I. Introduction
The predominant type of industrial controller in use today is the PID controller, with approximately 90% of controllers in commercial operation employing the PID algorithm. This widespread adoption can be attributed to the controller's straightforward construction, suitability for industrial applications, operational transparency, versatility in addressing practical issues, and cost-effectiveness [1], [2]. However, existing methods for computing PID controller parameters are tailored to linear systems, as the controller itself is considered a linear dynamic component in such cases. In instances where the control object is fundamentally nonlinear, achieving satisfactory control quality becomes challenging. When tasked with regulating complex nonlinear systems, such as helicopters turboshaft engines (TE), PID controllers may fall short in delivering the requisite control precision for the parameters of helicopters TE, system stability, and robustness under varying operational conditions and malfunctions. Thus, the modification of the PID controller by using neural network technologies to control the helicopters TE is an urgent scientific and practical task.