Describing function
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Review of Small-Signal Modeling Methods Including Frequency-Coupling Dynamics of Power Converters Open
Over the past years, the linearized modeling techniques for power converters have been continuously developed to capture the small-signal dynamics beyond half the switching frequency. This paper reviews and compares the small-signal modeli…
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Time domain simulations of nonlinear thermoacoustic behaviour in a simple combustor using a wave-based approach Open
Lean premixed combustion chambers are susceptible to combustion instabilities arising from the coupling between the heat release rate perturbations and the acoustic disturbances. These instabilities are not desirable and knowledge of this …
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Nyquist Stability Analysis of an AC-Grid Connected VSC-HVDC System Using a Distributed Parameter DC Cable Model Open
In this paper, a two-terminal VSC-HVDC system embedded in a weak grid ac environment is considered, emphasizing modeling, controller design, and small-signal stability analysis. Traditionally, the dc cable is modeled by \\Pi -sections, imp…
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Design of Ship Course-Keeping Autopilot using a Sine Function-Based Nonlinear Feedback Technique Open
Course keeping for ships is the core of automatic navigation in sea transportation. Much work has concentrated on developing novel control strategies for closed loop systems. We have turned our attention the other way to improve the contro…
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“Constant in Gain Lead in Phase” Element– Application in Precision Motion Control Open
This work presents a novel 'Constant in gain Lead in phase' (CgLp) element\nusing nonlinear reset technique. PID is the industrial workhorse even to this\nday in high-tech precision positioning applications. However, Bode's gain phase\nrel…
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Frequency-Domain Stability Criteria for Converter-Based Power Systems Open
Frequency-domain stability criteria are developed for converter-based power systems with any number of converters. The converters may be grid following or grid forming, and the grid can be an ac or hybrid ac-dc network. The converters and …
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Characterization of Subsynchronous Oscillation with Wind Farms Using Describing Function and Generalized Nyquist Criterion Open
Eigen-analysis is widely used in the studies of power system oscillation and small-signal stability. However, it may give inaccurate analyses on subsynchronous oscillation (SSO) when nonlinearity is not negligible. In this paper, a nonline…
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Modeling nonlinear wave digital elements using the Lambert function Open
A large class of transcendental equations involving exponentials can be made explicit using the Lambert W function. In the last fifteen years, this powerful mathematical tool has been extensively used to find closed-form expressions for cu…
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Loop-shaping for reset control systems Open
The ever-growing demands on speed and precision from the precision motion industry have pushed control requirements to reach the limitations of linear control theory. Nonlinear controllers like reset provide a viable alternative since they…
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A Green’s function approach to the rapid prediction of thermoacoustic instabilities in combustors Open
The prediction of thermoacoustic instabilities is fundamental for combustion systems such as domestic burners and industrial gas turbine engines. High-amplitude pressure oscillations cause thermal and mechanical stress to the equipment, le…
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Feedback control of combustion instabilities from within limit cycle oscillations using H∞ loop-shaping and the <i>ν</i> -gap metric Open
Combustion instabilities arise owing to a two-way coupling between acoustic waves and unsteady heat release. Oscillation amplitudes successively grow, until nonlinear effects cause saturation into limit cycle oscillations. Feedback control…
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Linear and Non-Linear Stability Analysis of a Constrained Railway Wheelaxle Open
Railway wheel axle experiences the problem of hunting above a critical velocity, which is a kind of self-excited oscillation. This paper investigates the linear and non-linear stability analysis of wheel axle constrained within a fixed bog…
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Describing Function Approach with PID Controller to Reduce Nonlinear Action Open
The nonlinear effect in the control system is so important and it may have a hard or soft effect on the electrical, mechanical, biological, and many other systems. This paper analyzes the describing function (DF) which is the transfer func…
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Limit Cycle Elimination in Inverted Pendulums: Furuta Pendulum and Pendubot Open
This paper presents the design of a linear state feedback controller for the stabilization of two inverted pendulums, namely, Furuta pendulum and pendubot. Such a controller design allows eliminating the limit cycle that appears in the sys…
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A nonlinear controller based on saturation functions with variable parameters to stabilize an AUV Open
This paper deals with a nonlinear controller based on saturation functions with variable parameters for set-point regulation and trajectory tracking control of an Autonomous Underwater Vehicle (AUV). In many cases, saturation functions wit…
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<i>G</i>-equation modelling of thermoacoustic oscillations of partially premixed flames Open
Numerical simulations aid combustor design to avoid and reduce thermoacoustic oscillations. Non-linear heat release rate estimation and its modelling are essential for the prediction of saturation amplitudes of limit cycles. The heat relea…
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Review of general modeling approaches of power converters Open
The modeling approaches of power converters occupy an important position in power electronic systems and have made considerable progress over the past years. Continuous modeling approaches and linearization techniques are reviewed, includi…
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Linearization and Control of Series-Series Compensated Inductive Power Transfer System Based on Extended Describing Function Concept Open
The extended describing function (EDF) is a well-known method for modelling resonant converters due to its high accuracy. However, it requires complex mathematical formulation effort. This paper presents a simplified non-linear mathematica…
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Uncertainty Quantification of Thermoacoustic Instabilities in a Swirled Stabilized Combustor Open
Combustion instabilities can develop in modern gas-turbines as large amplitude pressure oscillations coupled with heat release fluctuations. In extreme cases, they lead to irreversible damage which can destroy the combustor. Prediction and…
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Accounting for Quasi-Static Coupling in Nonlinear Dynamic Reduced-Order Models Open
Engineering structures are often designed using detailed finite element (FE) models. Although these models can capture nonlinear effects, performing nonlinear dynamic analysis using FE models is often prohibitively computationally expensiv…
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Stability Analysis With Considering the Transition Interval for PWM DC-DC Converters Based on Describing Function Method Open
The nonlinearity of the switching process in DC-DC converters can result in the inaccuracy and invalidation of traditional stability criterion based on linear modeling, which is very harmful in practice, especially for the DC-DC converters…
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Nonlinear analytical flame models with amplitude-dependent time-lag distributions Open
In the present work, we formulate a new method to represent a given Flame Describing Function by analytical expressions. The underlying idea is motivated by the observation that different types of perturbations in a burner travel with diff…
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Accurate Loop Gain Modeling of Digitally Controlled Buck Converters Open
For the digitally controlled buck converters, the nonlinearity and time periodicity, caused by the pulsewidth modulator (PWM) and sample and hold, make the accurate frequency-domain analysis intractable. In this article, based on the harmo…
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Analysis of Actuator Rate Limit Effects on First-Order Plus Time-Delay Systems under Fractional-Order Proportional-Integral Control ⁎ ⁎This work was supported by China Scholarship Council (CSC) under Grant (201606090086). Open
Actuator rate limit deteriorates control performance, and may even lead to system instability in precision process control. In this paper, a first-order plus time-delay (FOPTD) system class with actuator rate limit is considered. The descr…
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Wave-shape function analysis -- when cepstrum meets time-frequency analysis Open
We propose to combine cepstrum and nonlinear time-frequency (TF) analysis to study mutiple component oscillatory signals with time-varying frequency and amplitude and with time-varying non-sinusoidal oscillatory pattern. The concept of cep…
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Low-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors Open
This paper analyzes transversal thermoacoustic oscillations in an experimental gas turbine combustor utilizing dynamical system theory. Limit cycle acoustic motions related to the first linearly unstable transversal mode of a given 3D comb…
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Closed-Loop Frequency Analysis of Reset Control Systems Open
This article introduces a closed-loop frequency analysis tool for reset control systems. To begin with sufficient conditions for the existence of the steady-state response for a closed-loop system with a reset element and driven by periodi…
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Frequency analysis of reset systems containing a Clegg integrator: An introduction to higher order sinusoidal input describing functions Open
PID is the most popular controller in the industry. PID controllers are linear, and thus have fundamental limitations, such that certain performance criteria cannot be achieved. To overcome these limitations, nonlinear reset control can be…
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Occasional coupling enhances amplitude death in delay-coupled oscillators Open
This paper aims to study amplitude death in time delay coupled oscillators using the occasional coupling scheme that implies intermittent interaction among the oscillators. An enhancement of amplitude death regions (i.e., an increment of t…
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Precision Calibration of the Duffing Oscillator with Phase Control Open
The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to…