TOWARDS THE STUDY OF THE DYNAMICS OF A SYSTEM WITH COMBINED FREQUENCY-PHASE CONTROL

Besklubnaya Antonina Vyacheslavovna, Bondar’ Elena Aleksandrovna

It is known that practical needs in developing a method for rapid restructuring of self-oscillating systems based on the use of information on the phase-frequency properties of their oscillations dictate the need to develop techniques for qualitative and numerical modeling of the dynamics of the corresponding control systems. At the same time, the control system should not only be simple to implement technically, but also close to the optimal control strategy. In this paper, using the example of studying the dynamics of a system with frequency-phase control, a method for constructing a mathematical model based on the application of the point mapping method is considered. The point mapping method makes it possible not only to use a piecewise constant form of the control signal, but also allows one to analyze the mechanism of interaction between phase and frequency control. As a result, the state space of the system consists of three main subspaces and two subspaces of transient motions, in each of which the behavior of phase trajectories is determined by equations with a constant structure. Due to the fundamental nonlinearity of processes in the system, the development of a procedure for their modeling is relevant. And especially important is the modeling of the process of transition from the phase control mode to the frequency control mode

Keywords:mathematical modeling, system dynamics, synchronization system, combined pulse-width modulation of the control signal