150 research outputs found
Fast periodic oscillations in singularly perturbed relay control systems and sliding modes
As a mathematical model of chattering in the small neighbourhood of switching surface in the sliding mode systems we examine the singularly perturbed relay control systems (SPRCS). The sufficient conditions for existence of fast periodic solutions in such systems are found. Their stability is investigated. It is proved that the slow motions in such SPRCS are approximately described with equations obtained from the equations for the slow variables of SPRCS by averaging along fast periodic motions. It is shown that in the case when the original SPRCS contains the relay control linearly the averaged equations and equations which describe the motions of the reduced system in the sliding mode are coincide. The algorithm is proposed which allows to solve the problem of eigenvalues assignment for averaged equations using the additional dynamics of fast actuator
Analysis of relay-based feedback compensation of Coulomb friction
Standard problem of one-degree-of-freedom mechanical systems with Coulomb
friction is revised for a relay-based feedback stabilization. It is recalled
that such a system with Coulomb friction is asymptotically stabilizable via a
relay-based output feedback, as formerly shown in [1]. Assuming an upper
bounded Coulomb friction disturbance, a time-optimal gain of the relay-based
feedback control is found by minimizing the derivative of the Lyapunov function
proposed in [2] for the twisting algorithm. Furthermore, changing from the
discontinuous Coulomb friction to a more physical discontinuity-free one, which
implies a transient presliding phase at motion reversals, we analyze the
residual steady-state oscillations. This is in the sense of stable limit
cycles, in addition to chattering caused by the actuator dynamics. The
numerical examples and an experimental case study accompany the provided
analysis.Comment: 6 pages, 5 figure
Robust exact differentiators with predefined convergence time
The problem of exactly differentiating a signal with bounded second
derivative is considered. A class of differentiators is proposed, which
converge to the derivative of such a signal within a fixed, i.e., a finite and
uniformly bounded convergence time. A tuning procedure is derived that allows
to assign an arbitrary, predefined upper bound for this convergence time. It is
furthermore shown that this bound can be made arbitrarily tight by appropriate
tuning. The usefulness of the procedure is demonstrated by applying it to the
well-known uniform robust exact differentiator, which the considered class of
differentiators includes as a special case
Use of second-order sliding mode observer for low-accuracy sensing in hydraulic machines
submittedVersionNivĂĄ
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