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Value of system parameter. PID controller gave optimal control for 1 st order system without and delays. There are three classes of PID in this work; the class chosen has the generic form: The variable e t represents the tracking error, the difference between the desired value r and the actual output y. This error signal will be used by PID controller.

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PID will take appropriate action according to the law and pass the signal u to the plant to adjust the appropriate manipulated variable. Reference model is a desired forward dynamic response. In model reference control; ANN controller is designed to make the process output behaves similar to the reference model. In this work, we consider optimal model for our design. Model is said to be optimal with respect to cost criteria J, if the cost is lowest when using that model. The IAE and ISE cost criteria weight the initial values of the error more than the later value while the time weighted criteria such as the ITAE criteria weight the later values of the error more.

Minimizing the integral constraint tries to keep the error small in general sense. In this work, we used ITAE as our cost criterion. The n th order model considered has the form: For some n th order monic denominator poly nominal D is given by. Bandwidth, which measure the effectiveness of dynamic polynomial of system of the can be adjusted through this parameter.

Here the numerator is constant hence relative degree of the model is equal to the order of the denominator. Optimization computation using a Monte-Carlo method of optimization called a random neighborhood search RSN Franklin, et al; involved searching for the best set of coefficient to satisfy the given cost criteria that will provide zero steady state error.

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The system was simulated and the cost associated with that polynomial was computed. A polynomial with coefficient near the previous randomly chosen was obtained and the system re simulated and the cost recalculated. This process was continued until the set criteria were met. Network Structure and Representation. In this work, the type of network structure employed is multi layer, layer perception MLP ,which is one type of feed forward network.

A MLP consists of an input layer, several hidden layers, and an output layer. Node i , also called a neuron, in a MLP network is shown in Fig.

It includes a summer and a nonlinear activation function g. Single node in a MLP network. Input to the preceptor are individually weighted and summed. The preceptor computes the output as a function g of the sum. The activation energy, g in needed to introduce non-linear into the network. Thin makes multilayer network a powerful representation of nonlinear system. The output from the single node is computed by: A multilayer perceptron network with one hidden layer; the same activation function g is used in both layers.

Training is the process of adjusting the weights. The training is intended to steadily adjust the connection weight in order to minimize the mean square error between target value output and predicted value output. Training usually begins with random values for the weights of NN. There are two moves before the weights are updated.

In the first move forward move the outputs of all neurons are calculated by multiplying the input vector by the weights and the error is calculated for each of the output layer neuron. In the backward move, the error is passed through the network layer and the weight are updated according to the gradient steepest rule, so that the actual output of the MLP moves closer to the desire output.

The difference between the target output and the computed output is known as error, this error is computed as: The errors are back propagated through the layers and the weight adjustments are made. The formula for adjusting the weight is: The training is interned to gradually adjust the connection weight in order to minimize the mean square error. The main advantages of neural network are its ability to supply fast answers to a problem and its capability to generalize answers thus providing acceptable result for unknown samples Cholamreza Zahedi et al, An illustration of model reference control is presented in figure 4.

In the figure the network has two inputs, one of the inputs is difference between plant output and model reference output and second input is difference between model output and reference signal. ANN controller will have two input, error signal from reference model output, and plant output, the second error signal comes from difference between reference signal and plant output.

The procedures involved in training the network are generation and validation of training data sets; preprocessing of data set and training and validation of network. To have good representation of the model, two data sets were generated from the system to train the network, one data set for validation and another one testing.

Uniform random input signals, which span the upper and lower limit of operating range, were used to excite the system.

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This was done to enable network learn the nonlinear nature of the system. Before incorporating the network into the control scheme the networks was trained offline using the Gauss-Newton based Levenberg Marquardt algorithm K. Leleberg and D. The essence is to let the network learn the functional nonlinearities to a certain degree of accuracy before implementing into the controller, and thus can give faster online adaptation as need. In this study data sets for the training were obtained by carrying out simulation on the open loop of the system.

The network considered was MLP with a single hidden layer.

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  • The activation function used in study is nonlinear sigmoid function in hidden layer and the linear function in the output layer. Neural network with large enough number of hidden neurons, which has continuous and differentiable transfer function can approximate any continuous function over a closed interval Cybenko, The numbers of nodes are initially fixed at small numbers, the number was increased in order to have a proper trained network. Satisfactory networks model were obtained when the sum of squared errors of the validation data set was satisfactorily small. Simulation Result and Discussion.

    The open loop simulation of CSTR for reversible reaction is shown in figure 5. Here, the product concentration is plotted against time. The reaction considered was 1: This is not so because the reaction considered is a reversible reaction and there is backward reaction after a long period of time. Figure 6 shows the temperature profile of the system; it is observed that the system is unstable because the temperature is infinitely increasing for the system. Temperature profile for open loop simulation of CSTR for reversible reaction. In order to bring the reaction to complete conversion and to prevent backward reaction, the flow rate of reactant was used as manipulated variable in the control design.

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    Neural Network Control of CSTR for Reversible Reaction Using Reverence Model Approach

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