Control of nonlinear absorption and amplification of light in Er3+-doped fluoroindate glass

Nonlinear absorption and amplification of a probe laser beam can be controlled by adjustment of the intensity-modulation frequency and the wavelength of a pump laser beam. A demonstration of this effect in Er3+-doped fluoroindate glass is presented. The results show maximum amplification of the probe beam (∼12%) when a pump laser emitting 16 mW of power is modulated at ∼30 Hz. In the limit of low modulation frequencies, or cw pumping, induced absorption of the probe beam is the dominant nonlinear process. © 1999 Optical Society of America.

A nonlinear and non-ideal wind generator supporting structure

We present a simple mathematical model of a wind turbine supporting tower. Here, the wind excitation is considered to be a non-ideal power source. In such a consideration, there is interaction between the energy supply and the motion of the supporting structure. If power is not enough, the rotation of the generator may get stuck at a resonance frequency of the structure. This is a manifestation of the so-called Sommerfeld Effect. In this model, at first, only two degrees of freedom are considered, the horizontal motion of the upper tip of the tower, in the transverse direction to the wind, and the generator rotation. Next, we add another degree of freedom, the motion of a free rolling mass inside a chamber. Its impact with the walls of the chamber provides control of both the amplitude of the tower vibration and the width of the band of frequencies in which the Sommerfeld effect occur. Some numerical simulations are performed using the equations of motion of the models obtained via a Lagrangian approach.

Coordination, cooperation and control within decentralized fiscal systems

Includes bibliography

Observer-based control design for switched affine systems and applications to DC-DC converters

This paper deals with the problem of establishing a state estimator for switched affine systems. For that matter, a modification on the Luenberger observer is proposed, the switched Luenberger observer, whose idea is to design one output gain matrix for each mode of the original system. The efficiency of the proposed method relies on a simplification on estimation error which is proved always valid, guaranteeing the estimation error to asymptotically converge to zero, for any initial state and switching law. Next, a dynamic output-dependent switching law is formulated. Then, design methodologies using linear matrix inequalities are proposed, which, to the authors's knowledge, have not yet been applied to this problem. Finally, observers for DC-DC converters are designed and simulated as application examples. © 2013 Brazilian Society for Automatics - SBA.

On Switched Regulator Design of Uncertain Nonlinear Systems Using Takagi-Sugeno Fuzzy Models

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

A fuzzy Lyapunov function approach for stabilization and control of switched TS fuzzy systems

In this work, sufficient conditions for the existence of switching laws for stabilizing switched TS fuzzy systems via a fuzzy Lyapunov function are proposed. The conditions are found by exploring properties of the membership functions and are formulated in terms of linear matrix inequalities (LMIs). Stabilizing switching conditions with bounds on the decay rate solution and H1 performance are also obtained. Numerical examples illustrate the effectiveness of the proposed design methods.

Nonlinear state estimation and control for chaos suppression in MEMS resonator

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

Nonlinear ball and beam control system identification

The Ball and Beam system is a common didactical experiment in control laboratories that can be used to illustrate many different closed-loop control techniques. The plant itself is subjected to many nonlinear effects, which the most common comes from the relative motion between the ball and the beam. The modeling process normally uses the lagrangean formulation. However, many other nonlinear effects, such as non-viscous friction, beam flexibility, ball slip, actuator elasticity, collisions at the end of the beam, to name a few, are present. Besides that, the system is naturally unstable. In this work, we analyze a subset of these characteristics, in which the ball rolls with slipping and the friction force between the ball and the beam is non-viscous (Coulomb friction). Also, we consider collisions at the ends of the beam, the actuator consists of a (rubber made) belt attached at the free ends of the beam and connected to a DC motor. The model becomes, with those nonlinearities, a differential inclusion system. The elastic coefficients of the belt are experimentally identified, as well as the collision coefficients. The nonlinear behavior of the system is studied and a control strategy is proposed.

On nonlinear dynamics behavior and control of a new model of a magnetically levitated vibrating system, excited by an unbalanced DC motor of limited power supply

We analyze new results on a magnetically levitated body (a block including a magnet whose bottom pole is set in such a way as to repel the upper pole of a magnetic base) excited by a non-ideal energy source (an unbalanced electric motor of limited power supply). These new results are related to the jump phenomena and increase of power required of such sources near resonance are manifestations of a non-ideal system and they are referred as the Sommerfeld effect, which emulates an energy sink. In this work, we also discuss control strategies to be applied to this system, in resonance conditions, in order to decrease its vibration amplitude and avoiding this apparent energy sink.

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.

An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Model and control of tendon actuated robots

The use of tendons for the transmission of the forces and the movements in robotic devices has been investigated from several researchers all over the world. The interest in this kind of actuation modality is based on the possibility of optimizing the position of the actuators with respect to the moving part of the robot, in the reduced weight, high reliability, simplicity in the mechanic design and, finally, in the reduced cost of the resulting kinematic chain. After a brief discussion about the benefits that the use of tendons can introduce in the motion control of a robotic device, the design and control aspects of the UB Hand 3 anthropomorphic robotic hand are presented. In particular, the tendon-sheaths transmission system adopted in the UB Hand 3 is analyzed and the problem of force control and friction compensation is taken into account. The implementation of a tendon based antagonistic actuated robotic arm is then investigated. With this kind of actuation modality, and by using transmission elements with nonlinear force/compression characteristic, it is possible to achieve simultaneous stiffness and position control, improving in this way the safety of the device during the operation in unknown environments and in the case of interaction with other robots or with humans. The problem of modeling and control of this type of robotic devices is then considered and the stability analysis of proposed controller is reported. At the end, some tools for the realtime simulation of dynamic systems are presented. This realtime simulation environment has been developed with the aim of improving the reliability of the realtime control applications both for rapid prototyping of controllers and as teaching tools for the automatic control courses.

Seizure prediction and control in epilepsy

The first part of my thesis presents an overview of the different approaches used in the past two decades in the attempt to forecast epileptic seizure on the basis of intracranial and scalp EEG. Past research could reveal some value of linear and nonlinear algorithms to detect EEG features changing over different phases of the epileptic cycle. However, their exact value for seizure prediction, in terms of sensitivity and specificity, is still discussed and has to be evaluated. In particular, the monitored EEG features may fluctuate with the vigilance state and lead to false alarms. Recently, such a dependency on vigilance states has been reported for some seizure prediction methods, suggesting a reduced reliability. An additional factor limiting application and validation of most seizure-prediction techniques is their computational load. For the first time, the reliability of permutation entropy [PE] was verified in seizure prediction on scalp EEG data, contemporarily controlling for its dependency on different vigilance states. PE was recently introduced as an extremely fast and robust complexity measure for chaotic time series and thus suitable for online application even in portable systems. The capability of PE to distinguish between preictal and interictal state has been demonstrated using Receiver Operating Characteristics (ROC) analysis. Correlation analysis was used to assess dependency of PE on vigilance states. Scalp EEG-Data from two right temporal epileptic lobe (RTLE) patients and from one patient with right frontal lobe epilepsy were analysed. The last patient was included only in the correlation analysis, since no datasets including seizures have been available for him. The ROC analysis showed a good separability of interictal and preictal phases for both RTLE patients, suggesting that PE could be sensitive to EEG modifications, not visible on visual inspection, that might occur well in advance respect to the EEG and clinical onset of seizures. However, the simultaneous assessment of the changes in vigilance showed that: a) all seizures occurred in association with the transition of vigilance states; b) PE was sensitive in detecting different vigilance states, independently of seizure occurrences. Due to the limitations of the datasets, these results cannot rule out the capability of PE to detect preictal states. However, the good separability between pre- and interictal phases might depend exclusively on the coincidence of epileptic seizure onset with a transition from a state of low vigilance to a state of increased vigilance. The finding of a dependency of PE on vigilance state is an original finding, not reported in literature, and suggesting the possibility to classify vigilance states by means of PE in an authomatic and objectic way. The second part of my thesis provides the description of a novel behavioral task based on motor imagery skills, firstly introduced (Bruzzo et al. 2007), in order to study mental simulation of biological and non-biological movement in paranoid schizophrenics (PS). Immediately after the presentation of a real movement, participants had to imagine or re-enact the very same movement. By key release and key press respectively, participants had to indicate when they started and ended the mental simulation or the re-enactment, making it feasible to measure the duration of the simulated or re-enacted movements. The proportional error between duration of the re-enacted/simulated movement and the template movement were compared between different conditions, as well as between PS and healthy subjects. Results revealed a double dissociation between the mechanisms of mental simulation involved in biological and non-biologial movement simulation. While for PS were found large errors for simulation of biological movements, while being more acurate than healthy subjects during simulation of non-biological movements. Healthy subjects showed the opposite relationship, making errors during simulation of non-biological movements, but being most accurate during simulation of non-biological movements. However, the good timing precision during re-enactment of the movements in all conditions and in both groups of participants suggests that perception, memory and attention, as well as motor control processes were not affected. Based upon a long history of literature reporting the existence of psychotic episodes in epileptic patients, a longitudinal study, using a slightly modified behavioral paradigm, was carried out with two RTLE patients, one patient with idiopathic generalized epilepsy and one patient with extratemporal lobe epilepsy. Results provide strong evidence for a possibility to predict upcoming seizures in RTLE patients behaviorally. In the last part of the thesis it has been validated a behavioural strategy based on neurobiofeedback training, to voluntarily control seizures and to reduce there frequency. Three epileptic patients were included in this study. The biofeedback was based on monitoring of slow cortical potentials (SCPs) extracted online from scalp EEG. Patients were trained to produce positive shifts of SCPs. After a training phase patients were monitored for 6 months in order to validate the ability of the learned strategy to reduce seizure frequency. Two of the three refractory epileptic patients recruited for this study showed improvements in self-management and reduction of ictal episodes, even six months after the last training session.

Optimal polygonal L1 linearization and fast interpolation of nonlinear systems

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L1 norm. A thorough error analysis is developed to guide an optimal design of two kinds of polygonal approximations in the asymptotic case of a large budget of evaluation subintervals N. The method allows the user to obtain the level of linearization (N) for a target approximation error and vice versa. It is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), allowing real-time performance of computationally demanding applications. The quality and efficiency of the technique has been measured in detail on two nonlinear functions that are widely used in many areas of scientific computing and are expensive to evaluate.