Switching-off in a minimal time a fitzhugh-nagumo system

This paper deals with a system that describes an electrical circuitcomposed by a linear system coupled to a nonlinear one involving a tunneldiode in a flush-and-fill circuit. One of the most comprehensive models for thiskind of circuits was introduced by R. Fitzhugh in 1961, when taking on carebiological tasks. The equation has in its phase plane only two periodic solutions,namely, the unstable singular point S0 and the stable cycle Γ. If the system isat rest on S0, the natural flow of orbits seeks to switch-on the process by going- as time goes by - toward its steady-state, Γ. By using suitable controls it ispossible to reverse such natural tendency going in a minimal time from Γ toS0, switching-off in this way the system. To achieve this goal it is mandatorya minimal enough strength on controls. These facts will be shown by means ofconsiderations on the null control sets in the process.

On an energy exchange process and appearance of chaos in a non-ideal portal frame dynamical system

In this paper, we consider non-ideal excitation devices such as DC motors with restrictenergy output capacity. When such motors are attached to structures which needexcitation power levels similar to the source power capacity, jump phenomena and theincrease in power required near resonance characterize the Sommerfeld Effect, actingas a sort of an energy sink. One of the problems often faced by designers of suchstructures is how to drive the system through resonance and avoid this energy sink.Our basic structural model is a simple portal frame driven by a num-ideal powersource-(NIPF). We also investigate the absorption of resonant vibrations (nonlinearand chaotic) by means of a nonlinear sub-structure known as a Nonlinear Energy Sink(NES). An energy exchange process between the NIPF and NES in the passagethrough resonance is investigated, as well the suppression of chaos.

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.

Suppression of vibrations in a nonlinear half-car model using a magneto-rheological damper

The present work investigates the nonlinear response of a half-car model. The disturbances of the road are assumed to be sinusoidal. After constructing the bifurcation diagram, we use the 0-1 test to identify chaotic motions. The main objective of this study is to eliminate chaotic behavior of the chassis and reduce its vibrations. To accomplish this, a semi-active vehicle suspension control system, using magneto-rheological dampers, is proposed. The proposed semi-active control strategy consists of two nonlinear control laws: a feedforward control, and a feedback control. They are obtained by considering the SDRE (State Dependent Riccati Equation) control, where the control parameter is the voltage applied to the coils of the magneto-rheological dampers. Numerical results show that the proposed control method is effective in significantly reducing of the chassis vibration, increasing, therefore, passenger comfort.

Chaos control and sensitivity analysis of a double pendulum arm excited by an RLC circuit based nonlinear shaker

In this paper the dynamical interactions of a double pendulum arm and an electromechanical shaker is investigated. The double pendulum is a three degree of freedom system coupled to an RLC circuit based nonlinear shaker through a magnetic field, and the capacitor voltage is a nonlinear function of the instantaneous electric charge. Numerical simulations show the existence of chaotic behavior for some regions in the parameter space and this behaviour is characterized by power spectral density and Lyapunov exponents. The bifurcation diagram is constructed to explore the qualitative behaviour of the system. This kind of electromechanical system is frequently found in robotic systems, and in order to suppress the chaotic motion, the State-Dependent Riccati Equation (SDRE) control and the Nonlinear Saturation control (NSC) techniques are analyzed. The robustness of these two controllers is tested by a sensitivity analysis to parametric uncertainties.

Taylor's power law for ecological communities: an explanation on nonextensive/nonlinear statistical grounds

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