Limit cycle oscillator in nonlinear systems with multiple time delays

Hakimi, Ali Reza; Azhdari, Meysam; Binazadeh, Tahereh

doi:10.1016/j.chaos.2021.111454

Cited by 7 publications

(3 citation statements)

References 37 publications

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“…Considering the efficiency of the feedback mechanism in controlling unstable periodic orbits of dynamical systems, it is hypothesised that an appropriate feedback strategy can effectively suppress the disturbances generated during transient events in microgrids involving combinations of reactive elements. Self-feedback in a system provides flexibility in the output produced by systems in terms of diverse nature and stabilisation (Lazarus et al 2016;Hakimi et al 2021). Highly periodic stable waveforms can be obtained by adjusting the delay and the feedback gain even in chaotic systems (Peng et al 2020;Kashchenko 2023).…”

Section: Research Articlementioning

confidence: 99%

Virtual oscillator with delayed feedback for transient mitigation in inverter-based islanded microgrids

Salim,

Babu,

Krishna

2024

Int. J. Renew. Energy Dev.

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In recent years, the conventional control schemes for renewable energy-based inverter-dominated microgrids have been expeditiously replaced by Virtual Oscillator-based Control (VOC). The method of VOC ensures fast synchronisation and efficient load-sharing capabilities in inverter-based renewable energy systems. This work evaluates the effectiveness of VOC-based inverters in mitigating the transient dynamics of power system parameters like voltage, frequency and current under different types of switching events involving active and reactive load combinations. Further, to enhance the control efficiency of VOC under such load-switching scenarios a modified form of VOC is proposed utilizing the ability of the feedback mechanism to strengthen the state space trajectory of dynamical systems. In the proposed method, the control oscillator of conventional VOC driven by the inverter current is modified by providing a feedback signal in the form of an integral function of the error between the drive oscillator and the trajectory of the inverter output. The efficiencies of different forms of feedback are quantified in terms of percentage deviation in power system parameters as well as THD. The proposed feedback strategy can improve the control performance by bringing down the voltage deviation from 57 % in conventional VOC to around 4%. Likewise, the frequency deviation is brought down to 0.14% from 19.26 %. These advantages are achieved without any significant adverse impact on the THD. The proposed approach can be utilized in multi-inverter-based systems serving sensitive loads in microgrids.

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Section: Research Articlementioning

confidence: 99%

Virtual oscillator with delayed feedback for transient mitigation in inverter-based islanded microgrids

Salim,

Babu,

Krishna

2024

Int. J. Renew. Energy Dev.

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“…Authors in [5] designed a sliding mode controller for the LC with dead-zone nonlinearity. The design procedure was also developed for time-delay systems [6] using concept of positive limit sets. Moreover, synthesizing stable LC has been investigated for discrete-time dynamics and in versus disturbances [7], [8].…”

Section: Introductionmentioning

confidence: 99%

Generation of Limit Cycles in Nonlinear Systems: Machine Leaning Based Type-3 Fuzzy Control

et al. 2023

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A limit cycle is a cyclic path of oscillation on which the states of a nonlinear system settle. A considerable number of practical systems such as robots, converters, and heartbeat require generating the sustainable oscillatory behaviours. The objective is to design a controller to generate limit cycle with specific behaviours. In this paper, a novel fuzzy control (FC) strategy is introduced to create the limit-cycle for nonlinear complex dynamics with unknown uncertainties. The suggested controller benefits from new interval type-3 fuzzy logic, allowing the control synthesis to improve the quality of closed-loop response and robust performance. The adaptively learned backstepping controller based on FC is employed to analyze the convergence and robustness. Various simulations are proposed to ensure the efficiency of the fuzzy-based control law and adaption rules.

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“…The authors of [41] investigated this problem for the non-linear systems with dead-zone non-linearity. In [42,43] a backstepping method is proposed for limit cycle control of non-linear time-delay systems. Moreover, the limit cycle control approach is extended in [44] and [45] for the class of non-linear sandwich systems.…”

Section: Introductionmentioning

confidence: 99%

Robust adaptive finite‐time control design for the generation of stable oscillations in the strict‐feedback form non‐linear systems with input dead‐zone non‐linearity

Azhdari

Binazadeh

2022

IET Control Theory & Appl

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This paper presents a novel finite‐time limit cycle control for a class of strict‐feedback non‐linear systems with input dead‐zone non‐linearity, parameter uncertainties, and unknown disturbances. Creating attractive limit cycles in the phase plane of dynamical systems leads to generating sustained oscillations in the system's output. Achieving the finite‐time limit cycle is an extremely challenging problem because existing finite‐time theorems cannot be applied directly. To solve this difficulty, a novel structure of the sliding surface is introduced concerning the shape of the desired limit cycle. Then, to achieve the control objective, the sliding mode and backstepping control techniques are employed throughout the finite‐time stability concept. Simultaneously, to deal with the parameter uncertainties in the system's dynamic, the adaptive scheme is utilized. Moreover, a finite‐time command filter is introduced to cope with the trouble of the explosion of complexity in the backstepping method. The presented method rigorously ensures that the trajectories of the closed‐loop system converge to a small boundary region of the desired stable limit cycle within a finite time and equivalently the system's output reaches the desired periodic oscillation after a finite time. The applicability and effectiveness of the proposed method are validated by providing the comparative simulation results.

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Limit cycle oscillator in nonlinear systems with multiple time delays

Cited by 7 publications

References 37 publications

Virtual oscillator with delayed feedback for transient mitigation in inverter-based islanded microgrids

Virtual oscillator with delayed feedback for transient mitigation in inverter-based islanded microgrids

Generation of Limit Cycles in Nonlinear Systems: Machine Leaning Based Type-3 Fuzzy Control

Robust adaptive finite‐time control design for the generation of stable oscillations in the strict‐feedback form non‐linear systems with input dead‐zone non‐linearity

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