BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi Tomul LV (LIX), Fasc. 4, 2009 Secţia AUTOMATICĂ şi CALCULATOARE APPLICATION OF NEURO-PREDICTIVE APPROACH FOR DISTURBANCE REJECTION IN A STEAM DRUM BOILER BY CRISTINA BUDACIU Abstract. In this paper a neuro-predictive method is proposed in order to control the water level in the steam drum boiler system being in use at a Power Plant of Iaşi, Romania. The steam boiler provides thermal and electrical power and it works under complex technology in order to satisfy numerous technical, security and economical requirements. A nonlinear dynamic simulator for the proposed steam drum boiler was used in order to build up the neuro-predictive structure. Based on the data taken from the simulator, the adopted strategy was tested and simulation results are given. Key words: steam drum boiler, neural model, neuro-predictive strategy, drum level control, steam flow disturbance. 2000 Mathematics Subject Classification: 93C10, 93C40, 93C83. 1. Introduction Process control is an efficient expression of improving the operation of a process, the productivity of a plant, and the quality of products. In Power Plant systems, even a small improvement in the operation of a process can have great economic and environmental influences. As there is no universal best solution that would apply to all control problems, knowledge of different model structures and alternative methods can be used to offer advice on the choice of the most suitable technique for a specific application. According with this idea, the paper proposes a solution for controlling the water level in a steam drum boiler system. The drum boiler being a complex and dangerous component of the power plant offers nonlinearities and non-minimum phase response and therefore needs carefully choice of a control strategy. Although the power plant 10 Cristina Budaciu models are very complex and are suitable for simulators, they are of little interest for different control strategies because of their complexity. Such particularly models can be found in [1],…,[4]. The nonlinearity of a steam drum boiler-turbine unit was analyzed in [5] and [6], using a nonlinear state space reduced model and a multivariable controller designed via loop-shaping H∞ approach. An output tracking control system for improving the load-following capability of boiler-turbine units has been developed in [7]. A suitable multivariable model is derived in [8] for designing a life extending controller. For a typical nonlinear drum boiler-turbine unit model in [9], the feedback linearization theory is used to deduce a pseudo-linear system of the model for implementing a two-degree of freedom control structure. In the last decade many researchers concentrates their work towards identification and adaptive control using neural networks due to the computational ability and universality. Moreover, little knowledge about the problems specifications is required. Therefore a very complex system model can be replaced with a neural network model having a known structure, but containing a number of unknown parameters such as weights and biases. The use of neural networks for nonlinear drum boiler process modeling and identification is justified by their capability to approximate unknown nonlinear systems. In [10], a recurrent neural network is used in the form of a multistep-ahead predictor to model the drum level process dynamics. For the drum level process, a NNARMAX (neural nonlinear ARMAX) model was presented in [11] and employed to develop a neuro predictive tuner for optimizing the drum level controller. Others neural based models are used for modeling a drum boiler–turbine–generator unit using physical principles and different control strategies for level control are found in [12],…,[15]. This paper proceeds from [11] and expands the neuro-predictive method to the case when the nonlinear system – the steam drum boiler is affected by steam flow disturbances. The controller design uses a neural network to model the nonlinear steam drum boiler system. Based on the neural model, the process output prediction will be achieved considering a set of command and disturbance values which act on the process. The presence of the load disturbance, assumed to be known, influences the process parameters, these changing once disturbance modifies. Therefore, the controller should compensate the variations of the process dynamics by adapting its parameters. By the minimization of the predicted error calculated through the prediction horizon the controller tuning parameters are obtained. The paper is organized as follows: Section 2 presents the description of the steam drum boiler system and the neural model obtained; in Section 3 the proposed solution for drum level control based on neuro-predictive approach is discussed in detail and some simulation results are performed, and Section 4 concludes the paper. Bul. Inst. Polit. Iaşi, t. LV (LIX), f. 4, 2009 11 2. The Neural Model of the Steam Drum Boiler The industrial process analyzed in this paper is a steam drum boiler system which ensures the steam flow to the industrial consumers. Based on the nonlinear mathematical model of the plant, the data set for neural network test was achieved from the simulator designed in [10]. The data set for training the neural network from the boiler simulator are utilized to estimate the neural model of the steam boiler. The main objectives of the drum boiler system are to produce steam and to ensure safety operational functionality. In order to understand the steam boiler dynamics, some basic information about the process description is given as follows. In Fig. 1 it is illustrated a schematic structure for a steam generation system, considering the main subsystems: the risers - downcomers, the steam drum and the superheater. It is worth mentioning that the complete system is more complicated than shown in Fig.1. A complete description of the system and the suitable mathematical model which includes the main parts of the boiler using the characteristics for risers, downcomers and for the superheater can be found in [2], [10]. Qir We, he L RisersDowncomers Wd Drum Wr Wv Superheater Ws Pv Fig. 1 − The Drum, Risers-Downcomers and the Superheater block diagram. Fig. 1 shows the interconnections between the modules mentioned above: the Drum, the Risers-Downcomers assembly and the Superheater subsystem. The Risers-Downcomers module has a principal input variable, the heat energy Qir provided from combustion conversion of fuel chemical energy and some variables incoming from the Drum outputs. The Drum module has some input variables, the feed water flow We with the feed water enthalpy he and the variable incoming in the drum from the Risers - Downcomers subsystem. Wr is the liquid - vapour mixture mass flow from the Risers Downcomers subsystem The main output variables are the drum water level L, steam pressure in the drum Pv and the water flow through downcomers Wd. The superheater assures the steam flow quantity Ws. to the consumer. In order to implement the neuro-predictive strategy, the neural model of the plant based on the real plant data must to be developed. The model of the proposed steam drum boiler being in use being in use 12 Cristina Budaciu at the Power Plant of Iasi is obtained with a MLP neural network with two neurons in the hidden layer and one neuron on the output layer. The artificial neural network used in process identification is able to identify NARXNARMAX models. Therefore, the NARMAX model can be described by: y N (k ) = f [ y (k − 1),..., y (k − n), u (k − d ),...u (k − d − m), (1) p (k ),K p (k − h)] where f (.) is a nonlinear function. The inputs of the neural network are the past values of the command input u ( k − d ), u ( k − d − 1),..., u (k − d − m) , the disturbances p (k ), p (k − 1),..., p (k − h) and the output regresor vector y (k − 1), y (k − 2),..., y (k − n) . Steam flow 1 0 Drum water level Feedwater flow -1 0 100 200 300 400 500 600 700 100 200 300 400 500 600 700 100 200 300 400 500 600 700 1 0 -1 0 1 0 -1 0 Time [s] Fig. 2 − The open loop data set for training the neural network. In a first iteration, the off-line parametric identification around a nominal point has been performed in order to find the number of past outputs, past values of input and past values of disturbance, respectively. The data set used for identification are the feedwater mass flow, the steam mass flow and the level in the drum as is ilustrated in the Fig. 2. As is shown the input quantities Bul. Inst. Polit. Iaşi, t. LV (LIX), f. 4, 2009 13 are represented in normal range [-1 1], the feedwater flow coming in the drum and the steam flow disturbance signal to the consumer. The dynamic of the drum level is influenced by the feed water flow changes at variation of heat flow and in the presence of steam flow disturbance. The variation in feedwater flow input is justified by the fact that the feed water flow is varying in order to control manually, in open-loop, the drum water level around a nominal point, otherwise the drum water level would increase outside the safe limit. Steam flow 1 0 -1 0 50 100 150 200 250 300 350 400 450 50 100 150 200 250 300 350 400 450 50 100 150 200 250 Time [s] 300 350 400 450 Steam flow 1 0 Drum water level -1 0 1 0 -1 0 Fig. 3 − The open loop data set from simulator for testing the neural network. The neural network has been created using functions from Matlab Neural Network toolbox. For the training and validation of the neural network that models the process the data set illustrated in the Fig. 2 and Fig. 3 was used. After several simulations was seen that a neural network with only 1 hidden layer with 2 neurons and one neuron on the output layer is sufficient to describe the dynamics of the system. Therefore the neural network output, with the number of neurons on the hidden layer ns = 2, can be expressed as: ns u T p T y T (2) y pred (k ) = ∑ w j tansig(w j u(k − d − 1) + w j p(k − h) + w j y (k − 1) + b j ) + b, j =1 where: 14 Cristina Budaciu u(k − d − 1) = [u ( k − d ) u (k − d − 1) K u ( k − d − m)] , p(k ) = [ p (k ) p ( k − 1)K p ( k − h)] y (k − 1) = [ y ( k − 1) y (k − 2)K y (k − n)] - w uj is the weights vector associated with u(k-d-1) inputs in connection with jth neuron on the hidden layer. - w pj is the weights vector associated with p(k) disturbance in connection with jth neuron on the hidden layer y - w j is the weights vector associated with the past values of the output. - bj represents the biases for jth node on the hidden layer and b represents the bias for the output neuron. Open loop data set for training 1 Drum level 0.5 0 -0.5 -1 0 50 100 150 200 250 300 350 400 300 350 400 Simulator data set for testing 1 Drum level 0.5 0 -0.5 -1 0 50 100 150 200 250 Time [sec] Fig. 4 − The simulation results for neural network validation. The hyperbolic tangent function is used as the activation function in the artificial neural network for hidden layer. During the Backpropagation stage of the neural network training, the output layer of neurons is adjusted, to make the Bul. Inst. Polit. Iaşi, t. LV (LIX), f. 4, 2009 15 output closer to the desired output. In order to test the neural network, the Fig. 3 illustrates the data set taken from the steam drum boiler simulator developed in [10]. In the Fig. 4 are plotted comparatively the responses of the neural network with circle and the data set used with solid line. The simulation results from Fig. 4 indicate a good agreement, between neural network response and the desired output. 3. The Neuro-Predictive Structure for Drum Level Control The neuro-predictive structure that permits the on line design of the controller parameter is illustrated in Fig. 5. The figure shows an existing controller with tunable gains in a closed-loop configuration which has a known parametric structure. Its parameters will be modified at each sample time as a result of an optimization method. This strategy presented in [11] proposes the existing of two feedback loops, the real time control loop with the real process and the controller, and the prediction control loop with the predictor and the gain adaptation law with the simulated controller. upred(k+i|k) epred(k+i|k) r(k+i|k) + Controller p(k+i|k) Neural model ypred(k+i|k) Neuro-predictive control loop q Cost function Constraints Optimization block qopt e(k) r(k) + p(k) y(k) u(k) Controller Process Real-time control loop Fig. 5 − The Neuro-Predictive strategy for drum level control. The neuro-predictive control loop is used to make a prediction, at each sample time, over a certain horizon, of the future behavior of the real time control loop. The future response of neural model of the process and the predicted error are obtained at each time instant of the prediction horizon. 16 Cristina Budaciu The future control u pred ( k + i | k ) is calculated at each time instant in predictive control loop considering a smaller sampling time than the one from the real-time control loop. Therefore, the predicted output ypred(k+i|k) is determined over a finite horizon, with i = N1 , N 2 , N1 and N2 being the prediction horizons. The neural model design in Section 2 for the steam drum boiler is used in predictive control loop, so that at each time instant k, the predicted behavior of the process is obtained by the form: (3) y pred = [ y ( k + N1 | k ) y ( k + N1 + 1| k ) ... y ( k + N 2 | k )]T . The predicted disturbance p(k+i/k) meaning the steam mass flow is assumed to be known so that the predicted output can be calculated. The controller used in the both loops is of PI type and the control law is given by (4) u (k ) = u (k − 1) + q0 e(k ) + q1e(k − 1) The vector q = [ q0 q1 ] contains the controller parameters and are obtained at each sample time, using numeric minimization of a cost function, over prediction horizon N2. The cost function is considered the mean squared prediction error over a prediction horizon: (5) J= 1 N2 2 ∑ e pred (k + i | k ), 2 i = N1 where (6) e pred (k + i | k ) = y pred (k + i | k ) − r (k + i | k ) , i = N1 , N 2 is the prediction error over prediction horizon N2 between the predicted output and the reference. In the optimization block the optimal tuning parameters qopt are obtained, taking into account the process predictable dynamics variations. For the next time instant, k+1, the tuning parameters qopt are transferred to real time control loop and the simulated control loop. At each sample time, the controller parameters must respect the relations that characterizes the discrete PI controller: Bul. Inst. Polit. Iaşi, t. LV (LIX), f. 4, 2009 17 q0 > 0 (7) q1 < −q0 The neuro-predictive method for controller parameters tuning is advantageous because it allows on line adjustment of parameters to change the dynamics of the process, thereby avoiding the off line identification stage. The performances depend of the data set and the accuracy of results obtained from minimizing criterion function depends on the quality of the model obtained. 4. Simulation Results Feedwater and steam flow Drum level [0-100]% The neuro-predictive approach presented in Section 3 was applied to the steam drum boiler system in order to obtain better performances for level control subject to steam flow disturbances. The steam boiler provides thermal and electrical power and it works under complex technology in order to satisfy numerous technical, security and economical requirements. The simulation results are shown in the Fig. 6, considering a step variation in level reference values subject to a step variation of 10% in steam demand. 40 20 0 100 Drum level Reference 150 200 250 300 350 400 100 Feedwater flow 50 Steam flow 0 100 150 200 250 300 350 400 200 250 Time [s] 300 350 400 PI Parameters 20 10 0 qo q1 -10 100 150 Fig. 6 − Simulation results and PI controller parameters for the adaptive discrete PI controller. 18 Cristina Budaciu As it is shown in the Fig. 6, at t = 200 , the reference of the level is increase from 10% to 25% , so that the control action of the level controller will force the closing of the feed water valve. At moment t = 300 the steam flow is suddenly increased in the drum. A decreased of the feed water flow is accompanied by an increase of the drum level as was expected because due to the drop in the pressure, more steam bubbles will appear making the steamwater mixture to swell. The steam disturbance is rejected by the PI controller with adapted parameters, proving its capacity to keep the level at desired values. The PI controller parameters are adjusted according to the change in the process dynamics, thus compensating for variations that occur in both set point change and an increase in steam consumption. 5. Conclusions This paper reports an application of a neuro-predictive method for a nonlinear physical model with a high complexity - the steam drum boiler system being in use at the Power Plant from Iasi area. It is well known that in Power Plant systems, even a small improvement in the operation of a process can have great economic and environmental influences. This approach for self-tuning controllers demonstrates a good performance for processes having predictable dynamics variations. The method was applied to a 420t/h steam drum boiler system in order to obtain better performances for level control subject to steam flow disturbances. Received: August 5, 2009 “Gheorghe Asachi” Technical University of Iaşi, Department of Automatic Control and Applied Informatics e-mails: chalauca@ac.tuiasi.ro REFERENCES 1. Leva A., Maffezzoni C., Benelli G., Validation of Drum Boiler Models Through Complete Dynamic Tests. Control Engineering Practice, Vol. 7, 1, 1999, 11−26. 2. Ordys W., Pike A.W., Johnson M.A, Katebi R.M., Grimble M.J., Modelling and Simulation of Power Generation Plant. U.K., Springer-Verlag, 1994. 3. Åström K.J., Bell R., Drum-boiler Dynamics. Automatica, Vol. 36, 3, 2000, 363−378. 4. Kim H., Choi S., A model on Water Level Dynamics in Natural Circulation DrumType Boilers. 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Li D., Chen T., Marquez H.J., Gooden R.K., Life Extending Control of Boiler– Turbine Systems Via Model Predictive Methods. Control Engineering Practice, 2006, 319−326. STRUCTURĂ NEURO-PREDICTIVĂ PENTRU REJECŢIA PERTURBAŢIILOR DE SARCINA ÎN TAMBURUL UNUI BOILER DE ABUR (Rezumat) În această lucrare a fost testată o structură neuro-predictivă de acordare a parametrilor unui regulator PI discret. Metoda permite adaptarea on-line a parametrilor regulatorului atât la modificarea dinamicii procesului cât şi la apariţia unei perturbaţii de sarcină. Metoda de reglare neuro-predictivă propusă pentru reglarea nivelului în tamburul unui boiler în prezenţa unui consum de abur a fost testată prin simulare, considerând seturi de date preluate din functionarea în timp real a procesului existent la CET 1 S. A. Iasi. Pentru implementarea structurii de reglare adaptive s-a determinat un model neuronal care să modeleze dinamica procesului neliniar. Setul de date folosit 20 Cristina Budaciu pentru antrenarea reţelei neuronale a fost preluat din funcţionarea reală a unui boiler de abur industrial, iar setul de date de testare a fost preluat dintr-un simulator proiectat pentru tamburul boilerului considerat. Rezultatele experimentale au demonstrat că schimbările în dinamica procesului sunt compensate prin variaţii ale parametrilor regulatorului discret PI. Rezultatele prezentate subliniază avantajele folosirii acestei tehnici de acordare pentru a controla procese neliniare în toata zona de operare a acestora precum şi capacitatea de a rejecta perturbaţiile de sarcină în comparaţie cu alegerea unui regulator cu parametri ficşi determinaţi în jurul unui punct de operare.