A simple feedback control for a chaotic oscillator with limited power supply

We proposed a simple feedback control method to suppress chaotic behavior in oscillators with limited power supply. The small-amplitude controlling signal is applied directly to the power supply system, so as to alter the characteristic curve of the driving motor. Numerical results are presented showing the method efficiency for a wide range of control parameters. Moreover, we have found that, for some parameters, this kind of control may introduce coexisting periodic attractors with complex basins of attraction and, therefore, serious problems with predictability of the final state the system will asymptote to.     

On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. , where , are T periodic functions of t and there is a ₀ ∈ Ω such that f ( a ₀) = 0 and f ′( a ₀) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x ₃) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits.     

Suppression of vibrations in strongly nonhomogeneous 2DOF systems

In this work we analyze the effects of an optimal linear control for nonlinear systems under the vibrations of a strongly nonhomogeneous nonlinear two-degree-of-freedom system with single anchor spring under condition of initial impact. We compare the results with those obtained for (a) when using only a passive broadband boundary controller which, in essence, corresponds to a one-way passive and almost irreversible energy flow from a heavy or main system to a nonlinear energy sink (NES), and (b) when using the nonlinear energy sink in combination with the optimal linear control for nonlinear system.     

On energy pumping, synchronization and beat phenomenon in a nonideal structure coupled to an essentially nonlinear oscillator

In this paper, we investigated the effectiveness of the linear electromechanical vibration absorber (LEVA) and a nonlinear electromechanical vibration absorber (NEVA) in the vibration attenuation for nonideal structures (NIS). This electromechanical damping device consists of an electrical system coupled magnetically to a mechanical structure under a nonideal excitation. An analysis of the effects of the parameters of coupling and of nonlinear coefficients with increasing of constant torque of the DC motor is presented.     

Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part II: Nonideal energy source

In Part II of this two-part work, we apply an optimal linear control technique to suppress chaotic behavior in a SMA oscillator, driven by a DC motor with limited power supply (Nonideal sources). Nonideal sources of vibrations of structures are those whose characteristics are coupled to the motion of the structure. Thus, in this case, an additional equation of motion is written, related to the motor rotation. Special attention is focused into the resonance region, when the nonideal excitation frequency is near the natural frequency of the SMA oscillator. Numerical results are presented, which show the efficiency of the method in resonance region. The ideal case, when we do not consider the interaction between an energy source and structure was considered in Part I of this paper.     

An overview on the appearance of the Sommerfeld effect and saturation phenomenon in non-ideal vibrating systems (NIS) in macro and MEMS scales

This paper was written in honor of Prof. Viktor Olimpanovich Kononenko from Ukraine and takes into account reports of recent progress about non-ideal vibrating systems (NIS) published in the period from 2004 to 2017. New and old studies of NIS, with limited power supply (small DC motors or electrodynamical shakers), are usually used in laboratory tests, and therefore, the investigation of mutual interactions of driven and driving sub-system is very important. In this paper, main properties of NIS have been reviewed, such as the Sommerfeld effect, i.e., jump phenomena and the increase in power supply that is required by an excitation source operating near resonance; the possibility of saturation phenomenon occurrence, i.e., the transference of energy from higher frequency and lower amplitude to lower frequency and higher amplitude mode; and the existence of regular (periodic motion) and irregular (chaotic motion) behaviors, depending on the value of control parameters (voltage of a DC motor). This paper is divided into two goals: on the one hand will be treated about NIS and on the other hand will be provided an overview of the main engineering applications, analyzing their physical phenomena involved and the adequate methodologies to deal with them.     

Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

An analytical and numerical investigation into the dynamic interaction between a cantilever beam with nonlinear damping and stiffness behavior, modeled by the Duffing-Rayleigh equation, and a non-ideal motor that is connected to the end of the beam, is presented. Non-stationary and steady-state responses in the resonance region as well as the passage through resonance behavior when the frequency of the excitation is varied are analyzed. The influences of nonlinear stiffness, nonlinear damping and the extent of the unbalance in the motor are examined. It is found that in this situation so-called Sommerfeld effects may be observed; the increase required by a source operating near the resonance results in a small change in the frequency, but there is a large increase in the amplitude of the resultant vibration and the jump phenomenon occurs.     

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.     

On suppression of chaotic motion of a nonlinear MEMS oscillator

Nonlinear Dynamics - The present novel coronavirus (SARS-CoV-2) infection has created a global emergency situation by spreading all over the world in a large scale within very short time period....