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Aerospace Instrument-Making

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SYNTHESIS OF NONLINEAR CONTROL IN AUTOMATIC SYSTEMS WITH OSCILLATIONS HAVING SIGNIFICANT HIGHER HARMONICS
Yu.Yu. Shumilov

The article deals with the modifi cation of nonlinear homogeneous control for solving problems of ensuring the stability of aircraft stabilization systems. A generalization of homogeneous control is developed for the case of signifi cant higher harmonics of nonlinear oscillations. A method is proposed for the exact separation of a finite set of self-excited oscillation harmonics using even-order derivatives for the subsequent direction of each of them to a nonlinear dynamic element, the parallel connection of which is a nonlinear homogeneous control. The possibility of approximate separation of self-oscillation harmonics using standard first-order filters with subsequent correction of the frequency characteristics of the automatic system by nonlinear homogeneous control to ensure the desired region of system stability is substantiated. An estimate of the error of the output signal of a nonlinear homogeneous control is proposed when the higher harmonics of the input signal are discarded, which allows, in the case of a small deviation of the control output without taking into account the higher harmonics of the input signal from the control output, taking into account all the harmonics of the input signal, not to use the harmonic separation procedure and synthesize control based only on parameters of the first harmonic of the input signal. The limiting properties of homogeneous control and the possibility of passing to piecewise continuous control are investigated. The connection is established between nonlinear homogeneous control and control built on «quorum elements».
Keywords: nonlinear system, self-oscillation, nonliner control, splitting of oscillation harmonics, quorum-element.


DOI: 10.25791/aviakosmos.2.2022.1265

Pp. 20-28.

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