2,060 research outputs found
A globally exponentially stable position observer for interior permanent magnet synchronous motors
The design of a position observer for the interior permanent magnet
synchronous motor is a challenging problem that, in spite of many research
efforts, remained open for a long time. In this paper we present the first
globally exponentially convergent solution to it, assuming that the saliency is
not too large. As expected in all observer tasks, a persistency of excitation
condition is imposed. Conditions on the operation of the motor, under which it
is verified, are given. In particular, it is shown that at rotor
standstill---when the system is not observable---it is possible to inject a
probing signal to enforce the persistent excitation condition. {The high
performance of the proposed observer, in standstill and high speed regions, is
verified by extensive series of test-runs on an experimental setup
Inversely Unstable Solutions of Two-Dimensional Systems on Genus-p Surfaces and the Topology of Knotted Attractors
In this paper, we will show that a periodic nonlinear, time-varying
dissipative system that is defined on a genus-p surface contains one or more
invariant sets which act as attractors. Moreover, we shall generalize a result
in [Martins, 2004] and give conditions under which these invariant sets are not
homeomorphic to a circle individually, which implies the existence of chaotic
behaviour. This is achieved by studying the appearance of inversely unstable
solutions within each invariant set.Comment: 19 pages with 20 figures, AMS La-TeX, to be published in
International Journal of Bifurcation and Chao
Immersion and invariance orbital stabilization of underactuated mechanical systems with collocated pre-feedback
In this note we study the generation of attractive oscillations of a class of
mechanical systems with underactuation one. The proposed design consists of two
terms, i.e., a partial linearizing state feedback, and an immersion and
invariance orbital stabilization controller. The first step is adopted to
simplify analysis and design, however, bringing an additional difficulty that
the model loses its Euler-Lagrange structure after the collocated pre-feedback.
To address this, we propose a constructive solution to the orbital
stabilization problem via a smooth controller in an analytic form, and the
model class identified in the paper is characterized via some easily apriori
verifiable assumptions on the inertia matrix and the potential energy function
On the equivalence of contraction and Koopman approaches for nonlinear stability and control
In this paper we prove new connections between two frameworks for analysis
and control of nonlinear systems: the Koopman operator framework and
contraction analysis. Each method, in different ways, provides exact and global
analyses of nonlinear systems by way of linear systems theory. The main results
of this paper show equivalence between contraction and Koopman approaches for a
wide class of stability analysis and control design problems. In particular:
stability or stablizability in the Koopman framework implies the existence of a
contraction metric (resp. control contraction metric) for the nonlinear system.
Further in certain cases the converse holds: contraction implies the existence
of a set of observables with which stability can be verified via the Koopman
framework. We provide results for the cases of autonomous and time-varying
systems, as well as orbital stability of limit cycles. Furthermore, the
converse claims are based on a novel relation between the Koopman method and
construction of a Kazantzis-Kravaris-Luenberger observer. We also provide a
byproduct of the main results, that is, a new method to learn contraction
metrics from trajectory data via linear system identification
On IMU preintegration: A nonlinear observer viewpoint and its application
The inertial measurement unit (IMU) preintegration approach nowadays is
widely used in various robotic applications. In this article, we revisit the
preintegration theory and propose a novel interpretation to understand it from
a nonlinear observer perspective, specifically the parameter estimation-based
observer (PEBO). We demonstrate that the preintegration approach can be viewed
as recursive implementation of PEBO in moving horizons, and that the two
approaches are equivalent in the case of perfect measurements. We then discuss
how these findings can be used to tackle practical challenges in estimation
problems. As byproducts, our results lead to a novel hybrid sampled-data
observer design and an approach to address statistical optimality for PEBO in
presence of noise
A novel model for layer jamming-based continuum robots
Continuum robots with variable stiffness have gained wide popularity in the
last decade. Layer jamming (LJ) has emerged as a simple and efficient technique
to achieve tunable stiffness for continuum robots. Despite its merits, the
development of a control-oriented dynamical model tailored for this specific
class of robots remains an open problem in the literature. This paper aims to
present the first solution, to the best of our knowledge, to close the gap. We
propose an energy-based model that is integrated with the LuGre frictional
model for LJ-based continuum robots. Then, we take a comprehensive theoretical
analysis for this model, focusing on two fundamental characteristics of
LJ-based continuum robots: shape locking and adjustable stiffness. To validate
the modeling approach and theoretical results, a series of experiments using
our \textit{OctRobot-I} continuum robotic platform was conducted. The results
show that the proposed model is capable of interpreting and predicting the
dynamical behaviors in LJ-based continuum robots
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