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Л.К. Кузьмина
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Инженерный журнал: наука и инновации
# 9·2016
On the problem of motion separation
in gyrostabilization system dynamics
© L.K. Kuzmina
Kazan Aviation Institute (KNRTU – KAI), Kazan, 420015, Russia
The article describes developing concepts and methods of classical stability theory with a
generalization of the principle of reduction for the general qualitative analysis applied to
problems of modeling the dynamics of stabilization, guidance and control systems. On
the basis of developed universal approach the original formulation is proposed
combining the ideology of Lyapunov’s stability theory and asymptotic perturbation
theory methods, which allows reducing solving the problems of simulation and analysis
of the multiscale system dynamics to a regular circuit with decomposition of the system.
Systematic procedures for constructing simplified equivalent systems are presented as
comparison systems. At the same time the shortened system (non-linear on the basis of
combination of all input variables) and its solution are assumed as the generating system
and generating solution. Unlike traditional approaches the generating system is
singularly perturbed, generating solution is not degenerate. With regard to the problems
of the dynamics of mechanical and mathematical models for the stabilization, guidance
and control systems, taking into account their specific structural features, the algorithm
is designed using simplified models as the computational ones. Proprietary methodology
based on the development of N.G. Chetaev’s and V.V. Rumyantsev’s ideas allows, using
the developed scheme in the framework of the posed dynamic problem, multirate
components in system motion to be separated, parameters and variables in the original
system to be distinguished as essential and nonessential, "irrelevant" degrees of freedom
to be identified in the framework of the problem being solved, with a subsequent
transition to the correct shortened model (idealized in the appropriate sense), elucidating
the effect of the discarded "inaccuracy" on the dynamic properties. The problems of
constructing an optimal mechanical- mathematical model, minimal model (according to
N.N. Moiseyev) are solved. The results brought to the engineering level are obtained.
There are examples for the gyrostabilization system computational models with the
identification of various subclasses of stabilized objects (small satellites, large space
stations ), with the possibility of separating motions in the dynamics of the stabilization
and control systems in the dynamics of multi-axis systems, for small and large objects
being stabilized (satellites and space stations) [1–25].Using the fundamental theoretical
results in gyrostabilization system engineering problems will provide new solutions for
applications in the stabilization, orientation and control problems with the possibility of
separation of stabilization and control channels in a nonlinear formulation.
Keywords:
gyrostabilization systems, multiscale systems, decomposition, Liapunov's
methods.
REFERENCES
[1]
Lyapunov A.M.
Sobranie sochineniy v 5 tomakh. Tom 2: Obshchaya zadacha ob
ustoychivosti dvizheniya
[Five-book collected edition. Vol. 2: The general
problem of motion stability]. Moscow, USSR Academy of Sciences Publ., 1956,
pp. 7–264.
[2]
Chetaev N.G.
Prikladnaya matematika i mekhanika — Applied Mathematics and
Mechanics,
1957, vol. 21, no. 3, pp. 419–421.