On nonlinear dynamics and control of a robotic arm with chaos

J Braz. Soc. Mech. Sci. Eng.

et al. 2018

This study analyzes a nonlinear system with a crankshaft -slider mechanism linked to a pendulum. The crank is powered by a DC motor that moves horizontally the pendulum pivot. The speed of the motor is influenced by the pendulum dynamics, reason for calling the system as nonideal. In literature, the vibration of the pendulum support by a crank-shaftslider is generally considered as harmonic what neglects the real complexity of the mechanism. It is also common, for the crank speed or the excitation frequency to be considered constant, so a unique degree-of-freedom can take place. The novelty in this research is the analysis of the feedback effect of the pendulum over the crank speed and the complexity of crank-slider mechanism without approaching to a harmonic motion. Different types of motion occur as oscillations, rotations, and chaos. Results with different initial conditions are worked out and basins of attractions plotted. Chaos was obtained when small variations of parameters are made. The methods of analysis include phase portraits, time histories, bifurcations diagrams, and basins of attraction. The verification of chaotic phenomena is performed through the 0-1 test. By the end, the feedback control is applied using the method of Tereshko by altering the energy of the chaotic system, leading the pendulum to a limit cycle.

Section: Nonlinear Dynamical Analyses Using 0-1 Testmentioning

confidence: 99%

On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors

Avanço

Tusset

J Braz. Soc. Mech. Sci. Eng.

et al. 2018

“…To check which variation of chaotic behavior is considered the 0-1 test. The 0-1 test for chaos takes as input a time series of measurements and returns a single scalar value of either 0 for periodic attractors or 1 for chaotic attractors [31,34]. According to [35] value of (K c ) can be obtained from: …”

Section: Dynamic Analysis Of a Fractional-ordermentioning

confidence: 99%

Dynamics behaviour of an elastic non-ideal (NIS) portal frame, including fractional nonlinearities

Brasil

Félix

et al. 2016

J. Phys.: Conf. Ser.

Abstract. This paper overviews recent developments on some problems related to elastic structures, such as portal frames, taking into account the full interactions of the vibrating systems, with an energy source of limited power supply (small motors, electro-mechanical shakers). We include a discussion on fractional (rational) damping and stiffness effects on the adopted modelling. This was a plenary lecture, delivered in the event titled: Mechanics of Slender Structures, organized in Northampton, England from 21-22, September 2015. IntroductionThis paper shows a series of problems related to nonlinear dynamics and control, correlated to Electromechanical Systems [1] using an elastic support. Here, we analyzed such systems those fall into three groups: the conventional MACRO, MEMS and NEMS electro-mechanical systems, taking into account the existence of a full interaction between mechanical and electrical field quantities. The aim of this paper is to describe a large number of phenomena caused by the action of vibrations on nonlinear electro-mechanical systems and the energy source supply to it. This paper gives a general description of this class of phenomena which has been discussed in recent years.

“…The implementation of saturation as a control method was proposed by Golnaraghi (1991), Oueini et al (1997), Oueini (1999) and Pai and Schulz (2000), and studied by Pai et al (1998), Felix at al. (2005), Shoeybi and Ghorashi (2005), Warminski et al (2013), Felix et al (2014) and Tusset et al (2015), among others.…”

Section: Introductionmentioning

confidence: 98%

Using passive control by a pendulum in a portal frame platform with piezoelectric energy harvesting

Rocha

Journal of Vibration and Control

Tusset

et al. 2017

This work presents a passive control strategy using a pendulum on a simple portal frame structure, with two-to-one internal resonance, with a piezoelectric material coupling as a means of energy harvesting. In addition, the system is externally base-excited by an electro-dynamical shaker with harmonic output. Due to internal resonance the system may present the phenomenon of saturation, which provides some nonlinear dynamical behavior to the system. A pendulum is coupled to control nonlinear behaviors, leading to a periodic orbit, which is necessary to maintain energy harvesting. The results show that the system presents, most of the time, as being quasiperiodic. However, it does not present as being chaotic. With the pendulum, it was possible to control most of these quasiperiodic behaviors, leading to a periodic orbit. Moreover, it is possible to eliminate the need for an active or semi-active control, which are usually more complex. In addition, the control provides a way to detune the energy captured to the desired operating frequency.