Grid synchronization algorithms are important in control systems of power electronic converters. These algorithms must ensure proper synchronization even in the case of disturbances such as ...voltage-sags and phase-jumps, which are common in high-voltage and low-voltage ride-through applications. Therefore, the development of robust synchronization algorithms in these situations is of interest. In this article, a nonlinear synchronization algorithm suitable for application in grid-following inverters operating under fault ride-through conditions is proposed. This algorithm is called multilevel limit cycle oscillator frequency-locked loop (MLCO-FLL), and it is used as a prefilter for a synchronous reference frame phase-locked loop (SRF-PLL). This algorithm is robust against phase-jumps and variations in the voltage, both representing important features for fault ride-through applications. Also, it automatically detects the operation at different voltage levels without state machines or logic conditions. These features might be of interest in other research fields, where the detection of orbits is important. A comparison with other linear and nonlinear synchronization algorithms showed that MLCO-FLL features important advances. Moreover, in future, it is possible to improve its performance once its characteristics and parameters are examined in detail. Simulations and experimental results obtained from a 15 kW inverter connected to a grid-emulator were used to validate the MLCO-FLL.
The aim of this paper is to prove Llibre–Valls’s conjecture for the Brusselator system. By transforming the Brusselator system into Liénard equation and applying the limit cycle theory of Liénard ...equation, we give a positive answer to this conjecture. Numerical simulations are also given to illustrate our theoretical results.
•Positive answer of Llibre–Valls’s conjecture for the Brusselator system.•Developed a new technique to prove the nonexistence of limit cycle for Liénard equation.•The exact number of limit cycles of Brusselator system.
This paper reviews the design, implementation, and demonstration of energy harvesting devices that exploit flow-induced vibrations as the main source of energy. Starting with a presentation of ...various concepts of energy harvesters that are designed to benefit from a general class of flow-induced vibrations, specific attention is then given at those technologies that may offer, today or in the near future, a potential benefit to extend the operational capabilities and to monitor critical parameters of unmanned aerial vehicles. Various phenomena characterized by flow-induced vibrations are discussed, including limit cycle oscillations of plates and wing sections, vortex-induced and galloping oscillations of bluff bodies, vortex-induced vibrations of downstream structures, and atmospheric turbulence and gusts. It was found that linear or linearized modeling approaches are commonly employed to support the design phase of energy harvesters. As a result, highly nonlinear and coupled phenomena that characterize flow-induced vibrations are neglected in the design process. The Authors encourage a shift in the current design paradigm: considering coupled nonlinear phenomena, and adequate modeling tools to support their analysis, from a design limitation to a design opportunity. Special emphasis is placed on identifying designs and implementations applicable to aircraft configurations. Application fields of flow-induced vibrations-based energy harvesters are discussed including power supply for wireless sensor networks and simultaneous energy harvest and control. A large body of work on energy harvesters is included in this review journal. Whereas most of the references claim direct applications to unmanned aerial vehicles, it is apparent that, in most of the cases presented, the working principles and characteristics of the energy harvesters are incompatible with any aerospace applications. Finally, the challenges that hold back the integration of energy harvesting technologies in the aerospace field are discussed.
This paper mainly deals with the prediction and suppression of limit cycle oscillation existed in the two-mass system with nonlinear backlash. To improve position control precision of the drive ...system, the full-closed-loop feedback scheme is considered. Then, a comprehensive and definite prediction of limit cycle is given via the describing function method. In order to compensate backlash nonlinearity, the state feedback control method is employed. To overcome the insufficient application of the state feedback control in the complex nonlinear system, a novel design concept is proposed. The influence of backlash on the nonlinear system is substituted with an additional compensation component to the control signal, making the system approach a linear one. Following this, a pole placement scheme is designed, which aims to establish a feedback structure that can make the system equivalent to a rigid system. In such a case, the limit cycle oscillation can be eliminated; thus, the position control precision can also be enhanced. In all cases, the validity of the proposal is verified by experimental results.
We propose a method for designing 2-D limit-cycle oscillators with prescribed periodic trajectories and phase response properties based on the phase reduction theory, which gives a concise ...description of weakly perturbed limit-cycle oscillators and is widely used in the analysis of synchronization dynamics. We develop an algorithm for designing the vector field with a stable limit cycle that possesses a given shape and also a given phase sensitivity function. The vector field of the limit-cycle oscillator is approximated by polynomials whose coefficients are estimated by convex optimization. The linear stability of the limit cycle is ensured by introducing an upper bound to the Floquet exponent. The validity of the proposed method is verified numerically by designing several types of 2-D existing and artificial oscillators. As applications, we first design a limit-cycle oscillator with an artificial star-shaped periodic trajectory and demonstrate global entrainment. We then design a limit-cycle oscillator with an artificial high-harmonic phase sensitivity function and demonstrate multistable entrainment caused by a high-frequency periodic input.
The existing division of system stability region does not fully consider the influence of nonlinear characteristics of the system. To address the challenge that it is difficult to inscribe the ...stability region of wind power grid-connected systems accurately and quantitatively, this paper proposes a nonlinear system multi-parameter practical stability region analysis method based on limit cycle amplitude tracking. Firstly, the nonlinear dynamic model of multi-machine system with doubly fed induction generator (DFIG) is established, and the bifurcation diagram of the system is obtained by nonlinear analysis of the model. Then, the limit cycle-parameter diagram is obtained by tracking the limit cycle of the Hopf bifurcation point of the system, and the problem of how the system oscillation evolves with the change of operating parameters is analyzed. Afterwards, the single parameter practical stability region of the nonlinear system is obtained by combining the system equilibrium manifold. Finally, the multi-parameter practical stability region of the nonlinear system is obtained by the three-dimensional bifurcation map with the system time delay, DFIG output active power and reactive load as the bifurcation parameters. The division of the stability region has important guiding significance for the parameter adjustment in the actual operation of the system.
The mathematical model of vortex-induced vibrations (VIV) on long-span bridges is important to predict nonlinear structural responses. Such models can be divided into two categories: wake-oscillator ...and single-degree-of-freedom (SDOF) models. The SDOF model is widely used for wind-induced vibration calculations. However, the traditional SDOF model based on the standard van der Pol oscillator cannot simulate VIVs with multistability. In this study, a newly generalized van der Pol model is proposed to incorporate the limit-cycle oscillation (LCO) with multiple amplitudes, and the nonlinear damping is expressed by polynomial expansion. Next, the multiple LCO amplitudes can be determined from the energy evolution formula derived from the averaging method. Similarly, the evolution of the vibration amplitude during the transient response is also derived by the same method. Subsequently, nonlinear parameter identification methods based on constraint optimization are derived according to both the LCO amplitude and transient responses. In the last part of this study, the “energy map” is proposed to present the energy extracted from the fluid–structure interaction with different wind speeds and vibration amplitudes, and it is constructed by the parameters identified in the lock-in range of VIV. The “energy map” can provide a complete picture of the evolution of the energy of VIVs on bridge decks.
The synchronization stability of the system that one single VSC is connected to an infinite source via the line is studied in this letter. Based on Bendixson criterion, closed orbit (limit cycle) ...does not exist in the derived stable region, while may exist in the region between the conservative stable boundary and the unstable equilibrium point (UEP). Nonlinear damping effect on the system stability is analytically defined, and an unstable limit cycle appears when the positive and negative damping effect of the system over one period is mutually balanced. Numerical results verify the existence of limit cycle and nonlinear damping property of VSC.
High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important concept in a ...nonlinear setting. We show that dominance can be studied through linear dissipation inequalities and an interconnection theory that closely mimics the classical analysis of stability by means of dissipativity theory. In this approach, stability is seen as the particular situation where the dominant behavior is 0-dimensional. The generalization opens novel tractable avenues to study multistability through 1-dominance and limit cycle oscillations through 2-dominance.
This paper presents an analog-assisted (AA) output-capacitor-free digital low-dropout (D-LDO) regulator with tri-loop control. For responding to instant load transients, the proposed high-pass AA ...loop momentarily adjusts the unit current of the power switch array, and significantly reduces the voltage spikes. In the proposed D-LDO, the overall 512 output current steps are divided into three sub-sections controlled by coarse/fine loops with carry-in/out operations. Therefore, the required shift register (SR) length is reduced, and a 9-bit output current resolution is realized by using only 28-SR bits. Besides, the coarse-tuning loop helps to reduce the recovery time, while the fine-tuning loop improves the output accuracy. To eliminate the limit cycle oscillation and reduce the quiescent current, a freeze mode is added after the fine-tuning operation. To reduce the output glitches and the recovery time, a nonlinear coarse word control is designed for the carry-in/out operations. The D-LDO is fabricated in a 65-nm general purpose CMOS process. A maximum voltage undershoot/overshoot of 105 mV is measured with a 10-mA/1-ns load step and a total capacitor of only 100 pF. Thus, the resulting figure-of-merit is 0.23 ps.
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