Application of the Harmonic Linearization Method to the Study a Control Systems with a Self-Oscillatory Regime
Dmitry S. Kulyabov, Anna V. Korolkova, Tatyana R. Velieva · Вестник Российского университета дружбы народов. Серия: Математика, информатика, физика · 2017
In data transmission networks implemented as systems with control, the phenomenon of global synchronization can occur. Outwardly, this phenomenon manifests itself as a self-oscillating mode in the system. This mode negatively affects the characteristics of the entire system, such as throughput and transmission delays. Relevant is the problem of finding the areas of occurrence of self-oscillation. The authors investigated this problem for the system as a whole. Also, the problem of isolating the elements of the system responsible for the appearance of an autooscillatory regime is urgent. The complexity of this problem is caused by the essentially nonlinear character of the system and its elements. Often, the linearization method is used for the decomposition of the system. But with the linearization, the self-oscillatory regime disappears. There is a need to find a method of decomposition, non-destructive self-oscillating mode of the system. As such a method, the authors suggest using the method of harmonic linearization. This method is used in the control theory. However, we must admit that this mathematical apparatus is little known to researchers specializing in the study of networks. The authors tried to describe in as much detail the process of research using the method of harmonic linearization. The method is used to study the influence of the form of RED-type function on the occurrence of self-oscillation mode. Thus, this material is more methodical than exploratory one.