2. Application of artificial neural network

investigating the steady state column temperature profile, the sensing element should be located at the tray from the end, at a point where the gradient is large. At this point, a fixed change in product composition causes a larger temperature change. Controlling the temperature gives tight control on product composition despite wide variations in other factors such as internal reflux ratio [1]. The variables that need to be controlled are the top and bottom temperatures and the variables that need to be estimated is top and bottom compositions. Application of composition control to both ends of a debutanizer column has been considered with generally little success. The difficulty results because two individual control loops interact. The top loop controls the heavy key in the overhead stream and the bottom loop controls the light key in the bottom stream. Some disturbances cause the light key concentration in the bottom stream to increase. The lower loop acts to reduce the concentration by adding heat. This action lowers the light key concentration sends more heavy key up the column. If both loops are tuned tightly, the column becomes unstable, and the system can be stable by detuning one loop. Processes with only one output being controlled by a single manipulated variable are classified as single-input singleoutput (SISO) system. Many processes do not conform to such a simple control configuration. In the process industries, any unit operation cannot do so with only a single loop. In fact each unit operation requires control over at least two variables, product rate and product quality. Systems with more than one control loop are known as multi-input multi-output (MIMO) or multivariable control system. There will therefore be a composition control loop and temperature control loop. Minimization of energy usage is achievable if the compositions of both the top and bottom product streams are controlled to their design values, which are called dual composition control [1]. A common scheme to overcome this problem is to use reflux flow to control top product composition while the heat input is used to control bottom product composition. Loop interaction may also arise as a consequence of process design, typically the use of recycle streams for heat recovery purposes. Changes in the feed temperature will in turn influence bottom product composition. It is clear that interaction exists between the composition and pre heat control loops. The simple approach in dealing with loop interactions is by the design of multivariable control strategies. This is to eliminate interactions between control loops [1]. The outline in the book for this chapter is the multivariable controller used consists of neural network equation based for the forward model and inverse model. The multivariable control system is to control the top and bottom temperature and estimating the top and bottom composition. The use of the neural network-based controller compared to conventional PID controllers is because all the process variables surrounding the debutanizer column are non-linear in nature and PID could

The use of neural network models and controllers from available literature involve the use of black box models. This method is non-versatile and non-robust in nature and difficult to handle due to the relationship between the inputs and outputs of the system, which are important for industry. In this book, the main contribution and novelty, the proposed is to use an equation based inverse neural network models in a multi-input multi-output (MIMO) system to control the top and bottom temperature of the column simultaneously. The control structure is by using the direct inverse control (DIC) and internal model control (IMC) approach. Neural network equation-based models have also been used for the column to estimate the compositions as estimator. The other contribution of this book is that it utilizes a

not handle non-linearities.

142 Advanced Applications for Artificial Neural Networks

Artificial neural network (ANN) is a reliable and popular tool when dealing with problems involving prediction of variables in engineering at the present age. Details of the ANN application can be found in literature [2–7]. The main advantage of ANN is in its ability to estimate an arbitrary function mechanism that learns from data that is input to the network. However, it is not an easy step to apply neural network for control purposes. Good understanding of the underlying theory is essential and important. The first important criteria are the model selection which depends on the data representation and its application. A significant number of experiments are required for selecting and tuning an algorithm for training. The other criteria that are involve for training is robustness analysis. For the model, cost function and learning algorithm are important to be selected appropriately, so that the ANN final result can be robust. Neural network has been extensively used for a wide of chemical engineering applications which involve identification, control and prediction. Work has been done of various applications using neural network for control simulation and online implementation for chemical processes can be seen in literature [2].

As for today feed forward neural network (FANN) architecture is the widely used neural network architecture. It has a global approximation model for a multi-input multi-output function for fitting a low-order polynomial through a set of data. Various collection of different learning and network algorithms are available [8, 9] but the network is important to be selected as the basic building block. The formula describing the networks in mathematical form takes the following equation

$$y = F\_i \left[ \sum\_{j=1}^{m\_k} W\_{i,j} f\_j \left( \sum\_{l=1}^{n\_\psi} w\_{j,l} \rho\_l + w\_{j,0} \right) + W\_{i,0} \right] \tag{1}$$

where ϕ is the external input, n<sup>ϕ</sup> is the number of input in an input layer, nk is the number of hidden neurons in a hidden layer, W and w are the weights. The activation functions for hidden layer and output layer are f and F, respectively.

In order to model the system dynamically using recurrent neural network (ELMAN) or neural network with ARX, in this book neural network with non-linear autoregressive network with exogenous inputs (NARX) structure which are used to model the dynamic system based on time-series data gives optimum result. The equations describing the NARX structure can be expressed as follows

$$Y = f(Y\_1, Y\_2, \dots, Y\_n, \ U\_1, \mathcal{U}\_2, \dots, \mathcal{U}\_m) \tag{2}$$

where Y= [y1(k + 1) y2(k + 1)]<sup>T</sup> ; Y<sup>1</sup> = [y1(k), y1(k � 1), …, y1(k � ny1)] , … ,Yn = [yn(k), yn(k � 1), …, yn(k � nyn)]; U<sup>1</sup> = [u1(k), u1(k � 1), …, u1(k � nu1)] , … , Um = [um(k), um(k � 1), …, um(k � num)] and m is number of input variables n is number of output variables and ny and nu are the history length for output variables and input variables, respectively. The model was trained, validated and test for different number of neurons together with the ny and nu values. The time lags in the input and manipulated variables, that is, ny and nu are chosen based on trial and error and the values are give to be ny = 3 and nu = 2, respectively, on the combination that gives the lowest RMSE values with the least lag time. It is observed that the lowest RMSE for the top and bottom temperature during training, validation and test occurs at same configuration. This is also based on experience from various literatures on dynamic modeling using NN-based models for nonlinear chemical processes [10, 11].

However, the applications used previously have neural network utilized as a black box model, which has its own disadvantages. This limitation using black box model is due to robustness. In this book, the proper choice of the activation function and the neural network model can be represented by equation in form of algebraic. The equation used to approximate the output from the neural network model can estimate for a two layer network as follows

$$y = f^2 \left(LW^{2,1} f^1 \left( lW^{1,1} p + b^1 \right) + b^2 \right) \tag{3}$$

where IW1,1 = weight at layer 1; b<sup>1</sup> = bias value at layer 1; LW2,1 = weight at layer 2 (hidden layer); b<sup>2</sup> = bias value at layer 2; p = inputs to the neural network; y = outputs from the neural network; f = activation function at layer i.

By multiplying the matrix input layer and the biases value with the matrix hidden layer, the f <sup>1</sup> and f <sup>2</sup> are simplified. By choosing the activation function to be linear, the equation can be simplified in the form of

$$\mathbf{y} = \begin{bmatrix} y\_1 \\ y\_2 \end{bmatrix} = \begin{bmatrix} L\mathcal{W}^{2,1} \begin{bmatrix} I\mathcal{W}^{1,1}p + b^1 \end{bmatrix} + b^2 \end{bmatrix} \tag{4}$$

where the matrix definition LW2,1, IW1,1, b<sup>1</sup> and b<sup>2</sup> are given as

IW1,1 = weight at layer 1 (input layer); b<sup>1</sup> = bias value at layer 1; LW2,1 = weight at layer 2 (hidden layer); b<sup>2</sup> = layer 2 bias value.

These representations can also be used in this book to estimate the top and bottom compositions. While the multivariable controllers are used to control the top and bottom temperatures simultaneously that will be shown in the next sections.

#### 3. Control strategies neural network

There are two types of control strategies which are direct inverse control (DIC) and internal model control (IMC) methods are to be implemented for neural networks, which is the inverse model-based control schemes. These methods are described briefly in Figures 1 and 2.

Figure 1. Control loop of neural network-based direct inverse model control (DIC).

m is number of input variables n is number of output variables and ny and nu are the history length for output variables and input variables, respectively. The model was trained, validated and test for different number of neurons together with the ny and nu values. The time lags in the input and manipulated variables, that is, ny and nu are chosen based on trial and error and the values are give to be ny = 3 and nu = 2, respectively, on the combination that gives the lowest RMSE values with the least lag time. It is observed that the lowest RMSE for the top and bottom temperature during training, validation and test occurs at same configuration. This is also based on experience from various literatures on dynamic modeling using NN-based models for non-

However, the applications used previously have neural network utilized as a black box model, which has its own disadvantages. This limitation using black box model is due to robustness. In this book, the proper choice of the activation function and the neural network model can be represented by equation in form of algebraic. The equation used to approximate the output

where IW1,1 = weight at layer 1; b<sup>1</sup> = bias value at layer 1; LW2,1 = weight at layer 2 (hidden layer); b<sup>2</sup> = bias value at layer 2; p = inputs to the neural network; y = outputs from the neural

By multiplying the matrix input layer and the biases value with the matrix hidden layer, the f <sup>1</sup> and f <sup>2</sup> are simplified. By choosing the activation function to be linear, the equation can be

<sup>¼</sup> LW<sup>2</sup>,<sup>1</sup> IW<sup>1</sup>, <sup>1</sup>

IW1,1 = weight at layer 1 (input layer); b<sup>1</sup> = bias value at layer 1; LW2,1 = weight at layer 2

These representations can also be used in this book to estimate the top and bottom compositions. While the multivariable controllers are used to control the top and bottom temperatures

There are two types of control strategies which are direct inverse control (DIC) and internal model control (IMC) methods are to be implemented for neural networks, which is the inverse

model-based control schemes. These methods are described briefly in Figures 1 and 2.

are given as

<sup>p</sup> <sup>þ</sup> <sup>b</sup><sup>1</sup> <sup>þ</sup> <sup>b</sup><sup>2</sup> (3)

<sup>p</sup> <sup>þ</sup> <sup>b</sup><sup>1</sup> <sup>þ</sup> <sup>b</sup><sup>2</sup> (4)

from the neural network model can estimate for a two layer network as follows

<sup>2</sup> LW<sup>2</sup>,<sup>1</sup> f <sup>1</sup> IW<sup>1</sup>, <sup>1</sup>

y ¼ f

<sup>y</sup> <sup>¼</sup> <sup>y</sup><sup>1</sup> y2 

where the matrix definition LW2,1, IW1,1, b<sup>1</sup> and b<sup>2</sup>

simultaneously that will be shown in the next sections.

3. Control strategies neural network

(hidden layer); b<sup>2</sup> = layer 2 bias value.

linear chemical processes [10, 11].

144 Advanced Applications for Artificial Neural Networks

network; f = activation function at layer i.

simplified in the form of

Figure 2. Control loop of neural network-based internal model controller (IMC).
