113 research outputs found
Parameter Estimation-Based Extended Observer for Linear Systems with Polynomial Overparametrization
We consider a class of uncertain linear time-invariant overparametrized
systems affected by bounded disturbances, which are described by a known
exosystem with unknown initial conditions. For such systems an exponentially
stable extended adaptive observer is proposed, which, unlike known solutions,
simultaneously: (i) allows one to reconstruct original (physical) states of the
system represented in arbitrarily chosen state-space form rather than virtual
states of the observer canonical form; (ii) ensures convergence of the state
observation error to zero under extremely weak requirement of the regressor
finite excitation; (iii) does not include Luenberger correction gain and forms
states estimate using algebraic rather than differential equation; (iv)
additionally reconstructs the unmeasured external disturbance. Illustrative
simulations support obtained theoretical results.Comment: 6 pages, 2 figure
An Adaptive Observer-based Robust Estimator of Multi-sinusoidal Signals
This paper presents an adaptive observer-based
robust estimation methodology of the amplitudes, frequencies
and phases of biased multi-sinusoidal signals in presence of
bounded perturbations on the measurement. The parameters of
the sinusoidal components are estimated on-line and the update
laws are individually controlled by an excitation-based switching
logic enabling the update of a parameter only when the measured
signal is sufficiently informative. This way doing, the algorithm
is able to tackle the problem of over-parametrization (i.e., when
the internal model accounts for a number of sinusoids that is
larger than the true spectral content) or temporarily fading
sinusoidal components. The stability analysis proves the existence
of a tuning parameter set for which the estimator\u2019s dynamics are
input-to-state stable with respect to bounded measurement disturbances.
The performance of the proposed estimation approach
is evaluated and compared with other existing tools by extensive
simulation trials and real-time experiments
Monotonous Parameter Estimation of One Class of Nonlinearly Parameterized Regressions without Overparameterization
The estimation law of unknown parameters vector is proposed for
one class of nonlinearly parametrized regression equations . We restrict our attention
to parametrizations that are widely obtained in practical scenarios when
polynomials in are used to form . For
them we introduce a new 'linearizability' assumption that a mapping from
overparametrized vector of parameters to
original one exists in terms of standard algebraic functions. Under
such assumption and weak requirement of the regressor finite excitation, on the
basis of dynamic regressor extension and mixing technique we propose a
procedure to reduce the nonlinear regression equation to the linear
parameterization without application of singularity causing operations and the
need to identify the overparametrized parameters vector. As a result, an
estimation law with exponential convergence rate is derived, which, unlike
known solutions, (i) does not require a strict P-monotonicity condition to be
met and a priori information about to be known, (ii) ensures
elementwise monotonicity for the parameter error vector. The effectiveness of
our approach is illustrated with both academic example and 2-DOF robot
manipulator control problem.Comment: 7 pages, 2 figure
Nonlinear adaptive estimation with application to sinusoidal identification
Parameter estimation of a sinusoidal signal in real-time is encountered in applications
in numerous areas of engineering. Parameters of interest are usually amplitude, frequency
and phase wherein frequency tracking is the fundamental task in sinusoidal estimation. This thesis deals with the problem of identifying a signal that comprises n (n ≥ 1) harmonics from a measurement possibly affected by structured and unstructured disturbances. The structured perturbations are modeled as a time-polynomial so as to represent, for example, bias and drift phenomena typically present in applications, whereas the unstructured disturbances are characterized as bounded perturbation. Several approaches upon different theoretical tools are presented in this thesis, and classified into two main categories: asymptotic and non-asymptotic methodologies, depending on the qualitative characteristics of the convergence behavior over time.
The first part of the thesis is devoted to the asymptotic estimators, which typically consist
in a pre-filtering module for generating a number of auxiliary signals, independent of
the structured perturbations. These auxiliary signals can be used either directly or indirectly
to estimate—in an adaptive way—the frequency, the amplitude and the phase of the
sinusoidal signals. More specifically, the direct approach is based on a simple gradient
method, which ensures Input-to-State Stability of the estimation error with respect to the
bounded-unstructured disturbances. The indirect method exploits a specific adaptive observer scheme equipped with a switching criterion allowing to properly address in a stable way the poor excitation scenarios. It is shown that the adaptive observer method can be applied for estimating multi-frequencies through an augmented but unified framework, which is a crucial advantage with respect to direct approaches. The estimators’ stability properties are also analyzed by Input-to-State-Stability (ISS) arguments.
In the second part we present a non-asymptotic estimation methodology characterized by
a distinctive feature that permits finite-time convergence of the estimates. Resorting to the
Volterra integral operators with suitably designed kernels, the measured signal is processed, yielding a set of auxiliary signals, in which the influence of the unknown initial conditions is annihilated. A sliding mode-based adaptation law, fed by the aforementioned auxiliary signals, is proposed for deadbeat estimation of the frequency and amplitude, which are dealt with in a step-by-step manner. The worst case behavior of the proposed algorithm in the presence of bounded perturbation is studied by ISS tools.
The practical characteristics of all estimation techniques are evaluated and compared
with other existing techniques by extensive simulations and experimental trials.Open Acces
Control of flexible joint robotic manipulator using tuning functions design
The goal of this thesis is to design the controller for a single arm manipulator having a flexible joint for the tracking problem in two different cases. A controller is designed for a deterministic case wherein the plant parameters are assumed to be known while another is designed for an adaptive case where all the plant parameters are assumed to be unknown. In general the tracking problem is; given a smooth reference trajectory, the end effector has to track the reference while maintaining the stability. It is assumed that only the output of the manipulator, which is the link angle, is available for measurement. Also without loss of generality, the fast dynamics, that is the dynamics of the driver side of the system are neglected for the sake of simplicity; In the first case, the design procedure adopted is called observer backstepping. Since the states of the system are unavailable for measurement, an observer is designed that estimates the system states. These estimates are fed to the controller which in turn produces the control input to the system; The second case employs a design procedure called tuning functions design. In this case, since the plant parameters are unknown, the observer designed in case one cannot be used for determining the state estimates. For this purpose, parameter update laws and filters are designed for estimation of plant parameters. The filters employed are k-filters. The k-filters and the parameter update laws are given as input to the controller, which generates the control input to the system; For both cases, the mathematical models are simulated using Matlab/Simulink, and the results are verified
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