State Dependent Riccati Equation (SDRE) control method applied in cancellation of a parametric resonance in a magnetically levitated body

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design. Copyright © 2011 by ASME.

Control design applied to a non-ideal structural system with behavior chaotic

In this paper we study the behavior of a structure vulnerable to excessive vibrations caused by an non-ideal power source. To perform this study, the mathematical model is proposed, derive the equations of motion for a simple plane frame excited by an unbalanced rotating machine with limited power (non-ideal motor). The non-linear and non-ideal dynamics in system is demonstrated with a chaotic behavior. We use a State-Dependent Riccati Equation Control technique for regulate the chaotic behavior, in order to obtain a periodic orbit small and to decrease its amplitude. The simulation results show the identification by State-Dependent Riccati Equation Control is very effective. © 2013 Academic Publications, Ltd.

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.

GLOBAL DYNAMICS of THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

LOSS of EXPONENTIAL STABILITY FOR A THERMOELASTIC SYSTEM WITH MEMORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

PRODUCTION of THERMAL PHOTONS IN VISCOUS FLUID DYNAMICS WITH TEMPERATURE-DEPENDENT SHEAR VISCOSITY

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

Charged three-body system with arbitrary masses near conformal invariance

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

On the control of a non-ideal engineering system: A friction-driven oscillating system with limited power supply

In this work a switching feedback controller for stick-slip compensation of a 2-DOF mass-spring-belt system which interacts with an energy source of limited power supply (non-ideal case) is developed. The system presents an oscillatory behavior due to the stick-slip friction. As the system equilibrium for a conventional feedback controller is not the origin, a switching control law combining a state feedback term and a discontinuous term is proposed to regulate the position of the mass. The problem of tracking a desired periodic trajectory is also considered. The feedback system is robust with respect to the friction force that is assumed to be within known upper and lower bounds.

Classes of exact Klein-Gordon equations with spatially dependent masses: Regularizing the one-dimensional inversely linear potential

In this work we consider the effect of a spatially dependent mass over the solution of the Klein-Gordon equation in 1 + 1 dimensions, particularly the case of inversely linear scalar potential, which usually presents problems of divergence of the ground-state wave function at the origin, and possible nonexistence of the even-parity wave functions. Here we study this problem, showing that for a certain dependence of the mass with respect to the coordinate, this problem disappears. (c) 2006 Elsevier B.V. All rights reserved.

Exact solvability of potentials with spatially dependent effective masses

We discuss the relationship between exact solvability of the Schroedinger equation, due to a spatially dependent mass, and the ordering ambiguity. Some examples show that, even in this case, one can find exact solutions. Furthermore, it is demonstrated that operators with linear dependence on the momentum are nonambiguous. (C) 2000 Elsevier Science B.V.

An overview on a nonideal system with three and a half degrees of freedom

The present paper studies a system comprised of two blocks connected by springs and dampers, and a DC motor with limited power supply fixed on a block, characterizing a non-ideal problem. This DC motor exciting the system causes interactions between the motor and the structure supporting it. Because of that, the non-ideal mathematical formulation of the problem has one and a half extra degree of freedom than the ideal one. A suitable choice of physical parameters leads to internal resonance conditions, that is, its natural frequencies are multiple of each other, by a known integer quantity. The purpose here is to study the dynamic behavior of the system using an analytical method based on perturbation techniques. The literature shows that the averaging method is the more flexible method concerning non-ideal problems. Summarizing, an steady state solution in amplitude and phase coordinates was obtained with averaging method showing the dependence of the structure amplitudes with the rotation frequency of the motor. Moreover, this solution shows that on of the amplitude coordinates has influence in the determination of the stationary rotation frequency. The analytical solution obtained shows the presence of the rotation frequency in expressions representing the oscillations of the structure, and the presence of amplitude coordinates in expressions describing the dynamic motion of the DC motor. These characteristics show the influence not only of the motor on structure but also of the response of the structure on dynamical behavior of the motor. Copyright © 2005 by ASME.

LMI-based digital redesign of linear time-invariant systems with state-derivative feedback

A simple method for designing a digital state-derivative feedback gain and a feedforward gain such that the control law is equivalent to a known and adequate state feedback and feedforward control law of a digital redesigned system is presented. It is assumed that the plant is a linear controllable, time-invariant, Single-Input (SI) or Multiple-Input (MI) system. This procedure allows the use of well-known continuous-time state feedback design methods to directly design discrete-time state-derivative feedback control systems. The state-derivative feedback can be useful, for instance, in the vibration control of mechanical systems, where the main sensors are accelerometers. One example considering the digital redesign with state-derivative feedback of a helicopter illustrates the proposed method. © 2009 IEEE.

A comparison of performance indexes in DC-DC converters under different stabilizing state-dependent switching laws

This paper deals with the problem of establishing stabilizing state-dependent switching laws in DC-DC converters operating at continuous conduction mode (CCM) and comparing their performance indexes. Firstly, the nature of the problem is defined, that is, the study of switched affine systems, which may not share a common equilibrium point. The concept of stability is, therefore, broadened. Then, the central theorem is proposed, from which a family of switching laws can be derived, namely the minimum law and the hold state law. Some of these are proved to stabilize the basic DC-DC converters and then, their performances are compared to another law, from a previous work, by simulation, where a great reduction in overshoot is obtained. © 2011 IEEE.

Sliding Mode Control for Active Suspension System with Data Acquisition Delay

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Spatial dynamics of a population with stage-dependent diffusion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)