State and parameter estimation based on a nonlinear filter applied to an industrial process control of ethanol production

STATE AND PARAMETER ESTIMATION BASED ON A NONLINEAR FILTER APPLIED TO AN INDUSTRIAL PROCESS CONTROL OF ETHANOL PRODUCTION

L.A.C.Meleiro1^* and R.Maciel Filho¹

¹State University of Campinas (UNICAMP), School of Chemical Engineering,

Department of Chemical Processes

¹Laboratory of Optimization, Design and Advanced Control (LOPCA)

Cidade Universitária Zeferino Vaz - CP 6066 ,CEP 13081-970, Fax +(55) (19) 289-717

Campinas - SP, Brasil.

E-mail: [e-mail]

(Received: November 10, 1999; Accepted: May 18, 2000)

Abstract - Most advanced computer-aided control applications rely on good dynamics process models. The performance of the control system depends on the accuracy of the model used. Typically, such models are developed by conducting off-line identification experiments on the process. These experiments for identification often result in input-output data with small output signal-to-noise ratio, and using these data results in inaccurate model parameter estimates [1]. In this work, a multivariable adaptive self-tuning controller (STC) was developed for a biotechnological process application. Due to the difficulties involving the measurements or the excessive amount of variables normally found in industrial process, it is proposed to develop "soft-sensors" which are based fundamentally on artificial neural networks (ANN). A second approach proposed was set in hybrid models, results of the association of deterministic models (which incorporates the available prior knowledge about the process being modeled) with artificial neural networks. In this case, kinetic parameters – which are very hard to be accurately determined in real time industrial plants operation – were obtained using ANN predictions. These methods are especially suitable for the identification of time-varying and nonlinear models. This advanced control strategy was applied to a fermentation process to produce ethyl alcohol (ethanol) in industrial scale. The reaction rate considered for substratum consumption, cells and ethanol productions are validated with industrial data for typical operating conditions. The results obtained show that the proposed procedure in this work has a great potential for application.

Keywords: Adaptive control, Artificial Neural Networks, Hybrid Models, Fermentation processes.

INTRODUCTION

The industrial application considered here is concerned with a biotechnological process. Biotechnology has become increasingly important in the activities of contemporary society as a "clean" and safe technology when compared to traditional chemical processes. Moreover, it provides extremely useful and valuable products in several industrial areas (pharmaceutical, foods, fuels, etc.). Biotechnological processes are characterized by their complex dynamics, such as inverse response, dead time and strong nonlinearities, especially because the main driving force of these processes is microorganisms (cells) that are very sensitive to any environmental variations in the fermentation broth (e.g., temperature, substrate concentration, pH, among others). For these reasons modeling, simulation, and control of those systems are problems that have not yet been totally resolved. Therefore, they are still a relevant and timely research theme.

The underlying problem here refers to an important class of biotechnological industrial processes. The case study is a typical large-scale industrial plant to produce ethanol from sugar cane syrup. The process operational conditions are those typically found in the Brazilian industrial distilleries. As the literature has been showing, it is necessary to develop control algorithms based on the advanced control concepts to obtain system’s operation at high performance levels harmonized to safe conditions for the microorganisms [2].

It is well known that bioprocess are difficult to model and, consequently, troublesome to monitor and control. Generally, this kind of process is nonlinear, the involved biological mechanisms are far from being well understood, and the available on-line sensors are usually very expensive and/or inaccurate. The recent scientific literature has presented a considerable number of works that have proposed different strategies to overcome these difficulties. However, a general and efficient solution is still being pursuit. For such a system, since conventional PID controllers tend to fail because of time varying parameters of the process, high performance operating conditions can be achieved only with application of modern control strategies. The performance of the STC was analyzed through the process computer simulation under industrial operating conditions. The STC was applied considering measurement of TRS (Total Reducing Sugar) with High Performance Liquid Chromatography (HPLC) considering the time-delay observed in the industrial plant. The results obtained show that the STC has improved the control capability of this industrial process [3].

INDUSTRIAL PROCESS FOR ETHANOL PRODUCTION

General View of the Process

The Brazilian alcoholic fermentation processes arose from the production of the sugar cane liquor (aguardiente). Later, these processes were applied to the production of ethanol from molasses obtained from the sugar production plants. In the 1980s, the Federal Government’s "Pro-Alcohol" program created an incentive for the use of ethanol as an alternative fuel in automobiles. As a consequence, there was an increase in research focusing on improving the productivity and yield of these processes. Current research concentrates on the optimization of continuous operation of the processes.

As stated previously, an industrial plant for the production of ethanol is considered in the present work. Because of difficulties encountered when working directly with the plant in operating mode, especially because of the high costs involved in interruptions in its operation for tests, it has been chosen to work with a simulator whose kinetic parameters have already been validated in the real plant. This simulator was developed by Andrietta and Maugeri [4] who modeled the set of biochemical reactions of the process by means of a set of nonlinear ordinary differential equations and optimized an operational region. This optimized region was further implemented in the plant in such a way so as to achieve satisfactory productivity values without affecting its operational and economic feasibility. Within this pre-optimized operational region, controllers should be applied to act on the manipulated variables of the process to optimize its real time yield, even in the presence of disturbances [2].

Plant Description

The fermentative process for ethanol production is illustrated in Figure 1. The system is a typical large-scale industrial process composed of four tank reactors (fermenters) arranged in series and operated with cell recycling to produce ethanol from sugar cane syrup. The process is fed with a mixture composed of sugars (TRS) as well as sources of nitrogen and mineral salts, called feed medium. The feed medium is converted into ethanol by a fermentation process carried out using the yeast Saccharomyces cerevisae.

Since the behavior of the microorganisms is very sensitive to their environmental conditions, some of them are purged and the remaining cells are submitted to an acid treatment and dilution before being recycled into the first reactor. The recycling procedure is important because the generation of new microorganism colonies is an expensive and time-consuming process. A set of centrifuges split the fermented medium, which is formed of a mixture of water, CO₂, sugars, microorganisms (30-45g/l of cells), and alcohol, into two phases. The heavy phase contains most of the cells (160-200g/l) while the light phase contains at most 3g/l of cells and is 9-12% alcohol. The light phase is then sent to the distillation unit, where the alcohol is extracted. Each reactor has an external system of heat exchangers with independent control loops (PI controllers) whose objective is to maintain the temperature of the reactants (fermentation broth) constant at an ideal level for the fermentation process. The set point for the temperature was optimized by Andrietta and Maugeri [4] to maximize the efficiency of the reactions (conversion) of the industrial plant.

In the simulator of the plant some simplifications related to apparatus that are not represented in Fig. 1 are also considered. One of them is an independent internal control loop to regulate the liquid volumes of the tanks, which are represented in the simulator by the condition of equal flow rates in all the tanks. Another simplification refers to the flow control valves of the feed medium and recycling. The dynamics of these devices can be neglected without loss of generality since they are much faster than the other dynamics of the process. In addition, the hypothesis of perfect stirred tanks is adopted, i.e., it is assumed that the reactions occur homogeneously inside the tanks. This is a good approximation with respect to the kinetic model, but it influences the dynamic representation of the process by the elimination of the transport delays existing in real situations. Therefore, this simplification is going to be reconsidered in future work [2].

As mentioned previously, the industrial process for ethanol production is a highly nonlinear process. The main nonlinearities arise from the behavior of the microorganisms. Increasing the feed medium flow rate, for example, the TRS concentration inside the tanks also increases. Under this condition, ethanol production from the biological conversion of the sugar tends to increase. However, an excessive amount of sugar, which exceeds the microorganisms’ processing capacity, will not be converted into ethanol (substrate inhibition phenomenon). This excess of sugar will appear in the final product, thus characterizing a drop in the conversion efficiency as well as a waste of raw material and energy. Another problem caused by the substrate inhibition effect is a decrease in the microorganism reproduction, which is reflected directly in the alcohol production. This inhibitory effect can also be caused by an excess of alcohol in the fermentative broth, which in turn can cause the death of cells. Besides, low levels of substrate can also cause the death of cells. All of these factors influence the dynamics and the efficiency of the fermentation process. More details on this process can be found in [4], and a set of trials illustrating its inverse responses and/or strongly nonlinear behavior is presented in [5].

Considering these characteristics, the fundamental objective of the study of the fermentative process for ethanol production is to generate models and controllers in such a way so as to maximize its efficiency, i.e., to maximize ethanol concentration and minimize TRS concentration in the outlet of the fourth tank, while maintaining the stability of the microorganism colony.

Input, Output, and Disturbances Variables

Considering the pre-optimized operational conditions of the plant discussed above, the input, output, and disturbance variables of the process are [2]:

1. Feed Medium Flow Rate (F_a [m³/h]): This is the main manipulated input variable. The universe of discourse of this variable is the interval [40,140]. This interval is conservative in terms of the economic and operational viability of the plant. It represents the upper and lower bounds for the substrate feed flow of the microorganisms and comprises the limitations related to valve operation and tank volumes as well.

2. Recycle Rate (t_r [dimensionless]): This variable relates the feed medium flow rate, F_a, with the cell recycle flow rate (F_r [m³/h]) and, accordingly, with the real inlet feed flow rate in the first tank (F₀ [m³/h]), as shown in Fig. 1. This relationship is given by . The usual value of t_r in real operational conditions is 0.3. Thus, a recycle rate of 0.3 implies F_a = 0.7F₀ and F_r = 0.3F₀.

3. TRS Concentration in the Feed Medium (S₀ [g/l]): The nominal value of this variable under real operational conditions is 180g/l. However, since it depends on the sugar cane used, it is important to take into account possible disturbances of at least ±5% around this value. In this case, this variable becomes a measurable disturbance (input) belonging to the interval [170,190].

The output variables of interest according to the control objectives are

1. Outlet Ethanol Concentration in the Fourth Tank (P₄ [g/l]).

2. Outlet TRS Concentration in the Fourth Tank (S₄ [g/l]).

3. Outlet Cells Concentration in the Fourth Tank (X₄ [g/l]).

where the outlet product of the fourth tank is the fermented medium (see Fig. 1).

MATHEMATICAL MODELING

The mathematical modeling of the process is based on mass and energy balances on the reactors, (equations 1 to 7).

(1)

(2)

(3)

(4)

(5)

(6)

(7)

where the subscripts i refer to each stage, j and je are fresh water to cooler and from cooler, respectively, c is the reacting mean to cooler; V is the reactor volume; T is the temperature; F is the flow rate; S, X and P are the substrate, cells and ethanol concentration, respectively; r, C_p and DH are the physical parameters: density, specific heat and reaction heat, respectively; and Y_X/S and Y_P/S are the kinetic parameters of the yield.

To model each stage, seven differential equations are required and the Runge Kutta algorithm was used to integrate the global system of ordinary differential equations. The kinetic model is based on the Monod equation (8), and the kinetic parameters were obtained carefully to represent typical industrial conditions.

(8)

where m is specific growth of cells, m_max, P_max and X_max are fixed kinetic parameters and n and m are coefficients from inhibitor terms.

SOFT-SENSORS

Soft-Sensors are sophisticated monitoring systems that can relate state variables less accessible and the variables that can be measured during the process. These computational tools are useful to applications in fermentative process control, whose state variables are not always available. The control of these processes around the optimum increases the yield and reduces the operational costs. However, to operate at this point is a difficult task, because it involves a number of biochemical complex reactions that are difficult to monitor [6]. Soft-Sensors apply process models and estimation algorithms to estimate variables and parameters that are not easily measured or that are available only after a significant time delay from the on-line measured data. In biotechnological processes, the main variables (such as kinetic parameters, biomass, substrate, and metabolite concentrations) are usually determined by laboratory analysis. The cost and the time required for these analysis limits the sampling frequency. Soft-Sensors can be used to estimate these variables through on-line data available.

In order to develop such a soft-sensors, two neural networks were developed in this work. The first one, named "States Network", was used to overcome one of the main obstacles in bioprocess monitoring and control: the lack of reliable measurements of important process state variables (S, X and P concentrations). The second ANN, named "Kinetic Network", was developed to provide the specific growth rate of the cells (m) and was further used in a hybrid (ANN + deterministic) dynamical model of the system. For these purposes, soft-sensors based on ANN were used in this work in a way to provide both, the state variables of the process and the kinetic growth rate whose estimate are essential for advanced control and practical operational purposes.

Both of the networks used in this work are Multi-Layer Perceptron (MLP) Networks with hidden nodes (eight and two, respectively) in a single layer using Levenberg-Marquardt learning algorithm and the nonlinear sigmoid transfer function as activation function. Training data was obtained from computer simulation based on procedure described by Fonseca [7] using the deterministic model validated with industrial data. A training data set with over than 11000 input/output patterns was generated and used to train the ANNs. Partial training data are showed in Figure 2. A different test data set, but inside the same range, with 3000 input/output patterns was used to evaluate the performance of the ANNs in terms of the sum of the mean squared output errors (MSE). The obtained MSE after training processes were 1.5x10^-5 for the State Network and 2.35x10^-9 for the Kinetic Network.

In the State Network case (Fig. 3), soft-sensor was used as a source of predictive data for the controller, so that even it being a self-tuning type, predictive characteristics are incorporated in the decision of the controller. This ANN was trained with input changes in F_a and S₀ ranging from 40-140 g/l and 170-190 g/l, respectively, and the outputs of the ANN were the S, P, and X concentrations in fourth tank.

Figures 4 to 6 showed the capability of the soft-sensor to predict the state variables needful for the control algorithm under several input changes. The results show the excellent agreement between real values, provided by the deterministic model, and the predict ones, estimated by the soft-sensor [3].

It is already very established and quite direct the deduction of an approximate model of a bioreactor through mass balance equations in the variables of state of the system. The critical factor in the determination of the dynamic behavior of this process type is its kinetics [8]. Thus, in the hybrid model approach, the ANN is responsible for the prediction of the specific rates of microbial growth. In the Kinetic Network case, soft-sensor was coupled to the deterministic model in order to obtain the hybrid model of the process. This ANN was trained accordingly to the procedure above-mentioned. The architecture of the Kinetic Network is show in Figure 7 and its predictions for the test data set are shown in Figures 8 and 9.

THE CONTROLLER

The STC developed can be described as a control structure and a relationship between the states of the plant and the parameters of the controller. Since the states of the plant are unknown, they are obtained using an ANN for system identification. The parameters of the controller are then set from the estimated states of the process (equivalence principle). The controller is called "self-tuning" due to its ability to adjust its own parameters, and it is constituted by two branches. The inner one, is formed by a conventional controller, but with variable parameters, and the external branch is composed by an estimator and a design stage (representing the design of the controller in real time) which is responsible for the adjustment of the controller’s parameters [9].

Due to the basic characteristic of feedback controller, compensation was proposed in the performance of the controller through the incorporation of the predictions provided by the soft-sensor for the states of the process that are considered important. With this procedure, a robust and more stable controller, whose structure is shown in Figure 10, was obtained. The developed controller is a MIMO type (multi-input multi-output) and different control structures are proposed seeking to obtain high operational performance (high performance and the required yield) while adequate conditions for the microorganisms development are kept [3].

The Control Algorithm

The proposed control system consists on two loops. The first one controls the temperature of each fermenter by manipulating the cooling water flow. Since the temperature control loop is simpler, the control law used was the classical "PI" control, because it exhibits a good performance and it is easy to implement for this purpose. The another loop, the main one, controls TRS concentration in the fourth reactor, S₄, by handling the feed flow rate of syrup, F_a. The control algorithm was especially designed to take into account the relatively low dynamic response of the system, and high time delay measurement analysis of TRS, so that higher operational efficiency is obtained. In this work, it is considered time delay of 15-30 minutes to obtain the concentration value at S₄. The time delay in real cases is around 12 minutes [3].

The STC developed took into account the nonlinearity of the system by using a nonlinear control law in the control algorithm. Assis [10] proposed a methodology that uses the minimization of error covariance between the desired output and the output obtained by the model as an auxiliary variable "f" for controller design purposes defined as:

(9)

where S_i(t+1) is the correct value of S_i, is the desired set point for the substrate concentration, q is a scalar factor (reduction factor), and z^-1 is the back shift operator.

If the control objective is to minimize the variance of the "f(t)", the control law is specified by the choice of the control signal, F_a(t), which satisfy the equation f(t + 1) = 0. So, the control law can be described as:

(10)

where, Dt is the sampling time, and R is the recycle ratio.

The last term in equation (9) is used to reduce the control action by handling F_a. The higher is q, the less is the control action and vice-versa. The back shift term (1-z^-1) provides an integral action, eliminating offsets in servo problems. As can be seen, the flexibility of this control algorithm is great despite its simplicity [3].

RESULTS

In this work, the behavior of a continuous system of alcoholic fermentation was investigated under the action of the adaptive controller in the same way as described by Meleiro and Maciel Filho [3]. Here, however, the plant model adopted was that provided by the hybrid model. The ability of both the proposed approaches for soft-sensors developments were tested. The ANNs were able to predict the desired state variables as well as the kinetic of the process in a very accurate way. No significant differences were noticed between simulations with deterministic (used in [3]) and hybrid models.

Closed Loop Process Simulations

Simulations of the process were carried out varying the main parameters that are usually subject to perturbation. These variables are the inlet feed temperature, feed flow, feed substrate concentration, sampling time, and cooling fluid temperature.

Results are presented for dynamic response of the closed-loop system according to variations in the sampling time, delay in the instrument measurements, capacity of the controller to reject disturbances and to take the system to a new set point. For testing the closed loop behavior of this system, it was applied step changes in the feed concentration S₀, and set-point changes (servo control).

Figure 11 shows the performance of the STC in servo problems where several set points were set during process simulation.

Performance of the STC algorithm under load changes can be seen in Figure 12, and Figure 13 depicts the ethanol production in the fourth tank.

The objectives of the soft-sensor approach was achieved since the process simulations based on hybrid model reproduced the system behavior adequately as well as the control strategy based on "State Network" predictions allowed a high operation performance, even under long time delay measurement of S₄ and disturbances in the S₀.

CONCLUDING REMARKS

To obtain information about the states of the system, since the restrictions and difficulties in the monitoring of biochemical processes are well known, the development of soft-sensors showed an appropriate solution. It could be seen that soft-sensors based on ANN are a reliable computational tool for on-line system identification and that it can be used as a good support to adaptive control strategies. Application of the proposed strategies to the continuous ethanol production system provides on-line values available for the desirable variables. These values allow a good description of the state variables of the system and its kinetics, enabling comprehensive monitoring and implementation of an efficient automatic control of the process.

ACKNOWLEDGMENTS

The authors gratefully acknowledge CNPq by financial support.

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To whom correspondence should be addressed

Publication Dates

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

History

• Received
  10 Nov 1999
• Accepted
  18 May 2000