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Nonlinear energy sink (NES) is a device used for structural vibration reduction, which can not only achieve targeted energy transfer, but also has many advantages such as wide working frequency band, high reliability and strong robustness. In a fractional-order differential system, the historical memory of fractional-order differential operators enables us to more accurately simulate and study physical phenomena in actual systems. With this in mind, the vibration suppression performance of the fractional-order damping system coupled with NES is considered. However, random vibrations are everywhere and systems are susceptible to random excitations. Therefore, this paper conducts a numerical and analytical investigation into the dynamic response mechanism of a fractional-order damping system excited by random excitation, which coupled with a NES. Firstly, The Fokker–Planck–Kolmogorov equation and stationary probability density function expression are derived by using stochastic averaging method. Secondly, The effectiveness of this approach is confirmed by the concurrence between the analytical solutions and the numerical solutions obtained through Monte Carlo simulation. Subsequently, the effects of system parameters and noise intensity on the stationary response of the system are discussed, as well as stochastic P-bifurcation caused by system parameters. Ultimately, the time histories of displacement and the energy transformation of the primary structure with changes in system parameters under the condition of coupled with NES and without NES are analyzed to verify that NES can achieve the desired goal of vibration reduction. [ABSTRACT FROM AUTHOR]

In this study, an electric oil and gas actuator based on fractional-order PID position feedback control is proposed, through which the damping coefficient of the suspension system is adjusted to realize the active control of the suspension. An FOPID algorithm is used to control the motor's rotational angle to realize the damping adjustment of the suspension system. In this process, the road roughness is collected by the sensors as the criterion of damping adjustment, and the particle swarm algorithm is utilized to find the optimal objective function under different road surface slopes, to obtain the optimal cornering value. According to the mathematical and physical model of the suspension system, the simulation model and the corresponding test platform of this type of suspension system are built. The simulation and experimental results show that the simulation results of the fractional-order nonlinear suspension model are closer to the actual experimental values than those of the traditional linear suspension model, and the accuracy of each performance index is improved by more than 18.5%. The designed active suspension system optimizes the body acceleration, suspension dynamic deflection, and tire dynamic load to 89.8%, 56.7%, and 73.4% of the passive suspension, respectively. It is worth noting that, compared to traditional PID control circuits, the FOPID control circuit designed for motors has an improved control performance. This study provides an effective theoretical and empirical basis for the control and optimization of fractional-order nonlinear suspension systems. [ABSTRACT FROM AUTHOR]

In this study, an electric oil and gas actuator based on fractional-order PID position feedback control is proposed, through which the damping coefficient of the suspension system is adjusted to realize the active control of the suspension. An FOPID algorithm is used to control the motor’s rotational angle to realize the damping adjustment of the suspension system. In this process, the road roughness is collected by the sensors as the criterion of damping adjustment, and the particle swarm algorithm is utilized to find the optimal objective function under different road surface slopes, to obtain the optimal cornering value. According to the mathematical and physical model of the suspension system, the simulation model and the corresponding test platform of this type of suspension system are built. The simulation and experimental results show that the simulation results of the fractional-order nonlinear suspension model are closer to the actual experimental values than those of the traditional linear suspension model, and the accuracy of each performance index is improved by more than 18.5%. The designed active suspension system optimizes the body acceleration, suspension dynamic deflection, and tire dynamic load to 89.8%, 56.7%, and 73.4% of the passive suspension, respectively. It is worth noting that, compared to traditional PID control circuits, the FOPID control circuit designed for motors has an improved control performance. This study provides an effective theoretical and empirical basis for the control and optimization of fractional-order nonlinear suspension systems.

When a doubly-fed induction generator (DFIG) is connected to a weak grid, the coupling between the grid and the DFIG itself will increase, which will cause stability problems. It is difficult to maintain the tracking accuracy and ro-bustness of the phase-locked loop (PLL) in the weak grid, and the risk of instability of the current-controlled DFIG (CC-DFIG) system will increase. In this paper, a new type of voltage-controlled DFIG (VC-DFIG) mode is adopted, which is a grid-forming structure that can independently support the voltage and frequency with a certain adaptability in the weak grid. A small-signal impedance model of the VC-DFIG system is also established. The impedance of DFIG inevitably generates coupling with the grid impedance in the weak grid, especially in parallel compensation grids, and results in resonance. On the basis of the VC-DFIG, impedance stability analysis is performed to study the influences of the control structure and short-circuit ratio. Then, a feedforward damping method is proposed to modify the impedance of the VC-DFIG system at resonance frequencies. The proposed fractional order damping is utilized, which can enhance the robustness and rapidity of resonance suppression under parameter fluctuations. Finally, the experimental results are presented to validate the effectiveness of the proposed control strategy.

In this paper, nonlinear dynamic model of spur gear pairs with fractional-order damping under the condition of time-varying stiffness, backlash and static transmission error is established. The general formula of fractional-order damping term is derived by using the incremental harmonic balance method (IHBM), and the approximate analytical solution of the system is obtained by use of the iterative formula. The correctness of the results is verified by comparing with the numerical solutions in the existing literature. The effects of mesh stiffness, internal excitation amplitude and fractional order on the dynamic behavior of the system are analyzed. The results show that changing the fractional order can effectively control the resonance position and amplitude in the meshing process. Both the mesh stiffness and internal excitation can control the collision state and the stability. [ABSTRACT FROM AUTHOR]

In this paper we are interested in studying the effect of the fractional-order damping in the forced Duffing oscillator before and after applying a discretization process to it. Fixed points and their stability are discussed for the discrete system obtained. Finally, numerical simulations using Matlab are carried out to investigate the dynamic behavior such as bifurcation, chaos, and chaotic attractors. We note that on increasing the value of the fractional-order parameter, the resulting discrete system is stabilized. [ABSTRACT FROM AUTHOR]

Fractional-order derivative has been shown an adequate tool to the study of so-called "anomalous" social and physical behaviors, in reflecting their non-local, frequency- and history-dependent properties, and it has been used to model practical systems in engineering successfully, including the famous Bagley-Torvik equation modeling forced motion of a rigid plate immersed in Newtonian fluid. The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. Such forms of solutions are not good for engineers not only in understanding the solutions but also in investigation. This paper proves that for the linear SDOF oscillator with a damping described by fractional-order derivative whose order is between 1 and 2, the solution of its initial value problem free of external excitation consists of two parts, the first one is the 'eigenfunction expansion' that is similar to the case without fractional-order derivative, and the second one is a definite integral that is independent of the eigenvalues (or characteristic roots). The integral disappears in the classical linear oscillator and it can be neglected from the solution when stationary solution is addressed. Moreover, the response of the fractionally damped oscillator under harmonic excitation is calculated in a similar way, and it is found that the fractional damping with order between 1 and 2 can be used to produce oscillation with large amplitude as well as to suppress oscillation, depending on the ratio of the excitation frequency and the natural frequency. [ABSTRACT FROM AUTHOR]