3.3.1. Forward models

The procedure of training a neural network to represent the forward dynamics of a column is by predicting the outputs using the required inputs. This method is called forward modeling. The straightforward and good approach is to augment the network inputs data in real forms, from the model and system being identified [13, 14]. Other fundamental variables under state can also be fed into the network and considered as inputs. In this method, the network is fed with the present input, past inputs as well as the past outputs to predict the desired output. The neural network model is placed in parallel with the system. The error between the system output and network output are the prediction error which is used as the training signal for the network. The forward models that have been mentioned previously are used to determine the inverse model. The forward model which is inversed to get the inverse model is then changed to the equation based. The equation-based method has been used to replace the black box model neural network for IMC and DIC method. The inverse models as controllers are used in the IMC and DIC methods. The composition forward models are used as a neural network estimator to predict the top and bottom compositions.

The forward model for temperature is as follows

3.1. Method 1: direct inverse control (DIC)

146 Advanced Applications for Artificial Neural Networks

3.2. Method 2: internal model control (IMC)

3.3. Neural networks models

3.3.1. Forward models

This control strategy which is placed in series with neural network inverse models acts as a controllers. In this scheme, the outputs will predict the system input, while the desired set point acts as the output which is then fed to the network with the past plant inputs. In this case, the appropriate control parameter for the desired target will be predicted based on its input. Neural networks acting as the controller has to learn to supply at its input. As shown in Figure 1, the inverse model is then utilized in the control strategy by cascading it with the controlled system or plant. This method depends on the accuracy of the inverse model. The controlled variables used in this method are the top and bottom temperatures. The manipu-

Neural network-based IMC method highlighted in this book are presented in both inverse and forward model control scheme. The dynamic forward model of the process represents it is placed in parallel within the system. This is important to cater for mismatches of the model during implementation [12]. On the other hand, the inverse model could also be used as a controller. In this scheme, the error between the plant output and the neural network forward model is then subtracted from the set point before being fed into the inverse model, as shown in Figure 2. With this detection feature, the internal model-based controller can be used to move forward the controlled parameter to the desired set point even when disturbances and noise are present. The optimum performance for controller performance is the IMC method. The error produced by the process model could be minimized and compensated by the error produced by the neural network forward process model [12]. The controlled and manipulated

Before applying the inverse model neural network control strategies for the debutanizer column, it is crucial to discuss the development and configuration of the forward and inverse models. Using neural network architecture and equation-based neural network are important

The procedure of training a neural network to represent the forward dynamics of a column is by predicting the outputs using the required inputs. This method is called forward modeling. The straightforward and good approach is to augment the network inputs data in real forms, from the model and system being identified [13, 14]. Other fundamental variables under state can also be fed into the network and considered as inputs. In this method, the network is fed with the present input, past inputs as well as the past outputs to predict the desired output. The neural network model is placed in parallel with the system. The error between the system output and network output are the prediction error which is used as the training signal for the network. The forward models that have been mentioned previously are used to determine the inverse model. The forward model which is inversed to get the inverse model is then changed to the equation based. The equation-based method has been used to replace the black box

lated variables are the reflux and reboiler flow rate for the DIC method.

variables used in the IMC method are similar to the DIC method.

fundamentals to these model-based control strategies as necessary.

In this case, p is the input to the neural network temperature given by the vector

$$\begin{bmatrix} m\upsilon1(k) \ m\upsilon1(k-1) \ m\upsilon2(k) \ m\upsilon2(k-1) \ m\upsilon3(k) & & & \\ m\upsilon3(k-1) \ f(k) \ f(k-1) \ T\_{ttop}(k) \ T\_{ttop}(k-1) \ T\_{brt}(k) \ T\_{brt}(k-1) \end{bmatrix}^T \tag{5}$$

After pruning the neural network structure (simplifying the weights and biases values), p is given as matrix vector are defined in Eq. (6)

$$\begin{aligned} y = \begin{bmatrix} T\_1 \\ T\_2 \end{bmatrix} = \begin{bmatrix} -0.16 & -0.14 \ 0.04 & -0.002 & -0.094 & -0.95 \ 1.03 & -0.61 & -0.71 \ 0.81 \ 0.16 & -0.049 \\ 0.42 \ 0.07 \ 0.04 \ 0.20 & -0.30 & -0.19 \ 0.12 & -0.28 \ 0.35 & -0.29 & -0.48 \ 0.168 \end{bmatrix} p \\ &+ \begin{bmatrix} -0.28 \\ -0.22 \end{bmatrix} \end{aligned} \tag{6}$$

T<sup>1</sup> and T<sup>2</sup> is the output neural network top and bottom temperature prediction.

#### 3.3.2. Neural network estimator

The forward model for neural network for composition is composition n-butane used for control system IMC method is as follows

In this case, p is the input to the neural network composition given by the vector

$$\begin{bmatrix} m\upsilon2(k) \ m\upsilon2(k-1) \ m\upsilon3(k) \ m\upsilon3(k-1) \ f(k) \ f(k-1) \ p\_{hp}(k) \ p\_{hp}(k-1) \ p\_{bot}(k) \ p\_{bot}(k-1) \end{bmatrix}^T \tag{7}$$

After pruning the neural network structure (simplifying the weights and biases values), Eq. (7) can further be simplified to give the composition Eq. (8)

$$
\begin{bmatrix} y1 \\ y2 \end{bmatrix} = \begin{bmatrix} -0.26 \ 0.15 \ 0.37 \ 0.23 \ 0.38 \ 0.40 \ -0.50 \ 0.97 \ 0.12 \ -0.31 \\\\ -0.09 \ 0.006 \ 0.31 \ -0.10 \ 0.02 \ 0.02 \ -0.42 \ -0.12 \ 0.36 \ -0.085 \end{bmatrix} p + \begin{bmatrix} -0.28 \\\\ -0.21 \end{bmatrix} \tag{8}
$$

y<sup>1</sup> and y<sup>2</sup> is the output neural network bottom and top composition predictions.

#### 3.3.3. Models for inverse

Inverse models are basically the structure by representing the inverse of the network dynamics after the completion of training. The methods for inverse models are achieved by switching the required outputs and inputs. The important manipulated variable that is used for switching the inputs of the neural net is the manipulated variable reboiler and reflux. The outputs predicted are the future predictions of top and bottom temperatures are switched with the manipulated variables. The sequence of the inputs of the network needs to be maintained. The training procedure outlined in this book is called inversed modeling. y(k + 1) is the required set point. The network representation of the inverse is finally given below

$$u(k) = f^{-1}\left[y\_p(k+1), y\_p(k), y\_p(k-1), u(k), u(k-1)\right] \tag{9}$$

where f �<sup>1</sup> represents the inverse map of the forward model.

In this case the manipulated variable reboiler and reflux flow rate are the output variable which are used in inverse model. The one-step ahead prediction of the control output, mv2 (k) and mv3 (k) is performed inconformity with that of the forward model. The one-step ahead control action application in the control strategies involving the neural network-based strategies.

The training and validation data set are predicted for inverse model for the networks are similar to that used for forward modeling. Nevertheless, inverse model will have different input and output configuration.

The inverse model for temperature is as follows

In this case, p is the input to the neural network inverse temperature given by the vector

$$\begin{aligned} \begin{bmatrix} m\mathbf{v}1(k) & m\mathbf{v}1(k-1) & m\mathbf{v}2(k-1) & m\mathbf{v}3(k-1) & f(k) \ f(k-1) & T\_{hp}(k+1) & T\_{hp}(k)T\_{hp}(k-1) \end{bmatrix} \\ \begin{bmatrix} T\_{bot}(k+1) & T\_{bot}(k) & T\_{bot}(k-1) \end{bmatrix}^T \end{aligned} \tag{10}$$

After simplifying the weights and biases values by pruning the neural network structure Eq. (10) can further be simplified in order to give the inverse temperature below in a form of equation

Figure 3. Forward and inverse models to control temperature.

(11)

$$
\begin{aligned}
\begin{bmatrix}
m\mathbf{w}(k) \\
m\mathbf{w}(k)
\end{bmatrix} &= \begin{bmatrix}
0.42 & 0.077 & 0.039 & 0.20 & -0.30 & -0.19 & 0.13 & -0.27 & 0.34 & -0.28 & -0.47 & 0.16 \\
& & & & & & & \\
& & & & & & & -
\end{bmatrix} p \\
& \quad + \begin{bmatrix} -0.79 \\ -0.008 \end{bmatrix}
\end{aligned}
$$

mv2(k) and mv3(k) is the manipulated variable reflux and reboiler flow rate, respectively. The equation is implemented in SIMULINK in MATLAB by having the system with more than one control loop which are multi-input and multi-output (MIMO) or multivariable control. Figure 3 shows the forward and inverse model to control temperature.
