1,956 research outputs found
Design and frequency analysis of continuous finite-time-convergent differentiator
In this paper, a continuous finite-time-convergent differentiator is
presented based on a strong Lyapunov function. The continuous differentiator
can reduce chattering phenomenon sufficiently than normal sliding mode
differentiator, and the outputs of signal tracking and derivative estimation
are all smooth. Frequency analysis is applied to compare the continuous
differentiator with sliding mode differentiator. The beauties of the continuous
finite-time-convergent differentiator include its simplicity, restraining
noises sufficiently, and avoiding the chattering phenomenon
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
Rapid-convergent nonlinear differentiator
A nonlinear differentiator being fit for rapid convergence is presented,
which is based on singular perturbation technique. The differentiator design
can not only sufficiently reduce the chattering phenomenon of derivative
estimation by introducing a continuous power function, but the dynamical
performances are also improved by adding linear correction terms to the
nonlinear ones. Moreover, strong robustness ability is obtained by integrating
nonlinear items and the linear filter. The merits of the rapid-convergent
differentiator include the excellent dynamical performances, restraining noises
sufficiently, avoiding the chattering phenomenon and being not based on system
model. The theoretical results are confirmed by computer simulations and an
experiment.Comment: 26 pages, 15 figure
Design and analysis of continuous hybrid differentiator
In this paper, a continuous hybrid differentiator is presented based on a
strong Lyapunov function. The differentiator design can not only reduce
sufficiently chattering phenomenon of derivative estimation by introducing a
perturbation parameter, but also the dynamical performances are improved by
adding linear correction terms to the nonlinear ones. Moreover, strong
robustness ability is obtained by integrating sliding mode items and the linear
filter. Frequency analysis is applied to compare the hybrid continuous
differentiator with sliding mode differentiator. The merits of the continuous
hybrid differentiator include the excellent dynamical performances, restraining
noises sufficiently, and avoiding the chattering phenomenon
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