ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING Asia-Pac. J. Chem. Eng. 2007; 2: 536–543 Published online 29 October 2007 in Wiley InterScience (www.interscience.wiley.com) DOI:10.1002/apj.098 Research Article Dual-mode control with neural network based inverse model for a steel pickling process P. Thitiyasook,1 P. Kittisupakorn1 * and M. A. Hussain2 1 2 Department of Chemical Engineering, Chulalongkorn University, Bangkok, Thailand Chemical Engineering Department, University of Malaya, Kuala Lumpur, Malaysia Received 9 April 2007; Revised 25 July 2007; Accepted 13 August 2007 ABSTRACT: This article describes a novel implementation of the dual-mode (DM) control utilizing a neural network inverse model on a multivariable process (a steel pickling process). This process is highly nonlinear with variableinteraction, and is multivariable in nature, hence an accurately nonlinear model is required to provide acceptable control. The requirement of a true analytical inverse can be avoided when neural network models are used; they have the ability to approximate both the forward and the inverse system dynamics. Various changes in the open-loop dynamics are performed before implementation of the inverse neural network modeling technique. DM control based on neural network inverse model strategy is used to design the controllers to control concentration and pH of the process, which is guaranteed to remove steady-state offset in the controlled variables to obtain the maximum reaction rate and to comply with limits imposed by legislation. The robustness of the proposed DM control is investigated with respect to changes in disturbances and model mismatch. Comparisons are also made with the conventional inverse neural network controller (NNDIC) and other conventional controller proportional-integral (PI). Simulation results show the superiority of the DM controller in the cases involving disturbance and model mismatch, while the conventional controller gives better results in the nominal case. 2007 Curtin University of Technology and John Wiley & Sons, Ltd. KEYWORDS: steel pickling process; neural network inverse modeling; dual-mode control strategy INTRODUCTION Since the main reason for obtaining large uncertainties in a system is due to poor modeling, one possible method to solve this problem is by using neural networks to model the system. A neural network (NN), which is a black-box modeling tool, has found wide application in the fields of process identification and process control due to its superb ability in representing arbitrary nonlinear relationships.[1 – 3] A NN has been shown to model dynamic models (forward modeling techniques) well if time-delayed data are used as inputs to it in many cases.[3,4] The ability of NNs to model dynamic nonlinear mappings/functions makes them attractive for use in nonlinear system control strategies. The use of a NN for modeling the inverse of input–output relationship is also highly promising.[4 – 6] In this approach, the NN is trained with observed inputoutput data from the system to represent its inverse dynamics. In other words, given the current state of the dynamic system and the target state (e.g., set-point) *Correspondence to: P. Kittisupakorn, Department of Chemical Engineering, Chulalongkorn University, Bangkok, Thailand. E-mail: paisan.k@chula.ac.th 2007 Curtin University of Technology and John Wiley & Sons, Ltd. for the next sampling instant, the network is trained to produce the control action that drives the system to this target state. The resulting inverse model NN can then be used as a controller, typically in a feed-forward fashion. However, it is also widely recognized that the modeling accuracy of a network depends on the quality of the data presented to it during the training phase. Insufficient as well as noisy data can affect the accuracy of the network in the modeling of the inverse function. This may cause offset in the control trajectory. This limitation can be overcome by using dual-mode (DM) control[7] which incorporates both, inverse NN control mode, and the proportional-integral (PI) control mode. To this effect, the application of a DM controller based on the inverse NN model for a steel pickling plant, a fundamental industry in Thailand, is investigated in this work. The structure of the article is as follows. It starts with process description of the steel pickling process. Then, the general idea of inverse NN is reviewed, and further proceeds with the inverse modeling design of the system. The designed DM approach is implemented for process control. For comparison purposes, the conventional inverse NN and the PI controller that is used in many industries these days are also implemented, as discussed in the final section. Asia-Pacific Journal of Chemical Engineering NEURAL INVERSE MODEL IN STEEL PICKLING PROCESS • The deterioration of pickling efficiency resulting from iron concentration is considered negligible. THE STEEL PICKLING PROCESS The steel pickling process consists of two major steps: pickling and rinsing.[8] The purpose of the pickling step is to remove surface oxides (scales) and other contaminants from the metals by immersion of the metals into an aqueous acid solution. Metals are immersed in pickling baths containing 5, 10 and 15% by weight of hydrochloric acid (HCl), respectively, in order to remove scales from the metals. The metals move counter-current to the acid stream as can be seen in Fig. 1. The reaction occurring in the pickling baths is as follows: FeO + 2HCl −−→ FeCl2 + H2 O (1) Drag in-out pickling solution is removed from the metal surface using rinsing water in the rinsing step, which consist of three pure water baths. The metals move opposite to the rinse water flow as shown in Fig. 2. Here, the amount of drag-out solution of each bath is assumed to be equal to the amount of drag-in solution. The following assumptions are made for the purpose of this study. • The system is supposed to be perfectly mixed and isothermal. • All state variables are measurable directly. • Density of the liquid is assumed to be constant. Figure 1. Flow diagram of pickling baths control system. Based on the above assumptions, the mathematical model of the continuous steel pickling process as shown in Figs 1 and 2 for the change in volume and concentration can be derived for both, the pickling and rinsing steps, as follows: Pickling step (occurring in the 5, 10 and 15% HCl baths) dh1 dt dh2 A dt dh3 A dt dC1 V1 dt dC2 V2 dt dC3 V3 dt A = F2 − F1 − q (2) = F3 − F2 − F11 (3) = F4 + F5 − F3 − F10 (4) = F2 C2 − C1 (F1 + q) − V1 r1 (5) = qC1 + F3 C3 − C2 (F2 + F11 + q) − V2 r2 (6) = qC2 + F5 C20 + F4 C4 − C3 (F3 + F10 + q) − V3 r3 Rinsing step (occurring in three pure water baths) dh4 dt dh5 A dt dh6 A dt dC4 V4 dt dC5 V5 dt dC6 V6 dt A = F6 − F4 − F9 (8) = F7 − F6 (9) = F8 − F7 (10) = qC3 + F6 C5 − C4 (F4 + F9 + q) (11) = qC4 + F7 C6 − C5 (F6 + q) (12) = qC5 + F8 Cw − C6 (F7 + q) (13) The meanings of all these variables are specified in the nomenclature. To complete the mathematical modeling of this continuous process, the expression of the reaction rate, Eqn (1), in the pickling baths needs to be imposed. The reaction is assumed to be first order neglecting liquid diffusion and the deterioration of pickling acid resulting from the accumulation of oxide in the pickling bath. Therefore, the equation of the reaction rate studied here solely depends upon acid concentration as shown below: r = kC Figure 2. Flow diagram of rinsing baths control system. 2007 Curtin University of Technology and John Wiley & Sons, Ltd. (7) (14) The objective of this work is to control the concentration of HCl in all the pickling baths (C1 , C2 and C3 ) and Asia-Pac. J. Chem. Eng. 2007; 2: 536–543 DOI: 10.1002/apj 537 538 P. THITIYASOOK, P. KITTISUPAKORN AND M. A. HUSSAIN the pH (or H+ concentration (C4 )) in the first rinsing bath to a desired set-point by manipulating inlet flows F2 , F3 , F5 and F6 , respectively, as shown in Figs 1 and 2. Since the DM incorporating an inverse NN-based model is used for the control, we will first describe the procedure for inverse NN modeling and its use in control in the next section. Asia-Pacific Journal of Chemical Engineering F(k) C(k+1) PLANT + − Z−1 TRAINING SIGNAL ^ F(k) Z−k NEURAL NETWORK Z−1 NEURAL NETWORK The use of a NN in process engineering has increased considerably in the last decade. For a given set of inputs, NNs are able to produce a corresponding set of outputs according to some mapping relationship. This relationship is encoded into the network structure during a period of training (also called learning), and is dependant upon the parameters of the network, that is, weights and biases. Once the network has been trained (on the basis of known sets of input/output data), the input/output mapping is produced in a period of time that is faster than the time taken when using rigorous deterministic modeling.[9,10] Neural network inverse models Inverse models provide the NN structure, which represents the inverse of the system dynamics in the region of the training/identification. There are several ways to carry out this identification process. The technique used here is known as the generalized inverse learning method.[11,12] Here, the network is fed with the required future or reference output together with the past inputs and the past outputs to predict the current input or control action. The trained network represents the inverse model of the system. The assignment of the input nodes consists of the past and present values of the known flows and concentrations associated with the individual tanks and the desired value of the plant output, C (k + 1), corresponding to the required set-point or reference signal. The output node of the NN inverse model consists of the manipulated variable for the tank, i.e. flow entering the associated tank. Although various prediction horizons can be used for these inverse models, this study concentrates on a simple one-step-ahead horizon, which assumes that there is no additional time delay between the control action and the output. Procedure for obtaining neural network inverse models Inverse modeling refers to training the network models to predict the control actions, which are used as the controllers.[13,14] During training, each member of the 2007 Curtin University of Technology and John Wiley & Sons, Ltd. Z−k Figure 3. The method for the training of neural network inverse models. training set is presented to the network individually, and upon each input presentation, the weights are adjusted. The procedure is repeated until a certain performance index is achieved. In this case, the network is said to have converged to its targeted value. Initially, the adaptable weights and bias are set to small randomized values, and the network normally does not respond well mainly due to the random weights used. As the weights are adapted during training, the performance index will also improve. The training is stopped when the error rate is small or reaches its defined value. The method for training the NN inverse models is shown in Fig. 3. In this work, the single hidden layer feed-forward networks are used, which are trained using the Levenberg–Marquardt method. Mathematically, these four inverse models are expressed as functions of inputs to the model as below: Pickling Baths 5%HCl Bath F2 (k ) = f −1 (F2 (k − 1), C2 (k − 1), C2 (k ), C1 (k ), C1 (k + 1)) 10%HCl Bath F3 (k ) = f (15) −1 (F2 (k − 1), F2 (k ), F3 (k − 1), C1 (k − 1), C1 (k ), C3 (k − 1), C3 (k ), C2 (k ), C2 (k + 1)) (16) 15%HCl Bath F5 (k ) = f −1 (F3 (k − 1), F3 (k ), F5 (k − 1), C2 (k − 1), C2 (k ), C3 (k ), C3 (k + 1)) (17) Rinsing Baths 1# Rinsing Bath F6 (k ) = f −1 (F6 (k − 1), C3 (k − 1), C3 (k ), C5 (k − 1), C5 (k ), C4 (k ), C4 (k + 1)) (18) The stopping criteria for the training are set to either 1000 epochs or when the overall errors on the outputs are lower than 10−4 (where the errors are evaluated as the mean-squared error (MSE) function). The MSE is expressed mathematically below where n is the number Asia-Pac. J. Chem. Eng. 2007; 2: 536–543 DOI: 10.1002/apj Asia-Pacific Journal of Chemical Engineering NEURAL INVERSE MODEL IN STEEL PICKLING PROCESS of data, Ftg is the target/desired flow value and FN is the NN output. MSE = n 1 (Ftg (k ) − FN (k ))2 n (19) k =1 All the inputs and outputs are scaled between 0.05 and 0.95 to ensure that all the values computed in the network training are of the same order of magnitude. The inputs and outputs are scaled using the following equations: (valueAC − min value)(0.95 − 0.05) valueSD = (max value − min value) + 0.05 (20) The actual value is given by (valueSD − 0.05)(max value − min value) valueAC = 0.95 − 0.05 + min value (21) where valueSD is the scaled down value and valueAC is the actual value. The training is switched between the two sets of data until the MSE has been satisfied in both cases. They are switched between each other during training to improve the NN system identification capability. In obtaining the inverse model using a NN, the number of hidden nodes plays a very important role in the network performance. Currently, there are no specified methods in obtaining the correct number of nodes. In this work, the hidden nodes are chosen by the MSE minimization technique. In this technique, the hidden nodes are varied in various quantities and the MSE error is then monitored. The network with the corresponding hidden nodes that gives the minimum MSE value is selected as the final network configuration. As an example, Table 1 shows the MSE values obtained from the inverse NN model for the 15% HCl bath using different numbers of hidden nodes. Based on these minimizing MSE error values, it is found that 4, 8, 12 and 16 hidden nodes in the inverse NNs appear to be the best to be applied respectively, as Table 1. MSE value for different number of hidden nodes in the inverse neural network model for 15% HCl bath. Numbers of hidden nodes 4 8 12 16 20 Mean Squared Error (MSE) after validation 2.088 × 10−5 3.211 × 10−5 1.268 × 10−5 (least value) 2.214 × 10−5 1.082 × 10−4 2007 Curtin University of Technology and John Wiley & Sons, Ltd. Figure 4. Procedure for obtaining inverse neural network models. controllers for the 5, 10, 15% HCl and #1 rinsing bath in the control strategy. The NN inverse model-based control has constraints inherent in it since the constraint is set by the range of the training data. Detailed procedures to obtain reliable inverse NN models are summarized in Fig. 4. DUAL-MODE CONTROL BASED ON NEURAL NETWORK INVERSE MODEL STRATEGY Normally, the implementation of the inverse NN model to control the process gives some errors between set-point and control variable (offset) since an exact inverse model is difficult to obtain, as has been proved theoretically.[15] In order to remove this offset and improve the process response, PI controller is also implemented in this proposed DM control strategy which makes use of both, the inverse NN and PI controller. The basic concept of the DM algorithm can be divided into two modes of operation. That is, in the first mode, the inverse NN controller is applied whenever an error between the state (control variables) and set-point lies outside the limit values, E (Eqn (22)), while in the second mode, the PI controller is employed inside the limit error region to bring the state to the desired set-point. In this work, the limited value is set to ±3% of the set point in each bath, where E is defined as: (22) |Csp − C (k )| = E Asia-Pac. J. Chem. Eng. 2007; 2: 536–543 DOI: 10.1002/apj 539 540 P. THITIYASOOK, P. KITTISUPAKORN AND M. A. HUSSAIN The main benefit of the DM controller is that, under nominal operating conditions, when the state is located far away from set-point, the inverse NN controller can bring the state to the desired set-point without a drastic change of the manipulated variable and oscillation. However, when the state is located within a limited region (E ), the PI controller starts to gain control and brings the state to the desired set-point without offset, which normally occurs when controlling using the inverse NN controller only. In addition, the control action given by the PI controller in DM gradually changes and is less drastic when compared to using the conventional controller PI alone. Due to such advantages, the DM control offers an attractive control methodology for process control application. RESULTS AND DISCUSSION The objective of the simulation studies is to control the concentration of HCl in the 5, 10, 15% HCl and #1 rinsing bath to nominal values of 1.40, 2.87, 4.41 and 1 × 10−3 mol/l (pH 3) by adjusting the manipulated variables F2 , F3 , F5 and F6 , respectively. They are divided into three cases of control studies, which are the nominal case, disturbance case and model mismatch case, respectively. Asia-Pacific Journal of Chemical Engineering Nominal case The controllers are designed to bring the concentration of HCl in each bath to the desired value when the initial condition is set at the steady state for 20 min from the start. Figure 5(a), (b) and (c) show the control of HCl concentration in 15% HCl bath using DM control, NNDIC and PI control, respectively. The results in these figures indicate that the DM controller can bring the concentration to the desired set-point without any offset and oscillation of manipulated variable, while the NNDIC brings the concentration closely to the setpoint with minimal offset. The PI controller brings the concentration to the set-point without offset, but however, there is drastic change of the manipulated variable and wide oscillation in the initial state of the control. These control strategies are also applied for the 5 and 10% HCl, and the #1 rinsing bath; however, only the 15% HCl bath control result is shown because this bath has the highest HCl concentration and is very difficult to control, from which we can observe the effect of the controllers. Their performances are also evaluated using the Integral Absolute Error (IAE). The IAE results for the nominal case of these four baths are summarized in Table 2. They showed that relatively, the PI controllers give slightly better results than the DM control and NNDIC in terms of lesser IAE values Figure 5. Concentration control in 15% HCl bath under the nominal case: (a) DM control (b) NNDIC (c) PI control. This figure is available in colour online at www.apjChemEng.com. 2007 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. 2007; 2: 536–543 DOI: 10.1002/apj Asia-Pacific Journal of Chemical Engineering NEURAL INVERSE MODEL IN STEEL PICKLING PROCESS Table 2. Performance comparison between dual mode, NNDIC and PI controls under the nominal case. IAE values Bath 5% HCl bath 10% HCl bath 15% HCl bath #1 Rinsing bath DM NNDIC PI 1.756 3.425 4.967 0.044 2.109 37.925 21.697 0.274 0.342 2.607 13.281 0.007 for the 5 and 10% HCl, and the #1 rinsing baths. For the 15% HCL bath, the control action of PI controller is very drastic causing overshoot of concentration, and therefore, a higher IAE value is obtained as compared to the DM controller. Disturbance case In this case, the disturbance, which is the change in the concentration of C20 in the stream F5 , is introduced by increasing and reducing 15% from its nominal operation values. Initially, the process is left under control until t = 200 min, at which instant, a disturbance is introduced. During the period t = 200–300 min, the control action is halted at the last value to allow the process to respond to the new load condition. At t = 300 min, the DM, NNDIC and PI control actions are reintroduced into the system. Figure 6 shows the results of the DM, NNDIC and PI controls for 15% HCl bath by increasing 15% of C20 from its nominal value. It can be seen from Fig. 6 that when the disturbance is introduced (t = 200–300 min), the process responds by the increase in concentration of the baths due to the increase of HCl concentration (C20 ) to 15% HCl bath. After t = 300 min, the DM strategy can bring back the concentrations to the required value without offset and oscillation, while NNDIC strategy bring back the concentrations close to the required value and give offsets and the PI control strategy could not bring the concentrations to the set-point. Relatively, similar results are obtained for the 10% HCl bath and the #1 rinsing bath. In the 5% HCl bath, the PI controller can bring the concentration to its set-point but there is rigorous adjusting of the F2 up to 4 l/min causing overshoot in concentration. In reducing the concentration C20 by 15%, the results show that the DM strategy can still control the process and bring the concentrations to their set-points, while the NNDIC strategy brings the concentrations to their set-points with slight offsets, but the PI controller cannot control the process. Table 3 summarizes the IAE values of DM, NNDIC and PI controls for the four baths. They indicate that the DM controller is most robust and gives Figure 6. Concentration control in 15% HCl bath under the disturbance case (15% increase of the concentration, C20 ): (a) DM control (b) NNDIC (c) PI control. This figure is available in colour online at www.apjChemEng.com. 2007 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. 2007; 2: 536–543 DOI: 10.1002/apj 541 542 P. THITIYASOOK, P. KITTISUPAKORN AND M. A. HUSSAIN Asia-Pacific Journal of Chemical Engineering Table 3. Performance comparison between DM, NNDIC and PI controls under the disturbance case (15% increasing of the concentration, C20 ). the model mismatch is introduced. During the period t = 200–300 min, the process control action is halted at the latest value to allow the process to respond to a new load condition. At t = 300 min, the DM, NNDIC and PI control actions are reintroduced into the system. Figure 7 shows the results of DM, NNDIC and PI controls for 15% HCl bath by increasing 15% of the kinetic rate constant. When the model mismatch is introduced (t = 200–300 min), the process responds by a decrease in concentration in baths due to the increase of rate of reaction in the acid bath. After t = 300 min, the DM control brings back the concentrations to their required values without the offset, while the NNDIC strategy brings back the concentrations close to their required values and gives offsets, but PI control strategy cannot bring the concentrations to the set-point. In reducing 15% of the kinetic rate constant, the results again show that the DM control can control the process and bring the concentrations to their set-points, while the NNDIC strategy can control the process and bring the concentrations close to their set-points with slight offsets, but the PI controller cannot control the process at all. Table 4 shows the IAE values of DM, NNDIC and PI controls for the four baths. They again indicate that the DM control has the most robustness and gives better IAE values Bath 5% HCl bath 10% HCl bath 15% HCl bath #1 Rinsing bath DM NNDIC PI 1.183 3.661 38.492 0.052 3.508 77.595 74.997 0.444 12.252 623.919 696.903 0.087 better control performance than the NNDIC and PI controllers with very much smaller IAE error values, when disturbances are present in the system. Model mismatch case In this work, the rate of reaction in the acid bath is considered as the model mismatch in the parameter under consideration. The model mismatch is introduced by increasing and reducing 15% of the kinetic rate constant from its nominal value. Initially, the process is left under control until t = 200 min, at which instant, Figure 7. Concentration control in 15% HCl under the model mismatch case (15% increase of reaction rate, k): (a) DM control (b) NNDIC (c) PI control. This figure is available in colour online at www.apjChemEng.com. 2007 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. 2007; 2: 536–543 DOI: 10.1002/apj Asia-Pacific Journal of Chemical Engineering NEURAL INVERSE MODEL IN STEEL PICKLING PROCESS Table 4. Performance comparison between DM, NNDIC and PI controls under the model mismatch case (15% increase of the reaction rate, k). IAE values Bath 5% HCl bath 10% HCl bath 15% HCl bath #1 Rinsing bath DM NNDIC PI 3.998 8.162 11.665 0.049 11.116 101.759 73.782 0.424 136.385 220.565 289.428 0.041 control performance than NNDIC and PI controller for the model-mismatch case as well. CONCLUSION In practice, most real chemical processes are nonlinear and multivariable in nature, which make them difficult to control by using conventional controllers. Modelbased advanced control techniques are then required to obtain tighter control. However, in many cases it is even impossible to obtain a suitable process model due to the complexity of the underlying processes or the lack of knowledge of critical parameters of the models. A promising way to overcome these problems is to use inverse NNs as nonlinear black-box inverse models of the inverse dynamic behavior of the process. Nevertheless, inverse a NN model cannot produce the exact model and offset which normally occurs when it is implemented in control of the process. Therefore, the DM is an attractive control methodology for process control application because it can get rid of the offset and improves robustness of the controller. In this work, DM control strategy is tested and implemented for controlling concentrations of pickling and rinsing baths in a steel pickling process, which is highly nonlinear and involves multivariable interactions in nature. It was observed that DM control strategy can bring the control variables to their set-points without offset and oscillations in all the cases studies, i.e. nominal case, disturbance case and model mismatch case. Comparison of performance with the NNDIC and the conventional PI controller indicates that the DM control strategy gave better results in cases involving disturbances and model mismatches, and gave lesser IAE values than 2007 Curtin University of Technology and John Wiley & Sons, Ltd. the NNDIC and PI control. These results show that the DM control strategy gives acceptable and encouraging results for highly nonlinear and multivariable system such as this steel pickling process and can improve the robustness of such control systems. NOMENCLATURE area of operating tank (= 7.29 × 10−2 m2 ) HCl concentration (mol/l) volumetric rate (l/min) height of operating tank (m) reaction rate constant (= 3.267 × 10−4 mol/(l min)) amount of acid solution that stuck with samples (= 5 × 10−3 l/ min) t time (min) V volume of operating tank (m3 ) Subscripts 20 20% by weight HCl w water sp set-point A C F h k q REFERENCES [1] K.J. Hunt, D. Sbarbaro, R. Zbikowski, P.J. Gawthrop, Automatica, 1992; 28(6), 1083–1112. [2] M.A. Hussain, Artif. Intell. Eng., 1999; 13, 55–68. [3] C.W. Ng, M.A. Hussain, Chem. Eng. Process., 2004; 43, 559–570. [4] M.A. Hussain, P. Kittisupakorn, W. Daosud, Sci. Asia, 2001; 27(1), 41–50. [5] J. Diron, M. Casassud, M. Le Lann, G. Casamatta, Comput. Chem. Eng., 1995; 19, 797–802. [6] D. 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