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.

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.

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.

Effects of inhibition gastric acid secretion on arterial acid-base status during digestion in the toad Bufo marinus

Digestion affects acid-base status, because the net transfer of HCl from the blood to the stomach lumen leads to an increase in HCO3- levels in both extra- and intracellular compartments. The increase in plasma [HCO3-], the alkaline tide, is particularly pronounced in amphibians and reptiles, but is not associated with an increased arterial pH, because of a concomitant rise in arterial Pco(2) caused by a relative hypoventilation. In this study, we investigate whether the postprandial increase in Paco(2) of the toad Bufo marinus represents a compensatory response to the increased plasma [HCO3-] or a state-dependent change in the control of pulmonary ventilation. To this end, we successfully prevented the alkaline tide, by inhibiting gastric acid secretion with omeprazole, and compared the response to that of untreated toads determined in our laboratory during the same period. In addition, we used vascular infusions of bicarbonate to mimic the alkaline tide in fasting animals. Omeprazole did not affect blood gases, acid-base and haematological parameters in fasting toads, but abolished the postprandial increase in plasma [HCO3-] and the rise in arterial Pco(2) that normally peaks 48 h into the digestive period. Vascular infusion of HCO3-, that mimicked the postprandial rise in plasma [HCO3-], led to a progressive respiratory compensation of arterial pH through increased arterial Pco(2) Thus, irrespective of whether the metabolic alkalosis is caused by gastric acid secretion in response to a meal or experimental infusion of bicarbonate, arterial pH is being maintained by an increased arterial Pco(2). It seems, therefore, that the elevated Pco(2), occuring during the postprandial period, constitutes of a regulated response to maintain pH rather than a state-dependent change in ventilatory control. (C) 2003 Elsevier B.V. All rights reserved.

Variational supersymmetric approach to evaluate Fokker-Planck probability

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Statements on chaos control designs, including a fractional order dynamical system, applied to a MEMS comb-drive actuator

In this work, we deal with a micro electromechanical system (MEMS), represented by a micro-accelerometer. Through numerical simulations, it was found that for certain parameters, the system has a chaotic behavior. The chaotic behaviors in a fractional order are also studied numerically, by historical time and phase portraits, and the results are validated by the existence of positive maximal Lyapunov exponent. Three control strategies are used for controlling the trajectory of the system: State Dependent Riccati Equation (SDRE) Control, Optimal Linear Feedback Control, and Fuzzy Sliding Mode Control. The controls proved effective in controlling the trajectory of the system studied and robust in the presence of parametric errors.

The rigid-flexible nonlinear robotic manipulator: Modeling and control

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

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.

Chaos suppression in NEMs resonators by using nonlinear control design

In this work the chaotic behavior of a micro-mechanical resonator with electrostatic forces on both sides is suppressed. The aim is to control the system in an orbit of the analytical solution obtained by the Method of Multiple Scales. Two control strategies are used for controlling the trajectory of the system, namely: State Dependent Riccati Equation (SDRE) Control and Optimal Linear Feedback Control (OLFC). The controls proved effectiveness in controlling the trajectory of the system. Additionally, the robustness of each strategy is tested considering the presence of parametric errors and measurement noise in control. © 2012 American Institute of Physics.

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.

On elimination of chaotic behavior in a non-ideal portal frame structural system, using both passive and active controls

In this paper, an application is considered of both active and passive controls, to suppression of chaotic behavior of a simple portal frame, under the excitation of an unbalanced DC motor, with limited power supply (non-ideal problem). The adopted active control strategy consists of two controls: the nonlinear (feedforward) in order to keep the controlled system in a desirable orbit, and the feedback control, which may be obtained by considering state-dependent Riccati equation control to bringing the system into the desired orbit using a magneto rheological (MR) damper. To control the electric current applied in control of the MR damper the Bouc-Wen mathematical model was used to the MR damper. The passive control was obtained by means of a nonlinear sub-structure with properties of nonlinear energy sink. Simulations showed the efficiency of both the passive control (energy pumping) and active control strategies in the suppression of the chaotic behavior. © The Author(s) 2012.

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 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.

Fenômenos não-lineares, incluindo-se os não-ideias, em captura de energia utilizando-se dispositivos piezoelétricos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)