Predictive control based on neural networks: an application to a fluid catalytic cracking industrial unit

PREDICTIVE CONTROL BASED ON NEURAL NETWORKS: AN APPLICATION TO A FLUID CATALYTIC CRACKING INDUSTRIAL UNIT

V.M.L.Santos¹, F.R.Carvalho¹ and M.B.de Souza Jr2^*

¹ Universidade Federal de Pernambuco, Departamento de Engenharia Química,

R. Prof. Artur de Sá S/N, Cidade Universitária, Fone/Fax: [phone],

[phone], 50.740-521, Recife – PE

² Universidade Federal do Rio de Janeiro, Escola de Química, Departamento de Engenharia Química,

Sala E-207, Cidade Universitária, Ilha do Fundão, 21949-900, Rio de Janeiro-RJ

Fone: [phone], E-mail: [e-mail]

(Received: December 3, 1999 ; Accepted: May 18, 2000)

Abstract - Artificial Neural Networks (ANNs) constitute a technology that has recently become the focus of great attention. The reason for this is due mainly to its capacity to treat complex and nonlinear problems. This work consists of the identification and control of a fluid cracking catalytic unit (FCCU) using techniques based on multilayered ANNs. The FCC unit is a typical example of a complex and nonlinear process, possessing great interaction among the operation variables and many operational constraints to be attended. Model Predictive Control is indicated in these occasions. The FCC model adopted was validated with plant data by Moro (1992); and was used in this work to replace the real process in the generation of data for the identification of the ANNs and to test the predictive control strategy. The results of the identification and control of the process through ANNs indicate the viability of the technique.

Keywords: artificial neural networks, predictive control, fluid catalytic cracking.

INTRODUCTION

The petroleum fluid catalytic cracking process has fundamental importance in the world economic scenery. The conventional control techniques, based on PID (or proportional-integral-derivative) controllers, have not led to satisfactory results in FCC units, because these units present the following characteristics: non-linearity; presence of restrictions etc. For processes with these features, it is indicated the utilization of advanced control techniques, such as MPC (or model predictive control). The MPC uses a process model, that can be linear or non-linear. A category of non-linear MPC can be obtained by the utilization of a neural network internal model.

In this work, a FCC model - developed by Kurihara (1967) and validated with operational data of the catalytic cracking unit of the Henrique Lage Refinery (REVAP) by Moro (1992) - was used to provide data for the identification using neural network and also as a substitute to the real process in the control simulation study.

In sections 2, 3 and 4, short descriptions of the process, neural networks and predictive control, are presented. In section 5, results of the application of neural networks for the identification and control of the FCC are shown. The conclusions are drawn in the last section.

CATALYTIC CRACKING

The FCC units differ among themselves by the geometric structure of the system reactor/regenerator. The schematic representation showed in Figure 1 presents the Kellogg Orthoflow F kind. This structure is located in the REVAP refinery and was used in this project.

To guarantee an adequate conversion and selectivity, the reaction temperature (riser temperature), must be kept between 520 and 550^oC. Secondary reactions produce coke that is deposited on the surface of the catalyst. The spent catalyst is continuously regenerated by burning the coke under controlled conditions to prevent the catalyst deactivation.

ARTIFICIAL NEURAL NETWORKS (ANNS)

Multilayered ANNs are formed by a dense network of interconnected processing elements, distributed in layers (input, hidden and output) and processing information from the input data to obtain an answer. The neuron output is a non-linear function (named "activation") of the inputs and of the network parameters (weights and biases).

The sigmoid function (Eq. 1), which has been successfully employed elsewhere (Rumelhart & McClelland (1986)), was chosen as the activation function here. This function is continuous and limited between 0 and 1. As in Fonseca (1998), the variables were normalized between 0.1 and 0.9. This interval avoids that very large weights are obtained.

(1)

The network stores knowledge that are available to be used. This storage process is known as training. Among the training methods, the backpropagation is the one that has received the largest attention. It is composed by two stages:

Stage 1 - The input patterns are presented and propagated forward the net until the output signs are computed, which are compared to target outputs, obtaining an error;

Stage 2 - The error obtained in the phase 1 is propagated backward and the weights are adjusted.

This backpropagation method was adopted in this project, minimizing the objective function through the conjugated gradient technique (Leonard & Kramer, 1990).

PREDICTIVE CONTROL

In the last decade, the predictive control was established as a powerful technique, with an enormous potential for application, specially for the control of FCCUs.

Based on input and output past information, and in projections for the future control actions, the output of an internal model, that represents the process, is predicted along a prediction horizon of H sampling times. A sequence of future set-points r is generated, called reference trajectory. An appropriate objective function of future errors and control actions is minimized to provide a sequence of future control actions. The control actions can vary in a horizon U£H, known as control horizon. Only the first control action of the calculated control sequence is in fact introduced in the real process to which the controlled variables are measured. In the next sample time, the same procedure is repeated ("receding horizon control").

APPLICATION TO A FCCU – REVAP

Identification

Narendra & Parthasaraty (1990) suggested four model classes for non-linear processes, which are described by difference equations. The most general one is showed in the Eq. 2:

(2)

where g are any non-linear functions and m and n, indicate the process order. The values of m and n must be chosen based on the analysis of the process data, previous knowledge and experimentation. The smaller the value of m=n, the smaller will be the computational work.

Moro & Odloak (1995) proposed 6 variables to be controlled: riser temperature, severity, temperature of the dense phase of the regenerator first stage, temperature of the regenerator dense phase of the second stage, the differential valve pressure of the regenerated catalytic and the rotation velocity of the gas compressor. They also proposed the following manipulated variables: feed flow rate to the unit, air flow rate to the regenerator, valve opening of the regenerated catalytic and the feed temperature.

The chosen controlled variable here was the temperature of the dense phase of the regenerator first stage, manipulating the air flow rate to the regenerator.

Considering m=n=1, the data were divided in two settings: one for training and another for testing.

The identification results for this variable - whose neural network presents two neurons in the input layer (Trg1(k) and Rai(k)), nh hidden neurons and one neuron in the output layer for the one-step-ahead prediction (Trg1(k+1)); that is (2:nh:1) - were obtained for the data of Figure 2 (14 successive steps between -10 and +5% or between 198.9 and 232.1kNm³/h). These maximum and minimum values were adopted by Moro and constitute restrictions of the air blower. These results were compared to the ones obtained using only 8 successive steps, but making sure that the new steady states were achieved (Figure 3). It is important to remember that the number of steps for the complete right answer was smaller because of the commitment with the number of generated patterns and computational demand.

Tables 1 and 2 show the results of training. It can be depicted from the analysis of them that:

- The attempt using only 1 neuron in the hidden layer was not successful;

- 5 hidden neurons would be indicated for the data of Figure 2, and 6 for the data of Figure 3;

- The smaller objective function was the one obtained for 5 hidden neurons (nh=5), using a bigger number of steps in the range.

In some cases a bigger number of trials was necessary for convergence, due to the impossibility of the method to decrease more the objective function, as the adopted criteria for stopping the training are:

1) Norm of the Gradient of the objective function smaller than 10^-8;

2) Impossibility of the method of the conjugated gradient to reduce further the objective function.

Despite the fact the identification results were satisfactory for the networks (2:5:1 – 14 steps/ANN-I and 2:6:1 – 8 steps/ANN-II) with respect to the other ones, a comparative analysis of the steady states of the model and of the trained networks was done.

The Figures 4 and 5 indicate that for the air flow rate varying from 232.0 to 200.0kNm³/h, from the actual steady states, the networks - despite the fact they present a smaller objective function - do not predict the same steady states of the model.

The steady state diagrams of the identified nets were compared with the one of the process. The smaller net that produced the best steady state agreement with the process was the one obtained for 8 successive steps between 198.0 and 232.0 kNm³/h (or ANN-II – nh=3). It can be concluded that, despite the fact the objective functions are smaller for the ANN-I, it is not necessary many steps in the operation range, or still, only this criterion does not define the choice of a network. Less conservative criteria like the ones adopted in this work must be considered.

Predictive Control Based On Neural Networks – Case SISO

The control scheme proposed is shown in Figure 7. The objective function in the Equation 3 below was minimized by the routine of optimization DNCONF of the IMSL library, generating the future control actions that minimize the errors between a reference trajectory and the predicted outputs.

where:

u(k + i) = u(k + U - 1), i = U,..., H

l is the parameter that penalizes the control action increments.

Submitted to input and output restrictions of the process:

(4)

(5)

(6)

The reference trajectory for the control strategy is given by the model:

(7)

(8)

Servo Control

The control parameters were tuned and the results for a + 5^oC step and - 5^oC step are shown in the Figures 8. The control parameters are H= 5.0, a= 0.5 and l= 1x10^-7. The bounds on the control actions are u_mín= 198.9kNm³/h, u_máx= 232.1kNm³/h and Du_máx= 1.3kNm³/h. The sampling time is Dt= 0.05h.

Regulatory Control

The regulatory case can have as a disturbance variable the air temperature for the regenerator. For a disturbance of 10^oC in the initial operation temperature of 190.0^oC, in the time t=50 min; -10^oC, in the time t= 250 min; with the same parameters used in the servo case, the behavior of temperature of temperature of the first stage of the regenerator is showed in the Figure 9.

Before the disturbance happens, the controller does not change the manipulated variable, as expected. For both disturbances, small magnitude closed loop oscillations are observed. Better results cold be obtained if a different tuning had been chosen However, it was intended to use the same control parameter for servo and regulatory control.

CONCLUSIONS AND PERSPECTIVES

The utilization of ANNs for control objectives needs another training criteria besides the analysis of the objective function, gradient and answer analysis using the test data. The comparison of bifurcation diagrams is a valuable tool for discrimination between ANNs.

From the data of Tables 1 and 2, it could be concluded that a bigger number of steps in the interest range should be used. However, the results predicted by the networks using 8 and 14 steps do not differ significantly in the prediction of the process steady state.

In the SISO case, the same tuning parameters were used for the servo and regulatory cases. The use of artificial neural networks as controller of the system proved to be efficient in the analyzed situation.

Presently, it has been initiated the development of the MIMO control strategy. Analyzing the MIMO identification results (not shown here), it was realized that the artificial neural network can describe well the behavior of the process for the important control variables in a simultaneous way, what allow the technique employment, in the MIMO case.

Future projects will also be developed in the hybrid-neural modeling area. In this case, the coke concentrations in the spent and regenerated catalysts can be obtained using artificial neural networks. This would avoid the laboratory analysis needs. For that, historic data would need to be provided by the interested industry. The hybrid-neural modeling technique has been successfully applied to several research projects (Zbicinski et al. (1996), and others).

NOMENCLATURE

f Sigmoid function with respect to the net input H Prediction horizon J Objective function to training of net. N_h Number of neurons in the hidden layer Rai Air flowrate to regenerator (kNm³/h) sp Set-point Trg1 Temperature of dense phase at regenerator first stage (K) Trg2 Temperature of dense phase at regenerator second stage (K) Trx Temperature of cracking mixture in riser (K) U Control horizon u Variables manipulated X Severity of the cracking reaction (%) x_i Activation of the i^th neuron y Variables controlled y^{^} Prediction of the net y_sp Reference trajectory given by the model

Greek symbols

a Parameter of agreement of the controller l Penalization control action

REFERENCES

• Baughman D. R. and Liu Y. A., Neural Networks in Bioprocessing and Chemical Engineering. Academic Press, Inc. (1995).
• Fonseca E. F., Controle Preditivo Baseado em Redes Neurais de Fermentação Alcoólica Contínua. MSc. Dissertation, DEQ/UFPE, Recife (1998).
• Kurihara H., Optimal Control of Fluid Catalytic Cracking Processes. ScD. Thesis, MIT (1967).
• Leonard J. and Kramer M. A., Improvement of the Backpropagation Algorithm for Training Neural Networks, Computers chem. Engng., 14, N^o3, 337-341 (1990).
• Moro L. F. L. and Odloak D., Constrained multivariable control of fluid catalytic crackink converters. J. Proc. Cont., 5, N^o 1, 29-39 (1995).
• Moro L. F. L., Desenvolvimento de um Controlador Preditivo Multivariável para um Conversor Industrial de Craqueamento Catalítico. MSc. Dissertation, USP, São Paulo (1992).
• Narendra K. S. And Parthasarathy K., Identification and Control of Dynamical Systems Using Neural Networks. IEEE Transactions on Neural Networks., 1, N^o1, 4-27 (1990).
• Rumelhart D. E. and McClelland, J. L., Parallel Distributed Processing: Explorations in the Microstructure of Cognition, 1, Foundations, The Mit Press, Cambridge (1986).
• Zbicinski I., Strumillo P. and Kaminski W., Hybrid Neural Model of Thermal Drying in a Fluidized Bed. Computers chem. Engng., 20, S695-S700 (1996).

*

To whom correspondence should be addressed

Publication Dates

• Publication in this collection
  16 Mar 2001
• Date of issue
  Dec 2000

History

• Accepted
  18 May 2000
• Received
  03 Dec 1999