Showing papers on "Transfer function published in 2021"

Impedance Circuit Model of Grid-Forming Inverter: Visualizing Control Algorithms as Circuit Elements

Abstract: The impedance model is widely used for analyzing power converters. However, the output impedance is an external representation of a converter system, i.e., it compresses the entire dynamics into a single transfer function with internal details of the interaction between states hidden. As a result, there are no programmatic routines to link each control parameter to the system dynamic modes and to show the interactions among them, which makes the designers rely on their experience and heuristic to interpret the impedance model and its implications. To overcome these obstacles, this article proposes a new modeling tool named as impedance circuit model , visualizing the closed-loop power converter as an impedance circuit with discrete circuit elements rather than an all-in-one impedance transfer function. It can reveal the virtual impedance essence of all control parameters at different impedance locations and/or within different frequency bandwidths, and show their interactions and coupling effects. A grid-forming voltage source inverter is investigated as an example, with considering its voltage controller, current controller, control delay, voltage/current $dq$ -frame cross-decoupling terms, output-voltage/current feedforward control, droop controllers, and three typical virtual impedances. The proposed modeling tool is validated by frequency-domain spectrum measurement and time-domain step response in simulations and experiments.

A Reduced-Order Electrochemical Model for All-Solid-State Batteries

Abstract: All-solid-state batteries (ASSBs) have been considered as the next generation of lithium-ion batteries. Physics-based models have the advantage of providing internal electrochemical information. To promote physics-based models in real-time applications, in this study, a series of model reduction methods are applied to obtain a reduced-order model (ROM) for ASSBs. First, analytical solutions of the partial differential equations (PDEs) are derived by the Laplace transform. Then, the Pade approximation method is used to convert the transcendental transfer functions into lower order fractional transfer functions. Next, the concentration distributions in electrodes and electrolytes are approximated by parabolic and cubic functions, respectively. Due to the fast calculation of concentration distributions in real time, the equilibrium potential, overpotentials, and battery voltage can now be directly calculated. Compared with the original PDE-based model, the voltage errors of the proposed ROM are less than 2.6 mV. Compared with the voltage response of experimental data, a good agreement can be observed for the ROM under three large C-rates discharging conditions. The calculation time of ROM per step is within 0.2 ms, which means that it can be integrated into a battery management system. The proposed ROM achieves excellent performance and a better tradeoff between model fidelity and computational complexity.

Fast and Accurate Optical Fiber Channel Modeling Using Generative Adversarial Network

Abstract: In this work, a new data-driven fiber channel modeling method, generative adversarial network (GAN) is investigated to learn the distribution of fiber channel transfer function. Our investigation focuses on joint channel effects of attenuation, chromic dispersion, self-phase modulation (SPM), and amplified spontaneous emission (ASE) noise. To achieve the success of GAN for channel modeling, we modify the loss function, design the condition vector of input, and address the mode collapse for the long-haul transmission. The effective architecture, parameters, and training skills of GAN are also displayed in the article. The results show that the proposed method can learn the accurate transfer function of the fiber channel. The transmission distance of modeling can be up to 1000 km and can be extended to arbitrary distance theoretically. Moreover, GAN shows robust generalization abilities under different optical launch powers, modulation formats, and input signal distributions. Comparing the complexity of GAN with the split-step Fourier method (SSFM), the total multiplication number is only 2% of SSFM and the running time is less than 0.1 seconds for 1000-km transmission, versus 400 seconds using the SSFM under the same hardware and software conditions, which highlights the remarkable reduction in complexity of the fiber channel modeling.

Virtual Damping Control Design of Three-Phase Grid-Tied PV Inverters for Passivity Enhancement

Abstract: The interconnection stability of a grid-tied inverter system can be investigated not only based on classical control theory, e.g., Nyquist criterion, but also from the energy dissipation point of view. If a critical resonance occurs within the regions, where the system equivalent impedance behaves passively, i.e., has only nonnegative real parts, the system stability can be guaranteed. Thus, it is preferred to design systems with passive regions over a wide-frequency range. This article investigates passivity properties influenced by different control loops and operating points in the $dq$ frame, which facilitates the stability assessment in the frequency domain. Based on this, a virtual damping control method is proposed to improve the stability by enhancing the system passivity. By implementing a damping transfer function in the $d$ - and $q$ -axis individually, nonpassive regions can be accordingly reduced over a specific frequency range. Asymmetrical designs can be considered in the $d$ - and $q$ -axis according to corresponding passivity properties, which is impossible to be realized through symmetric physical filter components. The design procedure is elaborated based on a 2 MW inverter system, which is based on a combined graphical and analytical approach. Verifications are conducted based on a 1 kW prototype including both simulations and experimental results. The method applies to all types of grid-tied inverters with multiple control loops. This article is accompanied by a video demonstrating the validations.

Power law filters: A new class of fractional-order filters without a fractional-order Laplacian operator

Abstract: A new category of fractional-order filters, realized without employing a fractional-order Laplacian operator is introduced in this work. This can be achieved through the utilization of an efficient curve fitting method which approximates the frequency-domain behavior of the filter and transposes the fractional-order transfer function into the integer-order domain. Thus, the procedure results in a rational integer-order transfer function and its implementation is possible using conventional integer-order realization techniques. Therefore, there is no need for fractional-order elements to realize this class of filters. Design examples of this new kind of filters are presented with the derived simulation and experimental results confirming their correct performance.

Parameter Design Oriented Analysis of the Current Control Stability of the Weak-Grid-Tied VSC

Abstract: This paper studies the dynamic behaviors of weak-grid-tied VSCs with simplified transfer functions, which provides an accurate stability analysis and useful indications for tuning system parameters. A reduced-order multi-input multi-output (MIMO) transfer function that contains four single-input single-output (SISO) transfer functions for the weak-grid-tied VSC is first presented. It is found that the four SISO transfer functions share the same equivalent open-loop transfer function, i.e., the same stability conclusion. The Bode plots of the equivalent open-loop transfer function show that the inner current loop behaves as a band-pass filter whose maximum gain is approximately at the frequency of the PLL's bandwidth. By stability criterion, the harmonic amplification and instability occur when its maximum gain exceeds 0 dB caused by high PLL's bandwidth, large grid impedance or high active power. It is also found that the target system is less stable when it works as an inverter than as a rectifier, due to the risk of the local positive feedback in the inverter mode. An effective criterion is further proposed to guide the selection of a proper PLL's bandwidth to ensure the stability of the VSC system. Simulation results validate the correctness of the analysis and the efficacy of the criterion.

EFTL: Complex Convolutional Networks With Electromagnetic Feature Transfer Learning for SAR Target Recognition

Abstract: Considering that synthetic aperture radar (SAR) images obtained directly after signal processing are in the form of complex matrices, we propose a complex convolutional network for SAR target recognition. In this article, we give a brief introduction to complex convolutional networks and compare them with the real counterpart. A complex activation function is applied to analyze the influence of phase information in complex neural networks. Inspired by the theory of network visualization, a special kind of transfer learning based on the electromagnetic property from the attributed scattering center model is applied in our networks to modulate the first convolutional layer. The experiment shows a better performance in terms of classification accuracy compared to random weight initialization.

The mathematical model and a block diagram of a synchronous motor compressor unit with a system of automatic control of the excitation

Abstract: The general requirements for the automatic excitation control system of synchronous motors of a compressor unit are shown, taking into account its operating modes. A mathematical model is presented, a block diagram of the excitation circuits of a synchronous motor of a compressor unit and an exciter, which characterizes the feedback of the internal properties of this part of the system in dynamics. A block diagram of a closed-loop automatic excitation control system is obtained, taking into account the elasticity of the mechanical part and a hard blow in the compressor gas pipeline. The obtained structural diagrams make it possible to determine the transfer functions of the considered system in terms of control and disturbing influences, the characteristic equation, as well as the dependencies of various frequency characteristics, which make it possible to investigate the dynamic indicators (stability, control quality, etc.) of the system.

Double Exponent Fractional-Order Filters: Approximation Methods and Realization

Abstract: The main goal of this work is to exploit different tools in order to approximate a general double exponent fractional-order transfer function Through the appropriate selection of the two fractional orders of this function, different types of filters can be derived The investigated approximation tools are either curve fitting based tools or the Pade approximation tool, and the derived approximated transfer functions in all cases have the form of rational integer-order polynomials, which can be easily realized electronically

A Novel Deconvolution Cascaded Variational Mode Decomposition for Weak Bearing Fault Detection With Unknown Signal Transmission Path

Abstract: Rolling element bearing is one of the most widely used component in mechanical equipment, whose reliability requirements are also increasing. In complex working conditions, the measured signals often contain so strong noisy interferences that the weak bearing fault features are difficult to be detected. Variational mode decomposition (VMD) is a widely used method for bearing fault features extraction. However, it also encountered some problems when dealing with weak fault signals, especially the number determination of decomposition modes, the influence of strong noise and unknown transmission path. In order to solve these problems, a novel deconvolution cascaded variational mode decomposition is proposed for weak bearing fault detection in this article. Considering the influence of transmission path and strong noise, a monitored signal is enhanced by compensation transfer function and optimized resonance component to reduce the impact of noise. Firstly, to compensate the transfer function of a complex unknown transmission path, a deconvolution method with multi-point kurtosis is used, which adjusts the filter adaptively to enhance the periodic impact component in the signal. Then, to determine the decomposition modes number and furtherly remove interferences noise, a cascaded variational mode decomposition is proposed for multi-layer noise suppression. Subsequently, a standardized square envelope spectrum is employed to detect fault characteristics of the resonant mode. Experiments verified the effectiveness of the proposed method, and comparisons show that the envelope factor is increased from 1.0762 to 34.8781, which mean that the fault signal is enhanced by the proposed method.

Photovoltaic System Power Reserve Determination Using Parabolic Approximation of Frequency Response

Abstract: The most commonly used method for including photovoltaic system in the control of system frequency is to operate a PV power plant at reduced power while maintaining a specific amount of available power reserve. Such operating regime, often referred to as de-loaded, can cause additional costs and, consequently, determining a required power reduction becomes vitally important. This paper introduces a method for determining the required minimum de-loaded reserve of a photovoltaic system. To achieve the desired result a parabolic approximation of the system frequency response is developed to derive an explicit function of the frequency nadir. Taking this approximation into consideration, a method for determining the required minimum de-loaded margin was developed and tested in a case-study which observed a small power system consisting of several power plants. To demonstrate the accuracy of the proposed parabolic approximation, the calculated approximate values of the frequency nadir were compared to the values of the frequency nadir obtained from the frequency response simulations performed on the power system model developed in MATLAB/Simulink.

Robustness Improvement of the Fractional-Order LADRC Scheme for Integer High-Order System

Abstract: This article deals with a novel fractional-order active disturbance rejection control (FADRC) scheme to handle a general integer-order system The proposed control structure enhances the robustness and performance of the classical active disturbance rejection control, especially for the open-loop gain variation Based on the Bode's ideal transfer function, an analytical design of a state-feedback control is proposed The integer-order model of the system to be controlled is first transformed to a noninteger-order one, where the introduced fractional order is a design parameter, which imposes the overshoot of the closed-loop step response In addition, because the model of the system is transformed to a cascade of integer- and fractional-order integrator (the model is noncommensurate), a commensurate fractional-order extended state observer is proposed to estimate the generalized disturbance To improve the robustness of the proposed FADRC scheme, an analytical design method of a noncommensurate state-feedback control is proposed The proposed design method is based on the Bode's ideal transfer function cascaded with an integer-order filter The proposed FADRC scheme is applied for a pendulum–cart test bed, and the effectiveness and robustness of the proposed control are examined by experiments

Large- and Small-Signal Average-Value Modeling of Dual-Active-Bridge DC–DC Converter With Triple-Phase-Shift Control

Abstract: This article presents a novel reduced order average model for dual-active-bridge converter which can be applied to all modulation methods, such as single-phase-shift modulation, dual-phase-shift modulation, extended-phase-shift modulation and triple-phase-shift modulation. This model considers conduction, inductance, and transformer power losses. Furthermore, the input–output filters are suitable for system performance analysis. Based on the large-signal average model, the small-signal model and the output transfer function are derived. The detailed model for predicting the large-signal transient is established and the small signal analysis in frequency domain is carried out. This model can accurately predict the steady-state and transient-state response of the system. The experimental results agreed well with the simulation results which proved the accuracy and correctness of the model.

Multidimensional Object Management

Abstract: The paper deals with the management of multi-connected objects with multiple inputs and outputs, the so-called MIMO (multi-input multi-output) systems. Special attention is paid to the adaptation of SISO (single-input single-output) technologies to control MIMO systems. For this, it is proposed to carry out dynamic decoupling of control channels using a pre-switched on cross-link compensator. For the technical implementation of the cross-link compensator, a method is proposed for approximating its transfer functions, which makes it possible to significantly reduce their order. All conclusions are confirmed by the results of mathematical modeling of output processes in closed and open control systems.

Synthesis of fractional order robust controller based on Bode's ideas.

Abstract: The basic Bode’s ideal transfer function (BITF) based controller may not guarantee sufficient disturbance rejection for a class of plants with a cascaded integrator. In this paper, an improved BITF based control method is proposed to enhance the disturbance rejection performance for this class of control systems. A fractional order proportional–integral controller and a Bode’s ideal cut-off filter are introduced into the BITF based control strategy, improving the open-loop magnitude characteristics of the control system in the low and high frequency ranges. Therefore, the disturbance rejection performance of the control system can be improved, with small impact on the system’s stability. The improved BITF based control method is applied to the speed control problem of a class of permanent magnet synchronous motor servo systems. The robustness and dynamic response performances of the improved BITF based control system are verified by simulation and experiments. Performance comparisons are performed between the system using the improved BITF based control method and those using some existing control methods. Simulation and experimental results both show that the improved BITF based controller can enhance the step response performance and robustness of the PMSM servo system simultaneously and make the system achieve better disturbance rejection performance than the systems using some existing methods.

Analog Modeling of Fractional-Order Elements: A Classical Circuit Theory Approach

Abstract: In this paper a comprehensive procedure for the analog modeling of Fractional-Order Elements (FOEs) is presented. Unlike most already proposed techniques, a standard approach from classical circuit theory is applied. It includes the realization of a system function by a mathematical approximation of the desired phase response, and the synthesis procedure for the realization of basic fractional-order (FO) one-port models as passive RC Cauer- and Foster-form canonical circuits. Based on the presented one-ports, simple realizations of two-port differentiator and integrator models are derived. Beside the description of the design procedure, illustrative examples, circuit diagrams, simulation results and practical realizations are presented.

Implementation of Cross-Coupling Terms in Proportional-Resonant Current Control Schemes for Improving Current Tracking Performance

Abstract: The proportional-integrator (PI) controller in the synchronous reference frame (dq-frame) and the proportional-resonant (PR) controller in the stationary reference frame (αβ-frame) are two typical linear current control schemes for three-phase voltage source converters. It is generally believed that the plant model is mathematically uncoupled in αβ-frame. Hence, the decoupling control required to attenuate the axis cross-coupling effect in dq-frame is regarded as not necessary in αβ-frame. However, detailed analysis with complex coefficient transfer functions reveals differences in the control performance between the fully decoupled PI control scheme in dq-frame and the PR control scheme in αβ-frame. When regulating sinusoidal currents in αβ-frame, the α-axis and β-axis current references are strongly correlated with each other, which implies a cross-coupling effect equivalent to that of dq-frame. In analogy to the dq-frame decoupling control, cross-coupling terms can be employed together with the conventional PR control scheme. It can bring the benefit of improving the transient response of current tracking and reducing the sensitivity of the resonant controller to frequency variation, especially for low-switching-frequency applications with limited current control bandwidth. Furthermore, the cross-coupling terms based on reference current feed-forward are proposed to improve the performance of both positive- and negative-sequence current control. Experimental results are shown to validate the analysis and the performance of the proposed control scheme.

An Analytical Approach of Discrete-Time Modeling of Fixed and Variable Frequency Digital Modulation

Abstract: This paper proposes an analytical approach of discrete-time (DT) large-signal and small-signal modeling of digitally controlled DC-DC converters operated under different fixed-frequency and variable-frequency modulation techniques using uniform and event-based sampling. The proposed framework (i) provides a mathematical basis for existing approximate DT small-signal modeling and (ii) further improves accuracy, (iii) allows natural extensions to a wider class of fixed and variable frequency digital modulators, sampling techniques and converter topologies, and finally provides (iv) DT large-signal models for nonlinear analysis and high performance digital controller design. Boost converter design cases studies are considered, and the usefulness of variable frequency modulation is demonstrated using simulation and experimental results over its fixed-frequency counterpart. The proposed approach provides a basis to develop, analyze, and design of future high performance digital control.

On Bilinear Time-Domain Identification and Reduction in the Loewner Framework

Abstract: The Loewner framework (LF) in combination with Volterra series (VS) offers a non-intrusive approximation method that is capable of identifying bilinear models from time-domain measurements. This method uses harmonic inputs which establish a natural way for data acquisition. For the general class of nonlinear problems with VS representation, the growing exponential approach allows the derivation of the generalized kernels, namely, symmetric generalized frequency response functions (GFRFs). In addition, the homogeneity of the Volterra operator determines the accuracy in terms of how many kernels are considered. For the weakly nonlinear setup, only a few kernels are needed to obtain a good approximation. In this direction, the proposed adaptive scheme is able to improve the estimations of the computationally nonzero kernels. The Fourier transform associates these measurements with the derived GFRFs and the LF makes the connection with system theory. In the linear case, the LF associates the so-called S-parameters with the linear transfer function by interpolating in the frequency domain. The goal of the proposed method is to extend identification to the case of bilinear systems from time-domain measurements and to approximate other general nonlinear systems (by means of the Carleman bilinearizarion scheme). By identifying the linear contribution with the LF, a considerable reduction is achieved by means of the SVD. The fitted linear system has the same McMillan degree as the original linear system. Then, the performance of the linear model is improved by augmenting a special nonlinear structure. In a nutshell, we learn reduced-dimension bilinear models directly from a potentially large-scale system that is simulated in the time domain. This is done by fitting first a linear model, and afterward, by fitting the corresponding bilinear operator.

On error estimation for reduced-order modeling of linear non-parametric and parametric systems

Abstract: Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Moreover, we propose several variants of the error estimator, and compare those variants with the existing ones both theoretically and numerically. It is shown that some of the proposed error estimators perform better than or equally well as the existing ones. All the error estimators considered can be easily extended to estimate the output error of reduced-order modeling for steady linear parametric systems.

Best Linear Time-Varying Approximation of a General Class of Nonlinear Time-Varying Systems

Abstract: This article presents a method for estimating a linear time-varying approximation of a general class of nonlinear time-varying (NLTV) systems. It starts from noisy measurements of the response of the NLTV system to a special class of periodic excitation signals. These measurements are subject to measurement noise, process noise, and a trend. The proposed method is a two-step procedure. First, the disturbing noise variance is quantified. Next, using this knowledge, the linear time-varying dynamics are estimated together with the NLTV distortions. The latter are split into even and odd contributions. As a result, the signal-to-nonlinear-distortion ratio is quantified. It allows one to decide whether or not a linear approximation is justifiable for the application at hand. The two-step algorithm is fully automatic in the sense that the user only has to choose upper bounds on the number of basis functions used for modeling the response signal. The obtained linear time-varying approximation is the best in the sense that the difference between the actual nonlinear response and the response predicted by the linear approximation is uncorrelated with the input. Therefore, it is called the best linear time-varying approximation (BLTVA). Finally, the theory is validated on a simulation example and illustrated on two measurement examples: the crystallographic pitting corrosion of aluminum and copper electrorefining.

Rapid Yield Estimation of Microwave Passive Components Using Model-Order Reduction Based Neuro-Transfer Function Models

Abstract: In this letter, we propose a novel technique for rapid and accurate yield estimation of microwave passive components using model-order reduction (MOR)-based neuro-transfer function (neuro-TF) models. In the proposed technique, the frequency responses of microwave components are represented by transfer functions in the pole-zero-gain format. The poles, zeros, and gain in the transfer functions are computed by the MOR technique. Neural networks are trained to capture the dynamic changes of the poles/zeros/gain as the statistical/geometrical variables change. A refinement training process is designed to further align the outputs of the neuro-TF model. Once developed, the MOR-based neuro-TF model can provide rapid and accurate prediction of electromagnetic (EM) behavior of microwave passive components, thereby accelerating EM-based yield estimation. To achieve similar yield estimation accuracy, the proposed technique requires a shorter CPU time than existing yield estimation methods. The advantages of the proposed technique are illustrated by two microwave examples.

Pseudo-Differential (2 + α)-Order Butterworth Frequency Filter

Abstract: This paper describes the design of analog pseudo-differential fractional frequency filter with the order of $(2+\alpha)$ , where $0 . The filter operates in a mixed-transadmittance mode (voltage input, current output) and provides a low-pass frequency response according to Butterworth approximation. General formulas to determine the required transfer function coefficients for desired value of fractional order $\alpha $ are also introduced. The designed filter provides the beneficial features of fully-differential solutions but with a less complex circuit topology. It is canonical, i.e. it employs a minimum number of passive elements, whereas all are grounded, and current conveyors as active elements. The proposed structure offers high input impedance, high output impedance, and high common-mode rejection ratio. By simple modification, voltage response can also be obtained. The performance of the proposed frequency filter is verified both by simulations and experimental measurements proving the validity of theory and the advantageous features of the filter.

Order-of-magnitude differences in computational performance of analog Ising machines induced by the choice of nonlinearity

Abstract: Ising machines based on nonlinear analog systems are a promising method to accelerate computation of NP-hard optimization problems. Yet, their analog nature is also causing amplitude inhomogeneity which can deteriorate the ability to find optimal solutions. Here, we investigate how the system’s nonlinear transfer function can mitigate amplitude inhomogeneity and improve computational performance. By simulating Ising machines with polynomial, periodic, sigmoid and clipped transfer functions and benchmarking them with MaxCut optimization problems, we find the choice of transfer function to have a significant influence on the calculation time and solution quality. For periodic, sigmoid and clipped transfer functions, we report order-of-magnitude improvements in the time-to-solution compared to conventional polynomial models, which we link to the suppression of amplitude inhomogeneity induced by saturation of the transfer function. This provides insights into the suitability of nonlinear systems for building Ising machines and presents an efficient way for overcoming performance limitations. Analog Ising machines are promising fast computing schemes for some difficult optimization problems, yet their analog nature is known to cause errors and inhibit computational performance. Here, the authors investigate how the choice of nonlinear transfer functions partly suppresses errors caused by analog amplitude inhomogeneity, which leads to order-of-magnitude differences in the computation time.

Extending the Model-Based Controller Design to Higher-Order Plant Models and Measurement Noise

Abstract: The article extends a model-based controller design to higher-order systems, focusing on the speed and shapes of the closed loop responses, including the noise attenuation. It shows that, to obtain simple but reliable results, it is necessary to pay attention to the initial process identification and modelling and also to modify the target closed-loop transfer functions, which must remain causal. To attenuate high initial control signal peaks, appropriate pre-filters are introduced. In order to work with as few parameters as possible, all higher-order transfer functions (process models, target closed loops, pre-filters and noise-attenuation filters) are selected in the form of binomial filters with multiple time constants. Consequently, the so-called “half-rule”, used to reduce too complex process transfer functions, has been modified accordingly. Because derived controllers can lead to different transient dynamics depending on the context of use, the article recalls the need to introduce dynamic classes of control to clarify the mission of individual types of controllers. Consequently, also the performance evaluation using the total variation (TV) criterion had to be refined. Indeed, in its original version, TV is not suitable to distinguish between reasonable and excessive control effort due to improper tuning and noise. The modified TVs allow evaluating higher order systems with multiple changes in direction of their control signal increase without contributing to the excessive control increments. The advantages of the proposed modifications, compared to the traditional approaches, are made clear through simulation examples.