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)

Lyapounov stability for impulsive dynamical systems

This article addresses the problem of stability of impulsive control systems whose dynamics are given by measure driven differential inclusions. One important feature concerns the adopted solution which allows the consideration of systems whose singular dynamics do not satisfy the so-called Frobenius condition. After extending the conventional notion of control Lyapounov pair for impulsive systems, some stability conditions of the Lyapounov type are given. Some conclusions follow the outline of the proof of the main result.

Discrete-time sliding mode control of input-delay systems applied on a power generation system

This paper presents two discrete sliding mode control (SMC) design. The first one is a discrete-time SMC design that doesn't take into account the time-delay. The second one is a discrete-time SMC design, which takes in consideration the time-delay. The proposed techniques aim at the accomplishment simplicity and robustness for an uncertainty class. Simulations results are shown and the effectiveness of the used techniques is analyzed. © 2006 IEEE.

Comparative study of LMI-based output feedback spr synthesis for plants with different numbers of inputs and outputs

New Linear Matrix Inequalities (LMI) conditions are proposed for the following problem, called Strictly Positive Real (SPR) synthesis: given a linear time-invariant plant, find a constant output feedback matrix Ko and a constant output tandem matrix F for the controlled system to be SPR. It is assumed that the plant has the number of outputs greater than the number of inputs. Some sufficient conditions for the solution of the problem are presented and compared. These results can be directly applied in the LMI-based design of Variable Structure Control (VSC) of uncertain plants. ©2008 IEEE.

Structural real time control using fluid magnetorheologic damper

In the last decades there was a great development in the study of control systems to attenuate the harmful effect of natural events in great structures, as buildings and bridges. Magnetorheological fluid (MR), that is an intelligent material, has been considered in many proposals of project for these controllers. This work presents the controller design using feedback of states through LMI (Linear Matrix Inequalities) approach. The experimental test were carried out in a structure with two degrees of freedom with a connected shock absorber MR. Experimental tests were realized in order to specify the features of this semi-active controller. In this case, there exist states that are not measurable, so the feedback of the states involves the project of an estimator. The coupling of the MR damper causes a variation in dynamics properties, so an identification methods, based on experimental input/output signal was used to compare with the numerical application. The identification method of Prediction Error Methods - (PEM) was used to find the physical characteristics of the system through realization in modal space of states. This proposal allows the project of a semi-active control, where the main characteristic is the possibility of the variation of the damping coefficient.

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.

On the Chaotic Suppression of Both Ideal and Non-ideal Duffing Based Vibrating Systems, Using a Magnetorheological Damper

In this paper the dynamics of the ideal and non-ideal Duffing oscillator with chaotic behavior is considered. In order to suppress the chaotic behavior and to control the system, a control signal is introduced in the system dynamics. The control strategy involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system in a periodic orbit, obtained by the harmonic balance method, and a state feedback control, obtained by the state dependent Riccati equation, to bring the system trajectory into the desired periodic orbit. Additionally, the control strategy includes an active magnetorheological damper to actuate on the system. The control force of the damper is a function of the electric current applied in the coil of the damper, that is based on the force given by the controller and on the velocity of the damper piston displacement. Numerical simulations demonstrate the effectiveness of the control strategy in leading the system from any initial condition to a desired orbit, and considering the mathematical model of the damper (MR), it was possible to control the force of the shock absorber (MR), by controlling the applied electric current in the coils of the damper. © 2012 Foundation for Scientific Research and Technological Innovation.

Nonlinear control system applied to atomic force microscope including parametric errors

The performance of the optimal linear feedback control and of the state-dependent Riccati equation control techniques applied to control and to suppress the chaotic motion in the atomic force microscope are analyzed. In addition, the sensitivity of each control technique regarding to parametric uncertainties are considered. Simulation results show the advantages and disadvantages of each technique. © 2013 Brazilian Society for Automatics - SBA.

Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen's theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov's stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.

Vibration Control Applied in a Semi-Active Suspension using Magneto Rheological Damper and Optimal Linear Control Design

In this paper we study the behavior of a semi-active suspension witch external vibrations. The mathematical model is proposed coupled to a magneto rheological (MR) damper. The goal of this work is stabilize of the external vibration that affect the comfort and durability an vehicle, to control these vibrations we propose the combination of two control strategies, the optimal linear control and the magneto rheological (MR) damper. The optimal linear control is a linear feedback control problem for nonlinear systems, under the optimal control theory viewpoint We also developed the optimal linear control design with the scope in to reducing the external vibrating of the nonlinear systems in a stable point. Here, we discuss the conditions that allow us to the linear optimal control for this kind of non-linear system.

NASH game and mixed H2/H∞ control

In this work a Nonzero-Sum NASH game related to the H2 and H∞ control problems is formulated in the context of convex optimization theory. The variables of the game are limiting bounds for the H2 and H∞ norms, and the final controller is obtained as an equilibrium solution, which minimizes the `sensitivity of each norm' with respect to the other. The state feedback problem is considered and illustrated by numerical examples.

Linear matrix inequality-based robust model predictive control for time-delayed systems

This work addresses the solution to the problem of robust model predictive control (MPC) of systems with model uncertainty. The case of zone control of multi-variable stable systems with multiple time delays is considered. The usual approach of dealing with this kind of problem is through the inclusion of non-linear cost constraint in the control problem. The control action is then obtained at each sampling time as the solution to a non-linear programming (NLP) problem that for high-order systems can be computationally expensive. Here, the robust MPC problem is formulated as a linear matrix inequality problem that can be solved in real time with a fraction of the computer effort. The proposed approach is compared with the conventional robust MPC and tested through the simulation of a reactor system of the process industry.

Stabilization for an ensemble of half-spin systems

Feedback stabilization of an ensemble of non interacting half spins described by the Bloch equations is considered. This system may be seen as an interesting example for infinite dimensional systems with continuous spectra. We propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibrium in the H-1 topology. This local convergence is shown to be a weak asymptotic convergence for the H-1 topology and thus a strong convergence for the C topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the equilibrium. (C) 2011 Elsevier Ltd. All rights reserved.

Improved low-voltage-ride-through capability of fixed-speed wind turbines using decentralised control of STATCOM with energy storage system

The design and implementation of a new control scheme for reactive power compensation, voltage regulation and transient stability enhancement for wind turbines equipped with fixed-speed induction generators (IGs) in large interconnected power systems is presented in this study. The low-voltage-ride-through (LVRT) capability is provided by extending the range of the operation of the controlled system to include typical post-fault conditions. A systematic procedure is proposed to design decentralised multi-variable controllers for large interconnected power systems using the linear quadratic (LQ) output-feedback control design method and the controller design procedure is formulated as an optimisation problem involving rank-constrained linear matrix inequality (LMI). In this study, it is shown that a static synchronous compensator (STATCOM) with energy storage system (ESS), controlled via robust control technique, is an effective device for improving the LVRT capability of fixed-speed wind turbines.