Nonlinear control in an electromechanical transducer with chaotic behaviour

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the contact stiffness and nonlinear vibration of an elastic body with a rough surface in contact with a rigid flat surface

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear dynamics and control strategies: On a energy harvester vibrating system with a linear form to non-ideal motor torque

In this paper, we deal with the research of a vibrating model of an energy harvester device, including the nonlinearities in the model of the piezoelectric coupling and the non-ideal excitation. We show, using numerical simulations, in the analysis of the dynamic responses, that the harvested power is influenced by non-linear vibrations of the structure. Chaotic behavior was also observed, causing of the loss of energy throughout the simulation time. Using a perturbation technique, we find an approximate analytical solution for the non-ideal system. Then, we apply both two control techniques, to keep the considered system, into a stable condition. Both the State Dependent Ricatti Equation (SDRE) control as the feedback control by changing the energy of the oscillator, were efficient in controlling of the considered non-ideal system.

Potenciais singulares na equação de Schrodinger unidimensional via transformada de Laplace

The present work has as its goal to treat well known and interesting unidimensional cases from quantum mechanics through an unusual approach within this eld of physics. The operational method of Laplace transform, in spite of its use by Erwin Schrödinger in 1926 when treating the radial equation for the hydrogen atom, turned out to be forgotten for decades. However, the method has gained attention again for its use as a powerful tool from mathematical physics applied to the quantum mechanics, appearing in recent works. The method is specially suitable to the approach of cases where we have potential functions with even parity, because this implies in eigenfunctions with de ned parity, and since the domain of this transform ranges from 0 to ∞, it su ces that we nd the eigenfunction in the positive semi axis and, with the boundary conditions imposed over the eigenfunction at the origin plus the continuity (discontinuity) of the eigenfunction and its derivative, we make the odd, even or both parity extensions so we can get the eigenfunction along all the axis. Factoring the eigenfunction behavior at in nity and origin, we take the due care with the points that might bring us problems in the later steps of the solving process, thus we can manipulate the Schrödinger's Equation regardless of time, so that way we make it convenient to the application of Laplace transform. The Chapter 3 shows the methodology that must be followed in order to search for the solutions to each problem

SDRE control strategy applied to a nonlinear robotic including drive motor

A robotic control design considering all the inherent nonlinearities of the robot-engine configuration is developed. The interactions between the robot and joint motor drive mechanism are considered. The proposed control combines two strategies, one feedforward control in order to maintain the system in the desired coordinate, and feedback control system to take the system into a desired coordinate. The feedback control is obtained using State-Dependent Riccati Equation (SDRE). For link positioning two cases are considered. Case I: For control positioning, it is only used motor voltage; Case II: For control positioning, it is used both motor voltage and torque between the links. Simulation results, including parametric uncertainties in control shows the feasibility of the proposed control for the considered system.

Scalar-bipolar asymptotic modules for solving (2+1)-dimensional nonlinear evolution equations with constraints

An infinite hierarchy of solvable systems of purely differential nonlinear equations is introduced within the framework of asymptotic modules. Eacy system consists of (2+1)-dimensional evolution equations for two complex functions and of quite strong differential constraints. It may be interpreted formally as an integro-differential equation in (1+1) dimensions. © 1988.

Nonlinear state estimation and control for chaos suppression in MEMS resonator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear state estimation and control applied to a manipulator robotic including drive motor

A robotic control design considering all the inherent nonlinearities of the robot engine configuration is developed. The interactions between the robot and joint motor drive mechanism are considered. The proposed control combines two strategies, one feedforward control in order to maintain the system in the desired coordinate, and feedback control system to take the system into a desired coordinate. The feedback control is obtained using State Dependent Riccati Equation (SDRE). For link positioning two cases are considered. Case 1: For control positioning, it is only used motor voltage; Case 2: For control positioning, it is used both motor voltage and torque between the links. Simulation results, including parametric uncertainties in control shows the feasibility of the proposed control for the considered system.

Suppression of vibrations in a nonlinear half-car model using a magneto-rheological damper

The present work investigates the nonlinear response of a half-car model. The disturbances of the road are assumed to be sinusoidal. After constructing the bifurcation diagram, we use the 0-1 test to identify chaotic motions. The main objective of this study is to eliminate chaotic behavior of the chassis and reduce its vibrations. To accomplish this, a semi-active vehicle suspension control system, using magneto-rheological dampers, is proposed. The proposed semi-active control strategy consists of two nonlinear control laws: a feedforward control, and a feedback control. They are obtained by considering the SDRE (State Dependent Riccati Equation) control, where the control parameter is the voltage applied to the coils of the magneto-rheological dampers. Numerical results show that the proposed control method is effective in significantly reducing of the chassis vibration, increasing, therefore, passenger comfort.

Chaos control and sensitivity analysis of a double pendulum arm excited by an RLC circuit based nonlinear shaker

In this paper the dynamical interactions of a double pendulum arm and an electromechanical shaker is investigated. The double pendulum is a three degree of freedom system coupled to an RLC circuit based nonlinear shaker through a magnetic field, and the capacitor voltage is a nonlinear function of the instantaneous electric charge. Numerical simulations show the existence of chaotic behavior for some regions in the parameter space and this behaviour is characterized by power spectral density and Lyapunov exponents. The bifurcation diagram is constructed to explore the qualitative behaviour of the system. This kind of electromechanical system is frequently found in robotic systems, and in order to suppress the chaotic motion, the State-Dependent Riccati Equation (SDRE) control and the Nonlinear Saturation control (NSC) techniques are analyzed. The robustness of these two controllers is tested by a sensitivity analysis to parametric uncertainties.

Existência e concentração de soluções para uma equação de schrödinger estacionária

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo de sistemas não-lineares em mecânica quântica

The main goal of this work is to investigate the effects of a nonlinear cubic term inserted in the Schrödinger equation for one-dimensional potentials studied in Quantum Mechanics textbooks. Being the main tool the numerical analysis in a large number of works, the analysis of this effect by this term in the potential itself, in order to work with an analytical solution, can be considered something new. For the harmonic oscillator potential, the analysis was made from a numerical method, comparing the result with the known results in the literature. In the case of the infinite well potential and the step potential, hoping to work with an analytical solution, by construction we started with the known wavefunction for the linear case noting the effects in the other physical quantities. The coupling of the physical quantities involved in this work has yielded, besides many complications in the calculations, a series of conditions on the existence and validity of the solutions in regard to the system possible configurations

Estudo de sistemas não-lineares em mecânica quântica

The main goal of this work is to investigate the effects of a nonlinear cubic term inserted in the Schrödinger equation for one-dimensional potentials studied in Quantum Mechanics textbooks. Being the main tool the numerical analysis in a large number of works, the analysis of this effect by this term in the potential itself, in order to work with an analytical solution, can be considered something new. For the harmonic oscillator potential, the analysis was made from a numerical method, comparing the result with the known results in the literature. In the case of the infinite well potential and the step potential, hoping to work with an analytical solution, by construction we started with the known wavefunction for the linear case noting the effects in the other physical quantities. The coupling of the physical quantities involved in this work has yielded, besides many complications in the calculations, a series of conditions on the existence and validity of the solutions in regard to the system possible configurations

Additional scaled solutions to Richards' equation for infiltration and drainage

Warrick and Hussen developed in the nineties of the last century a method to scale Richards' equation (RE) for similar soils. In this paper, new scaled solutions are added to the method of Warrick and Hussen considering a wider range of soils regardless of their dissimilarity. Gardner-Kozeny hydraulic functions are adopted instead of Brooks-Corey functions used originally by Warrick and Hussen. These functions allow to reduce the dependence of the scaled RE on the soil properties. To evaluate the proposed method (PM), the scaled RE was solved numerically using a finite difference method with a fully implicit scheme. Three cases were considered: constant-head infiltration, constant-flux infiltration, and drainage of an initially uniform wet soil. The results for five texturally different soils ranging from sand to clay (adopted from the literature) showed that the scaled solutions were invariant to a satisfactory degree. However, slight deviations were observed mainly for the sandy soil. Moreover, the scaled solutions deviated when the soil profile was initially wet in the infiltration case or when deeply wet in the drainage condition. Based on the PM, a Philip-type model was also developed to approximate RE solutions for the constant-head infiltration. The model showed a good agreement with the scaled RE for the same range of soils and conditions, however only for Gardner-Kozeny soils. Such a procedure reduces numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils. (C) 2011 Elsevier B.V. All rights reserved.

Invariant Solutions of Richards' Equation for Water Movement in Dissimilar Soils

Scaling methods allow a single solution to Richards' equation (RE) to suffice for numerous specific cases of water flow in unsaturated soils. During the past half-century, many such methods were developed for similar soils. In this paper, a new method is proposed for scaling RE for a wide range of dissimilar soils. Exponential-power (EP) functions are used to reduce the dependence of the scaled RE on the soil hydraulic properties. To evaluate the proposed method, the scaled RE was solved numerically considering two test cases: infiltration into relatively dry soils having initially uniform water content distributions, and gravity-dominant drainage occurring from initially wet soil profiles. Although the results for four texturally different soils ranging from sand to heavy clay (adopted from the UNSODA database) showed that the scaled solution were invariant for a wide range of flow conditions, slight deviations were observed when the soil profile was initially wet in the infiltration case or deeply wet in the drainage case. The invariance of the scaled RE makes it possible to generalize a single solution of RE to many dissimilar soils and conditions. Such a procedure reduces the numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils.