Synthesis methods of controllers based on the use of frequency characteristics or root hodographs are considered classic or traditional. Frequency methods are available in practical applications, and most control systems are designed based on various modifications to these methods. A distinctive feature of these methods is the so-called robustness, which means that the characteristics of a closed system are insensitive to the minor errors of the model of the real system. This feature is significant because of the complexity of constructing an accurate model of the real system, as well as the fact that many systems are inherent in all kinds of nonlinearities, which complicate their analysis and synthesis. In recent years, many attempts have been made to develop new methods of synthesis, commonly referred to as modern control theory. One synthesis method is like the root hodograph method, which allows positioning the poles of the closed-loop transfer function at predetermined points.

In the article on the basis of information about the desired transient characteristic of the reference, which is obtained on the basis of a dynamic neural network, using the Ackerman formula, a procedure for calculating the coefficient matrix, whose introduction in the structure of the object model provides the specified dynamics of the process. On the base of the reference mathematical model is created the architecture of the corresponding dynamic neural network. During training, there is the target function as a numerical sequence that corresponds to the desired transient characteristic of the system, and the input signal is given in the form of a numerical sequence that reproduces jump function. Using the values of the weight coefficients obtained in the course of learning the neural network, the coefficients of the mathematical model of the reference and the roots of its characteristic equation are calculated, with the following calculation using the Ackerman formula of the coefficients of the matrix, whose values are entered into the structure of the model ensuring the specified dynamics of the process in it.

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