Rodrigo Tumolin Rocha

On nonlinear dynamics of a parametrically excited pendulum using both active control and passive rotational (MR) damper

This paper presents two control strategies for a parametrically excited pendulum with chaotic behavior. One of them considers active control obtained by nonlinear saturation control (NSC) and the other a passive rotational magnetorheological (MR) damper. Firstly, the active control problem was formulated in order to design the external torque for the pendulum, considering the NSC. Numerical simulations were carried out in order to show the effectiveness of this method for the active control of the pendulum oscillation. The ability of the control of the proposed NSC in suppression of the chaotic behavior, considering the proposed parameters, was tested by a sensitivity analysis to parametric uncertainties. In the case of the passive rotational MR damper, firstly the influence of the introduction of the MR in a pendulum was performed considering the 0-1 test. Different electric currents are applied to suppress the chaotic behavior of the system. The numerical results showed that the simple introduction of a passive rotational MR damper without electric current did not change the chaotic behavior of the system. However, it is possible to keep the pendulum oscillating with periodic behavior using the rotational MR damper with energizing discontinuity.

Dynamical Analysis and Control of a Chaotic Microelectromechanical Resonator Model

The dynamic analysis and control of a nonlinear MEM resonator system are considered. Phase diagram, bifurcation diagram, and the 0-1 test are applied to the analysis of the influence of the parameters on the dynamics of the system, whose parameters are damping coefficient, polarization of the voltage, and nonlinear stiffness term. The bifurcation diagram is used to demonstrate the existence of the pull-in effect. Numerical results showed that the parameters, which were taken into account, were significant, indicating that the response can be either chaotic or periodic behavior. In order to bring the system from a chaotic state to a periodic orbit, two controls are considered: the time-delayed feedback control and the sliding mode control.

On an Optimal Control Applied in MEMS Oscillator with Chaotic Behavior including Fractional Order

The dynamical analysis and control of a nonlinear MEMS resonator system is considered. Phase diagram, power spectral density (FFT), bifurcation diagram, and the 0-1 test were applied to analyze the influence of the nonlinear stiffness term related to the dynamics of the system. In addition, the dynamical behavior of the system is considered in fractional order. Numerical results showed that the nonlinear stiffness parameter and the order of the fractional order were significant, indicating that the response can be either a chaotic or periodic behavior. In order to bring the system from a chaotic state to a periodic orbit, the optimal linear feedback control (OLFC) is considered. The robustness of the proposed control is tested by a sensitivity analysis to parametric uncertainties.

Optimal Control for Robot Manipulators with Three-Degress-of-Freedom

This work presents the modeling and simulation of a manipulator robot with three degrees of freedom and considering its structures with rigid behavior. The concepts of kinematics for the mathematical deduction and the Lagrangian mechanics were used to obtain the dynamic models of the manipulator and the DC actuators with permanent magnet. Due to nonlinearity and dynamics characteristics, both the states observer and the control used were based on State Dependet Ricatti Equation (SDRE). The simulations made for constant performance parameters demonstrated the effectiveness of the optimal control applied to the manipulator and to the chosen DC actuator models. The applications of trajectories to the manipulator enrich the applicability of the project and the results obtained with the techniques chosen show his efficiency.