Implementation of NARMA-L2 Controller for Shell ... - ACS Publications

Article pubs.acs.org/IECR

Implementation of NARMA-L2 Controller for Shell and Tube Heat Exchanger Temperature Process Rajarshi Paul* and Shreesha Chokkadi Department of Instrumentation and Control Engineering, Manipal Institute of Technology, Manipal, 576104, India ABSTRACT: In this research, the authors present the tuning and implementation of the nonlinear moving average autoregressive-linearization level 2 (NARMA-L2) controller for a shell and tube heat exchanger (STHE) temperature process. A mathematical model of the process plant is considered for simulation, and the model is discretized for the controller operation. The NARMA-L2 controller computes a sequence of control variable (the cold water inflow rate) adjustments in order to optimize the future performance of STHE process. The selected controller is trained to provide a quick control over the process variable in the nominal operating range of STHE by selecting appropriate constraints for NARMA models. The paper compares the performance of the selected NARMA-L2 controller with that of a benchmark controller, and the comparative results are presented.

Dudzik3 investigated the application of artificial neural networks to heat exchangers. In his experiments, data acquisition and analysis were done by LabVIEW software. He incorporated the concept of quasi-static heat transfer process for the heat consumption rate calculations. The neural network has been developed and trained based on the thermographic images of the heat exchanger. The autoregressive moving average models using fuzzy logic and ANN has been explained by Khashei et al.4 In their work, the model future values were predicted by several observations. The conventional method of using a linear regression model to predict future values was considered inadequate because every real world application involves nonlinearities. Therefore, to yield better results, the authors designed a hybrid autoregressive integrated moving average (ARIMA) combined with fuzzy and ANN. To model the nonlinear parameters of ARIMA, neural networks were designed. Optimum values of the model parameters were calculated by fuzzy regression. Ahilan et al.5 examined the intelligent controller implementation for observing the degradation of the heat exchanger, and their online monitoring system was designed for energy performance improvement. In their work particle swarm optimization algorithm was used for the fouling factor measurement. Varshney and Panigrahi6 have also investigated the neural network controller design for heat exchanger using LabVIEW software simulation. The heat exchanger was used with closed air inflow. On the basis of their paper, the neural network can be accepted as the good controller with the stable response and low value of error compared to conventional controllers.

1. INTRODUCTION The nonlinearity and delay involved in the heat exchanger process make the controller design complex. Hence, these issues give scope for artificial intelligence based controllers to be implemented on a real-time process plant. The artificial neural network (ANN) based controller provides satisfactory results on the nonlinear behavior of the plant. It has the capability to identify dynamic behavior and control the nonlinear systems. The neural network is one of the current topics of research. This work explores the possibility of applying it to process control problems. In this paper, an attempt has been made to handle the slow process dynamics with neural network based nonlinear moving average autoregressive-linearization level 2 (NARMA-L2) controller. The input−output data have been collected from the shell and tube heat exchanger (STHE) setup, and the NARMA-L2 controller has been trained and validated. Several research activities have been carried out in order to incorporate the neural network based controllers to the real world applications. Diaz et al.1 proposed the concept of the adaptive neural controller for the STHE plant. The work projected the idea toward online adaptation of neural networks for better performance. Two vital criteria that followed in their adaptation method were the accuracy in prediction and stability of the system. Due to neural network’s approximation property, it is easy to control the chemical processes. The neural network controller cancels all nonlinearities of the plant and transforms the nonlinear system dynamics into linear dynamics. Sometimes neural network controllers could not respond satisfactorily due to the generalization of the training data. When the network has been trained with appropriately obtained data set, it produces the desired output as a controller. Moreover neural networks have the capability to approximate functions that can be used for system identification.2 © XXXX American Chemical Society

Received: October 12, 2015 Revised: April 17, 2016 Accepted: April 19, 2016

A

DOI: 10.1021/acs.iecr.5b03791 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

has been designed to control the flow rate of the cold water by regulating the pneumatic valve. In this paper, the simulation results are obtained from the mathematical model of the heat exchanger. The mathematical model is developed after studying the working principle and dynamics of the heat exchanger. The model obtained is called first order plus dead time (FOPDT). By use of MATLAB/ SIMULINK, process response was obtained by manipulating the flow rate of cold water. Section 2 of the paper discusses the dynamics of heat transfer that takes place in heat exchangers along with the mathematical model. Training and implementation of NARMA-L2 are discussed in section 3 and section 4. Comparison of simulation results and real-time results are shown in section 5 and section 6. Finally, the conclusion is given in section 7 discussing the real-time applications results.

Several other methods for nonlinear system control using neural networks have been reported in the literature.7 The application of a neural network based controller for the heat exchanger process has been explored.8−10 The authors produced satisfactory results with a neural network predictive controller and a fuzzy controller for auxiliary manipulated variable. A sliding mode controller for the support of heat exchanger process has also been tried. Almutairi et al.11 designed terminal sliding mode (TSM) control for heat exchanger where it regulated the output to a certain time period. For a nonlinear process like heat exchanger, TSM produced desired results. Oliveira and Bauchspiess12 adapted the NARMA-L2 controller for the fourth order liquid level control process. Their proposed controller produced satisfactory results compared to conventional control algorithm. Also noticeable results13,14 were found through nonlinear autoregressive algorithm implementation for nonlinear process plants. The nonlinear autoregressive moving average (NARMA) based controller was first proposed by Narendra and Parthsarathy.15 The main objective reported in their work was to identify and control the nonlinear dynamical systems by neural networks. The delayed input and output were used as a method to identify nonlinear plants. The identified model proposed was capable of computing partial derivatives of the performance index with respect to the controller parameters. In their work back-propagation algorithm was extensively used to design the neural network. Due to the training of dynamic backpropagation and minimization of the error, NARMA based controller performance was slower. To overcome this drawback, NARMA-L2 based controller was proposed by Narendra and Mukhopadhya.16 The authors reported that a two-step linearization of NARMA controller produced a faster response, and hence NARMA was modified to be used as NARMA-L2. Many types of research have been tried on NARMA-L2 based neural network controller for the process control applications, but the implementation of this controller for the shell and tube heat exchanger process has not been seen in the literature. To identify the manipulated variable which controls the output variable, design of experiments (DOE) is performed. Experiments are described as a series of tests where purposeful changes are included on the inputs of the process to observe and identify the reasons for change in response variables.17,18 The experiments were designed with an objective of the controller design. In the DOE, we investigated the various aspects of plant control. It provided the scope to understand the relationships between process parameters. The techniques can be related back to real time experimentation with the aid of software tools. Thus, we explored more on the adaptation and implementation of the methods to control STHE. Many researchers adopted statistical analysis for their experimentation. The objective of the experiment is to correlate input variables and output variables for the control of STHE. When the variation of controlled variables affects the response variable, then the controlled variables are called factors.19 The values of the factors are called levels. Through the experimental design, the influence of the change in factors on the response is observed as described by Cox and Reid.20 We adopted a full factorial design technique that evaluates the combinations of all input variables.21−23 Statistical analysis gives the validation of the simulation results which helps to draw the definite conclusive statement. Through DOE, we found the cold water inflow rate was the most effective manipulated variable. It has the maximum influence on the process. Hence, the controller

2. SHELL AND TUBE HEAT EXCHANGER PLANT DYNAMICS Shell and tube heat exchanger (STHE) is one of the widely used equipment in the process industry. The satisfactory performance of the STHE is ensured by the design of the controller. The experimental setup has specification as shown in Table 1. Table 1. System Hardware Specifications type shell material tube material tube length shell diameter number of tubes passes diameter of tube input output sensor transmitter characteristics valve action characteristics valve action

Heat Exchanger shell and tube in cocurrent and countercurrent SS 316 copper 750 mm 150 mm 32 single 6 mm PID Controller 24 V 4−20 mA Temperature Sensor PT-100, 3-wire 4−20 mA, 0−5 V Control Valve for Hot Water equal percentage air to open Control Valve for Cold Water equal percentage air to close

The structure of the STHE is having 32 copper tubes and steel shell coated with carbon. Inside the heat exchanger, hot fluid flows through the tubes and cold fluid simultaneously flows from the shell side. The fluids are separated by a solid wall. The heat transfer process can be briefly explained as follows. • The hot fluid releases the heat to the wall by convection. • The wall absorbs the heat by conduction phenomenon. • Heat is transferred to the cold fluid in the shell by convection. Hence, the total heat transfer rate is given by eq 1. Q = ΔT /R = UAΔT = UA i ΔT = UAoΔT

(1)

By use of the law of energy conservation, eq 2 and eq 3 are obtained. mh Cph B

dTh + UA(Th − Tc) = 0 dx

(2)


Article

Industrial & Engineering Chemistry Research mcCpc

dTc + UA(Th − Tc) = 0 dx

(3)

The objective of this work is to keep the hot water outlet temperature at a desired operating temperature by manipulating the cold water inflow. In the work setup, the inflow rate of the two streams is measured by the differential pressure transmitters DPT1 and DPT2, which are connected to the orifice. Simultaneously at the hot water inlet, the temperature is measured with resistance temperature detector (RTD). The manipulated variable (cold water flow rate) is changed through I/P converter actuated by the control action given from the controller algorithms. The control algorithm is designed with an objective to achieve the desired set point value for the hot water outlet temperature. The data acquisition from the STHE was done with ADμC 841 microcontroller. FOPDT model is given by eq 4 and has been obtained by following the guidelines given by the two-point method.24

G (s ) =

kp τs + 1

e−tds

Figure 1. NARMA-L2 controller schematics.

The nonlinear autoregressive moving average controller was proposed before NARMA-L2. The main drawback of NARMA controller was the high value of the mean squared error. Hence, the NARMA controller with two steps of linearization as NARMA-L2 was proposed. The system output can be represented as in eq 6, y(k + d) = f [y(k), y(k − 1), ..., y(k − n + 1), u(k − 1), ..., u(k − n + 1)]

(4)

+ g[y(k), y(k − 1), ..., y(k − n + 1), u(k),

where G(s) is the ratio of the hot water outlet temperature to the cold water flow rate, kp is the process gain, τ is the time constant (in seconds), td is the time delay of the process (in seconds). The mathematical modeling was done with the step change in the input to the process. In real time the control valve opening for cold water flow was varied from 50% to 80% to 30% and the following conditions are considered: (1) Hot water inlet and outlet flow is 75 L/h. (2) Cold water temperature is 35 °C. (3) Cold water input flow rate varied from 500 to 95 L/h. (4) Maximum and minimum values of the outlet hot water are noted with 100% and 0% opening of the cold water valve (with 100% opening at 42 °C and 0% opening at 62 °C) The process is allowed to settle to the steady state value. When the process variable (hot water outlet temperature) reaches steady state value, the parameter values have been calculated from the response and substituted the values in eq 4 to obtain the final model transfer function eq 5 as G (s ) =

0.505 e−62.73s 612.84s + 1

..., u(k − n + 1)]·u(k)

(6)

The representation is called companion form. u(k) is the control input to the plant, and y(k) is the plant output. When the plant output follows the reference values or set points, then

y(k + d) = yr (k + d)

(7)

The resulting controller has the form:

{

u(k) = yr (k + d) − f [y(k), y(k − 1), ..., y(k − n + 1),

}

u(k − 1), ..., u(k − n + 1)]

/{g[y(k), y(k − 1), ..., y(k − n + 1), u(k − 1), ..., u(k − n + 1)]}

(8)

The validation of the neural network is shown in Figure 2. In Figure 3, three lines show the training, test, and validation processes. It can be noted that the MSE values decrease from higher values to a lower value. The network has been validated with 75 epochs, but the best validation happens at epoch 32. The learning process of the network is indicated by the performance during training. The best MSE value obtained was 0.000 162. During the training procedure, the network learns about the plant behavior by fitting the data on the target output. The training output estimates the response of the future plant behavior by reduction of the MSE values. The performance of the NARMA-L2 is also measured by the regression plots for the training, test, and validation (see Figure 4). The corresponding regression values (R-values) are 1.000 00, 0.999 98, and 0.999 96. Figure 4 justifies the correlation between the network output and target value. The R-value close to 1.000 means the ideal correlation which is indicated also by the perfect fit of the data points over the solid dashed line.

(5)

The FOPDT model obtained was used for simulation experiment, and in the real time the model was replaced by the physical plant. In our work, we carried out the simulation first to validate the controller design and calculations of gain values for conventional controllers. After validating the controllers in the simulation, we replaced the model and used the controller for real-time control of STHE temperature process.

3. NARMA-L2 NEURAL NETWORK CONTROLLER DESIGN AND TRAINING This section proposes the NARMA-L2 neural network control technique. The feedback linearization technique forms the basis of controller algorithm. In this controller, the neural network is approximated with a companion form. The controller operates on the nonlinear system by canceling the nonlinearities and transforming it into linear dynamics. The schematic of the controller is shown in Figure 1. The reference model will be given as the set-point values for tracking in real time, and the control signal will be passed to the plant.

4. SIMULATION DESIGN WITH NARMA-L2 The simulation is done using variable-step solver, ODE45 mode. The NARMA-L2 controller was designed with Bayesian regularization algorithm with five hidden layers. The sampling rate was fixed to 0.01 s for all the simulations. The implementation of NARMA-L2 is shown in Figure 5. The controller acts on the C


Article


Figure 2. Validation of NARMA-L2.

Figure 3. Training NARMA-L2 using MATLAB.

obtained plant model in the simulation process. The workflow schematics of the controller for real-time implementation have been depicted in Figure 6. The controller communicates with the heat exchanger by sending the signals through the microcontroller based data acquisition card. The interfacing from the data acquisition card to the computer happens through the RS232 serial port. The objective of the proposed controller is to send signals to the cold water valve to regulate the hot water outlet temperature. The NARMA-L2 controller is a discrete-time controller that has internal feedback from plant output to compare with reference input. It has the ability to transform the nonlinear system dynamics into an implicit algebraic model which can effectively track the reference values of the temperature. In the closed loop simulation, the controller tracks the set point with no overshoot as shown in Figure 7.

5. COMPARISON OF SIMULATION RESULTS To compare the performance of the proposed method with conventional and benchmark controllers, the performance of STHE

Figure 4. Training, testing, and validation neural network with R ≤ 1. D


Article


Figure 5. Implementation of NARMA-L2 in SIMULINK.

Figure 6. Workflow schematics with the NARMA-L2 controller and the plant.

Figure 7. Simulation results with the plant model.

For the process it is defined as

was examined with PID controller tuned with Ziegler−Nichols (ZN) method and Skogestad’s method. However, Skogestad’s PI(D) method has been preferred over ZN method and was implemented in a closed loop for real-time implementation. For simulation, both controllers were used with the plant model.25,26 The Skogestad’s controller comparatively produced better results in the simulation with faster disturbance rejection capabilities and has been chosen as the benchmark controller for further work comparison (see Figure 8). The servo response with set point tracking using a conventional controller is shown in Figure 9. The method proposed by Skogestad was further modified by Finn27 for the process defined by “time constant plus delay”. The process is defined by eq 9, and the gain values of controller were found using eq 10.

K e−θs τs + 1 τ kp = , K (Tc + θ )

(9)

Ti = min[τ , c(Tc + θ )],

Td = 0 (10)

where c = 1.5 and Tc is the time constant calculated at the 63.2% of the closed loop response. In order to compare the results, we also have implemented NN-predictive controller (see Figure 10). This controller predicts the output of the plant on the basis of the previous plant inputs and outputs. The FOPDT model obtained was the initial step to design this controller. The NNPC was trained with E


Article


Figure 8. Skogestad’s PI(D) controller SIMULINK design.

Figure 9. Nominal plant FOPDT model servo response with PID control.

Figure 10. Simulation workflow using NN-predictive controller for FOPDT model with disturbance.

of the data set are 1.0000, 1.0000, and 0.999 64. The perfect fit of the solid dashed line over the data points in Figure 12 justifies the correlation with network output with the target values. After the training of the network, it has been used as the controller. The controller acts on the plant model with the reference set point temperature and disturbances during simulation. The controller adjusts the manipulated variable with reference to the change in the set point and rejects the disturbances. In the simulation, the disturbance was introduced at t = 650 s and t = 1100 s after observing the process behavior (see Figure 13).

reference to the error between the predicted plant output and actual output. The Levenberg−Marquardt algorithm updates the weights and bias in the NNPC. The minimization of error was attained by the continuous feedback. The NNPC was trained with the set of plant data collected from the previous behavior. The performance and training procedure for the NNPC have been shown in the Figure 11. The MSE values decreased during the learning process to 3.2594 at the maximum epoch of 75. The regression values obtained for training, validation, and testing F


Article


Figure 11. Performance determination of the NNPC with MSE value.

Table 2. NARMA-L2 Specifications no. of delayed inputs no. of delayed outputs sampling interval training algorithm hidden activation function no. of hidden neurons output layer activation function learning rate objective function

2 1 0.01 s Bayesian regularization algorithm tran sigmoid function 5 pure line linear function 0.5 mean squared error (MSE)

Table 3. Proposed Controller vs the Benchmark Controllers: Performance Index Skogestad PID Controller control action set point (40 °C) step change (5 °C)

Figure 12. Regression plots of the NNPC for training, testing, and validation.

control action set point (40 °C) step change (5 °C)

overshoot (%)

rise time tr (s)

7 1100 9 900 NN-Predictive Controller mp (%)

rise time tr (s)

9 750 10 600 NARMA-L2 Controller

settling time ts (s) 700 1020 settling time ts (s) 900 770

control action

mp (%)

rise time tr (s)

settling time ts (s)

set point (40 °C) step change (5 °C)

3 3

587 390

723 685

the plant model in the form of a pulse and the controllers were able to track the set point; however, NARMA-L2 provided a faster response with minimum overshoot.

6. REAL TIME RESULTS ANALYSIS In order to work with the real-time control, the plant model has been removed and controller proposed was interfaced using “query instrument block”. The photographic view of the experimental setup has been shown in Figure 14. For interfacing and simulation in real time MATLAB/SIMULINK code has been developed separately (see Figure 15). For the real-time

Figure 13. Simulation results of all the controllers for the process plant model.

The performance of the controllers is summarized in Table 3. The disturbance rejection capabilities of the control system are noticed when the step inputs are applied at different temperature levels, respectively. In this test, a disturbance is applied to G


Article


Figure 14. Real-time experimental setup.

implementation of the controllers the cold water inflow to the heat exchanger has been chosen as the manipulated variable. The desired temperature of the hot water outlet was maintained by the controller action. In Figure 16, the three controllers were used to run the process with the same settings in the set-point temperature from the outlet. The manipulated variable, that is, cold water inflow to the system, was regulated by the opening of the air-to-close control valve. The variable marked “MV” shows the maximum value corresponding to the minimum opening of the valve. As the process runs and heat absorption happens to the running cold water, the valve action reciprocates. The controller output of the three controllers is shown in Figure 17. It can also be noted that the cold water temperature rises to the higher value in order to set the outlet temperature of the hot water. The NARMA-L2 controller with the settings in Table 2 was implemented in a closed loop with the real system. In the realtime it has been observed that the STHE response tracks the set point temperature values applied at different instants. The control action of the proposed controller has shown the sharp variation with the step change at every instant. In order to analyze it, the NARMA-L2 function was compared with Skogestad’s

Figure 16. (a) Real-time response of the Skogestad’s PI(D) controller, (b) NARMA-L2 controller, and (c) NN-predictive controller for the STHE temperature process.

PI(D) and NNPC controller. Table 4 projects the performance measures of the three controllers.

Figure 15. Real-time SIMULINK controller design. H



■

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +919035673329. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors would like to acknowledge Dr. I. Thirunavukkarasu, Department of Instrumentation and Control Engineering, Manipal Institute of Technology, Manipal, 576104, India for technical guidance and Manipal University, Manipal, 576104, India for infrastructure support to carry out this research work.

■

■

Figure 17. (a) Skogestad’s PID controller output, (b) NARMA-L2 controller output, and (c) NN predictive controller output.

controller

ISE

IAE

ITAE

497 511 486

876 968 759

1503 1412 1387

REFERENCES

(1) Diaz, G.; Sen, M.; Yang, K. T.; McClain, R. L. Adaptive neurocontrol of heat exchangers. J. Heat Transfer 2001, 123 (3), 556−562. (2) Diaz, G.; Sen, M.; Yang, K. T.; McClain, R. L. Simulation of Heat Exchanger Performance by Artificial Neural Networks. HVACR Res. 1999, 5 (3), 195−208. (3) Dudzik, S. Investigations of a heat exchanger using infrared thermography and artificial neural networks. Sens. Actuators, A 2011, 166 (1), 149−156. (4) Khashei, M.; Bijari, M.; Raissi Ardali, G. A. Improvement of AutoRegressive Integrated Moving Average models using Fuzzy logic and Artificial Neural Networks (ANNs). Neurocomputing 2009, 72 (4), 956−967. (5) Ahilan, C.; Dhas, J. E. R.; Somasundaram, K.; Sivakumaran, N. Performance assessment of heat exchanger using intelligent decisionmaking tools. Appl. Soft Comput. 2015, 26, 474−482. (6) Varshney, K.; Panigrahi, P. K. Artificial Neural Network Control of a Heat Exchanger in a closed air-flow circuit. Appl. Soft Comput. 2005, 5 (4), 441−465. (7) Ramírez, D. R.; Arahal, M. R.; Camacho, E. F. Min−Max Predictive Control of a Heat Exchanger Using a Neural Network Solver. IEEE Trans. Control Sys. Technol. 2004, 12 (5), 776−786. (8) Vasickaninová, A.; Bakošová, M. Control of a heat exchanger using neural network predictive controller combined with auxiliary fuzzy controller. Appl. Therm. Eng. 2015, 89 (1), 1046−1053. (9) Vasickaninová, A.; Bakošová, M.; Meszaros, A.; Klemes, J. Neural network predictive control of a heat exchanger. Appl. Therm. Eng. 2011, 31 (13), 2094−2100.

Table 4. Performance on the Basis of Error Reduction Skogestad PI(D) NN predictive NARMA-L2

NOMENCLATURE Q = total amount of heat transferred during the process (W) U = overall heat transfer coefficient (W/(m2K)) R = thermal resistance encountered by each fluid (m2K/W) Th = hot water temperature (K) Tc = cold water temperature (K) ΔT = temperature difference between the bulk mean temperatures of the two fluids on the two sides of the elementary area (K) Cpc = specific heat of the cold water (J/K) Cph = specific heat of the hot water (J/K) A = area of the wall across which heat is transferred (m2) Ai = inlet area of the wall across which heat is transferred (m2) Ao = outlet area of the wall across which heat is transferred (m2) mh = mass transfer of the hot fluid (kg) mc = mass transfer of the cold fluid (kg) SP = set point MV = manipulated variable MP% = maximum peak value DOE = design of experiment

7. CONCLUSION In this work, we concentrated on the NARMA-L2 based controller implementation for the shell and tube heat exchanger. To implement NARMA-L2 controller, we used the MATLAB/ SIMULINK. The NARMA-L2 controller was trained with Bayesian regularization algorithm, and the tuned controller was used for real time STHE process control. On the basis of simulation results and actual performance data, the effectiveness of the NARMA-L2 controller was established. With set-point tracking method, it has been found that the controller produced better responses in terms of settling time, ISE, IAE, and ITAE values and minimal overshoot. The controller was capable of rejecting several disturbances during simulation. In real time implementation of the system operated with the NARMA-L2 controller, process response was found to track steady state condition. I


Article

Industrial & Engineering Chemistry Research (10) Vasičkaninová, A.; Bakošová, M. Fuzzy Model-based Neural Network Predictive Control of a Heat Exchanger. Chem. Eng. Trans 2015, 45, 313−318. (11) Almutairi, B. N.; Zribi, M. Control of plate heat exchanger using the terminal sliding mode technique. Ind. Eng. Chem. Res. 2012, 51, 4610−4623. (12) Oliveira, J C.P.; Bauchspiess, A. Neural Control of 4th order level process. ABCM Symp. Ser. Mechatronics 2008, 3, 197−206. (13) Inoan, I.; Abrudean, M. Design of NARMA-L2 Neural controller for an Induction Motor’s Speed Control. J. Comput. Sci. Control Syst. 2013, 6 (2), 18−21. (14) George, M.; Basu, K. P. NARMA-L2 Controlled Variable Frequency Three-Phase Induction Motor Drive. Eur. J. Sci. Res. 2012, 70 (1), 98−111. (15) Narendra, K. S.; Parthasarathy, K. Identification and Control of Dynamical Systems Using Neural Networks. IEEE Trans. Neural Networ. 1990, 1 (1), 4−27. (16) Narendra, K. S.; Mukhopadhyay, S. Adaptive Control using Neural Networks and Approximate Models. IEEE Trans. Neural Networ. 1997, 8, 475−485. (17) Mason, R. L.; Gunst, F.; James, L. Statistical Design and Analysis of Experiments: With Applications to Engineering and Science, 2nd ed.; Wiley Publication: New York, 2003. (18) Law, A. M.; Kelton, W. D. Simulation Modeling and Analysis, 3rd ed.; McGraw-Hill: Boston, MA, 1999. (19) Kleijnen, J. P.C.; Sargent, R. G. A methodology for fitting and validation metamodels in simulation. Eur. J. Operational Res. 2000, 120, 14−29. (20) Cox, D. R.; Reid, N. The Theory and Design of Experiments, 3rd ed.; Chapman and Hall/CRC: Boca Raton, FL, 2000. (21) Ravikumar, K.; Kim, S.-H.; Son, Y. Design of experiments for the optimization and statistical analysis of Berberine finishing of polyamide substrates. Dyes Pigm. 2007, 75 (2), 401−407. (22) Douglas, C. M. Design and Analysis of Experiments, 5th ed.; John Wiley and Sons: New York, 2001. (23) Sanchez, S.; Moeeni, M. F.; Sanchez, P. J. So many factors, so little time: Simulation experiments in the frequency domain. Int. J. Prod. Economics 2006, 103 (1), 149−165. (24) Malleswararao, Y. S. N.; Chidambaram, M. Nonlinear Controllers for a Heat Exchanger. J. Process Control 1992, 2 (1), 17−21. (25) Ziegler, J. G.; Nichols, N. B. Optimum Settings for Automatic Controllers. Trans. ASME 1942, 64 (1), 759−768. (26) Skogestad, S. Simple analytic rules for model reduction and PID controller tuning. J. Process Control 2003, 13, 291−309. (27) Finn, H. The Good Gain method for PI(D) controller tuning. TechTeach, 2010; http://techteach.no/presentations/tekna_olje_ gass_04/lecture/documents/skogestad.pdf.

J


Implementation of NARMA-L2 Controller for Shell ... - ACS Publications

Recommend Documents