Using Neural Networks to Address Nonlinear pH Control in Wet

Ind. Eng. Chem. Res. 2010, 49, 2263–2272

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Using Neural Networks to Address Nonlinear pH Control in Wet Limestone Flue Gas Desulfurization Plants A. L. Villanueva Perales,* F. J. Gutie´rrez Ortiz, F. Vidal Barrero, and P. Ollero Department of Chemical and EnVironmental Engineering, UniVersity of SeVille, Camino de los Descubrimientos s/n, 41092, SeVille, Spain

In previous articles,1-3 we evaluated the performance of different linear control strategies (decentralized feedback control and multivariable predictive control) in wet limestone flue gas desulfurization (WLFGD) plants based on a pilot plant study. Although these control strategies show good performance, they may not be suitable if the oxidation tank pH is significantly nonlinear, which depends on many plant operating factors. Control of oxidation tank pH is important since it is related to the quality of gypsum, a byproduct of the WLFGD process. In this work, we propose and assess a combined control strategy for dealing with nonlinear pH control in WLFGD plants, based on a decentralized strategy composed of a neural predictive controller and a feedback controller, which control the oxidation tank pH and SO2 concentration of the desulfurized gas, respectively. 1. Introduction Wet limestone flue gas desulfurization (WLFGD) is the most widespread technology for controlling SO2 emission in coalfired power stations, and it is also widely used in process plants such as smelters, sulphuric acid plants, refineries, and pulp and paper mills. In the wet limestone desulfurization process, the flue gas is scrubbed with slurry containing limestone particles (CaCO3). The SO2 absorbed from the flue gas reacts with limestone, and gypsum (CaSO4 · 2H2O) is produced according to the following overall reaction: SO2 + CaCO3(s) + 0.5O2 + 2H2O f CaSO4 · 2H2O(s) + CO2 (1) The main components of a WLFGD plant are the absorber, where flue gas is brought into contact with the scrubbing slurry, and the oxidation tank, where air is sparged to promote the oxidation of the absorbed SO2 to sulfate, which ends up as gypsum (Figure 1). The most important controlled variable in a WLFGD plant is the SO2 concentration in the desulfurized gas because regulation SO2 emission limits must be fulfilled. The oxidation tank pH must also be controlled because it has a significant influence on limestone utilization and, therefore, on gypsum quality.1 The main manipulated variables are the fresh limestone slurry flow rate to the oxidation tank and the slurry recycle flow rate in the absorber. The main control problem in a WLFGD plant is the rejection of its most important disturbance, the inlet SO2 load to the absorber. In coal-fired power stations, this disturbance is a consequence of large changes in the boiler load in order to meet power grid demand but also changes in sulfur content of coal, boiler air intake, etc. Recently, more stringent SO2 regulations have come into force, both in Europe and the U.S.A.1 Meeting the new SO2 emission limits entails higher operating costs related to limestone consumption and pumping of absorbent slurry. In fact, the outlet SO2 set point is lower than the SO2 emission limit to provide a safety margin against changes in the inlet SO2 load to the absorber that could result in violation of the SO2 emission limit. However, the higher the safety margin, the higher are the * To whom correspondence should be addressed. Tel.: +0034 954487223. E-mail: [email protected].

operating costs. How much larger the safety margin needs to be depends on selection and design of the control strategy and the dynamic properties of the WLFGD plant to be controlled. Considering that there are no experimental studies addressing these issues in the literature, we published a series of paper dealing with modeling of WLFGD plants for control purposes1 as well as selection, design, and comparison of suitable control strategies for these kinds of plants based on a pilot plant study2,3 (Figure 1). In the first paper,1 we analyzed the dynamic features of WLFGD plants with regard to the physical-chemical phenomena of the WLFGD process. It was reasoned that, due to the complex chemistry of the WLFGD process, an empirical approach was more suitable than a first-principles approach when obtaining a dynamic model of WLFGD plants for control purposes. We gave general recommendations on linear identification of WLFGD plants, and a linear multivariable dynamic model of the WLFGD pilot plant was identified. The model predicted the dynamics of the plant very well in spite of the somewhat nonlinear dynamics of the oxidation tank pH. In our second paper,2 we studied the control limitations of WLFGD plants and assessed the suitability of decentralized feedback control, the most common control strategy in WLFGD plants. First, a general controllability analysis revealed that, in general, good SO2 control in WLFGD plants can be achieved mainly because WLFGD plants are not difficult to control (RGA elements are not large) and the main disturbance of the process is well aligned with the plant. Then, we provided advice on how to design decentralized feedback control for the WLFGD plant through controllability analysis. This revealed that (1) suitable pairings can be selected in these plants that are both beneficial for SO2 control and avoid instability due to interactions, and (2) good control of the WLFGD plant is possible for reference tracking and disturbance rejection, something that was checked in actual plant experiments. In our third paper,3 a model predictive control (MPC) strategy based on a dynamic matrix (DMC) was designed and applied to the WLFGD pilot plant to evaluate the enhancement that could be achieved in control performance as compared to conventional decentralized control strategy. The pilot plant experiments showed that MPC can significantly improve both reference tracking and disturbance rejection.

10.1021/ie9007584  2010 American Chemical Society Published on Web 01/20/2010

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Ind. Eng. Chem. Res., Vol. 49, No. 5, 2010

Figure 1. Pilot plant flowsheet and general view. AT: SO2 sensor, M: variable speed motor, FT: gas flowmeter, pHT: pH sensor.

In general, linear control techniques should suffice to obtain good control of WLFGD plants because commercial wet flue gas desulfurization plants usually operate within a narrow range of oxidation tank pH in order to obtain good gypsum quality. However, the oxidation tank pH in commercial plants can be significantly nonlinear with regard to the fresh limestone slurry flow rate.4 This depends on many factors, such as chemical composition of slurry, limestone reactivity, and operating pH. Hence, in some cases, linear control techniques may be not suitable for pH control and it may be necessary to use nonlinear control techniques. To the best of our knowledge, only a few patents by Almston Technologies propose a control strategy to address nonlinear control of WLFGD plants, based on a multivariable linear predictive controller with a dynamic model which is updated from a steady-state nonlinear model.5-8 Unfortunately, no information about real application of the invention is provided in those patents. We propose a combined control strategy of the WLFGD plant where oxidation tank pH is controlled by a neural predictive controller manipulating the fresh limestone flow rate while the outlet flue gas SO2 concentration is controlled by a feedback controller which manipulates the slurry recycle flow rate. Of course, other approaches would be possible, for example, a multivariable nonlinear predictive control, but (1) a decentralized control strategy is suitable for controlling WLFGD plants, as reasoned above, and (2) nonlinear multivariable controllers are based on MIMO nonlinear models, which are much more difficult to build than SISO models. For the sake of simplicity, we propose the simplest nonlinear control strategy that seems plausible for nonlinear pH control. The main objective of this paper is to assess the aforementioned control strategy for nonlinear pH control in WLFGD plants. For this purpose, the control strategy is applied to a WLFGD pilot plant. The paper is organized into three parts. In the first part, a procedure for nonlinear identification of the oxidation tank pH in WLFGD plants is proposed and applied to the pilot plant. On the basis of the nonlinear model (neural network) and a linear model of the plant, previously identified by the authors,1 the combined control strategy is tuned. Finally, the performance of this strategy is assessed for inlet SO2 load rejection at different operating pHs.

We must point out that, due to the type of limestone used, to obtain good gypsum quality, the WLFGD pilot plant had to be operated in a pH range where the pH turned out to be mildly nonlinear. Therefore, application of the proposed control strategy is not really necessary to achieve acceptable pH control in the pilot plant.2,3 In any event, the proposed control strategy provided excellent pH control, better than the linear control strategies assessed in previous papers in the same pH range,2,3 and similar performance is expected when the pH is highly nonlinear. We must also mention that the pilot plant used in this series of papers (Figure 1) is basically similar to an industrial plant, but there are a few differences: (1) in industrial plants, the most common absorber is a spray scrubber, although packed scrubbers are also used, and (2) in the pilot plant, the fresh limestone slurry is produced by mixing limestone and tap water in a continuous stirred tank. However, in an industrial plant, recycled water from the gypsum dehydration system is used instead of tap water in order to minimize water consumption. This affects the chemical composition of the oxidation tank and, therefore, the performance of the pilot plant may differ slightly from that of an industrial plant under the same operating conditions. However, since the comparison of the control strategies is relative, the conclusions are expected to be correct for fullscale plants. 2. Nonlinear Identification of Oxidation Tank pH for Predictive Control In this section, we discuss the nonlinear identification of oxidation tank pH in WLFGD plants using a neural network, based on the pilot plant study. The section is divided according to the steps that are usually followed to identify a dynamic process:9 (1) selection of the inputs and outputs of the dynamic model; (2) design of identification experiments; (3) selection of neural network architecture; (4) estimation of model parameters; (5) validation of the model. Each step is explained in detail in the following subtopics of this section. 2.1. Selection of Inputs and Outputs of the Neural Network Model. The neural predictive controller will use the neural network model to control the oxidation tank pH by


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Table 1. Nominal Operating Point of the Desulfurization Pilot Plant treated flue gas flow rate, G (Nm3/h) inlet flue gas SO2 concentration (ppmv) L/G ratio in the absorber (L/Nm3) oxidation tank pH SO2 removal efficiency (%) outlet flue gas SO2 concentration (ppmv) reagent ratio (Ca/S)

250 1500 12 3.9 95 70 1.03

manipulating the fresh limestone slurry flow rate. Therefore, at the least, the neural network must model the dynamics between the oxidation tank pH (pH) and the fresh limestone flow rate. This means that the output of the neural network must be the oxidation tank pH while the fresh limestone slurry flow rate (Q) must be one of the inputs to the neural network model. However, since a WLFGD plant is a multivariable plant from a control point of view, changes in the recycle flow rate (L) and inlet SO2 load (load) also affect the oxidation tank pH. Including them as inputs to the neural network would imply developing a multivariable nonlinear model, which entails a more difficult identification procedure since (1) multivariable identification experiments are much more complex than in the linear case due to the “curse of dimensionality”,10 and (2) a larger neural network must be trained. For these reasons, it was decided to develop a nonlinear SISO model of the oxidation tank pH with the fresh limestone slurry flow rate as the only input. As will be shown later, good pH control was achieved in the pilot plant with this model. It should be pointed out that not including the inlet SO2 disturbance as input to the neural network model is acceptable in our case because large changes in the inlet SO2 load are not possible in the pilot plant, 8% at most. Nevertheless, the inlet SO2 load varies significantly in coal-fired power plants, and it must also be included as input to the nonlinear pH model. The reason is that the relation between oxidation tank pH and the fresh limestone slurry flow rate depends greatly on the amount of SO2 absorbed. If the inlet SO2 load varies significantly and the neural network has no information about that, then the fresh limestone supply predicted by the neural network to maintain the operating pH will be highly erroneous. This would probably result in poor pH control. Therefore, inlet SO2 load must be an input to the neural network pH model in full-scale plants. For the neural network to learn the dynamics between pH and inlet SO2 load, the latter should be excited within its operation range in the identification experiments. However, this is not possible in coal-fired power plants as the inlet SO2 load depends on the boiler load, which is changed only to meet power grid demand. A possible solution is that the neural network can learn at least the steady-state effect of the inlet SO2 load on the pH by carrying out the identification experiments at the most common load levels. Since the load is kept constant in these experiments, the same identification experiments that were carried out in the pilot plant could also be used, which is described in the next subtopic. 2.2. Design of Identification Experiments. In the identification experiments, the fresh limestone flow rate must be varied in order to excite the dynamics of the oxidation tank pH. The experiments are carried out around a nominal operating point (Table 1), which was previously determined to meet the new European SO2 emission limit for large power plant stations (outlet SO2 concentration e70 ppmv) and obtain commercialquality gypsum.1 The input/output data generated in these identification experiments must be informative in order to estimate a reliable nonlinear model. This means that the input signal of the identification experiments should meet the following requirements:11,12

Figure 2. RAS identification experiment. pH: oxidation tank pH; Q: rotating speed of the fresh limestone peristaltic pump.

(1) Excite the process in the frequency range important for control. The power spectrum of the input signal should be high in the frequency band (eq 2): 1 R eωe βτhigh τlow

(2)

where τlow and τhigh are the high and low estimates of the time constant over the entire operation range and β is an integer factor representing a high percentage (greater than 95%) of the settling time of the process (normally equal to 3, 4, or 5), while R represents the desired closed-loop speed of response as a multiple of the open-loop response (normally equal to 2). (2) Excite the process over the entire operating range of interest by keeping the input signal amplitude within certain limits due to safety reasons (“plant friendly” amplitude). A random amplitude signal (RAS) meets these requirements since its amplitude is uniformly distributed within two limits, switching from one level to another every clock period (Ts).12,13 The clock period, or switching time, can be adjusted to excite the process at frequencies of interest. It is normally set equal to the time constant12 or the settling time13 of the process. In the pilot plant experiments, a RAS signal was applied to the fresh limestone flow rate (Q) from the nominal operating point, keeping the rest of the variables (L, load) constant so the oxidation tank pH was excited in the operating range of 3.8-4.5. The clock period was set at 40 min which is the settling time of the pH around the nominal operating point.1 The identification experiment is shown in Figure 2. A second kind of experiment was also carried out so the neural network could learn the expected closed-loop performance of the pH controller. In this experiment, the fresh limestone flow rate was manually varied to emulate tracking control of pH step set point changes within the operating range (Figure 3). The system was kept at each set point for a while after it was stabilized, because the dynamic predictions of neural networks are better if the neural network is also trained with steady-state information.14,15 Figure 4 shows the power spectrum of the input signal for each experiment. The frequency range important for control is also shown; it was calculated from eq 2, by selecting R ) 2, β ) 4, and considering that the time constant of the pH barely changes within the operating range and, hence, is equal to the nominal time constant (10 min), that is, τlow ≈ τhigh ≈ 10 min. It can be observed that in both identification experiments the frequency range important for control is considerably excited. During these experiments, it is necessary to monitor those disturbances and secondary process variables that may vary so

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Figure 3. Manual control of pH for set point step changes between 3.8, 4.2, and 4.5.

Figure 5. Linear model fitting to RAS experiment.

neurons was selected because of its capability of acting as a universal approximator.21 The inputs of the ERNN are a set of past plant inputs and predicted outputs, also known as a regression vector (φ(t)). A first estimation of the ERNN regression vector was obtained from the regression vector of the output error model, the linear counterpart of an ERNN model, which best fit the identification experiment data. This linear model is shown in eq 3 (sample time ) 120 s), where the oxidation tank pH (pH) and the rotating speed of the fresh limestone peristaltic pump (Q) are expressed as deviation variables from the nominal operating point (pH ) 3.8; Q ) 44 rpm). The circumflex accent in eq 3 means that the pH value is a prediction by the model.

Figure 4. Power spectrum of input signal in the identification experiments.

much as to perturb the dynamics between the oxidation tank pH and fresh limestone flow rate, invalidating the collected data. This is an important issue because an experiment usually lasts for several hours, due to the slow response of the pH for changes in the fresh limestone flow rate, and unwanted changes in disturbances and secondary process variables are likely to occur. The SO2 load is the most important disturbance of the process and the experiments should be carried out in periods where the boiler load is expected to be constant. The level and density of the oxidation tank will tend to vary notably in the experiments because large changes in the flow rate of fresh limestone are made. As we did in our experiments, we recommend controlling the level and density of the oxidation tank implementing feedback loops. The dynamics of these loops is so fast that they do not affect the experiments. 2.3. Selection of Neural Network Architecture. An external recurrent neural network16 (ERNN) was the type of neural network chosen for modeling the dynamics between the oxidation tank pH and the fresh limestone flow rate. This kind of neural network offers some advantages: (1) ERNNs are more suitable for model predictive control than feedforward neural networks (FNN) since they are naturally capable of providing long-range predictions;14,17-20 (2) A neural predictive controller based on an ERNN can be tuned off-line. Once the type of neural network has been selected, the number of inputs, layers, and neurons must be chosen. In this work, a multilayer perceptron (MLP) neural network with one hidden layer of sigmoidal neurons and one output layer of linear

Figure 5 shows the fitting of the linear model to the RAS experiment. It can be observed that the nonlinearity of the pH is moderate in the pH range studied since the linear model prediction is fairly good. Therefore, we can expect a neural network model with the same regression vector to predict the dynamics of pH even better. If the nonlinearity of the pH had been more severe, a good estimation of the regression vector using a linear model would not have been possible. In that case, advanced methods, such as false nearest neighbors,22,23 their variations,24-26 or those based on identification of local linear models27,28 would be necessary to estimate the regression vector. These methods are advantageous since they allow determination of the regression vector without a priori selection of the number of layers and neurons, therefore decoupling both tasks. Finally, the number of neurons in the hidden layer was selected using a heuristic rule29 which states that the ratio between the number of training patterns and parameters of the neural networks should be around 10. This means that the hidden layer should be composed of eight neurons. This choice was right because the prediction capability of the neural network did not improve when the number of neurons was increased but got worse as the number decreased. Before training the neural network, the experimental data were scaled to zero mean and unit variance. Then, patterns were created on the basis of the aforementioned regression vector. 2.4. Neural Network Parameter Estimation. The neural network was trained using a weight decay method with the Levenberg-Marquardt algorithm. Weight decay is a regularization method which avoids overfitting of the neural network in the training process but also offers other advantages, as will be


Figure 6. Mean square prediction error (V) and Aikake’s final prediction error (AFPE) as a function of the weight decay (R).

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Figure 7. Effective number of parameters in the neural network as a function of the weight decay.

discussed later. The training objective function to be minimized (W) is composed of two terms: one term (V) penalizes the prediction error, while the other (a regularization term) penalizes the use of excessive neural network parameters for the fitting (eq 4):

In eq 4, N is the number of training patterns, ε is the prediction error, θ is the neural network parameter vector, and D is a diagonal matrix, which is usually D ) RI, where R is the weight decay. The correct value of the weight decay is that which minimizes the generalization error of the neural network, which is usually estimated from validation patterns or, if not available, from the training patterns.6 The use of the weight decay method was also motivated because we realized that it was difficult to partition the available experimental data into large enough training and validation data sets so that both the training and validation results were reliable. This situation can also occur in full-scale plants if there is limited time to carry out identification experiments. We decided to use all the experimental data to train the neural network while its validation would be carried out from the training results.10 The weight decay method does not need a validation data set since the neural network is trained until the regularized objective function reaches a minimum. Under these circumstances, the average generalization error can be estimated from Akaike’s final prediction error (AFPE), which makes use of the mean square prediction error (V) based on the training data set.6 The objective of the training process presented here is to find a weight decay R which results in a neural network with minimum AFPE. For this purpose, sensitivity analysis was carried out by evaluating the AFPE for 10-3 < R < 1. In order to avoid local minima in the training objective function, for each value of R, the neural network was trained 3 or 4 times from different initial parameters. In Figure 6, it can be observed that the minimum AFPE was achieved for R ) 10-2, although it is barely noticeable since the AFPE is almost constant for 10-3 < R < 10-1. However, in that range, the effective number of parameters in the neural networks significantly decreases as R increases (Figure 7) since the larger the R, the larger the penalization in the objective function for the use of an excessive number of parameters. For optimum weight decay R ) 10-2, the number of effective

Figure 8. Neural network fitting to training data and associated modeling error.

parameters is 33 while the total number of parameters of the starting neural network was 44. This does not mean that it is appropriate to retrain a network with an initial size of 33 parameters because the use of a smaller network could entail removing not only superfluous parameters but effective ones as well, thus worsening the flexibility of the network for fitting the data.30 Figure 8 shows the fitting of the optimum ERNN (R ) 10-2) to the training data. It can be observed that the neural network perfectly captures the pH dynamics much better than the linear model (eq 3) and that the modeling error is due practically to measurement noise. 2.5. Acceptance of the Model for Control Purposes. Since no validation data set was available, it was decided to accept the ERNN as a dynamic model for controlling the oxidation tank pH if good pH control in the pilot plant was possible using a nonlinear model predictive controller based on the ERNN. Figure 9 shows the neural predictive controller performance for a step change in the pH set point. The control performance is quite good; the closed-loop response is fast (the closed-loop time constant is 50% of the open-loop time constant, i.e., from 10 to 5 min) with neither overshoot nor offset at steady state. Since good control was achieved with the trained ERNN, it was accepted as a model for controlling the pH. 3. Combined Control Strategy of the WLFGD Pilot Plant For controlling nonlinear pH in WLFGD plants, we propose a combined control strategy where oxidation tank pH is

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Figure 9. Neural predictive controller performance for changes in pH set point.

Figure 10. Neural predictive control strategy implemented in the pilot plant.

controlled by a neural predictive controller, which manipulates the fresh limestone flow rate (Q) while the outlet flue gas SO2 concentration is controlled by a feedback controller which manipulates the slurry recycle flow rate (L). A computer (control station) of the pilot plant communication network was used to execute the control algorithms. The control algorithms were implemented in Simulink, which was installed in the control station. Communication between Simulink and the programmable logic controller (PLC) of the plant was by means of a Profibus-DP fieldbus and OPC protocol. Real-time execution of Simulink is possible using a Real Time Blockset31 which synchronizes Simulink with the computer processor clock. In this section, we first describe the features of the neural predictive controller implemented in the WLFGD pilot plant. Then, we address the tuning of the controllers. After that, the performance of the combined control strategy in the pilot plant for disturbance rejection is shown. Finally, the results are compared with other control strategies previously implemented in the pilot plant.2,3 3.1. Neural Predictive Control of the Oxidation Tank pH. The neural predictive control strategy implemented in the pilot plant is shown in Figure 10. An optimizer calculates the changes in the rotating speed of the fresh limestone pump (∆Q) to minimize an objective function (J), which penalizes pH control errors from a reference (r) over a prediction horizon (p), and aggressive control moves over a control horizon (m) through a move suppression coefficient (λ2) (eq 5). p

J)

m

∑ [r(t + k) - pH(t + k|t)]

2

k)1

+ λ2

∑ [∆Q(t + k - 1)]

2

k)1

(5) The optimizer uses the neural network model to predict the future behavior of oxidation tank pH for changes in the fresh

limestone flow rate. The predictions of the neural network are not directly used in eq 5 but are corrected to take into account modeling errors and unmeasured disturbances (w) and to prevent the controller from exhibiting steady-state offset. The most common correction used in nonlinear predictive control is the addition of a bias correction to the predictions based on the prediction error32,33 (eq 6), that is, the difference between the current measured pH (pHm) and the current predicted pH by the neural network model (from eq 3). This correction corresponds to the standard DMC correction and is equivalent to shifting the reference, as shown in Figure 10. This approach assumes that unmeasured disturbances are constant over the prediction horizon, and under these circumstances, the correction provides integral action to the controller, resulting in no steadystate offset regardless of process/model mismatch.34 It should be pointed out that this correction modifies the prediction of the neural network by adding a corrective term and, hence, is not suitable for highly nonlinear processes.35

In the case of the WLFGD pilot plant, the correction was suitable since the pH is moderately nonlinear, as will be shown in Section 4. If good performance of the controller had not been achieved, alternative corrections could have been selected, such as regressions based on past prediction errors to estimate future prediction errors36,37 or corrections directly based on past predictions.38 The optimization problem was posed as shown in eq 7: min

∆Q(t+1),...,∆Q(t+m)

subject to

J ∆Q(t + k - 1) e ∆Qmax k ) 1, ..., m k ) m, ..., p ∆Q(t + k) ) 0

(7) A constraint on the maximum allowable change in rotating speed of the fresh limestone pump was imposed, as will be explained later. At each sample time, this nonlinear programming problem was solved using the fmincon function from Matlab’s Optimization Toolbox,39 which implements a sequential quadratic programming (SQP) algorithm. 3.2. Tuning of the Combined Control Strategy. The tuning of the combined control strategy was carried out in two steps. First, the neural predictive controller and the feedback controller were independently tuned. Then the combined control strategy was simulated for fine-tuning. 3.2.1. Tuning of the Neural Predictive Controller. The setting of the model predictive controller was determined by evaluating the performance of the controller for reference tracking over the entire operating range by means of simulations. It should be noted that the tuning is carried out taking into account that in the objective function J (eq 5), pH and Q are scaled so that both of them are of the order of one. The scaling factors are those used for scaling the inputs and outputs of the neural network in the training. Thus, (1) tuning is more intuitive since both terms in the objective function are of the same order, and (2) the optimizer directly uses the inputs and outputs of the neural network, without needing intermediate scaling. First, the sample time of the predictive controller is set to be equal to that of the neural network, that is, 120 s. Initial values for the prediction horizon (p) and control horizon (m) were chosen on the basis of the rules of thumb10,13 before performing the simulations. The prediction horizon is recommended to be at least the desired rise time of the system. In this case, it was

Ind. Eng. Chem. Res., Vol. 49, No. 5, 2010 Table 2. Setting of the Neural Predictive Controller sample time (s) prediction horizon (p) control horizon (m) move suppression factor (λ2)

120 5 2 0.04

set at 10 min (5 intervals). In general, the prediction horizon can be set as large as one wants it to be, as this tends to smooth the controller performance, but it should bear in mind that a very large prediction horizon may result in excessive computational burden for solving the optimization problem within the sampling time. Regarding the control horizon, it is recommended to set it initially at 1 interval (in this case 2 min) because the larger the control horizon the more complex the optimization problem. After setting the prediction and control horizon, the control performance of the predictive controller can be inspected for reference tracking by means of simulations where the move suppression factor (λ2) is changed between 0 and 1. In this case, it was not possible to find a relatively fast response without very large control moves. A possible solution is to increase the degrees of freedom of the controller by increasing the control horizon from 1 to 2 intervals and perform the simulations again. However, a good trade-off was not found either. Instead of increasing the control horizon, which would entail a more complex optimization problem, it may be better to constrain the maximum change in the manipulated variable to prevent very large control moves. Thus, the maximum change in rotating speed of the fresh limestone pump (∆Qmax) was constrained to 4 rpm, and then, a good trade-off was found for λ2 ) 0.04. This initial setting (Table 2) was used for tuning the combined control strategy, as explained in section 3.2.3. 3.2.2. SO2 Feedback Controller. The SO2 feedback controller is the one used in a decentralized feedback control previously implemented in the WLFGD plant. The controller manipulates the frequency of the slurry recirculation pump motor (Hz). It was designed on the basis of IMC-PID tuning rules from a linear dynamic model of the pilot plant identified around the nominal operating point. A thorough description of the controller design has been provided elsewhere.2 Only the discrete form of the controller implemented in the pilot plant is shown here: k(z) ) -0.0013

1 + 0.01248z-1 - 0.988z-2 1 - 1.999z-1 + 0.995z-2

(8)

The sample time of the SO2 controller was 30 s. The drawback of this controller is that its performance may not be guaranteed at operating pHs different from the nominal one, unlike the nonlinear predictive controller, since the effect of the slurry recycle flow rate on the outlet flue gas SO2 concentration may change significantly with the operating pH. In that case, a gain scheduling approach should be taken. This was not necessary in the WLFGD pilot plant, as will be explained next. 3.2.3. Fine-Tuning of the Controllers Settings. The performance of the combined control strategy for rejecting the maximum expected changes in the inlet SO2 load to the absorber was assessed by means of simulations in order to determine whether fine-tuning of controllers settings was necessary. Because a nonlinear dynamic model of the whole plant was not available, a dynamic model of the plant comprising the neural network and linear models previously determined1 was used. Although this is a rough dynamic model, it was useful to assess the performance of the combined control strategy. With the initial settings, the performance of the combined control strategy for disturbance rejection was good. As expected,

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no adjustment of the settings was necessary, since WLFGD plants are not highly interactive.1,2 Setting the control horizon at 4 min (two intervals) provided the predictive controller with enough degrees of freedom to handle changes in the inlet SO2 load while the constraint in the maximum change of the rotating speed of the fresh limestone pump prevented very large control moves. 3.2.4. Verifying the Use of the Neural Network. Once the neural network predictive controller has been tuned by simulations, the next step is its implementation in the WLFGD plant. To prevent that any implementation error may cause unexpected variation of the manipulated variable by the predictive controller, it is recommended to implement the neural predictive controller in three steps. First, the neural network should be run online and its pH predictions based on the actual fresh limestone flow rates should be compared with actual pH when the plant is at the nominal operating point. If the error between model predictions and plant output is similar to that observed in the validation of the neural network, this has been correctly implemented. The second step is to run the neural predictive controller in open-loop: when control is transferred from manual to automatic, the inputs of the neural network are initialized with past plant values of the fresh limestone flow rate and pH; then the neural predictive controller, on the basis of the information from the plant, calculates the change in the fresh limestone flow rate, but this is not implemented. If the plant operates at steady state, the fresh limestone flow rate predicted by the controller should be similar to the actual fresh limestone flow rate. If so, the neural predictive controller is correctly implemented and ready to run in closed-loop. 4. Performance of the Combined Control Strategy in the Pilot Plant The performance of the combined control strategy was only assessed for rejecting changes in the inlet SO2 load to the absorber since it is the most important control objective in WLFGD plants. To study the robustness of the control strategy, the control experiments were carried out at different oxidation tank pHs, namely, 3.8, 4.05, and 4.3, so at each pH, changes of different magnitude in the inlet SO2 load were applied. Feedforward action was not added to the control system in order to evaluate the maximum rejection capacity of the combined control strategy by itself. According to our previous papers,2,3 the criterion for achieving acceptable control of the WLFGD pilot plant was to keep the control error of tank pH and outlet flue gas SO2 concentration below 0.12 and 50 ppmv, respectively, considering a maximum expected change of 8% in the treated flue gas flow rate. Since the inlet flue gas SO2 concentration is assumed to be constant at its nominal value (1500 ppmv), the maximum expected change in the inlet SO2 load is 30 000 N m3 · ppmv/h. The results of the control experiments are shown in Figures 11-16. Figures 11 and 12 show the performance of the control strategy for rejection of 74% and 87% of the maximum expected change in the inlet SO2 load, respectively, at a fixed pH set point of 3.8. In both experiments, the pH control is very good, much better than with a decentralized feedback control strategy2 and similar to multivariable linear model predictive control.3 On the other hand, there is disparity in the control of the outlet flue gas SO2 concentration for both experiments. In the experiment where the change in the inlet SO2 load is smaller, the maximum SO2 control error is 40 ppmv, 20% lower than the maximum allowable one, while in the other experiment the maximum SO2 control error is 75 ppmv, 50% larger than the

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Figure 11. Performance of combined control strategy for 74% of maximum expected step change in the inlet SO2 load. Set points: pH ) 3.8, SO2 ) 78 ppmv.


maximum allowable. Therefore, the SO2 control is not completely satisfactory, similar to the results observed with a decentralized feedback control strategy.2 Figures 13, 14, and 15 show the performance of the control strategy for rejection of 75%, 85%, and 94% of the maximum expected change of the inlet SO2 load, respectively, at a fixed pH set point of 4.05. The same conclusions for pH and SO2 control can be drawn as those at a pH set point of 3.8. It could be expected that the SO2 control would improve over the previous experiments because the alkalinity of the slurry is somewhat higher. However, it seems that such an increase in the pH is negligible at a low operating pH. This is also true



even operating at a tank pH of 4.3, as can be observed in Figure 16. That is the reason why the performance of the SO2 controller did not change with the operating pH. Thus, at a low operating pH (4.5-5), gain scheduling may be necessary. From the control experiments, it can be concluded that replacing a feedback controller with a neural predictive controller in a decentralized control strategy greatly improves pH control. However, “perfect” control of tank pH does not entail



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Figure 17. Simulations of disturbance rejection with and without SO2 feedforward action (dashed red and solid blue line, respectively) for 85% of maximum expected step change in the inlet SO2 load.

17. It can be observed that the SO2 feedforward action greatly improves the SO2 control while the pH control by the neural predictive controller remains excellent. The control experiments also reveal that the neural predictive controller is robust for the pH range studied, successfully handling changes in the slurry recycle flow rate and the inlet SO2 load, which are unmeasured disturbances to the neural predictive controller. We can conclude that the choice of DMC correction was right. This was expected, as the DMC correction, when used with a predictive controller based on an ERNN, is an effective way of dealing with modeling errors, as previously reported by other authors.18 5. Conclusions


better SO2 control, mainly because changes in the fresh limestone flow rate to control tank pH affect the outlet flue gas SO2 concentration1 slowly due to the slow dissolution rate of limestone in WLFGD plants. Only rapid changes in the slurry recycle flow rates can significantly reduce the initial effect of inlet SO2 load changes on the outlet flue gas SO2 concentration.1,2 Therefore, feedforward control should be added to the SO2 control loop to achieve acceptable control. This was checked by carrying out simulations of the combined control strategy with and without feedforward action for SO2, as shown in Figure

In this work, we propose and assess a combined control strategy for nonlinear pH control in WLFGD plants. The necessary steps for designing and implementing the combined control strategy in a WLFGD plant have been described, based on a pilot plant study. When comparing the performance of the combined control strategy with control strategies previously applied to the WLFGD pilot plant, namely, decentralized feedback control2 and linear multivariable predictive control,3 it can be concluded that it is better than decentralized feedback control but worse than linear multivariable predictive control. The combined control strategy improves the oxidation tank pH control as compared to decentralized feedback control but lacks good SO2 control for changes in the inlet SO2 load. This comparison is carried out without the use of feedforward control in the control system. However, if feedforward action is added to the SO2 control loop, the SO2 control improves so much2 that the performance of the combined control strategy is practically equal to that of linear multivariable predictive control. Of course, it makes no sense to choose a combined control strategy instead of a linear multivariable predictive controller unless the nonlinearity of the tank pH is so high that the linear predictive controller cannot deal with it. In that case, a pH

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nonlinear predictive controller and a SO2 feedback controller with feedforward action suffice to achieve acceptable control. Using more complex control strategies, such as nonlinear multivariable predictive controllers is probably not worthwhile. Acknowledgment This work is part of the research project “Advanced control of wet flue gas desulfurization units” (PPQ2001-1106) funded by the Science and Technology Ministry of Spain. Initial guidance by Dr. M. R. Arahal of the Department of System Engineering and Automatic Control of the University of Seville is gratefully acknowledged. Literature Cited (1) Villanueva Perales, A. L.; Ollero, P.; Gutie´rrez Ortiz, F. J.; Vidal, F. Dynamic analysis and identification of a wet limestone flue gas desulfurization pilot plant. Ind. Eng. Chem. Res. 2008, 47 (21), 8263–8272. (2) Villanueva Perales, A. L.; Gutie´rrez Ortiz, F. J.; Ollero, P.; Munõz Gil, F. Controllability analysis and decentralized control of a wet limestone flue gas desulfurization plant. Ind. Eng. Chem. Res. 2008, 47 (24), 9931– 9940. (3) Villanueva Perales, A. L.; Ollero, P.; Gutie´rrez Ortiz, F. J.; Go´mezBarea, A. Model predictive control of a wet limestone flue gas desulfurization pilot plant. Ind. Eng. Chem. Res. 2009, 48 (11), 5399–5405. (4) Radian International LLC. Electric Utility Engineer’s FGD Manual: Volume 1-FGD Process Design; U.S. Department of Energy Office of Fossil Energy: West Virginia, 1996. (5) Boyden, S. A.; Piche, S. Optimized air pollution control. U.S. Patent 2006/0045800, March 2, 2006. (6) Boyden, S. A.; Piche, S. Maximizing Profit and Minimizing Losses in Controlling Air Pollution. U.S. Patent 2006/0047607, March 2, 2006. (7) Boyden, S. A.; Piche, S. Cost based control of air pollution control. U.S. Patent 2006/0047526, March 2, 2006. (8) Boyden, S. A.; Piche, S. Control of rolling or moving average values of air pollution control emissions to a desired value. U.S. Patent 2006/ 0047347, March 2, 2006. (9) Ljung, L. System Identification - Theory For the User, 2nd ed; PTR Prentice Hall: Upper Saddle River, N.J., 1999. (10) Nørgard, M.; Ravn, O.; Poulsen, N. K.; Hansen, L. K. Neural Networks for Modelling and Control of Dynamic Systems; Springer-Verlag: London, 2003. (11) Rivera, D. E.; Braun, M. W.; Stenman, A. A “Model-on-Demand” identification methodology for non-linear process systems. Int. J. Control 2001, 74 (18), 1708–1717. (12) Ling, W.-M.; Rivera, D. E. A methodology for control-relevant non-linear system identification using restricted complexity models. J. Proc. Control 2001, 11, 209–222. (13) Doherty, S. K. Control of pH in chemical processes using artificial neural networks. Ph.D. Thesis. Liverpool John Moores University. 1999. (14) Himmelblau, D. M.; MacMurray, J. C. Modeling and Control of a Packed Distillation Column Using Artificial Neural Network. Comput. Chem. Eng. 1995, 19, 1077–1088. (15) Zhang, J. Developing Robust Neural Networks Models by Using Both Dynamic and Static Process Operating Data. Ind. Eng. Chem. Res. 2001, 40, 234–241. (16) Narendra, K. S.; Parthasarathy, K. Identification and control of dynamic systems using neural networks. IEEE Trans. Neural Networks 1990, 1, 4–27.

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ReceiVed for reView May 11, 2009 ReVised manuscript receiVed December 21, 2009 Accepted December 21, 2009 IE9007584

Using Neural Networks to Address Nonlinear pH Control in Wet

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