Search results for "linearization"
showing 10 items of 115 documents
On Leonov’s method for computing the linearization of the transverse dynamics and analysis of Zhukovsky stability
2019
The paper focuses on a comprehensive discussion of G. A. Leonov’s results aimed at analyzing the Zhukovsky stability of a solution to a nonlinear autonomous system by linearization. The main contribution is deriving the linear system that approximates dynamics of the original nonlinear systems transverse to the vector-flow on a nominal behavior. As illustrated, such a linear comparison system becomes instrumental in the analysis and re-design of classical feedback controllers developed previously for the stabilization of motions of nonlinear mechanical systems.
A New Look at the Stochastic Linearization Technique for Hyperbolic Tangent Oscillator
1998
Abstract Stochastic linearization technique is reconsidered for oscillator with restoring force in form of hyperbolic tangent. We show that a subtle error was made in the previously known procedure for derivation of the linearized system parameters. Two new error-free procedures, namely, those based on minimization of mean square difference between (a) restoring force or (b) potential energy of the original non-linear system and their linear counterparts, are suggested. The results of numerical analysis are shown.
Amplification of Interstory Drift and Velocity for the Passive Control of Structural Vibrations
2008
Mitigation of structural damage due to earthquake ground motion may be performed by inserting dampers in the structure. In order to enhance the damping effect various toggle brace configurations have been recently proposed. In this paper these equipments are analyzed in detail and compared with a new one here proposed. The analysis is performed by taking into account the inherent nonlinearities of the damper by means of stochastic analysis and validated by using time histories of recorder accelerograms and by the stochastic analysis using spectrum consistent power spectral density.
Gluon mass scale through nonlinearities and vertex interplay
2019
We present a novel analysis of the gluon gap equation, where its full nonlinear structure is duly taken into account. In particular, while in previous treatments the linearization of this homogeneous integral equation introduced an indeterminacy in the scale of the corresponding mass, the current approach determines it uniquely, once the value of the gauge coupling at a given renormalization point is used as input. A crucial ingredient for this construction is the "kinetic term" of the gluon propagator, whose form is not obtained from the complicated equation governing its evolution, but is rather approximated by suitable initial {\it Ans\"atze}, which are subsequently improved by means of …
Comparing two methods of analysis of single-ring infiltrometer data for a sandy–loam soil
2009
Abstract The single-ring pressure infiltrometer (PI) with the steady-state Two-Ponding-Depth (TPD) application method were developed to simultaneously determine the saturated soil hydraulic conductivity, K fs , and the α ⁎-parameter in the field. Methods of analysis of transient PI data are also available but they have received little testing so far. The transient WU method and the TPD method were compared for a sandy-loam soil. A linearization technique of the infiltration curve yielded more reliable K fs and α ⁎ results (i.e., falling within expected ranges) than a non-linear optimization technique. The WU method gave both positive and reasonable K fs and α ⁎ values for all infiltration t…
Input-output feedback linearizing control of linear induction motor taking into consideration the end-effects. Part I: Theoretical analysis
2015
Abstract This first part of a paper, divided into two parts, deals with the theoretical formulation of the input–output feedback linearization (FL) control technique as to be applied to linear induction motors (LIMs). Linear induction motors, differently from rotating induction motors (RIMs), present other strong non-linearities caused by the so-called dynamic end effects, leading to a space-vector model with time-varying inductance and resistance terms and an additional braking force term. This paper, starting from a dynamic model of the LIM taking into consideration its dynamic end effects, previously developed by the same authors, defines a feedback linearization (FL) technique suited fo…
Input-Output Feedback Linearizing Control of Linear Induction Motor Taking into Consideration the End-Effects. Part II: Simulation and Experimental R…
2015
This is the second part of a paper, divided in two parts, dealing with the application of the input–output feedback linearization (FL) control technique to linear induction motors (LIMs). The first part has treated the theoretical formulation of the input–output feedback linearization control technique as to be applied to linear induction motors. This second part describes the set of tests, both in numerical simulations and experiments, performed to assess the validity of the control technique. In particular, it addresses the issues of the sensitivity of the FL control versus the LIM electrical parameters’ variations and the improvements achievable by considering the LIM dynamic end effects…
On the convergence of fixed point iterations for the moving geometry in a fluid-structure interaction problem
2019
In this paper a fluid-structure interaction problem for the incompressible Newtonian fluid is studied. We prove the convergence of an iterative process with respect to the computational domain geometry. In our previous works on numerical approximation of similar problems we refer this approach as the global iterative method. This iterative approach can be understood as a linearization of the so-called geometric nonlinearity of the underlying model. The proof of the convergence is based on the Banach fixed point argument, where the contractivity of the corresponding mapping is shown due to the continuous dependence of the weak solution on the given domain deformation. This estimate is obtain…
Statistic moments of the total energy of potential systems and application to equivalent non-linearization
2000
In this paper some properties of the total energy moments of potential systems, subjected to external white noise processes, are shown. Potential systems with a polynomial form of energy-dependent damping have been considered. It is shown that the analytical relations between the statistical moments of the energy associated with such systems can be obtained with the aid of the standard Ito calculus. Furthermore, it is shown that, for the stationary case, these analytical relations are very useful for the application of the equivalent non-linearization technique.
Iterative closure method for non-linear systems driven by polynomials of Gaussian filtered processes
2008
This paper concerns the statistical characterization of the non-Gaussian response of non-linear systems excited by polynomial forms of filtered Gaussian processes. The non-Gaussianity requires the computation of moments of any order. The problem is solved profiting from both the stochastic equivalent linearization (EL), and the moment equation approach of Ito's stochastic differential calculus through a procedure divided into two parts. The first step requires the linearization of the system, while retaining the non-linear excitation; the response statistical moments are calculated exactly, and constitute a first estimate of the moments of the actual non-linear system. In the second step, t…