**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

doi: 10.17586/2226-1494-2016-16-1-68-75

doi: 10.17586/2226-1494-2016-16-1-68-75

# RESEARCH OF FREE MOTION TRAJECTORIES FEATURES OF CONTINUOUS SYSTEM DEFINED AS A CONSECUTIVE CHAIN OF IDENTICAL FIRST-ORDER APERIODIC LINKS

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**Article in**Russian

**For citation:**Vunder N.A., Nuyya O.S., Pescherov R.O., Ushakov A.V. Research of free motion trajectories features of continuous system defined as a consecutive chain of identical first-order aperiodic links.

*Scientific and Technical Journal of Information Technologies, Mechanics and Optics*, 2016, vol. 16, no. 1, pp. 68–75.

**Abstract**

It is stated that the model of desired behavior has found a widespread usage in the theory and practice of control system design, with the state matrix having a binomial Newton placement of eigenvalues. A structural representation of these systems in the case of the transfer functions approach application leads to a system defined as a consecutive chain of identical first-order aperiodic links. Such model of the desired system behavior has the transient response of the system, which is characterized by the absence of overshoot, that is particularly valuable in the unique technological equipment control. Situation varies considerably when the control system with a binomial placement of eigenvalues has a nonzero initial state. Such situation may arise in the case of an unexpected power fail interrupt of the system electrical components followed by its recovery. This problem is especially important for remote online control of continuous plant in the case of the normal functioning disruption of the channel environment and its restoration in the future. The system in a form of consecutive chain of identical first-order aperiodic links mathematically has a three-parametric set as a module of the negative real eigenvalue, its multiplicity equal to the system dimension and aperiodic link gain. It was found that the three-parametric system may have trajectory emissions at any of negative eigenvalue module. The paper results are illustrated by the computer experiment.

**Keywords:**identical first-order aperiodic links, state matrix, modified canonical Jordan form, multiplicity of eigenvalues, free motion, norm, overshoot

**Acknowledgements.**This work was supported by the Government of the Russian Federation, Grant 074-U01 and the Ministry of Education and Science of the Russian Federation (Project 14. Z50.31.0031)

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