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.
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.
•A prey-predator model incorporating fear factor is developed.•A globally stable theorem of coexistence equilibrium is established.•The existences of Hopf bifurcation and limit cycle are shown.•The ...fear effect can not only reduce the population density of predator, but also stabilize the system by excluding the existence of periodic solutions.
In this paper, we investigate the influence of anti-predator behaviour due to the fear of predators with a Holling-type-II prey-predator model incorporating a prey refuge. We first provide the existence and stability of equilibria of the model. Next, we give the existence of Hopf bifurcation and limit cycle. In addition, we study the impact of the fear effect on the model analytically and numerically, and find that the fear effect can not only reduce the population density of predator at the positive equilibrium, but also stabilize the system by excluding the existence of periodic solutions. Moreover, we also find that prey refuge has great impact on the persistence of the predator.
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.
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 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 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.
We study the circle formation problem for a group of anonymous mobile agents in a plane, in which the agents are required to converge onto a circle with a preset target as the center, as well as to ...maintain the desired relative positions when rotating around the target at the same speed. Each agent is modeled as a kinematic point and can merely perceive the relative positions of the target and its limited neighbors. In order to solve the circle formation problem, a limit-cycle-based decoupled-design approach is delivered. We divide the overall control objective into two subobjectives, where the first is target circling that all agents converge onto the circle around the target, and the second is spacing adjustment that each agent maintains the desired distance from its neighbors. Then, we propose to use a controller comprised of converging part and layout part to deal with these two subobjectives, respectively. The former part is based on a limit-cycle oscillator using only the relative position from the target, and the latter is designed by also perceiving the relative position from the agent's neighbors. An important feature of the controller is that it guarantees that no collision between agents ever takes place throughout the system's evolution. Another feature is that some of the parameters in the proposed controller have explicit physical meanings related to the agents' rotating motion around the target, so that they can be set more reasonable and easily in real applications. Numerical simulations are given to show the effectiveness and performance of the proposed circle formation controller.
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.
The objective of this paper is to study the number and stability of limit cycles for planar piecewise linear (PWL) systems of node–saddle type with two linear regions. Firstly, we give a thorough ...analysis of limit cycles for Liénard PWL systems of this type, proving one is the maximum number of limit cycles and obtaining necessary and sufficient conditions for the existence and stability of a unique limit cycle. These conditions can be easily verified directly according to the parameters in the systems, and play an important role in giving birth to two limit cycles for general PWL systems. In this step, the tool of a Bendixon-like theorem is successfully employed to derive the existence of a limit cycle. Secondly, making use of the results gained in the first step, we obtain parameter regions where the general PWL systems have at least one, at least two and no limit cycles respectively. In addition for the general PWL systems, some sufficient conditions are presented for the existence and stability of a unique one and exactly two limit cycles respectively. Finally, some numerical examples are given to illustrate the results and especially to show the existence and stability of two nested limit cycles.
•The piecewise linear (PWL) system is of node–saddle type.•A necessary and sufficient condition is presented for the uniqueness of a limit cycle for Liénard PWL systems.•The number of limit cycles are given in different parameter regions for general PWL systems.•A Poincaré–Bendixon-like theorem for Filippov systems is successfully employed to obtain the existence of a limit cycle.
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