Artificial Neural Networks

In class activities

Activities

Single-layer perceptron neural network

In a chemical processing plant, a critical valve is controlled based on three parameters: temperature, pressure, and reactant concentration, all within normalized ranges. Each parameter is represented as a binary input: 1 if the parameter is within the desired range, indicating favorable conditions for opening the valve, and 0 if it is outside the range, indicating unfavorable conditions. The decision to open the valve depends on these inputs to ensure safe and efficient operation.

• Scenario 1: Low temperature, low pressure, optimal concentration.
• Scenario 2: Optimal temperature, optimal pressure, optimal concentration.
• Scenario 3: Optimal temperature, low pressure, optimal concentration.
• Scenario 4: Low temperature, optimal pressure, optimal concentration.

Expected valve position

Temperature	Pressure	Concentration	Valve Opens
0	0	1	0
1	1	1	1
1	0	1	1
0	1	1	0

Design a simple single-layer perceptron using MATLAB to learn this decision-making process based on the input parameters.

Solution

The code for single layer perceptron is in ann_single_layer_perceptron.mlx.

ANN modeling of Crystallization

To control the average crystal size in a crystallization process, it is essential to account for its dependence on two measurable variables:

1. Mother liquor temperature $T$
2. Mother liquor density $\rho$

Since average crystal size cannot be directly measured and requires offline laboratory analysis, there are inherent delays in controlling the crystallizer.

To predict crystal size using temperature $T$ and density $\rho$, consider the following:

1. Input transfer functions

   1. Feed flow rate (U₁)

   $$\begin{array}{}\text{(1)}& U_1(s)=\frac{1}{s+1}\end{array}$$

   2. Stirrer Speed (U₂)

   $$\begin{array}{}\text{(2)}& U_2(s)=\frac{1}{2s+1}\end{array}$$

2. Process Transfer functions

   1. Temperature (X₁) is influenced by U₁

   $$\begin{array}{}\text{(3)}& X_1(s)=(\frac{2}{3s+1}+\frac{-0.2}{2s^2+1.1s+1})e^{-s}\end{array}$$

   2. Density (X₂) is influenced by U₂

   $$\begin{array}{}\text{(4)}& X_2(s)=\frac{e^{-s}}{4s^2+3s+1}\end{array}$$

3. Dependency of average crystal size d_avg (Y) on temperature and density is given by

$$\begin{array}{}\text{(5)}& d_{avg}=10+(0.8T+1.3\rho +1.1T^2-1.9{\rho }^2+0.6T\rho )\end{array}$$

Develop an Artificial Neural Network (ANN) model to predict the average crystal size in a crystallization process based on measured temperature and density, which are influenced by feed flow rate and stirrer speed.

Solution

• Crystallizer model for training
• Crystallizer model control