CO2 losses can be done by designing ade˜ Guzmán, Berenguel, quate control algorithms. In Fernández, Pena, and Acién (2010), classical PID plus feedforward control strategies were developed to cope with this problem, where a simplified linear model of the pH evolution based on changes in CO2 injection was used for control design purposes. Moreover, in Romero-García, Guzmán, Moreno, Acién, and Fernández-Sevilla (2012) a FSP (Filtered Smith Predictor) approach has been used to improve control results in presence of significant time delay due to pH sensor location. In both cases, important improvements against on/off controllers were obtained. On the other hand, MPC (Model Predictive Control) techniques have also been used satisfactorily in pH control problems obtaining very good results (Lazar, Pintea, & Keyser, 2007; Oblak & Skrjanc, 2010; Senthil & Zainal, 2012). An example of pH control in photobioreactors using Generalized Predictive Controller (GPC) can be found in Berenguel et al. (2004). In that case, it was possible to improve the overall control performance respect to the classical on/off controller. This was possible thanks to the predictive algorithm that captures the process dynamics as well as considers the on/off valve limitation explicitly in the process constraints. Besides, CO2 losses were considerably reduced in comparison to the commonly used on/off controllers. The main advantage of MPC algorithms is their constraints handling capability, allowing to consider many physical limitations of the process as well as the used equipment. For that reason, these algorithms are very popular in chemical process control applica˜ ˜ & Liue, 2013; Hu tions (Christofides, Scattolini, Munoz de la Pena, & El-Farra, 2011). All previous control techniques for pH control provided promising performance results with an adequate CO2 losses reduction. However, as these control algorithms are time-based control approaches, the control action is always calculated and executed on the plant even for small control errors. Thus, the control effort, and therefore the CO2 losses, may be reduced even further if control techniques that only act when necessary (for instance, when the control error is relevant) are used. This is the case of event-based control approaches, which are becoming very popular from a practical point of view since they allow finding a tradeoff between performance and control effort in a very straightforward

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˚ manner (Arzén, 1999; Pawlowski et al., 2009a). As it is well-known, event-based control is characterized by the ability to adapt the timing of the control action to the current process state. When the controller is event triggered, the control actions will be applied to the process in an asynchronous way and only when it is strictly necessary (Varutti & Findeisen, 2009). This is contrary to the classical control systems, where new control actions are produced every sampling instant and even for very small errors, persistent movements of the actuator are required. The event-based control techniques can be especially useful in bio-process control systems, where some flexibility in control performance is allowed (Pawlowski, Cervin, Guzmán, & Berenguel, 2014; Pawlowski et al., 2009b). In such cases, it is possible to achieve minimum required performance and simultaneously reducing the resources utilization and control effort. This aspect is even more important in processes where electromechanical actuators are used. The event-based techniques allow to extend actuators lifetime as well as permitting to reduce the maintenance of the controlled process form an economical point of view. All those aspects of event-based control approach can be beneficial for pH regulation in tubular photobioreactors, especially when the compromise between control performance and resource utilization (CO2 ) need to be fulfilled. Therefore, this work presents the development and implementation of an event-based MPC algorithm to control the pH of an industrial photobioreactor. From the pH control point of view, the event-based MPC could reduce the controller attention (reducing computational costs) while limiting the resource utilization (applying new control values only if it is strictly necessary). Hence, the application of event-based control in tubular photobioreactors is motivated by reaching both, control effort reduction (minimization of CO2 losses) as well as to keep the pH level in a certain range. In this work, a recent event-based GPC control strategy (Pawlowski, Guzmán, Normey-Rico, & Berenguel, 2012b) is implemented to control the pH in a tubular photobioreactor and to achieve the system requirements. The event detection is based on the level ˚ crossing sampling technique with additional time limits (Arzén, 1999). With this idea, the control actions are only calculated when the process output is outside a certain band around the setpoint. The control law is computed fast when events are detected and slow when there are no events. On the other hand, controlled variable, pH, is regulated with established tolerance (determined by sensor virtual deadband), what allows to reduce the control effort. In this configuration, the control variable (state of on/off valve) is updated only when necessary, what reduces considerably the CO2 usage. This fact is directly reflected in CO2 loses, which makes the event-based controller a resource-aware control system. First, the presented control strategy is tested by simulations on a nonlinear tubular photobioreactor model (Fernández et al., 2012) to perform the event-based control analysis as well as to achieve optimal tuning of design parameters. Next, the event-based GPC is tested on an industrial photobioreactor to verify its performance against plant-model mismatch, process disturbances and measurement noise. Moreover, the obtained results are compared with classical on/off controllers and the classical time-based GPC.

2. Microorganism and photobioreactor used The freshwater strain Scenedesmus almeriensis CCAP 276/24 was used. This strain is characterized by high speed of growth, withstanding temperatures up to 45 ◦ C and pH values up to 10; its optimum conditions being temperature 35 ◦ C and pH 8 (Sánchez et al., 2008). The culture medium used was Mann & Myers, prepared using agricultural fertilizers instead of pure chemicals. The cultures were operated in continuous mode at a dilution rate of 0.34 1/day.

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is circulated at 0.9 m/s using a centrifugal pump located between the bubble column and the solar receiver. 3. System dynamics and models A microalgal culture is a three-phase system (solid, liquid and gas) on which cells (solids) are usually considered as part of the liquid fraction, its growth rate being a function of the nutrients concentration in the liquid. In this sense, the nutrients availability by the cells is a function of mixing degree into the liquid phase according to the design of the reactor. Regarding the gas phase, carbon dioxide and air are usually present in microalgae cultures. The carbon dioxide from the gas phase is transported to the liquid phase to provide the inorganic carbon to growth and to control the pH of the cultures. This inorganic carbon is incorporated into the cells at a specific rate, according to the photosynthesis rate (Acién et al., 1999). In the case of the oxygen, it is produced by photosynthesis and transferred in the opposite way, from the liquid culture to the gas phase when it is present, otherwise accumulating into the liquid. To remove oxygen generated by photosynthesis it is necessary to put in contact the liquid with a gas phase poor in oxygen, usually air. Therefore, a model of a microalgae culture must consider the photosynthesis rate, the mixing and the gas–liquid mass transfer into the system. According to these principles, a general non-linear model of growth for photosynthetic microorganisms in photobioreactors was developed in Fernández et al. (2012) and an improved version (by using partial differential equations) is used in this work as virtual plant for simulation purposes. In the following sections, the main parts of model are summarized describing only the balances related to the pH. For a more detailed information about the model, see Fernández et al. (2012). 3.1. Solid phase – photosynthesis rate The photosynthesis rate PO2 (t, x) is expressed according to the following equation: Fig. 1. Photobioreactor: plane and real view of the photobioreactor.

PO2 (t, x) =

PO2max Iav (t, x)n Ikn + Iav (t, x)n ×

The photobioreactor used is located at the facility at “Estación Experimental Las Palmerillas”, property of Fundación CAJAMAR (Almería, Spain). The facility consists in ten tubular fence-type photobioreactors, which detailed features can be found in Acién, Fernández, Sánchez, Molina, and Chisti (2001). Fig. 1 shows a scheme of the tubular photobioreactor (Molina, Fernández, Acién, & Chisti, 2001). The system is composed of a vertical external-loop airlift pump that drives the culture fluid through the vertical tubular solar receiver and a bubble column. The solar receiver is made of transparent tubes joined into a loop configuration to obtain a total horizontal length of 400 m and 0.09 m diameter. The total culture volume in the photobioreactor is 2600 l, it has a 19.0 m length and 0.7 m width. The loop is optimally arranged to maximize the interception of solar irradiance, minimize resistance to flow, and occupy minimum area to reduce the demand for land. The bubble column size is 3.5 m high and 0.4 m diameter for degassing and heat exchange. Liquid and gas flow rates entering the photobioreactor are measured using digital flowmeters; the temperature, dissolved oxygen and pH are measured using sensors located at the beginning and at the end of the loop. The photobioreactor is bubbled at constant airflow rate of 20 l/min in the bubble column, whereas the pH is controlled by on-demand injection of pure CO2 within a range of 5 l/min at the entrance of the solar receiver. The temperature of the culture is controlled through an internal heat exchanger located in the bubble column. Furthermore, the microalgal culture

pH(t, x) KSpH + pH(t, x) + (pH(t, x)2 /KIpH )

− rPO2max

(1)

In this model, PO2max is the maximum photosynthesis rate of the microorganisms at the culture conditions, Ik is the constant average irradiance or average irradiance required to achieve half of the maximum photosynthesis rate at culture conditions, Iav (t, x) is average irradiance available in each section of the reactor ((t, x) represents time t and point x along the tube), n is a form exponent, KSpH is the half saturation constant for pH, KIpH is the inhibition constant for pH, pH(t, x) is the pH value in the culture, and r is the respiration rate (Fernández et al., 2012). 3.2. Liquid phase – mass balance For the liquid phase, the biomass concentration depends directly on the photosynthetic rate of the culture; thus, the variation for each instant and each point of reactor is defined as: (1 − (t, x))S

∂[Cb ](t, x) ∂[Cb ](t, x) = −Ql (t) ∂t ∂x

+ (1 − (t, x))SP O2 (t, x)[Cb ](t, x)Yb/O2

(2)

where Yb/O2 is the yield coefficient of biomass produced by oxygen unit mass produced (stoichiometric value of 0.75 gbiomass /gO2 is used), whereas Ql (t) is the volumetric flow rate of liquid, which is constants along the tube, PO2 (t, x) is the oxygen production rate,

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(t, x) is the gas holdup, S is the cross-sectional area of the tube, and Cb (t, x) is the biomass concentration. Regarding the inorganic carbon concentration, this can be related to the gas–liquid mass transfer rate and the photosynthesis rate by the following mass balance: (1 − (t, x))S

∂[CT ](t, x) ∂[CT ](t, x) = −Ql (t) ∂t ∂x

+ (1 − (t, x))S

PCO2 (t, x)[Cb ](t, x) MCO2

+ (1 − (t, x))SK l al,CO2 ([CO∗2 ](t, x) − [CO2 ](t, x))

(3)

where [CT ](t, x) is the total inorganic carbon concentration, MCO2 is the molecular weight of CO2 , whereas PCO2 (t, x) is the carbon dioxide consumption rate, which is equal to PO2 (t, x) with reversed sign. Kl al,CO2 is the mass transfer coefficient of CO2 and finally [CO∗2 ](t, x) calculated as a function of the dioxide carbon concentration in the gas phase according to the Henry’s law. 3.3. Gas phase – mass balance For the gas phase, pure carbon dioxide is introduced into the system, thus these mass balances have to be taken into account. The mass balance for carbon dioxide can be related to the gas–liquid mass transfer rate as:

∂YCO2 (t,x) ∂YCO2 (t, x) (t, x)S = −Qgas (t, x) ∂t ∂x −

(1 − (t, x))SK l al,CO2 Vmol yN2

([CO∗2 ](t, x) − [CO2 ](t, x))

(4)

where YCO2 (t, x) is the molar carbon dioxide ratio to nitrogen in the gas phase, Qgas (t, x) is the volumetric flow rate of the gas, yN2 the nitrogen molar fraction in the gas phase, and Vmol the molar volume under reactor conditions (pressure and temperature). 3.4. Linear pH model for control purposes The non-linear model described in the previous sections has been used as virtual plant for simulation purposes. Regarding to control design purposes, a simplified model for the controlled variable, pH, is used. The pH of the culture is influenced mainly by two phenomena: CO2 supply and CO2 uptake as a function light availability. The supplied CO2 contributes to formation of carbonic acid causing a decrease in culture pH. On the other hand, microalgae performs photosynthesis in presence of solar radiation consuming CO2 and producing O2 , thus causing a gradual rise in pH. Finally, variations in solar radiation produce variations in the rate of photosynthesis and therefore the rate of rise in pH. Considering that the process output is the culture pH, the aperture of the on/off CO2 injection valve is the manipulated variable, and the solar irradiance is the main system disturbance, the process behavior can be represented by simplified linear models (Berenguel et al., 2004; Fernández et al., 2010; Sierra et al., 2008). The linear reduced-order model has been identified taking into account the layout of the photobioreactor, the local distribution of the sensor and actuator, and the dynamics observed in the data. The simplified model relates the outlet pH to the CO2 injection input around the operation point, and is represented by the following transfer functions (Berenguel et al., 2004; Fernández et al., 2010): pH =

k1 kr ωn2 e−tr s u + I 1 + 1 s s2 + 2ıωn s + ωn2 1 + r s

   TF 1 (s)



TF 2 (s)



   TF 3 (s)

(5)

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where pH is the culture pH, u is the control signal (0–100%), and I is the solar irradiance. As observed in (5), the pH evolution is governed by two main dynamics related with the mass transfer capacity of the system. A first-order dynamical term relating the pH dynamics to CO2 injections, TF1 , and a second-order oscillatory term describing the effect of multiple recirculation cycles of the culture affected by CO2 injection through the loop, TF2 Moreover, a time delay, tr , was observed, imposed by constant inlet air flow rate in the riser and the distance between the CO2 injection point and the pH sensor. Finally, the solar irradiance effect on pH is captured by a first-order model such as shown in TF3 . This linear model has been properly validated by the authors around the desired operating point, obtaining the following values of the parameters: k1 = −0.08 pH %−1 ,  1 = 28 min, ωn = 0.014 rad s−1 , ı = 0.042, tr = 7 min, kr = 0.002 pH m2 W−1 , and  r = 182 min. Notice that the small gain kr is logical as the influence of irradiance over pH is mainly through the photosynthesis activity. An example of the validation data can be seen in Fig. 2, where it can be observed how the model properly captures the dynamics of the real system (Berenguel et al., 2004; Fernández et al., 2010). Once the simplified models for pH control have been obtained, the event-based GPC control scheme is built. 4. Event-based GPC control scheme This section briefly summarizes the event-based GPC algorithm used in this work and that was developed in Pawlowski et al. (2012b). 4.1. Control structure In a general way, an event-based controller consists of two parts: ˚ 2007). The event detecan event detector and a controller (Aström, tor deals with informing the controller when a new control signal must be calculated due to the occurrence of a new event. In this work, the controller is composed by a set of GPC controllers, in such a way that one of them will be selected according to the time instant when a new event is detected, such as described below. The complete control structure is shown in Fig. 3, including the process, the actuator, the controller, and the event generator. This scheme operates using the following ideas: • The process output is sampled using a constant sampling time Tbase at the event generator block, while the control action is computed and applied to the process using a variable sampling time Tf , which is determined by an event occurrence. • Tf is multiple of Tbase (Tf = fTbase , f ∈ [1, nmax ]) and verifies Tf ≤ Tmax , being Tmax = nmax Tbase the maximum sampling time value. This maximum sampling time will be chosen to maintain a minimum performance and stability margins. • Tbase and Tmax are defined considering process data and closedloop specifications, following classical methods for sampling time choice. • After applying a control action at time t, the process output is monitored by the event generator block at each base sampling time, Tbase . This information is used by the event detector block, which verifies if the process output satisfies some specific conditions. If these conditions are satisfied, an event is generated with a sampling period Tf and a new control action is computed. Otherwise, the control action is only computed by a timing event, at t = t + Tmax . • Notice that according to the previous description, the control actions will be computed based on a variable sampling time, Tf . For that reason, a set of GPC controllers is used, where each GPC controller is designed for a specific sampling time Tf = fTbase , f ∈ [1,

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Fig. 2. Simplified model validation results.

nmax ]. On the other hand, resampling of the signals is necessary to avoid undesirable jumps in the control action at each change among controllers.

controller in that set is implemented as a classical GPC algorithm by using the model described by (5). The GPC controller consists of applying a control sequence that minimizes a multistage cost function of the form (Camacho & Bordóns, 2007):

4.2. GPC algorithm As pointed out above, the proposed control structure is based on the use of the GPC algorithm as the feedback controller. Specifically, a set of GPC controllers is used to implement the proposed strategy, one for each sampling time Tf , f ∈ [1, nmax ]. Each individual

N

J=

f

2 

f

f

f

2

ı [ˆy (t + j|t) − w(t + j)] +

f 1

j=N

Fig. 3. Event-based GPC control scheme.

Nu  j=1

f [uf (t + j − 1)]

2

(6)

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where yˆ f (t + j|t) is an optimum j step ahead prediction of the system output on data up to time t, uf (t + j − 1) are the future control increments and w(t + j) is the future reference trajectory, considering all signals with a sampling time Tf (t = kTf , k ∈ Z+ ). Moreover, the tuning parameters are the minimum and maximum prediction f f f horizons, N1 and N2 , the control horizon, Nu , and the future error f f and control weighting factors, ı and  , respectively (Camacho & Bordóns, 2007). The prediction horizons are defined, considering f f the discrete time delay df , as N1 = df + 1 and N2 = df + N f , and the f weighting factor ı = 1. The objective of GPC is to compute the future f control sequence uf (t), uf (t + 1), . . ., uf (t + Nu − 1) in such a way f that the future plant output y (t + j) is driven close to w(t + j). This is accomplished by minimizing J. The main difference between the event-based and the time based controller is the ability to adapt the controllers invocation, basing on the controlled variable dynamics. In such a case, the event-based controller will update the system in a fast way (with Tbase sampling frequency), when the controlled variable is outside established band. Otherwise, when the controlled variable is inside the band, the event-based controller will switch to the slowest sampling (Tmax ) in order to reduce the control effort. Additionally, the presented event-based control structure can work with variable sampling frequency between Tbase and Tmax to detect control system events. Considering this working principle, the event-based control structure can manage the control effort adapting it to the performance requirements of the controlled process. 4.3. Event-based signal sampling From the scheme in Fig. 3, it can be seen that the event-based sampling is governed by the event generator block. This block includes two different kinds of conditions in order to generate new events. When one of those conditions becomes true, a new event is generated, and then, the current signal values of the process variables are transmitted to the controller block being used to compute a new control action (CO2 injections in this case). The first condition focuses on checking the process variables. These conditions are based on the level crossing sampling technique (Miskowicz, 2006), that is, a new event is considered when the absolute value between two signals is bigger than a specific limit ˇ. For instance, in the case of the setpoint tracking, the condition would be the following |w(t) − y(t)| > ˇ

(7)

trying to detect that the process output, y(t) = pH(t), is tracking the reference, w(t) = wpH (t), within a specific tolerance ˇ. The second condition is a time-based condition, used for stability and performance reasons. This condition defines that the maximum period of time between two control signals computation, and thus between two consecutive events, is given by Tmax : t − tei ≥Tmax

(8)

where tei is the time when the last event ei was generated. These conditions are checked with the smallest sampling rate Tbase , where the detection of an event will be given within a variable sampling time Tf = fTbase , f ∈ [1, nmax ]. Notice that this variable sampling period determines the current closed-loop sampling time to be used in the computation of the new control action. 4.4. Signal sampling and resampling technique Such as described above, the computation of a new control action is done with a variable sampling period Tf . So, in order to implement the GPC control algorithm, the past values of the process variables and those of the control signals must be available

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sampled with Tf . Therefore, a resampling of the corresponding signals is required (Pawlowski et al., 2012b). 4.4.1. Resampling of process output As discussed previously, the controller block only receives the new state of the process output when a new event is generated. This information is stored in the controller block and is resampled to generate a vector yb including the past values of the process output with Tbase samples. The resampling of the process output is performed by using a linear approximation between two consecutive events and afterwards this linear approximation is sampled with the Tbase sampling period, resulting in yb (k) with k = 0, Tbase , 2Tbase , 3Tbase , . . .. Once the process output signal is resampled, the required past information must be obtained according to the new sampling time Tf , resulting in a new signal, yf , with the past information of the process output every Tf samples. Hence, the vector yf is obtained as a result, which contains the past process information with the new sampling period Tf to be used in the calculation of the current control action. 4.4.2. Reconstruction of past control signals The procedure is similar to that described for the resampling of the process output. There is a control signal, ub , which is always used to store the control signal values every Tbase samples. Nevertheless, the procedure for the control signal is done in the opposite way than for the process output. First, the required past information is calculated and afterwards the signal ub is updated. Lets consider that a new event is generated, what results in a new sampling period Tf = fTbase . Now, the past information for the new sampling period, Tf , is first calculated from the past values in ub and stored in f

a variable called up . Afterwards, this information, together with the past process output data given by yf , will be used to calculate the new control action, uf (Tf ) = ub (k). Once the new control action has been computed, uf (Tf ) = ub (k), the ub signal is updated by keeping constant the values between the two consecutive events. 5. Results This section shows both simulation and real experiments using the event-based control strategy applied to pH control in tubular photobioreactors. First, the event-based control strategy was tested in simulation, where the non-linear model described in Section 3 was used as virtual plant. Afterwards, the analyzed eventbased GPC algorithm was verified through real experiments on the industrial photobioreactor described in Section 2. All data used in the simulation study were collected from the real photobioreactor operating in continuous mode at real conditions in Almería (Spain). Moreover, in all considered control systems the continuous signal obtained from the controller must be translated into a discontinuous signal used to drive the valve. For this purpose, a PWM (Pulse Width Modulation) technique is used, with a frequency of 0.1 Hz. Notice that microalgae growth requires that the operation variables must be maintained at optimum values, where for the microalga used in this work, Scenedesmus almeriensis, an optimal value of wpH = 8 is required. 5.1. Simulation study The simulations were performed for a period of 7 days, where different profiles of solar irradiance have been considered, since it is the main disturbance that affects the pH control process during diurnal conditions (through the photosynthesis process). In this study, different control strategies, namely on/off controller, classical time-based GPC and event-based GPC controller, have been used for comparison purposes.

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The event-based GPC control structure with sensor deadband was implemented with Tbase = 1 min, Tmax = 5 min, nmax = 5, and thus Tf ∈ [1, 2, 3, 4, 5]. The control horizon was selected to Nunmax = 5 samples for all GPC controllers. The prediction horizon was set to N2c = 20 min in continuous time and was used to calculate the equivalent prediction horizon for each controller with a different sampling period (Pawlowski et al., 2012b). Finally, the control weighting factor was adjusted to f = 0.005 to achieve the desired closed-loop dynamics for the faster GPC controller with T1 = Tbase = 1 min. Due to the physical limitation of the actuator signal (PWM pulse width), the event-based GPC controller considers constraints on the control signal 0 < u(t) < 100%. Taking into account all design parameters, the control structure is composed of five controllers for each possible sampling frequency. Considering pH operating limits for tubular photobioreactor (7 < pH < 9) and the relationship of the pH with the photosynthesis rate (as will be described below), the ˇ parameter was set to ˇ = 0.075. In such a way, event-based configuration will keep pH close to its optimal value and allows to find an acceptable tradeoff between performance and control effort (Pawlowski et al., 2012b). For the time-based GPC, a sampling time of 1 min was used with following parameters: Nu = 5, N2 = 20,  = 0.005. The value of the solar irradiance in the prediction horizon is considered constant and equal to the last measured value. Additionally, an on/off controller was used in simulations, since it is the most common controller for pH control in algae production processes. The simulation results for all considered days, including the control performance indexes, are summarized in Table 1. This table shows the Integrated Absolute Error (IAE), the number of events (Event), the injection time (IT) in minutes, and the total CO2 supplied and the CO2 losses, both expressed in grams. Moreover, two complementary indexes are calculated for oxygen and biomass production, RO2 and Pb , respectively. Those measurements are used to demonstrate the influence of the evaluated algorithm on microalgae growth. The former one presents the overall oxygen production rate, which depends, among others, on pH and solar irradiance. The second index corresponds to the daily biomass production rate, which represents the overall performance of the photobioreactor. As expected, GPC-based controllers overcome the on/off controller, what can be appreciated analyzing the IAE index and CO2 losses. Additionally, it can be seen that event-based algorithm obtains inferior performance in comparison to the time-based GPC, but with an important reduction in events (changes in the control signal). This fact is confirmed by IAE and Event measures obtained for both control systems. In spite of performance degradation, the event-based configuration satisfies the control accuracy requirements for such application. The most important fact is that the event-based scheme reduces the control system events, and consequently reduces the control effort. Furthermore, it presents a promising tradeoff between control performance and the number of control actions, and thus reduction on CO2 injections. This configuration obtains the lowest number of control actions over the controlled system for all the analyzed days, reaching an average reduction of about 60%. From the obtained results, it can be deduced that for processes where some tolerance in setpoint tracking is permitted, an important reduction of control actions can be reached. In this case of pH control, this reduction can be translated into economic savings, reducing the electromechanical actuator wastage, and CO2 injection time (and thus CO2 losses). The microalgae growth performance is verified using RO2 and Pb indexes presented in Table 1. From the results it can be concluded that biomass production and photosynthesis rate have higher values for the control strategies based on GPC algorithm. In the case of the on/off controller those measures are significantly smaller, what is caused by a low pH control performance. It is confirmed through the relationship between pH value and normalized

Fig. 4. Influence of pH on the photosynthesis rate of S. almeriensis culture at 200 ␮E/m2 s, 25 ◦ C, and 100%Sat of dissolved oxygen.

photosynthesis rate illustrated in Fig. 4. This dependency was previously analyzed and confirmed through experiments by Costache et al. (2013). Moreover, the growth rate indexes for the event-based GPC controller are similar to the time-based GPC for all analyzed days. It is due to the fact that the deadband for event-based structure was established close to the optimal pH value being in the favorable range for photosynthesis rate (see Fig. 4). In such a case, even small desviations from the optimal value of (wpH = 8 ± ˇ), will keep the photosynthesis rate close to its optimal value. On the contrary, the on/off controller, which controls pH with a significant error (see IAE), drives system from its optimal operation condition and provokes production losses due to the nonlinear relationship between pH and photosynthesis rate. Since a graphical result for 7 days and all analyzed control techniques will not allow one to see the results properly, two representative days have been selected, which are shown in Figs. 5 and 6, respectively. These figures show the results of the event-based GPC control structure and of the time-based GPC for the selected days. The results for on/off controller are not included in the graphs due to its low control accuracy, what may hamper visual analysis. Fig. 5 shows the response of the event-based controller for a day with rapid changes in process disturbances (solar irradiance). In this particular day, the control performance was deteriorated from both configurations due to disturbance effects. Considering the control signal, it can be observed that the event-based control approach adapts the control system execution based on the controlled variable dynamics. These reductions in the control signal changes is beneficial for the actuator lifespan as well as reduce CO2 injection time (IT). Moreover, for this specific day, an additional simulation was performed for TB GPC with  = 0.05. This configuration was analyzed to demonstrate that the classical tuning does not allow to obtain a control performance similar to the event-based structure. In such a case, the control weighting parameter was increased (from  = 0.005 to  = 0.05) to reduce the controller sensibility and in consequence the control effort. For this specific day, it can be observed that TB-GPC with  = 0.05 obtains a lower performance. This fact is due to the penalization on the control signal imposed by the  value.

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Table 1 Performance indexes for the simulation results. Day 1

2

3

4

5

6

7

TB-GPC

IAE Event IT [min] CO2 [g/day] Lost CO2 [g/day] RO2 [kg[O2 ] /m3 day] Pb [kg[b] /m3 day]

804 656 336.6 1239 345 0.3425 0.2570

671 667 403.5 1485 423 0.4171 0.3143

616 671 408 1503 429 0.4244 0.3188

970 673 330.3 1215 342 0.3420 0.2560

1114 653 379.2 1395 381 0.4008 0.3012

806 659 357.9 1317 372 0.3690 0.2764

639 678 440.9 1495 426 0.4234 0.3158

EB-GPC

IAE Event IT [min] CO2 [g/day] Lost CO2 [g/day] RO2 [kg[O2 ] /m3 day] Pb [kg[b] /m3 day]

1404 207 310 1143 249 0.3419 0.2565

1146 193 376.5 1386 324 0.4163 0.3122

1118 173 381.9 1404 330 0.4236 0.3177

1196 194 306.9 1128 261 0.3409 0.2557

1506 210 355.1 1308 294 0.3997 0.2998

1247 170 333.7 1227 282 0.3679 0.2759

1096 158 379.3 1395 327 0.4201 0.3151

ON/OFF

IAE Event IT[min] CO2 [g/day] Lost CO2 [g/day] RO2 [kg[O2 ] /m3 day] Pb [kg[b] /m3 day]

5756 656 466.5 1719 825 0.2203 0.1653

7210 667 553.5 2037 975 0.2727 0.2045

7364 671 561 2064 990 0.2783 0.2088

6542 673 454.5 1674 801 0.2082 0.1561

7968 653 529.5 1950 936 0.2593 0.1945

8411 659 492 1812 867 0.2408 0.1806

7505 678 556.5 2049 981 0.2732 0.2049

When  is set to 0.05, the controller needs more time to respond to the system disturbances induced by changes in solar irradiance (Pawlowski, Guzmán, Normey-Rico, & Berenguel, 2012a). The lower control performance for this configuration is confirmed by IAE = 1774 index, which is worst from all GPC configurations. On the other hand, the CO2 injection time (IT) for this configuration is slightly lower IT = 332 min than for the TB-GPC with  = 0.005 (TI = 336 min), and higher in comparison to EB-GPC (IT = 310 min). Considering those results it can be deduced that increasing  parameter do not provide significant savings in CO2 utilization and in the same time produces a negative influence on the control performance due to its slower response to the disturbances. Contrary

to the EB-GPC, where control structure dynamically adapts the actuation frequency to the current state of the controlled variable. Moreover, in the analyzed event-based control structure, each GPC controller from the set can be tuned independently. Taking into account this feature, the GPC controller for the slowest sampling time can tuned with higher  value to achieve an additional savings. Fig. 6 shows the control performance for a clear day with smooth disturbance dynamics, where good overall control accuracy is achieved for both configurations. The event-based structure with sensor deadband maintains the controlled variable inside the

Fig. 5. Simulation results for a day with passing clouds.

Fig. 6. Simulation results for a clear day.

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established band, satisfying the design requirements. Analyzing the control signal for a clear day, one can see that the event-based controller actuates with the limit sampling time Tmax most of the time, what is reflected in the number of events presented in Table 1 and from the bottom graphic in Fig. 6. On the other hand, an environmental impact and economical interpretations of the control results can be performed taking in to account CO2 injection time (IT), CO2 usage, and CO2 losses presented in Table 1. The application of the event-based structure allows to reduce the IT and, in consequence, the minimization of the CO2 usage and CO2 losses. However, the obtained control performance is slightly worst in comparison to TB-GPC, and it is possible to obtain a tradeoff between control performance and cost of the plant maintenance. Moreover, the event-based configuration obtains better performance that commonly used on/off controller and at the same time reduces the daily CO2 consumption and losses around 30% (see Table 1). 5.2. Experimental study This section shows the results obtained when using the eventbased GPC and the classical time-based GPC to control pH in an industrial tubular photobioreactor. The experiments have been performed between 6 and 12 June 2013 at the plant described in Section 2. During this period, the photobioreactor plant worked in continuous mode. In this mode, 34% of the total volume of culture is harvested daily. The harvesting operation is done usually around midday and this influences on the pH value. From the control system point of view, this issue is considered as an unmeasurable disturbance, since the harvesting operation is performed by the plant operator to cover product demand. All control schemes are implemented on an industrial PC located at the plant facilities. The controller with Labview-based software executes the event-based GPC controller or classical GPC, which are coded in the Matlab environment. All control system sensors and actuator are connected to the Compact-FieldPoint unit from National Instruments. In such configuration, the controller node communicates with Compact-FieldPoint through a dedicated Ethernet network to perform sensing and control tasks. 5.2.1. Classic GPC The first tested control scheme was the classical time-based GPC. The control system configuration and algorithm tuning parameters are the same as in the simulation study described previously. This configuration was implemented and tested to assure the proper control system configuration and check the control performance in presence of measurement noise and external disturbances that affect controlled variable. Prior to the controller implementation, several tests were made to confirm the proper model validation around the operation point. This procedure confirmed the relatively good accuracy of model, to guarantee the desired control performance. The time-based GPC was tested during two different days and representative results of one of those days are shown in Fig. 7 (notice that classical GPC was already studied by the authors in previous works and for that reason it was only used here for comparisons (Berenguel et al., 2004)). It can be observed how GPC controller regulates the pH of the photobioreactor compensating the influence of the solar irradiance (main control system disturbance). On the other hand, it can observed how the controller reacts to the unmeasurable process disturbances (harvesting operation), between 12 and 15 h. It can be also seen, that despite of the disturbance, the controller maintains the pH close to the setpoint, due to aggressive compensation of the control signal. During this day, the classical GPC obtains a good control accuracy, comparable with the results obtained through simulations, what was

Fig. 7. Experiments control results for classical time-based GPC.

confirmed by IAE = 1357 index. The accumulated IT reaches 342 min that corresponds to 1262 g of pure CO2 . To achieve this performance, an amount of 350 g of CO2 was lost. The microalgae growth performance indexes for RO2 and Pb were 0.7509 kg[O2 ] /m3 day and 0.5572 kg[b] /m3 day, respectively. For this particular day, the classical GPC obtains a good accuracy in pH regulation. However, this good control performance is obtained through a high CO2 consumption, what also increases the CO2 losses. This fact confirms the results obtained through simulations. As mentioned previously, the CO2 losses is an important issue in photobioreactor pH control problem and any solution that face this problem is welcome. In such perspective, the event-based GPC arises as an interesting option to reduce the control effort at expense of a reasonable control performance accuracy degradation. 5.2.2. Event-based GPC The event-based GPC algorithm was implemented with the same configuration parameters as in the simulation study. Again, the control objective is to maintain the pH value close to the setpoint with a desired tolerance. Such tolerance is determined by the sensor deadband value, selected to ˇ = 0.075 for whole test period according to the relationship between the pH and the photosynthesis rate described in Fig. 4. The application of the event-based controller makes possible to establish the tradeoff between control performance accuracy and CO2 losses. The event-based configuration has been tested during five days and the overall control performance is shown in Fig. 8. It can be observed that for most of the time the controlled variable is inside the established band SP ±ˇ. The pH goes outside the band only a few times during the whole test period and this fact is induced by the external disturbances. This is especially visible during the second and third days, where solar irradiance is affected by passing clouds what changes the photosynthesis rates and affects the pH values. On the other hand, the obtained results show that the eventbased controller properly rejects unmeasurable disturbances due to microalgae harvesting action. During clear days, the event-based controller maintains the pH inside the band, updating the process

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37

Fig. 8. Experimental event-based control results for a five-day period.

control action at the low rate (with Tmax sampling time). When the pH crosses the sensor deadband limit, the control structure switches to the fastest sampling frequency Tbase to move back controlled variable into the setpoint tolerance band. Fig. 9 shows a detailed view for the fourth day. It can be observed that the event-based GPC provides a good control accuracy.

Fig. 9. Experimental control results for event-based GPC for forth day.

Moreover, it can be seen that each time the pH crosses the sensor deadband, the event-based control system increases the sampling frequency. Additionally, it can be observed how the load disturbance related to harvesting process is rejected properly by event-based controller around the midday. The event-based GPC controller generates less aggressive control signal as long as the pH is inside the limits. When the controlled variable goes out the limits, the event-based scheme increases sampling frequency to compensate for the disturbances. The bottom graph in Fig. 9 shows how events are generated and can be seen that the event generation frequency increases when the pH goes outside the limit. On the other hand, the sampling frequency decreases when pH is within the limits. In this way, it is possible to reduce the controlled system updates. Hence, as a consequence of the reduced number of process updates, the event-based control system reduces the required control effort related to the CO2 consumptions as well as CO2 losses. Table 2 collects the performance indexes for event-based GPC with sensor deadband in the experimental results. It can be observed that the overall IAE index is slightly worst in comparison with those obtained through simulations. This is mainly due to harvesting process that affects the pH control accuracy and was not considered during the simulation study. On the other hand, it can be observed how the event-based control scheme reduces the number of events in comparison to the SLT (Solar Light Time), which corresponds to the number of invocation of classical time-based control scheme. The CO2 usage was similar to the values obtained during simulation study, what confirms the reduction of its usage with respect to the time-based scheme. This fact is also confirmed by the accumulated IT for all considered days. At the same time, it can be see that the CO2 losses are reduced. On the other hand, the microalgae growth indexes, RO2 and Pb , were quite similar for the different days (as expected according to Fig. 4), and are comparable with the classical GPC, analyzed previously. All those benefits are obtained at expense of the control performance taking as a reference the time-based GPC controller. Moreover, event-based configuration is able to reduce around 30%

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Table 2 Performance indexes for the experimental results. Day

EB-GPC

IAE SLT [min] Event IT [min] CO2 [g/day] Lost CO2 [g/day] RO2 [kg[O2 ] /m3 day] Pb [kg[b] /m3 day]

1

2

3

4

5

1725 767 214 319.6 1177 235 0.8464 0.6196

1555 767 280 291.1 1072 216 0.9953 0.7445

1666 767 269 296.4 1091 213 0.9317 0.6783

1341 767 228 284.3 1047 208 0.7526 0.5532

1579 767 258 307.8 1134 227 0.7459 0.5378

CO2 losses obtained by classical GPC. Finally, notice that when event-based GPC controller is compared with on/off controllers (which are the typical used in industrial photobioreactor), the control accuracy is highly improved and the CO2 losses are reduced by more than 2 times. 6. Conclusions In this paper, an event-based GPC control strategy has been used to reduce CO2 losses in pH control of tubular photobioreactors by keeping an adequate control performance level. The core idea consists of updating the controlled process only when significant deviations from the setpoint occurs. The presented control scheme provides savings in plant maintenance cost, minimizing the CO2 losses. The obtained benefits are reached at the expense of control performance through control accuracy degradation. The desired tradeoff between control performance and CO2 losses can be easily implemented adjusting a sensor deadband value at the control system design stage. The experiments show that the eventbased GPC control scheme is suitable for pH control in tubular photobioreactors. The obtained reductions in CO2 losses are even more significant than in the case of the classical GPC analyzed in Berenguel et al. (2004). This is due to the event-based framework, which allows to reduce the resource utilization at expense of the control performance. In such case, it is possible to meet the compromise between control accuracy degradation and plant maintenance costs as well as environmental impact. The evaluation performed in this work is based on a single photobioreactor, but it can be easily extrapolated to industrial scale. In such case, the benefits are even more visible. Acknowledgments This work has been partially funded by the following projects: PHB2009-0008 (financed by the Spanish Ministry of Education; CNPq; CAPES-DGU 220/2010); DPI2010-21589-C05-04 and DPI2011-27818-C02-01 (financed by the Spanish Ministry of Economy and Competitiveness and ERDF funds); CENIT VIDA (financed by the Spanish Ministry of Economy and Competitiveness and CDTI funds) and supported by Cajamar Foundation. References Acién, F. G., Fernández, J. M., Magán, J. J., & Molina, E. (2012). Production cost of a real microalgae production plant and strategies to reduce it. Biotechnology Advances, 30, 1344–1353. Acién, F. G., Fernández, J. M., Sánchez, J. A., Molina, E., & Chisti, Y. (2001). Airlift-driven external-loop tubular photobioreactors for outdoor production of microalgae: Assessment of design and performance. Chemical Engineering Science, 56, 2721–2732. Acién, F. G., García, F., & Chisti, Y. (1999). Photobioreactors: Light regime, mass transfer, and scale-up. Progress in Industrial Microbiology, 35, 231–247. Acién, F. G., González-López, C. V., Fernández, J. M., & Molina, E. (2012). Conversion of CO2 into biomass by microalgae: How realistic a contribution may it be to significant CO2 removal? Applied Microbiology and Biotechnology, 96, 577–586.

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