PITTMAN MOTOR CONTROL USING NEURAL NETWORKS

: Neural networks are well-suited for the modeling and control of complex physical systems because of their ability to handle complex input-output mapping without detailed analytical model of the systems . In this paper internal model control associated with proportional gain is used to control the system implemented with two neural networks , model of the system and inverse model.


Introduction:
In the industrial processes there are many systems having nonlinear properties .Moreover, these properties are often unknown and time varying.The commonly used PID controllers are simple to be realized , but they suffer from poor performance if there are uncertainties and nonlinearities.
The neural network controllers have emerged as a tool for difficult control problems of unknown nonlinear systems.

Since multilayer neural networks can approximate arbitrary nonlinear mapping through a learning mechanism , they can compensate the nonlinearity [1].
There are several control strategies for neural networks which some of them are as: feed forward control , direct inverse control , indirect adaptive control based on neural network identification , and internal model control ( IMC ) [2].
IMC requires a forward model as well as a model of the inverse of the system to be controlled , and a low-pass filter, to impact on the behavior of the closed-loop system.
The following features are special to the IMC: • Off-set free response for systems affected by a constant disturbance.Pittman Motor: The system to be controlled is Pittman GM9413H529 DC motor with a simulated inertial load .The simulated moment of inertia is small , and is considerably less than the actual motor moment of inertia .The equivalent circuit diagram of the DC motor system is shown in fig.(1) [4].Neural Networks For Modeling: The use of neural networks for modeling and identification is justified by their capacity to approximate the dynamics of systems including those with high nonlinearities or dead time .In order to estimate the system dynamics , the neural network must be trained until the optimal values of the weights and biases are found .In most applications , feed forward neural networks are used , because the training algorithms are less complicated [5].

Several studies have founded that a three-layered neural networks with one hidden layer can approximate any nonlinear function to any desired accuracy [2]. The structure of three layer networks that used to identify the feed forward model and it's inverse are shown in fig.(2).[2]. It consists of an input layer , an output layer of linear activation function and one hidden layer of seven tanh units.
Where Ii(k) , Wj , Wij , Sj and O(k) are the ith input to the network , the connecting weight between jth hidden neuron and the output of the network , connecting weight between ith input to network and the jth hidden neuron , the output of jth hidden neuron and the output of the network .This network trained using back propagation algorithm as follows : The cost function Where yd(k) and e are the desired output and the error .
Where W(k) is any weight of network , η is the learning rate of this weight .Therefore; This network is trained for both the internal model and its inverse using arbitrary input data .

Control Scheme:
A control system consists of the process to be controlled and of a control device chosen by the designer , which computes the control input so as to convey the desired behavior to the control system .