Steady-state Oscillations Research Articles

Dynamic Nonlinear Gradient Observer Based Extremum Seeking Control for Optimum Braking

The application of extremum seeking control (ESC) algorithm to antilock braking systems (ABSs) is attractive for maximizing the longitudinal braking force. Most currently reported results suffer from the drawback of steady-state oscillations around the extremum or the need to have the gradient information. In this article, a new ESC algorithm is proposed for application to ABSs to overcome these two drawbacks. The proposed algorithm is based on a novel dynamic nonlinear gradient observer (DNGO) and a longitudinal braking force estimator. The performance and the ultimate boundedness of the proposed ESC, DNGO, and the force estimator are analyzed. The proposed method is validated by simulation for dry and wet road surfaces and compared with two established results. The method is further validated on an experimental setup in the laboratory for dry and oily surfaces.

Indirect P&O type-2 fuzzy-based adaptive step MPPT for proton exchange membrane fuel cell

The output power of the fuel cell depends on the operating conditions, such as the temperature and membrane water content. Therefore, a robust maximum power point tracking (MPPT) approach is highly required to ensure the operation of the proton exchange membrane fuel cell (PEMFC) at the maximum power point. A new hybrid perturb & observe and type-2 fuzzy-based adaptive step size MPPT for PEMFC system is proposed to enhance the dynamic response and eliminates the oscillations around maximum power point at steady state. The type-2 fuzzy approach has been used to scale the variable step size of conventional perturb & observe algorithm to extract the maximum available power of the PEMFC system. The proposed hybrid controller has been tested and validated using MATLAB software via modeling of the fuel cell power system composed of 7 kW PEMFC powering a resistive load through a DC-DC boost converter. Comparative simulation results prove that our proposed hybrid P&O type-2 fuzzy-based MPPT reduces the response time between 14.62 and 84.72% compared to the P&O type-1 fuzzy-based MPPT. The response time is also reduced between 43.99 and 88.04% compared to the conventional P&O fixed step size MPPT. In addition, the proposed controller decreases the steady-state oscillation to an interval of 66.67% to 70.97% compared to the P&O type-1 fuzzy-based MPPT and an interval of 72.73% to 84.85% compared to the conventional P&O fixed step size MPPT.

Voltage and Current Reference Based MPPT Under Rapidly Changing Irradiance and Load Resistance

This paper formulates a maximum power point tracking (MPPT) technique that accurately tracks the maximum power point of photovoltaic (PV), which undergoes simultaneous or independent sudden changes in load resistance and irradiance. The proposed algorithm is fundamentally divided into three parts; current and voltage perturbation algorithm (IPA/VPA), perturbation step-size reduction algorithm (PSSRA) and a deviation avoidance loop. The use of dual perturbation parameters using IPA and VPA ensures high tracking speed. PSSRA iteratively reduces the perturbation step-size of IPA and VPA and helps in reducing the power oscillations around MPP. Finally, a deviation avoidance loop is developed to detect a change in irradiance by examining the sign of the slope of the two power curves, namely P-V and P-I. The algorithm compares the per unit change in voltage and current of PV, to determine a simultaneous change in both irradiance and load resistance. The proposed algorithm is compared with two recently developed MPPT algorithms. The results show that the proposed technique can track the MPP with high speed and low steady-state oscillations and does not deviate from the MPP tracking path regardless of fast changes in irradiance and load resistance.

A hybrid of bio-inspired algorithm based on Levy flight and particle swarm optimizations for photovoltaic system under partial shading conditions

In this paper, a hybrid of bio-inspired control algorithm to track the maximum power point of photovoltaic (PV) system under partial shading conditions is proposed. Particle swarm optimization (PSO) is a well-known method due to its simplicity and ease of implementation. Levy flight optimization (LFO) is a random walk distribution which is also simple and able to provide fast response. In the proposed algorithm, these two methods are integrated together, noted as a hybrid of Levy flight and particle swarm optimization (LPSO) to extract the global maximum power point (GMPP). The proposed LPSO is evaluated under three conditions: (1) under uniform irradiance (2) under non-uniform irradiance and (3) under step-change of irradiance. A prototype is built to verify the effectiveness of the proposed LPSO. Based on the results obtained, it clearly shows that the hybrid LPSO can track the local and global maximum power point effectively. Both simulation and experimental results show that the proposed LPSO is stable and efficient with zero steady-state oscillation. The efficiency of the proposed LPSO is approximately 99.50% for all tested conditions.

Digital Pulsewidth Modulation (DPWM) Using Direct Digital Synthesis

Wide-bandgap semiconductor power devices are being adopted to increase efficiency and switching frequency for power converters. This requires a demand for higher resolution digital pulsewidth modulation (DPWM) in digitally controlled power converters. This is because, in a digitally controlled dc–dc converter, steady-state limit-cycle oscillations can exist if the resolution of DPWM is less than the ADC resolution. This article proposes a cost-competitive, high-performance, functionally integrated with a small package-sized, a complete direct digital synthesis-based DPWM architecture to achieve a high resolution, linear, monotonic behavior, and extremely fast frequency hopping ability. This article presents a detailed analysis of the new DPWM architecture. Simulation and experimental results are presented to verify the analysis. This article also discusses the various advantages and numerous applications addressed by the proposed method.

Quadratic Constrained Periodic Optimization for Bandlimited Linear Systems Via the Fourier-Based Method

AbstractMotivated by engineering applications, we address bounded steady-state optimal control of linear dynamical systems undergoing steady-state bandlimited periodic oscillations. The optimization can be cast as a minimization problem by expressing the state and the input as finite Fourier series expansions, and using the expansions coefficients as parameters to be optimized. With this parametrization, we address linear quadratic problems involving periodic bandlimited dynamics by using quadratic minimization with parametric time-dependent constraints. We hence investigate the implications of a discretization of linear continuous time constraints and propose an algorithm that provides a feasible suboptimal solution whose cost is arbitrarily close to the optimal cost for the original constrained steady-state problem. Finally, we discuss practical case studies that can be effectively tackled with the proposed framework, including optimal control of DC/AC power converters, and optimal energy harvesting from pulsating mechanical energy sources.

STATIC STRAINING AND LONGITUDINAL OSCILLATIONS OF UNDERGROUND PIPELINE BUILT ON BLOCK FOUNDATION

The article considers the issues of forecasting the strength of underground pipelines, which are operated on seismically active sections of the route, composed of relatively rigid mobile blocks. According to the literature, the problems of the influence of the interaction of base faults on the stress state of the pipeline have not been studied to date. The aim of the work is to develop a model for the analysis of abnormal stresses in the underground pipeline on a damaged basis caused by static or time-harmonious mutual movement of its blocks along the axis of the pipe in the presence of several faults. Boundary value problems for differential equations of static tensile-compression and steady-state longitudinal oscillations of a tubular rod with discontinuous right-hand sides are formulated. Based on the analytical solutions of these problems for the cases of antisymmetric and symmetric displacement of the foundation blocks, the distributions of axial displacement and equivalent stress in the pipe, depending on the distance between faults and the frequency of forced oscillations, are investigated.

Modified Levy Flight Optimization for a Maximum Power Point Tracking Algorithm under Partial Shading

This paper presents a novel modified Levy flight optimization for a photovoltaic PV solar energy system. Conventionally, the Perturb and Observe (P&O) algorithm has been widely deployed in most applications due to its simplicity and ease of implementation. However, P&O suffers from steady-state oscillation and stability, besides its failure in tracking the optimum power under partial shading conditions and fast irradiance changes. Therefore, a modified Levy flight optimization is proposed by incorporating a global search of beta parameters, which can significantly improve the tracking capability in local and global searches compared to the conventional methods. The proposed modified Levy flight optimization is verified with simulations and experiments under uniform, non-uniform, and dynamic conditions. All results prove the advantages of the proposed modified Levy flight optimization in extracting the optimal power with a fast response and high efficiency from the PV arrays.

Область стабилизации нелинейной модели синхронного генератора с ПИДД2-регулятором возбуждения

We take as the research object the well-known system of nonlinear differential and functional equations that describes a synchronous generator. PIDD2-control was carried out through the excitation block. Effective values of the steady state in relative units and the preliminary settings of suboptimal controllers were obtained earlier using a linearized model. Disturbing surges (spikes and slump) in bus voltages were modeled as line impedance changes. The system stabilization was studied at various surges values and controller parameters by means series of numerical experiments; the calculations were carried out by the methods of Runge-Kutta and Dorman-Prince. The main attention was paid to various transient types, both stabilizing and diverging, as well as a configuration of the stability region boundary in the controller parameters of and a surge magnitude; the paper presents the results for the proportional control parameter are as the most informative. We've identified five types of transients and several important features of the model's behavior near the stabilization area boundary. Thus, the nonlinear model turned out to be unstable to small and stable to bigger perturbations in the unstable area of its linearization. The steady-state oscillations at the boundary have a lower amplitude with increasing of an initial perturbation, etc.

Improved Proportional-Integral Coordinated MPPT Controller with Fast Tracking Speed for Grid-Tied PV Systems under Partially Shaded Conditions

When a photovoltaic (PV) system is exposed to physical objects and cloud coverage and connected to bypass diodes, a partial shading condition (PSC) occurs, which causes a global maximum power point (GMPP) and numerous local maximum power points (LMPPs) on the power-voltage (P-V) curve. Unlike conventional MPPT techniques that search for multiple LMPPs on the P-V curve, it is possible to track GMPP straightaway by designing a simple but robust MPPT technique that results in faster tracking speed and low power oscillations. Hence, in this study, an improved proportional-integral (PI) coordinated Maximum Power Point Tracking (MPPT) algorithm is designed to enhance the conversion efficiency of a PV system under PSC with fast-tracking speed and reduced power oscillations. Here, PI controllers are used to mitigating the steady-state errors of output voltage and current of PV system that later on passed through an incremental conductance (INC) algorithm to regulate the duty cycle of a dc–dc boost converter in order to ensure fast MPPT process. The PV system is integrated with the grid through an H-bridge inverter, which is controlled by a synchronous reference frame (SRF) controller. Tracking speed and steady-state oscillations of the proposed MPPT are evaluated in the MATLAB/Simulink environment and validated via a laboratory experimental setup using Agilent solar simulator and dSPACE (DS1104) controller. Results show that the proposed MPPT technique reduces the power fluctuations of PV array significantly and the tracking speed of the proposed method is 13% and 11% faster than the conventional INC and perturb and observe (P&O) methods respectively under PSCs.

Flexible Power Point Tracking for Solar Photovoltaic Systems Using Secant Method

Grid-connected photovoltaic (PV) systems impose challenges like voltage fluctuations, low system inertia, and power quality issues. The need to tackle these challenges led to the introduction of flexible power point tracking (FPPT), where the PV power output is controlled by an energy management system, rather than solely operating the PV systems on the maximum power point. The requirement of fast transient response implies that algorithms such as the one proposed in this article are desirable. The proposed algorithm uses the secant method to achieve significantly improved results in comparison to the existing methods. The method also simplifies the prediction of variations during changes in the environment and power reference, hence, results in reduced oscillation around the set-point and faster convergence. Experimental validation is presented in this article for supporting the claims. The results in terms of accuracy, convergence rate, steady-state oscillations, and cumulative error are bench-marked against one of the most recent FPPT methods.

Extremum seeking control with attenuated steady-state oscillations

We propose two perturbation-based extremum seeking control (ESC) schemes for general single input single output nonlinear dynamical systems, having structures similar to that of the classical ESC scheme. We propose novel adaptation laws for the excitation signal amplitudes in each scheme that drive the amplitudes to zero. The rates of decay for both the laws are governed by the gradient measures of the unknown reference-to-output equilibrium map We show that the proposed ESC schemes achieve practical asymptotic convergence to the extremum with a proper tuning of the parameters in the proposed schemes. As the extremum is reached, and the magnitudes of the gradient measures become small, the excitation signal amplitudes converge to zero. Thus, the proposed schemes ensure that the excitation signal is driven to zero as the system output converges to a neighborhood of the extremum and the steady-state oscillations about the extremum, typically observed for the classical ESC schemes, are attenuated. Simulation examples are included to illustrate the effectiveness of the proposed schemes.

Optimization Methods of MPPT Parameters for PV Systems: Review, Classification, and Comparison

To obtain efficient photovoltaic (PV) systems, optimum maximum power point tracking (MPPT) algorithms are inevitable. The efficiency of MPPT algorithms depends on two MPPT parameters, i. e., perturbation amplitude and perturbation period. The optimization of MPPT algorithms affect both the tracking speed and steady-state oscillation. In this paper, optimization methods of MPPT parameters are reviewed and classified into fixed and variable methods. The fixed MPPT parameters are constant during MPPT performance, and a trade-off should be made between the tracking speed and steady-state oscillation. However, the variable MPPT parameters will be changed to improve both the tracking speed and the steady-state oscillations. Moreover, some of them are simulated, compared, and discussed to evaluate the real contributions of the optimization methods to the MPPT efficiency. Furthermore, significant features of the optimization methods, i.e., noise immunity, robustness, and computation effort, are investigated.

An Effective Salp Swarm Based MPPT for Photovoltaic Systems Under Dynamic and Partial Shading Conditions

This study proposes a duty cycle-based direct search method that capitalizes on a bioinspired optimization algorithm known as the salp swarm algorithm (SSA). The goal is to improve the tracking capability of the maximum power point (MPP) controller for optimum power extraction from a photovoltaic system under dynamic environmental conditions. The performance of the proposed SSA is tested under a transition between uniform irradiances and a transition between partial shading (PS) conditions with a focus on convergence speed, fast and accurate tracking, reduce high initial exploration oscillation, and low steady-state oscillation at MPP. Simulation results demonstrate the superiority of the proposed SSA algorithm in terms of tracking performance. The performance of the SSA method is better than the conventional (hill-climbing) and among other popular metaheuristic methods. Further validation of the SSA performance is conducted via experimental studies involving a DC-DC buck-boost converter driven by TMS320F28335 DSP on the Texas Instruments Experimenter Kit platform. Hardware results show that the proposed SSA method aligns with the simulation in terms of fast-tracking, convergence speed, and satisfactory accuracy under PS and dynamic conditions. The proposed SSA method tracks maximum power with high efficiency through its superficial structures and concepts, as well as its easy implementation. Moreover, the SSA maintains a steady-state oscillation at a minimum level to improve the overall energy yield. It thus compensates for the shortcomings of other existing methods.

Unity Proportional Gain Resonant and Gain Scheduled Proportional (PR-P) Controller-Based Variable Perturbation Size Real-Time Adaptive Perturb and Observe (P&O) MPPT Algorithm for PV Systems

In this paper, Proportional Gain Resonant and Gain Scheduled Proportional (PR-P) Controller based variable perturbation size real-time adaptive perturb and observe (P&O) maximum power point tracking (MPPT) algorithm is presented. The proposed control scheme resolved the drawbacks of conventional P&O MPPT method associated with the use of constant perturbation size that leads to poor transient response and high continuous steady-state oscillations. The prime objective of using the PR-P controller is to utilize inherited properties of the signal produced by the controller’s resonant path and integrate it to update best estimated perturbation that represents the working principle of extremum seeking control (ESC) to use in P&O algorithm that characterizes the overall system learning-based real time adaptive (RTA). Additionally, utilization of internal dynamics of the PR-P controller overcome the challenges namely, complexity, computational burden, implantation cost and slow tracking performance in association with commonly used soft computing intelligent systems and adaptive control strategies. The proposed control scheme is verified using MATLAB/Simulink by applying comparative analysis with PI controlled conventional P&O MPPT algorithm. Moreover, performance of the proposed control scheme is validated experimentally with the implementation of MATLAB/Simulink/Stateflow on dSPACE Real-time-interface (RTI) 1007 processor board, DS2004 A/D and CP4002 Digital I/O boards. The experimental results and analysis reveal that the proposed control strategy enhanced the tracking speed five times with reduced steady-state oscillations around maximum power point (MPP) and more than 99% energy extracting efficiency.

Mode Analysis Theory of Small Disturbance Operation Process of Power System

The power system currently has the problem that transient steady-state low-frequency oscillations after the power system suffers from small disturbances will affect the normal operation of the power grid. This paper proposes a model analysis of engineering mathematics for the power system’s small-disturbance transient low-frequency oscillations. First, this paper constructs the mathematical model and simplified model of the power system. Next, this paper calculates the initial steady state of the model and builds a linearized model. Then small disturbances are added to the model in order to simulate the transient steady-state process of a single-machine infinite-bus system under real conditions. Finally, the power system stabilizer (Power system stabilizer PSS) is designed through model analysis. Compared the transient steady-state process the PSS isn’t installed and the PSS is installed in the singlemachine infinite power system, we can get experimental results, which show that the power system can obtain a new steady state after receiving small disturbances and eliminating small disturbances in time. At the same time, the installation of PSS can effectively increase the stability of the power system and the tolerance for the existence of interference.

A MODIFIED PERTURB AND OBSERVE TECHNIQUE FOR MPPT OF INTGRATED PV SYSTEM USING DC-DC BOOST CONVERTER

A photovoltaic system (PV) connected to the utility grid through three-phase voltage source inverter (VSI) has been controlled in this paper for achieving maximum power point tracking (MPPT). In this paper, a modified perturb and observe (P&O) technique has been proposed for achieving MPPT of PV system using DC-DC boost converter. The proposed algorithm is used to obtain better capture of energy with minimum steady state oscillations. In this technique, the duty cycle is determined using a variable step-size to achieve MPPT accurately. A digital simulation using Matlab/Simulink package is carried out to demonstrate the advantage of the proposed system performance compared to the conventional technique under varying irradiation and temperature levels. The obtained results investigate that the modified algorithm can track the maximum power point (MPP) accurately besides, it extracts the additional power during the variation in weather conditions as compared to the conventional P&O algorithm.

Reflection and refraction of a plane sound wave in an elastic plate with an inhomogeneous anisotropic coating

In paper the problem of the reflection and refraction of a plane harmonic sound wave by a homogeneous isotropic elastic plate with an continuously inhomogeneous anisotropic elastic coating is considered. It is assumed that the plate is adjoin to ideal fluids. The propagation of small perturbations in a ideal fluid in the case of steady state oscillations is described by Helmholtz’s equation. The propagation of elastic waves in a uniform isotropic elastic plate is described by scalar and vector Helmholtz’s equations for longitudinal and transverse waves. Oscillations of an inhomogeneous anisotropic elastic coating are described by general motion equations of the continuous medium. The boundary-value problem for the system of ordinary second order differential equations is constructed for determination of the displacement field in inhomogeneous anisotropic coating. An analytical description of the reflected and transmitted through the plate acoustic fields is obtained. Particular cases when the material of an inhomogeneous coating is transversely isotropic and isotropic are considered. The results of numerical calculations of dependence of reflection coefficient of a homogeneous isotropic plate with a transversely isotropic coating from the incidence angle of plane wave are presented.

Manometric Tubular Springs Oscillatory Processes Modeling with Consideration of its Viscoelastic Properties

This article is dedicated to the operation and management of systems of machine-building and aviation enterprises, systems of production, transport, storage of oil and gas, issues of control of technological processes are of great importance. Control of technological processes is carried out by monitoring the pressure and other parameters. These measuring instruments must have high reliability and the necessary accuracy. In this connection, there is a sharp increase in interest in determining the dynamic parameters of the elements of measuring devices. The main elements of such devices are monomeric tubular springs (Bourdon tubes). The paper considers the natural and forced steady-state oscillations of a thin curved rod interacting with a liquid. Based on the principle of possible displacements, a resolving system of partial differential equations and the corresponding boundary conditions are obtained. The problem is solved numerically by the Godunov orthogonal run method, and the Muller method and the Eigen frequencies found are compared with the experimental results. As a result, for a given axial perturbation, it was possible to select such an effect, in the orthogonal direction, that the amplitude of the longitudinal vibrations of the rod at the first resonance decreased by 20 times. The described vibration damping effect is due to the interrelation of transverse and longitudinal vibrations and is fundamentally impossible in the case of a straight rod.

Time-Delayed Nonlinear Integral Resonant Controller to Eliminate the Nonlinear Oscillations of a Parametrically Excited System

In this work, a nonlinear integral resonant controller is utilized for the first time to suppress the principal parametric excitation of a nonlinear dynamical system. The whole system is modeled as a second-order nonlinear differential equation (i.e., main system) coupled to a nonlinear first-order differential equation (i.e., controller). The control loop time-delays are included in the studied model. The multiple scales homotopy approach is employed to obtain an approximate solution for the proposed time-delayed dynamical system. The nonlinear algebraic equation that governs the steady-state oscillation amplitude has been extracted. The effects of the time-delays, control gain, and feedback gains on the performance of the suggested controller have been investigated. The obtained results indicated that the controller performance depends on the product of the control and feedback signal gains as well as the sum of the time-delays in the control loop. Accordingly, two simple objective functions have been derived to design the optimum values of the loop-delays, control gain, and feedback gains in such a way that enhances the efficiency of the proposed controller. The analytical and numerical simulations illustrated that the proposed controller could eliminate the system vibrations effectively at specific values of the control and feedback signal gains. In addition, the selection method of the loop-delays that either enhances the control performance or destabilizes the system motion has been explained in detail.