Analysis of Periodic Motions in Digital Self-Oscillating Control Systems

This paper is devoted to the investigation of relay systems with sample-data control. Self-oscillations in such systems are the operating mode. Time-sampling has a significant effect on the parameters of periodic oscillations. We propose an exact method for analyzing periodic regimes in digital self-oscillating control systems with a two-position relay element. The proposed approach extends the phase hodograph method to the class of systems operating in discrete time. A method for obtaining a phase locus for the case of self-oscillating systems with time-sampling and a linear control object is presented. The method for obtaining a phase locus for the case of self-oscillating systems with time-sampling and a linear control object is presented. The method for obtaining a phase locus for the case of self-oscillating systems with time sampling and a linear part is presented. The paper proposes a analytical procedure for constructing a family of phase locusers of a discrete relay system, both in the frequency domain and in the time domain. This approach makes it possible to isolate all possible symmetric periodic motions in the systems under consideration. The frequency approach is based on the allocation of a continuous linear object and a discrete control part. The output signal from the digital part in the batch mode can be decomposed into a discrete Fourier series. This allows obtaining analytical conditions for the output signal of the continuous part. The sampling of the control system causes a delay in the switching of the relay in a batch mode in comparison with the continuous case. The method allows to determine all symmetrical periodic oscillations in relay systems with time sampling. Similarly, we propose the approach of obtaining a family of phase travel curves for such systems in the time domain. The approach is based on the consideration of the control object in the state space. The approach is based on consideration in the state space of the control object. The phase locus is determined by solving the matrix equation. The stability and the attraction domain of limit cycles are discussed. The effect of sampling on periodic processes with an unstable control object is given. It is shown that in this case micro-chaotic oscillations arise in the system. An example is provided to demonstrate the application of the method.

Self-oscillations, relay control, discrete systems, limit cycle, phase locus method, relay-pulse systems

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