Search results for "Nonlinear system"
showing 10 items of 1446 documents
Steady-state dynamic response of various hysteretic systems endowed with fractional derivative elements
2019
In this paper, the steady-state dynamic response of hysteretic oscillators comprising fractional derivative elements and subjected to harmonic excitation is examined. Notably, this problem may arise in several circumstances, as for instance, when structures which inherently exhibit hysteretic behavior are supplemented with dampers or isolators often modeled by employing fractional terms. The amplitude of the steady-state response is determined analytically by using an equivalent linearization approach. The procedure yields an equivalent linear system with stiffness and damping coefficients which are related to the amplitude of the response, but also, to the order of the fractional derivativ…
Improving the speed estimation by load torque estimation in induction motor drives: an MRAS and NUIO approach
2021
This paper proposes the application of the NUIO inside a FOC induction motor drive for the simultaneous estimation of the load torque and the rotor speed. The idea is to estimate at first the speed with the current model in parallel with a reference model developed on the basis of the voltage model of the induction machine. Then, the estimated speed is given as input to a nonlinear unknown input observer (NUIO) to estimate the load torque. This estimation is then used to correct the previous estimation of the speed. Simulation and experimental results confirm the goodness of the method for an extended range of speed and different load torque, and they confirm the reduction of error in trans…
Numerical analysis of thermally induced optical nonlinearity in GaSe layered crystal
1996
A numerical approach to studying thermally induced optical nonlinearity in semiconductors is presented. A transient finite difference algorithm is applied to solve the thermal diffusion equation coupled with the nonlinear absorbance-transmittance of Au/GaSe/Au samples with an applied electric field. The presented analysis can deal with any arbitrary axisymmetric dependence of the input power over the sample and external electric field, and provides information about the steady state and transitory effects in the transmittance.
Probabilistic response of linear structures equipped with nonlinear damper devices (PIS method)
2008
Passive control introducing energy absorbing devices into the structure has received considerable attention in recent years. Unfortunately the constitutive law of viscous fluid dampers is highly nonlinear, and even supposing that the structure behaves linearly, the whole system has inherent nonlinear properties. Usually the analysis is performed by a stochastic linearization technique (SLT) determining a linear system equivalent to the nonlinear one, in a statistical sense. In this paper the effect of the non-Gaussianity of the response due to the inherent nonlinearity of the damper device will be studied in detail via the Path Integral Solution (PIS) method. A systematic study is conducted…
Statistics of residence time for Lévy flights in unstable parabolic potentials
2020
We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.
On stability and dissipativity of stochastic nonlinear systems
2012
Input-to-state stability of nonlinear control system is described in several different manners, and has been a central concept since the equivalences among them were verified. In this paper, a framework of stability and dissipativity for stochastic control systems is constructed on the maximal existence interval of behaviors (states and external inputs), by the aid of stochastic Barbalat lemma and stochastic dissipativity. The main work consists of three aspects. First, input-to-state stability and robust stability are extended to the stochastic case, and several criteria are established. Second, two forms of dissipativity and their criteria are presented. Third, the key relations among the…
Stochastic integro-differential and differential equations of non-linear systems excited by parametric Poisson pulses
1997
Abstract The connection between stochastic integro-differential equation and stochastic differential equation of non-linear systems driven by parametric Poisson delta correlated processes is presented. It is shown that the two different formulations are fully equivalent in the case of external excitation. In the case of parametric type excitation the two formulation are equivalent if the non-linear argument in the integral representation is related by means of a series to the corresponding non-linear parametric term in the stochastic differential equation. Differential rules for the two representations to find moment equations of every order of the response are also compared.
Einstein-Smoluchowsky equation handled by complex fractional moments
2014
In this paper the response of a non linear half oscillator driven by α-stable white noise in terms of probability density function (PDF) is investigated. The evolution of the PDF of such a system is ruled by the so called Einstein-Smoluchowsky equation involving, in the diffusive term, the Riesz fractional derivative. The solution is obtained by the use of complex fractional moments of the PDF, calculated with the aid of Mellin transform operator. It is shown that solution can be found for various values of stability index α and for any nonlinear function of the drift term in the stochastic differential equation.
Stochastic seismic analysis of multidegree of freedom systems
1984
Abstract A unconditionally stable step-by-step procedure is proposed to evaluate the mean square response of a linear system with several degrees of freedom, subjected to earthquake ground motion. A non-stationary modulated random process, obtained as the product of a deterministic time envelope function and a stationary noise, is used to simulate earthquake acceleration. The accuracy of the procedure and its extension to nonlinear systems are discussed. Numerical examples are given for a hysteretic system, a duffing oscillator and a linear system with several degrees of freedom.
Noise-enhanced propagation in a dissipative chain of triggers
2002
International audience; We study the influence of spatiotemporal noise on the propagation of square waves in an electrical dissipative chain of triggers. By numerical simulation, we show that noise plays an active role in improving signal transmission. Using the Signal to Noise Ratio at each cell, we estimate the propagation length. It appears that there is an optimum amount of noise that maximizes this length. This specific case of stochastic resonance shows that noise enhances propagation.