Sufficients conditions for analysis of extrema in the step-response of the linear control systems

This note deals whith the problem of extrema which may occur in the step-response of a stable linear system with real zeros and poles. Some simple sufficients conditions and necessary conditions are presented for analyses when zeros located between the dominant and fastest pole does not cause extrema in the step-response. These conditions require knowledge of the pole-zero configuration of the corresponding transfer-function.

Optimal laser control of molecular photoassociation along with vibrational stabilization

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Necessary conditions for optimal impulsive control problems

A Maximum Principle is derived for a class of optimal control problems arising in midcourse guidance, in which certain controls are represented by measures and, the state trajectories are functions of bounded variation. The optimality conditions improves on previous optimality conditions by allowing nonsmooth data, measurable time dependence, and a possibly time varying constraint set for the conventional controls.

On a control design to an AFM microcantilever beam, operating in a tapping-mode, with irregular behavior

In last decades, control of nonlinear dynamic systems became an important and interesting problem studied by many authors, what results the appearance of lots of works about this subject in the scientific literature. In this paper, an Atomic Force Microscope micro cantilever operating in tapping mode was modeled, and its behavior was studied using bifurcation diagrams, phase portraits, time history, Poincare maps and Lyapunov exponents. Chaos was detected in an interval of time; those phenomena undermine the achievement of accurate images by the sample surface. In the mathematical model, periodic and chaotic motion was obtained by changing parameters. To control the chaotic behavior of the system were implemented two control techniques. The SDRE control (State Dependent Riccati Equation) and Time-delayed feedback control. Simulation results show the feasibility of the bothmethods, for chaos control of an AFM system. Copyright © 2011 by ASME.

A new sufficient condition for optimal impulsive control problems

In this article we introduce the concept of MP-pseudoinvexity for general nonlinear impulsive optimal control problems whose dynamics are specified by measure driven control equations. This is a general paradigm in that, both the absolutely continuous and singular components of the dynamics depend on both the state and the control variables. The key result consists in showing the sufficiency for optimality of the MP-pseudoinvexity. It is proved that, if this property holds, then every process satisfying the maximum principle is an optimal one. This result is obtained in the context of a proper solution concept that will be presented and discussed. © 2012 IEEE.

Optimal impulsive control in a powered Swing-By

This paper studies the problem of applying an impulsive control in a spacecraft that is performing a Swing-By maneuver. The objective is to study the changes in velocity, energy and angular momentum for this maneuver as a function of the three usual parameters of the standard Swing-By plus the three parameters (the magnitude of the impulse, the point of its application and the angle between the impulse and the velocity of the spacecraft) that specify the impulse applied. The dynamics used is the restricted three body problem under the regularization of Lemaitre, made to increase the accuracy of the numerical integration near the primaries. The present research develops an algorithm to calculate the variation of energy and angular momentum in a maneuver where the application of the impulsive control occurs before or after the passage of the spacecraft by the periapsis, but within the sphere of influence of the secondary body and in a non-tangential direction. Using this approach, it is possible to find the best position and direction to apply the impulse to maximize the energy change of the total maneuver. The results showed that the application of the impulse at the periapsis and in the direction of motion of the spacecraft is usually not the optimal solution.

Dinâmica não linear, caos, e controle na microscopia de força atômica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Suppression of vibrations in strongly nonhomogeneous 2DOF systems

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

On energy transfer phenomena, in a nonlinear ideal and nonideal essential vibrating systems, coupled to a (MR) magneto-rheological damper

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

Otimizando vibrações sísmicas em estruturas através de controles híbridos

Pós-graduação em Engenharia Mecânica - FEIS

Active control in rotating machinery using magnetic actuators with linear matrix inequalities (LMI) approach

The recent years have seen the appearance of innovative system for acoustic and vibration attenuation, most of them integrating new actuator technologies. In this sense, the study of algorithms for active vibrations control in rotating machinery became an area of enormous interest, mainly due to countless demands of an optimal performance of mechanical systems in aircraft, aerospace and automotive structures. In this way, this paper presents an approach that is numerically verified for active vibration control in a rotor using Active Magnetic Bearings (AMB). The control design in a discrete state-space formulation is carried out through feedback technique and Linear Matrix Inequalities (LMI) approach. LMI is useful for system with uncertainties. The AMB uses electromagnetic forces to support a rotor without mechanical contact. By monitoring the position of the shaft and changing the dynamics of the system accordingly, the AMB keeps the rotor in a desired position. This unique feature has broadened for the applications of AMB and now they can be considered not only as a main support bearing in a machine but also as dampers for vibration control and force actuators. © 2009 Society for Experimental Mechanics Inc.

Parameter-dependent Lyapunov functions for state-derivative feedback control in polytopic linear systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times

This paper deals with a stochastic optimal control problem involving discrete-time jump Markov linear systems. The jumps or changes between the system operation modes evolve according to an underlying Markov chain. In the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (TN), or the occurrence of a crucial failure event (τΔ), after which the system is brought to a halt for maintenance. In addition, an intermediary mixed case for which T represents the minimum between TN and τΔ is also considered. These stopping times coincide with some of the jump times of the Markov state and the information available allows the reconfiguration of the control action at each jump time, in the form of a linear feedback gain. The solution for the linear quadratic problem with complete Markov state observation is presented. The solution is given in terms of recursions of a set of algebraic Riccati equations (ARE) or a coupled set of algebraic Riccati equation (CARE).

Optimal placement of sensors/actuators in truss structures with known disturbances

An important stage in the solution of active vibration control in flexible structures is the optimal placement of sensors and actuators. In many works, the positioning of these devices in systems governed for parameter distributed is, mainly, based, in controllability approach or criteria of performance. The positions that enhance such parameters are considered optimal. These techniques do not take in account the space variation of disturbances. An way to enhance the robustness of the control design would be to locate the actuators considering the space distribution of the worst case of disturbances. This paper is addressed to include in the formulation of problem of optimal location of sensors and piezoelectric actuators the effect of external disturbances. The paper concludes with a numerical simulation in a truss structure considering that the disturbance is applied in a known point a priori. As objective function the C norm system is used. The LQR (Linear Quadratic Regulator) controller was used to quantify performance of different sensors/actuators configurations.

Design of SPR systems with dynamic compensators and output variable structure control

This paper presents necessary and sufficient conditions for the following problem: given a linear time invariant plant G(s) = N(s)D(s)-1 = C(sI - A]-1B, with m inputs, p outputs, p > m, rank(C) = p, rank(B) = rank(CB) = m, £nd a tandem dynamic controller Gc(s) = D c(s)-1Nc(s) = Cc(sI - A c)-1Bc + Dc, with p inputs and m outputs and a constant output feedback matrix Ko ε ℝm×p such that the feedback system is Strictly Positive Real (SPR). It is shown that this problem has solution if and only if all transmission zeros of the plant have negative real parts. When there exists solution, the proposed method firstly obtains Gc(s) in order to all transmission zeros of Gc(s)G(s) present negative real parts and then Ko is found as the solution of some Linear Matrix Inequalities (LMIs). Then, taking into account this result, a new LMI based design for output Variable Structure Control (VSC) of uncertain dynamic plants is presented. The method can consider the following design specifications: matched disturbances or nonlinearities of the plant, output constraints, decay rate and matched and nonmatched plant uncertainties. © 2006 IEEE.