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Application of internal model control methods to industrial combustion
Applied Soft Computing 5 (2005) 223–233 www.elsevier.com/locate/asoc
Application of internal model control methods to industrial combustion M.M. Awais* Computer Science Department, Lahore University of Management Sciences (LUMS), Sector U, DHA, Lahore 54792, Pakistan Received 14 February 2004; received in revised form 16 June 2004; accepted 5 July 2004
Abstract Most practical systems are inherently non-linear to some extent in their behaviour and for their cost effective, smooth and safe operation, optimised control systems based on the non-linear models are required. To this end many useful techniques such as the stochastic modelling, sliding mode control and adaptive identification and control have been proposed in the literature. However, the high cost of implementation, the inability to capture imprecision with the required level of tolerance, and the inflexibility against distortions in the operating variables, make them less attractive. To this end new artificial intelligence based techniques such as fuzzy logic, neural networks and probabilistic reasoning, are becoming more and more popular. Among these techniques neural networks have an edge over the others, mainly because of their ability to process large amount of available data, subsequent to the development of some interpretable models for solving engineering problems. Moreover, the ability to capture the non-linearities of a real system accurately and the versatility in being able to accommodate with ease, the various conventional and advanced strategies within their structures, make them much more attractive. The problem becomes more computationally worse and uncontrollable when inverse of the system does not exist. This problem is resolved when neural network based techniques such as internal model control (IMC) are applied to the real systems. This paper outlines the application of neural networks based IMC methods for estimation/control of important input and output variables of a 0.5 MW laboratory scale industrial furnace. The application involves inputs such as the airflow rate, swirl number and momentum ratio. The outputs include emission levels of oxides of nitrogen especially nitric oxide. The response to step and staircase inputs has been analysed. The results have been compared with standard linear quadratic controller. The control output of the IMC methods has resulted in almost similar steady state error performance to the linear quadratic regulator. Although the development process of the IMC method might take longer time because of the training and data arrangement but has the capability of readjustment after being developed. # 2004 Elsevier B.V. All rights reserved. Keywords: Neural networks; Furnace; Internal model control; Burnout; Momentum ratio; Nitric oxides.
1. Introduction * Tel.: +92 42 5722670; fax: +92 42 5722591. E-mail address: [email protected].
In this paper, the variation in the optimising parameters, namely excess air, swirl number and
1568-4946/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2004.07.001
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M.M. Awais / Applied Soft Computing 5 (2005) 223–233
Fig. 1. Experimental furnace [1].
momentum ratio, are exploited to maintain lower emission levels and high thermal/combustion efficiencies for laboratory scale furnace at Imperial College of Science, Technology and Medicine (ICSTM), London, UK. Neural networks (NN) [9– 11] have been employed to model the nitric oxide (NO) emissions with regard to the operating and the measured conditions and then an optimiser has been developed that ensures the operating conditions to fall within the stability limits and high efficiency range. The control laws for the furnace optimiser are based on the stability performance curves discussed in the sequel.
laboratory scale coal fired furnace [1]. The experimental furnace on which the data were collected is shown in Fig. 1. The combustion chamber is
1.1. Experimental The data was collected through experiments that were conducted previously on 0.5 MW ICSTM
Fig. 2. Input/output data furnace model node assignment.
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Fig. 3. Input/output data controller node assignment.
cylindrical, with its axis vertically aligned to ensure flow symmetry and is down-fired. It consists of 10 water-cooled sections, of an internal diameter of 0.6 m and a height of 0.3 m. The upper five sections are refractory lined. All segments are provided with pairs of radially opposed 0.2 m windows for observation. Further details of this combustor and its instrumentation may be found in Abbas and co-workers [1,2]. 1.2. Stability performance curves During the data collection campaign two different types of burners were utilised i.e., a single annular orifice (SAO) burner and single central orifice (SCO) burner that depict high and low NO formation behaviours respectively, details about the burners can be found in [1,2]. The geometry of the two types of
225
burners and the internal dynamics within the near burner region (NBR) are shown in Fig. 5. A brief explanation is given here. The burner geometry is typically that of a wall fired power station boiler. The secondary air supply and the burner jet are part of the burner. The secondary air is preheated up to 300 8C, and passes through a swirl generator [1]. In the SAO burner, a centrally located tube is present which acts as a bluff body, conforming to the industrial practice. In the standard SCO burner the jet is a simple hollow tube. In the SAO burner, the combined influence of the annular jet, a strong, well defined and enclosed internal recirculation zone (IRZ) and the secondary air swirl results in the fuel particles being subjected to high radial forces. Thus few particles move axially and penetrate in the IRZ, in fact the majority of the particles move into the oxygen-rich zone inside the quarl between the outer boundary of IRZ and incoming secondary air. The environment in which the particles are trapped is very favourable for high NO formation. The fuel nitrogen is released during the devolatilisation in this oxygen-rich neighbourhood and subsequently produces fuel NO. For the SCO burner, the centrally located primary jet is relatively unaffected by the centrifugal-drag component exerted by the swirling secondary airflow. Therefore, the particles under the influence of the primary momentum penetrate into the IRZ further, having an average residence time of 200 ms compared with 20 ms for the SAO [3]. The burner jet provides a long, thin and fuel-rich region over a major portion of the primary jet. These conditions favour lower NO
Fig. 4. Close loop arrangement of the furnace.
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Fig. 5. SAO and SCO burner aero-dynamics.
formation due to the dearth of the oxygen in the initial combustion region, along with a higher NH3 formation downstream of the initial combustion region. It was observed that NO formation was minimum within certain ranges of swirl number (SN), excess air (EA) and momentum ratio (MR). The combustion efficiency of the furnace i.e., the burnout was also calculated and its variation was obtained against SN, EA and MR. The data obtained by these experiments has considered the variation of one of these variables while keeping the other two constant [1].
Fig. 6 shows the variation of NO with respect to the change in the excess air. As the excess air increases, the NOx emissions increase and vice-versa. The burnout variation with respect to the excess air shows the same trend but provides an asymptotic behavior with increase in excess air. Therefore, at low excess air levels the NO emissions can be reduced to the required levels. The limiting factor however, is the burnout as the reduction is observed at lower values of excess air. The threshold value observable for excess air from the study of the two figures is thus limited to 15% for an
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Fig. 6. Variation of burnout and NO w.r.t excess air, at swirl number = 1 and momentum ratio = 0.24, SAO (^), and SCO (&) [1].
acceptable and stable range of operation [1]. Further reduction in NO can be achieved by manipulating the factors, which strongly affect the near burner aerodynamics such as swirl number and/or momentum ratio while keeping the excess air at 15%. In Fig. 7 the minimum NO concentration and maximum burnout for both the burners occur at swirl number 1.0 for excess air of 15% and momentum ratio of 0.24. Above and below this swirl number, the NO concentration and the burnout values start to increase and decrease, respectively. From Fig. 8 the optimal operating point for momentum ratio can be seen as 0.24 because around this point maximum burnout is achieved and NO formation is low. From the above discussion we can prescribe three different NO reduction methodologies based on the exit conditions and near burner dynamics that are observable through the stability performance curves explained above, and are summarised in Table 1. The detailed deliberations
Fig. 7. Variation of burnout and NO w.r.t swirl number at momentum ratio = 0.24 and excess air = 15%, SAO (^), and SCO (&) [1].
and the implementation of control schemes based on these optimal operating ranges is the subject addressed in [4]. For the present study, the variation in MR is considered as a NO reduction methodology through, thus the controller realization considers MR as the input and NO as the only output.
2. Controller development The controller developed here advises the amount of variation in the input variables, required to maintain the optimised performance and set points of the combustion system under study. In this regard momentum ratio was taken as the input variable while keeping the excess air and swirl number at their optimal values obtained from the stability curves in
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the system have been realised. Instead of using static feed forward neural networks for the controller development, an inverse model of the systems has been developed by re-arranging the data. In the experimental facility under consideration i.e., the ICSTM furnace, the equipment for on-line identification was not available. Therefore, all efforts were diverted towards accomplishing the task of forward modelling via off-line neural network training and application. Subsequent to the development of the forward model, an inverse model was developed and finally, the two models were put together in a closedloop to check the performance of the overall system. In the discussion that follows, the methodologies adopted for the forward model, inverse model and the closedloop system development, are outlined. 2.1. Forward modelling In the forward modelling method the model is developed as a function of the past and present inputs, as well as the outputs to yield the future output of the system. In terms of the mathematics this is represented as Eq. (1) given further: ˆ m ðkÞ; ym ðk 1Þ; yˆ m ðk þ 1Þ ¼ f½y Fig. 8. Variation of burnout and NO w.r.t momentum ratio at swirl number = 1, and excess air = 15%, SAO (^), and SCO (&) [1].
Table 1 Optimum conditions
Variation in EA Variation in SN Variation in MR
EA
SN
MR
– 15% 15%
1.0 – 1.0
0.24 0.24 –
Figs. 6 and 7 i.e., 15% and 1.0, respectively. The controller is based on time series modelling and the internal model control (IMC) system through implementing neural networks [4–8]. In order to implement the IMC method, forward and the inverse models of
ym ðk iÞ; um ðkÞ; um ðk 1Þ;
(1) um ðk jÞ;
where ym ðkÞ, is the present output of the system and ym ðk þ 1Þ, is the one step ahead (future) output of the system, ym ðk 1Þ to ym ðk iÞ are the past outputs up to the ith time scale. Similarly the corresponding inputs are represented as um ðkÞfor the present time and, um ðk 1Þ to um ðk jÞ are the past inputs to the jth level in time. The validation and the training data for the above-mentioned problem was generated by discretizing the stability performance curves. The output was the value of future NO and the input values were the past and present MR and the NO values keeping the values of EA and SN uniform at 15% and 1.0, respectively (Table 1). The forward modelling approach was employed to predict one-step ahead NO
Table 2 Specs for forward model of furnace Type of NN
Data sets
Input/output
Weight initiation
Training algorithm
Validation
Recurrent
150
Inputs = 5/output = 1
1 to + 1
Back propagation
47%
M.M. Awais / Applied Soft Computing 5 (2005) 223–233 Table 3 NN forward model parameters for the furnace Input layer neurons (activation function) Output layer neurons (activation function) Hidden layer neurons (activation function) Number of hidden layers Global learning rate (adaptive) Global momentum rate Error at the end of iterations (mean sum squared error) Number of iterations
5 (inactive) 1 (linear) 3 (sigmoid) 1 0.01 0.98 0.00658 5000
values. Multi-step ahead predictions are not considered in the proposed control strategy. Fig. 2 represents the structure of the input and output data used for modelling the neural network-based forward model for the furnace. The training was carried out using cross-validation technique [4]. When a reasonably low mean sum squared error (MSE) was achieved, the training was stopped and the validation test for the two separate and distinctly arranged data sets, was carried out. The main features and specifications of the model developed are discussed in details further. Table 2 shows the specifications of neural network based forward model for the furnace. Recurrent network with back propagation based optimisation algorithm was used for the model development. The initiation of the weights ranged between 1 and +1, and 47% of the total data sets were used for validating the model. The input layer was kept inactive, as usual, while the hidden layer activation function was taken as
Fig. 9. Forward model prediction for training data of the furnace, experimental (continuous line) results and NN (dashed line).
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sigmoid (Table 3). The training process took 5000 iterations. The training results of the forward model are presented in Fig. 9, whereas the response of the model during the validation is presented in Fig. 10. The highest prediction error, as expected for both the cases, was observed at the transition of the response curve, which is without doubt the most difficult part to track. Several test runs were carried out and similar results were obtained. The available data sets were arranged differently for the training and validation runs in order to realise the change in the furnace output in a gradual manner. For validation, a ‘staircase’ model (Fig. 10) output with both ascending and descending values was placed in effect, whereas for the training data sets two consecutive loops of continuously increasing and decreasing data values were taken. During the model selection phase, various trials were carried out that included testing the model output with a different number of hidden neurons and activation functions. As a result a cascade of models was developed. The final selection of the forward model was based on the closed-loop performance of the model with the inverse model (controller) placed in series with the forward model. 2.2. Inverse modelling An inverse modelling technique basically involves prediction of the inputs to the plant given the past data
Fig. 10. Forward model prediction for validation data of the furnace, experimental (continuous line) results and nn (dashed line).
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Table 4 Specs for inverse model of furnace Type of NN
Data sets
Input/output
Weight initiation
Training algorithm
Validation
Recurrent
150
Inputs = 4/output = 1
1 to + 1
Back propagation
47%
of the plant’s inputs and the outputs together with the desired future outputs. Inverse modelling of the dynamical system plays a vital role in many control strategies and structures. These inverse models can be directly used as the controllers in direct inverse and internal model control schemes. Obtaining an inverse of many complex continuous systems is extremely difficult, especially in the field of combustion. The inverse modelling via neural networks is obtained by the direct manipulation of the data sets, achievable through considering the inputs of the system as the outputs and vice versa. This, however, can only be achieved in the region of the plant’s operation where one to one functional mapping between the inputs and the outputs exist. During the training of the inverse models the neural network is fed with the required future or the reference output/set point value together with past inputs and the past outputs to predict the current input of the system i.e., um ðkÞ. Thus the equation for the forward model can be altered accordingly and inverse model expression Eq. (2) can be obtained as: 1 um ðkÞ ¼ fˆ ½ym ðkÞ; ym ðk 1Þ;
(2)
ym ðk iÞ; ym ðk þ 1Þ; um ðk 1Þ; um ðk jÞ;
where the nomenclature is the same as explained 1 earlier for forward model, except for fˆ which is the inverse map of the forward model. The training methodology again employs the moving window Table 5 NN inverse model parameters for the furnace Input layer neurons (activation function) Output layer neurons (activation function) Hidden layer neurons (activation function) Number of hidden layers Global learning rate Global momentum rate Error at the end of iterations (mean sum squared error) Number of iterations
4 (inactive) 1 (linear) 3 (sigmoid) 1 0.01 0.98 0.0067 5000
approach similar to the one explained earlier. In the case study under consideration this mapping does exist and is evident from the stability performance curves of the system presented earlier. Fig. 3 represents the input/output (MR/NO) data arrangement of the control structure for obtaining the inverse model of the plant. The controller inputs also contain the steady state error between the set point chosen for plant operation and the future output of the plant at interval ‘k + 1’. Instead of using the error between the future value and the set point, the input can be replaced by only the future output (NO) of the plant. This will however, restrict the ability of the controller (inverse model) to track effectively the required set point for NO, which is tracked by manipulating/varying the controlling variable (MR). The inclusion of this error also makes it easier to obtain the closed-loop response of the plant and the controller. The details of the neural networkbased inverse model are presented in the Table 4. In this case, again, a recurrent network with back propagation algorithm was used for the inverse model development. The initiation of weights was ranged between 1 and +1, and 47% of the total data sets were used for validating the model. Other parameters regarding training performance are listed in Table 5. The controller response is depicted in Figs. 11 and 12. The controller output follows the set point initiated at the input domain and suggests the corresponding change required in the momentum ratio. The available data sets were arranged to realise the change in the set point of NO. Again, a ‘staircase’ arrangement was adopted for tracking the set points. During the controller selection phase, various trials were carried out under varying neural network parameters. A number of inverse models were developed and were tested for their closed-loop performance. 2.3. Closed-loop analysis In the closed-loop analysis, both the forward and the inverse models of the furnace were put in series with each other and the response of the closed-loop
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Fig. 11. Controller output for training data of the furnace, experimental (continuous starred line) results and NN (dashed line).
Fig. 12. Controller output for validation data of the furnace, experimental (continuous starred line) results and NN (dashed line).
system was checked for the set point variation. The arrangement of the closed-loop system is represented in Fig. 4 In this regard, the values of the set point of NO (NO_set) were varied and the response of the controller and the plant was plotted. Ideally the NO(k + 1) should converge to the set point value and the output of the controller should rest after fluctuating across the mean value of the corresponding momentum ratio. The results presented here are for three set points. The values of the NO_set were kept at 420, 415, and 410 ppm. For each set point the initialisation
point of the plant was different therefore the rise time in each case is different. For example for set point 410 the starting value of NO was kept at 402, similarly for 415 and 420 the initialisation of the output was kept at 411 and 414 respectively. The response of the closedloop system seen in Fig. 13 yields the expected results showing that the controller is sensitive to the set point change and tracks it by affecting a corresponding change in the momentum ratio. The corresponding changes recommended by the controller are 0.24, 0.23, and 0.22 for the above-mentioned set points. The
Fig. 13. Close loop simulation response for the furnace for three different set points.
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Table 6 Percentage error between set point and actual controller output Set point
Controller output
Absolute error (%)
410 415 420
412 415.5 418
0.48 0.12 0.47
error observed between the desired and the predicted experimental values is within 0.5% of the desired NO set points as shown in Table 6, which is acceptable.
2.4. Linear quadratic regulator For the furnace problem stated above a linear quadratic regulator (LQR) was also developed and the steady error of the IMC method and the LQR controller were compared. Here are some details of the controller that was developed using LQR method. Based on the given data the state space model of the furnace was developed. This state space model was used to obtain the gain matrix for the system using the LQR technique. Finally the state space model along with the gain matrix was used to calculate the regulator output. In the LQR the regulation perfor-
mance is measured by a quadratic performance criterion given in Eq. (3). Z 1 JðuÞ ¼ fxT Qx þ uT Rugdt (3) 0
The weighting matrices Q and R define the trade off between the regulation performance and control effort. In designing LQR controller the state-feedback was found through the control law u ¼ Kx, such that the objective function J(u) was minimized. Here K is the minimizing matrix obtained by solving the algebraic Riccati equation [12]. For the problem presented in this paper LQR controller performance was compared with the IMC controller. Fig. 14 represents the error for both the type of controllers. It is interesting to note that the performance of the IMC and LQR is almost similar after the steady state is reached. Both the controllers reach a zero steady state error. However, the IMC takes longer time and more input variations to reach the steady state. The settling period is almost linear in both the cases and variations in the errors are not fluctuating. Thus one may conclude that the IMC based controllers perform similar to the LQR controllers especially for the problem under consideration. The advantage of using IMC, however, is the ease with which the controller can be adjusted for
Fig. 14. Steady state error for (-) LQR control, (- -) IMC control.
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new set points. Moreover, the controller for IMC based method can easily be trained and deployed after including more input/output parameters provided the data for the new parameters is available.
3. Conclusions The modelling techniques mentioned in the above discussion, have revealed numerous advantages. The most appealing though, is the ease with which the forward model can be inverted to obtain the controller for the plant. The results of the controller show that it works well for any set point change prescribed within the limits of the training data. The set point tracking error observed is less than 0.5% for the closed-loop simulations. As far as the steady-state conditions of the furnace are concerned, the controller performed satisfactorily. The results compare well with LQR controller. The tests for the transient phase of operation of the system were not conducted, mainly because the available experimental data only accounted for the steady-state conditions. This simply means that the range of input excitation signal acceptable for the controller is limited. Therefore, the ramp-only data signals were not considered during the training and the validation phases. This study reveals that the successful application of the IMC technique relies heavily on the simultaneous accuracy of the forward and the inverse models. Since this is not easily achieved for many on-line applications especially noise-wrecked non-linear systems, a filter can be added prior to the controller to compensate for these inaccuracies and to sustain robustness in the control implementation. In order to make the controller more effective, the transient dynamics of the furnace should be included in the present control structure, once the data is available. This aspect of the controller development can be treated as an extension to the present research activity and may become a part of a future research work. In our case study, the inverse model obtained, performed reasonably well as the development was conducted off-line after pre-processing the data, thus
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the filter was not implemented. But the large spikes and oscillations in the control inputs could still be seen clearly at the instances where set point changes were made. This behaviour can certainly be improved by introducing the filtering option. The dynamics of the system with different coals was not considered in this study, thus the coal characteristics were kept constant during this development. Again, this was simply because of the lack of the training and the validation data.
References [1] T. Abbas, In-flame measurements of N-pollutants and burnout in a pulverised coal fired furnace. PhD Thesis, University of London, London, 1993. [2] F.C. Lockwood, Romo Millares, Combust. Sci. Technol. 102 (1994) 57. [3] M. Yehia, Modelling of pulverised coal swirling flames in axisymmetric furnaces. PhD Thesis, University of London, London, 1992. [4] M.M. Awais, Application of neural networks to combustion processes. PhD Thesis, Imperial College, London, 2000. [5] M.A. Hussain, Inverse-model control strategies using neural networks: analysis, simulation, and on-line implementation. PhD Thesis, University of London, London, 1996. [6] M.M. Awais, F.C. Lockwood, T. Abbas, Application of neural networks for coal combustor performance and control, in: Proceedings of the Fifth International Conference on Combustion Technology for Clean Environment, Lisbon, Portugal, 1999, p. 1239. [7] M.M. Awais, S. Godoy, F.C. Lockwood, The development of a neural network model for NOx predictions based on flat flame turbulent jet apparatus, in: Proceedings of the Fifth International Conference on Combustion Technology for Clean Environment, Lisbon, Portugal, vol. II, 1999, p. 825. [8] M.A. Aamir, M.M. Awais, A.P. Watkins, F.C. Lockwood, CFD and Neural Network Modelling of Dense Propane Spray, in: Proceedings of the 15th ILASS-Europe’99 Conference, Toulouse, France, 1999. [9] M.H. Hassoun, Fundamentals of Artificial Neural Networks, MIT Press, 1995. [10] J.M. Zurada, Introduction to Artificial Neural Systems, St. Paul: West Publishing Company, St. Paul, 1992. [11] I. Alexander, H. Morton, An Introduction to Neural Computing, Chapman and Hall, London, 1991. [12] J.E. Slotine, W. Li, Applied Nonlinear Control, Prentice-Hall, 1991.
Application of internal model control methods to industrial combustion M.M. Awais* Computer Science Department, Lahore University of Management Sciences (LUMS), Sector U, DHA, Lahore 54792, Pakistan Received 14 February 2004; received in revised form 16 June 2004; accepted 5 July 2004
Abstract Most practical systems are inherently non-linear to some extent in their behaviour and for their cost effective, smooth and safe operation, optimised control systems based on the non-linear models are required. To this end many useful techniques such as the stochastic modelling, sliding mode control and adaptive identification and control have been proposed in the literature. However, the high cost of implementation, the inability to capture imprecision with the required level of tolerance, and the inflexibility against distortions in the operating variables, make them less attractive. To this end new artificial intelligence based techniques such as fuzzy logic, neural networks and probabilistic reasoning, are becoming more and more popular. Among these techniques neural networks have an edge over the others, mainly because of their ability to process large amount of available data, subsequent to the development of some interpretable models for solving engineering problems. Moreover, the ability to capture the non-linearities of a real system accurately and the versatility in being able to accommodate with ease, the various conventional and advanced strategies within their structures, make them much more attractive. The problem becomes more computationally worse and uncontrollable when inverse of the system does not exist. This problem is resolved when neural network based techniques such as internal model control (IMC) are applied to the real systems. This paper outlines the application of neural networks based IMC methods for estimation/control of important input and output variables of a 0.5 MW laboratory scale industrial furnace. The application involves inputs such as the airflow rate, swirl number and momentum ratio. The outputs include emission levels of oxides of nitrogen especially nitric oxide. The response to step and staircase inputs has been analysed. The results have been compared with standard linear quadratic controller. The control output of the IMC methods has resulted in almost similar steady state error performance to the linear quadratic regulator. Although the development process of the IMC method might take longer time because of the training and data arrangement but has the capability of readjustment after being developed. # 2004 Elsevier B.V. All rights reserved. Keywords: Neural networks; Furnace; Internal model control; Burnout; Momentum ratio; Nitric oxides.
1. Introduction * Tel.: +92 42 5722670; fax: +92 42 5722591. E-mail address: [email protected].
In this paper, the variation in the optimising parameters, namely excess air, swirl number and
1568-4946/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2004.07.001
224
M.M. Awais / Applied Soft Computing 5 (2005) 223–233
Fig. 1. Experimental furnace [1].
momentum ratio, are exploited to maintain lower emission levels and high thermal/combustion efficiencies for laboratory scale furnace at Imperial College of Science, Technology and Medicine (ICSTM), London, UK. Neural networks (NN) [9– 11] have been employed to model the nitric oxide (NO) emissions with regard to the operating and the measured conditions and then an optimiser has been developed that ensures the operating conditions to fall within the stability limits and high efficiency range. The control laws for the furnace optimiser are based on the stability performance curves discussed in the sequel.
laboratory scale coal fired furnace [1]. The experimental furnace on which the data were collected is shown in Fig. 1. The combustion chamber is
1.1. Experimental The data was collected through experiments that were conducted previously on 0.5 MW ICSTM
Fig. 2. Input/output data furnace model node assignment.
M.M. Awais / Applied Soft Computing 5 (2005) 223–233
Fig. 3. Input/output data controller node assignment.
cylindrical, with its axis vertically aligned to ensure flow symmetry and is down-fired. It consists of 10 water-cooled sections, of an internal diameter of 0.6 m and a height of 0.3 m. The upper five sections are refractory lined. All segments are provided with pairs of radially opposed 0.2 m windows for observation. Further details of this combustor and its instrumentation may be found in Abbas and co-workers [1,2]. 1.2. Stability performance curves During the data collection campaign two different types of burners were utilised i.e., a single annular orifice (SAO) burner and single central orifice (SCO) burner that depict high and low NO formation behaviours respectively, details about the burners can be found in [1,2]. The geometry of the two types of
225
burners and the internal dynamics within the near burner region (NBR) are shown in Fig. 5. A brief explanation is given here. The burner geometry is typically that of a wall fired power station boiler. The secondary air supply and the burner jet are part of the burner. The secondary air is preheated up to 300 8C, and passes through a swirl generator [1]. In the SAO burner, a centrally located tube is present which acts as a bluff body, conforming to the industrial practice. In the standard SCO burner the jet is a simple hollow tube. In the SAO burner, the combined influence of the annular jet, a strong, well defined and enclosed internal recirculation zone (IRZ) and the secondary air swirl results in the fuel particles being subjected to high radial forces. Thus few particles move axially and penetrate in the IRZ, in fact the majority of the particles move into the oxygen-rich zone inside the quarl between the outer boundary of IRZ and incoming secondary air. The environment in which the particles are trapped is very favourable for high NO formation. The fuel nitrogen is released during the devolatilisation in this oxygen-rich neighbourhood and subsequently produces fuel NO. For the SCO burner, the centrally located primary jet is relatively unaffected by the centrifugal-drag component exerted by the swirling secondary airflow. Therefore, the particles under the influence of the primary momentum penetrate into the IRZ further, having an average residence time of 200 ms compared with 20 ms for the SAO [3]. The burner jet provides a long, thin and fuel-rich region over a major portion of the primary jet. These conditions favour lower NO
Fig. 4. Close loop arrangement of the furnace.
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Fig. 5. SAO and SCO burner aero-dynamics.
formation due to the dearth of the oxygen in the initial combustion region, along with a higher NH3 formation downstream of the initial combustion region. It was observed that NO formation was minimum within certain ranges of swirl number (SN), excess air (EA) and momentum ratio (MR). The combustion efficiency of the furnace i.e., the burnout was also calculated and its variation was obtained against SN, EA and MR. The data obtained by these experiments has considered the variation of one of these variables while keeping the other two constant [1].
Fig. 6 shows the variation of NO with respect to the change in the excess air. As the excess air increases, the NOx emissions increase and vice-versa. The burnout variation with respect to the excess air shows the same trend but provides an asymptotic behavior with increase in excess air. Therefore, at low excess air levels the NO emissions can be reduced to the required levels. The limiting factor however, is the burnout as the reduction is observed at lower values of excess air. The threshold value observable for excess air from the study of the two figures is thus limited to 15% for an
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Fig. 6. Variation of burnout and NO w.r.t excess air, at swirl number = 1 and momentum ratio = 0.24, SAO (^), and SCO (&) [1].
acceptable and stable range of operation [1]. Further reduction in NO can be achieved by manipulating the factors, which strongly affect the near burner aerodynamics such as swirl number and/or momentum ratio while keeping the excess air at 15%. In Fig. 7 the minimum NO concentration and maximum burnout for both the burners occur at swirl number 1.0 for excess air of 15% and momentum ratio of 0.24. Above and below this swirl number, the NO concentration and the burnout values start to increase and decrease, respectively. From Fig. 8 the optimal operating point for momentum ratio can be seen as 0.24 because around this point maximum burnout is achieved and NO formation is low. From the above discussion we can prescribe three different NO reduction methodologies based on the exit conditions and near burner dynamics that are observable through the stability performance curves explained above, and are summarised in Table 1. The detailed deliberations
Fig. 7. Variation of burnout and NO w.r.t swirl number at momentum ratio = 0.24 and excess air = 15%, SAO (^), and SCO (&) [1].
and the implementation of control schemes based on these optimal operating ranges is the subject addressed in [4]. For the present study, the variation in MR is considered as a NO reduction methodology through, thus the controller realization considers MR as the input and NO as the only output.
2. Controller development The controller developed here advises the amount of variation in the input variables, required to maintain the optimised performance and set points of the combustion system under study. In this regard momentum ratio was taken as the input variable while keeping the excess air and swirl number at their optimal values obtained from the stability curves in
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the system have been realised. Instead of using static feed forward neural networks for the controller development, an inverse model of the systems has been developed by re-arranging the data. In the experimental facility under consideration i.e., the ICSTM furnace, the equipment for on-line identification was not available. Therefore, all efforts were diverted towards accomplishing the task of forward modelling via off-line neural network training and application. Subsequent to the development of the forward model, an inverse model was developed and finally, the two models were put together in a closedloop to check the performance of the overall system. In the discussion that follows, the methodologies adopted for the forward model, inverse model and the closedloop system development, are outlined. 2.1. Forward modelling In the forward modelling method the model is developed as a function of the past and present inputs, as well as the outputs to yield the future output of the system. In terms of the mathematics this is represented as Eq. (1) given further: ˆ m ðkÞ; ym ðk 1Þ; yˆ m ðk þ 1Þ ¼ f½y Fig. 8. Variation of burnout and NO w.r.t momentum ratio at swirl number = 1, and excess air = 15%, SAO (^), and SCO (&) [1].
Table 1 Optimum conditions
Variation in EA Variation in SN Variation in MR
EA
SN
MR
– 15% 15%
1.0 – 1.0
0.24 0.24 –
Figs. 6 and 7 i.e., 15% and 1.0, respectively. The controller is based on time series modelling and the internal model control (IMC) system through implementing neural networks [4–8]. In order to implement the IMC method, forward and the inverse models of
ym ðk iÞ; um ðkÞ; um ðk 1Þ;
(1) um ðk jÞ;
where ym ðkÞ, is the present output of the system and ym ðk þ 1Þ, is the one step ahead (future) output of the system, ym ðk 1Þ to ym ðk iÞ are the past outputs up to the ith time scale. Similarly the corresponding inputs are represented as um ðkÞfor the present time and, um ðk 1Þ to um ðk jÞ are the past inputs to the jth level in time. The validation and the training data for the above-mentioned problem was generated by discretizing the stability performance curves. The output was the value of future NO and the input values were the past and present MR and the NO values keeping the values of EA and SN uniform at 15% and 1.0, respectively (Table 1). The forward modelling approach was employed to predict one-step ahead NO
Table 2 Specs for forward model of furnace Type of NN
Data sets
Input/output
Weight initiation
Training algorithm
Validation
Recurrent
150
Inputs = 5/output = 1
1 to + 1
Back propagation
47%
M.M. Awais / Applied Soft Computing 5 (2005) 223–233 Table 3 NN forward model parameters for the furnace Input layer neurons (activation function) Output layer neurons (activation function) Hidden layer neurons (activation function) Number of hidden layers Global learning rate (adaptive) Global momentum rate Error at the end of iterations (mean sum squared error) Number of iterations
5 (inactive) 1 (linear) 3 (sigmoid) 1 0.01 0.98 0.00658 5000
values. Multi-step ahead predictions are not considered in the proposed control strategy. Fig. 2 represents the structure of the input and output data used for modelling the neural network-based forward model for the furnace. The training was carried out using cross-validation technique [4]. When a reasonably low mean sum squared error (MSE) was achieved, the training was stopped and the validation test for the two separate and distinctly arranged data sets, was carried out. The main features and specifications of the model developed are discussed in details further. Table 2 shows the specifications of neural network based forward model for the furnace. Recurrent network with back propagation based optimisation algorithm was used for the model development. The initiation of the weights ranged between 1 and +1, and 47% of the total data sets were used for validating the model. The input layer was kept inactive, as usual, while the hidden layer activation function was taken as
Fig. 9. Forward model prediction for training data of the furnace, experimental (continuous line) results and NN (dashed line).
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sigmoid (Table 3). The training process took 5000 iterations. The training results of the forward model are presented in Fig. 9, whereas the response of the model during the validation is presented in Fig. 10. The highest prediction error, as expected for both the cases, was observed at the transition of the response curve, which is without doubt the most difficult part to track. Several test runs were carried out and similar results were obtained. The available data sets were arranged differently for the training and validation runs in order to realise the change in the furnace output in a gradual manner. For validation, a ‘staircase’ model (Fig. 10) output with both ascending and descending values was placed in effect, whereas for the training data sets two consecutive loops of continuously increasing and decreasing data values were taken. During the model selection phase, various trials were carried out that included testing the model output with a different number of hidden neurons and activation functions. As a result a cascade of models was developed. The final selection of the forward model was based on the closed-loop performance of the model with the inverse model (controller) placed in series with the forward model. 2.2. Inverse modelling An inverse modelling technique basically involves prediction of the inputs to the plant given the past data
Fig. 10. Forward model prediction for validation data of the furnace, experimental (continuous line) results and nn (dashed line).
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Table 4 Specs for inverse model of furnace Type of NN
Data sets
Input/output
Weight initiation
Training algorithm
Validation
Recurrent
150
Inputs = 4/output = 1
1 to + 1
Back propagation
47%
of the plant’s inputs and the outputs together with the desired future outputs. Inverse modelling of the dynamical system plays a vital role in many control strategies and structures. These inverse models can be directly used as the controllers in direct inverse and internal model control schemes. Obtaining an inverse of many complex continuous systems is extremely difficult, especially in the field of combustion. The inverse modelling via neural networks is obtained by the direct manipulation of the data sets, achievable through considering the inputs of the system as the outputs and vice versa. This, however, can only be achieved in the region of the plant’s operation where one to one functional mapping between the inputs and the outputs exist. During the training of the inverse models the neural network is fed with the required future or the reference output/set point value together with past inputs and the past outputs to predict the current input of the system i.e., um ðkÞ. Thus the equation for the forward model can be altered accordingly and inverse model expression Eq. (2) can be obtained as: 1 um ðkÞ ¼ fˆ ½ym ðkÞ; ym ðk 1Þ;
(2)
ym ðk iÞ; ym ðk þ 1Þ; um ðk 1Þ; um ðk jÞ;
where the nomenclature is the same as explained 1 earlier for forward model, except for fˆ which is the inverse map of the forward model. The training methodology again employs the moving window Table 5 NN inverse model parameters for the furnace Input layer neurons (activation function) Output layer neurons (activation function) Hidden layer neurons (activation function) Number of hidden layers Global learning rate Global momentum rate Error at the end of iterations (mean sum squared error) Number of iterations
4 (inactive) 1 (linear) 3 (sigmoid) 1 0.01 0.98 0.0067 5000
approach similar to the one explained earlier. In the case study under consideration this mapping does exist and is evident from the stability performance curves of the system presented earlier. Fig. 3 represents the input/output (MR/NO) data arrangement of the control structure for obtaining the inverse model of the plant. The controller inputs also contain the steady state error between the set point chosen for plant operation and the future output of the plant at interval ‘k + 1’. Instead of using the error between the future value and the set point, the input can be replaced by only the future output (NO) of the plant. This will however, restrict the ability of the controller (inverse model) to track effectively the required set point for NO, which is tracked by manipulating/varying the controlling variable (MR). The inclusion of this error also makes it easier to obtain the closed-loop response of the plant and the controller. The details of the neural networkbased inverse model are presented in the Table 4. In this case, again, a recurrent network with back propagation algorithm was used for the inverse model development. The initiation of weights was ranged between 1 and +1, and 47% of the total data sets were used for validating the model. Other parameters regarding training performance are listed in Table 5. The controller response is depicted in Figs. 11 and 12. The controller output follows the set point initiated at the input domain and suggests the corresponding change required in the momentum ratio. The available data sets were arranged to realise the change in the set point of NO. Again, a ‘staircase’ arrangement was adopted for tracking the set points. During the controller selection phase, various trials were carried out under varying neural network parameters. A number of inverse models were developed and were tested for their closed-loop performance. 2.3. Closed-loop analysis In the closed-loop analysis, both the forward and the inverse models of the furnace were put in series with each other and the response of the closed-loop
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Fig. 11. Controller output for training data of the furnace, experimental (continuous starred line) results and NN (dashed line).
Fig. 12. Controller output for validation data of the furnace, experimental (continuous starred line) results and NN (dashed line).
system was checked for the set point variation. The arrangement of the closed-loop system is represented in Fig. 4 In this regard, the values of the set point of NO (NO_set) were varied and the response of the controller and the plant was plotted. Ideally the NO(k + 1) should converge to the set point value and the output of the controller should rest after fluctuating across the mean value of the corresponding momentum ratio. The results presented here are for three set points. The values of the NO_set were kept at 420, 415, and 410 ppm. For each set point the initialisation
point of the plant was different therefore the rise time in each case is different. For example for set point 410 the starting value of NO was kept at 402, similarly for 415 and 420 the initialisation of the output was kept at 411 and 414 respectively. The response of the closedloop system seen in Fig. 13 yields the expected results showing that the controller is sensitive to the set point change and tracks it by affecting a corresponding change in the momentum ratio. The corresponding changes recommended by the controller are 0.24, 0.23, and 0.22 for the above-mentioned set points. The
Fig. 13. Close loop simulation response for the furnace for three different set points.
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Table 6 Percentage error between set point and actual controller output Set point
Controller output
Absolute error (%)
410 415 420
412 415.5 418
0.48 0.12 0.47
error observed between the desired and the predicted experimental values is within 0.5% of the desired NO set points as shown in Table 6, which is acceptable.
2.4. Linear quadratic regulator For the furnace problem stated above a linear quadratic regulator (LQR) was also developed and the steady error of the IMC method and the LQR controller were compared. Here are some details of the controller that was developed using LQR method. Based on the given data the state space model of the furnace was developed. This state space model was used to obtain the gain matrix for the system using the LQR technique. Finally the state space model along with the gain matrix was used to calculate the regulator output. In the LQR the regulation perfor-
mance is measured by a quadratic performance criterion given in Eq. (3). Z 1 JðuÞ ¼ fxT Qx þ uT Rugdt (3) 0
The weighting matrices Q and R define the trade off between the regulation performance and control effort. In designing LQR controller the state-feedback was found through the control law u ¼ Kx, such that the objective function J(u) was minimized. Here K is the minimizing matrix obtained by solving the algebraic Riccati equation [12]. For the problem presented in this paper LQR controller performance was compared with the IMC controller. Fig. 14 represents the error for both the type of controllers. It is interesting to note that the performance of the IMC and LQR is almost similar after the steady state is reached. Both the controllers reach a zero steady state error. However, the IMC takes longer time and more input variations to reach the steady state. The settling period is almost linear in both the cases and variations in the errors are not fluctuating. Thus one may conclude that the IMC based controllers perform similar to the LQR controllers especially for the problem under consideration. The advantage of using IMC, however, is the ease with which the controller can be adjusted for
Fig. 14. Steady state error for (-) LQR control, (- -) IMC control.
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new set points. Moreover, the controller for IMC based method can easily be trained and deployed after including more input/output parameters provided the data for the new parameters is available.
3. Conclusions The modelling techniques mentioned in the above discussion, have revealed numerous advantages. The most appealing though, is the ease with which the forward model can be inverted to obtain the controller for the plant. The results of the controller show that it works well for any set point change prescribed within the limits of the training data. The set point tracking error observed is less than 0.5% for the closed-loop simulations. As far as the steady-state conditions of the furnace are concerned, the controller performed satisfactorily. The results compare well with LQR controller. The tests for the transient phase of operation of the system were not conducted, mainly because the available experimental data only accounted for the steady-state conditions. This simply means that the range of input excitation signal acceptable for the controller is limited. Therefore, the ramp-only data signals were not considered during the training and the validation phases. This study reveals that the successful application of the IMC technique relies heavily on the simultaneous accuracy of the forward and the inverse models. Since this is not easily achieved for many on-line applications especially noise-wrecked non-linear systems, a filter can be added prior to the controller to compensate for these inaccuracies and to sustain robustness in the control implementation. In order to make the controller more effective, the transient dynamics of the furnace should be included in the present control structure, once the data is available. This aspect of the controller development can be treated as an extension to the present research activity and may become a part of a future research work. In our case study, the inverse model obtained, performed reasonably well as the development was conducted off-line after pre-processing the data, thus
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the filter was not implemented. But the large spikes and oscillations in the control inputs could still be seen clearly at the instances where set point changes were made. This behaviour can certainly be improved by introducing the filtering option. The dynamics of the system with different coals was not considered in this study, thus the coal characteristics were kept constant during this development. Again, this was simply because of the lack of the training and the validation data.
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