A lot of neural network articles deal with nonlinear dynamic controllers. Three main control methods are described: Model Predictive Control, Model Reference Control and NARMA Control. These methods are based on minimizing the Mean Square Error of some cost function. Eventually, the closed loop response may possess sustained oscillation and steady state deviations. Similar criterions for minimizations are widely used to control Linear Time Invariant dynamic systems, such as ISE, IAE etc. For better stability performance the factors of gain and phase margins must be applied as well. To achieve this kind of control, the method of poles and zeroes cancelation, pole placement and other methods are used. This paper deals with nonlinear controller design based on neural networks, for Thermal Treatment Furnaces, represented by a two layer neural network. The network is comprised of two nonlinear neurons in the hidden layer and one linear summing neuron in the output layer. Each nonlinear neuron represents a second order LTI system, multiplied by a nonlinear function. According to this architecture, the neural controller should be organized similarly. The purpose of this paper is to summarize the differences between neural network controllers using the MSE criterions only to those using gain and phase margin criterions as well.
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