Nonlinear Circuit Model Research Articles

Sampling the user controls in neural modeling of audio devices

This work studies neural modeling of nonlinear parametric audio circuits, focusing on how the diversity of settings of the target device user controls seen during training affects network generalization. To study the problem, a large corpus of training datasets is synthetically generated using SPICE simulations of two distinct devices, an analog equalizer and an analog distortion pedal. A proven recurrent neural network architecture is trained using each dataset. The difference in the datasets is in the sampling resolution of the device user controls and in their overall size. Based on objective and subjective evaluation of the trained models, a sampling resolution of five for the device parameters is found to be sufficient to capture the behavior of the target systems for the types of devices considered during the study. This result is desirable, since a dense sampling grid can be impractical to realize in the general case when no automated way of setting the device parameters is available, while collecting large amounts of data using a sparse grid only incurs small additional costs. Thus, the result provides guidance for efficient collection of training data for neural modeling of other similar audio devices.

A behavioral nonlinear modeling implementation for MEMS capacitive microphones

We are highlighting the behavioral nonlinear system-level modeling approach for MEMS capacitive microphones. The combination of finite element modeling and large signal nonlinear circuit modeling provides a strong capability to predict electroacoustical performance for capacitive transductions. Circuit simulation tools such as Cadence Virtuoso have emerged as powerful aids in designing behavioral models in both linear and nonlinear regimes. Typical small signal lumped element models fail to capture the MEMS behavior which changes over pressure and electrical bias conditions. The models described herein capture diaphragm displacement and capacitance change over large pressure ranges for a simply supported circular plate. This can be coupled with the electrostatic force, due to the applied bias voltage, and converted back to pressure, thereby realizing a feedback loop in the circuit model. The nonlinear model capability is extended to predict capacitance-bias behavior and estimate pull-in of the MEMS device. The microphone sensitivity, signal-to-noise ratio, and harmonic distortions are accurately predicted using the nonlinear large signal model when compared to measured microphone data.

Adaptive Models for Improved Battery Charging Systems / Adaptivni modeli za poboljšane sisteme punjenja baterija

During its operation, sometimes it is a needed to swiftly replenish the battery from a partially depleted state, while strictly adhering to its technological limitations such as the battery terminal voltage and rated continuous charging current. To achieve this goal, this contribution outlines the dynamic battery recharging system, utilizing feedback provided by the nonlinear estimator of the battery state-of-charge (SoC) or SoC-related open-circuit-voltage (OCV). In the former case, the estimator is realized as an extended Kalman filter (EKF), while in the latter case it is implemented using the methodology of a System Reference Adaptive Model (SRAM), whose design is based on the Lyapunov stability theory. Thus-obtained innovative adaptive battery chargers are compared against the conventional constant-current/constant-voltage (CCCV) charging system, which relies solely on battery voltage feedback. A comprehensive comparative analysis is conducted through extensive simulations utilizing the nonlinear equivalent circuit model of the lithium titanate battery (LTO) cell.

Shifted Legendre method for solutions of Riccati type functional differential equations and application of RL circuit model

AbstractIn order to solve the Riccati type functional differential equations under mixed condition, this research suggests a collocation approach based on shifted Legendre polynomials. These equations are seen in physics and electronic sciences. By means of the evenly spaced collocation points, the shifted Legendre polynomials, their derivatives and matrix forms, the method is constructed. It reduces the problem into a system nonlinear algebraic equations. Error analysis is made. The method is applied to numerical examples and their results are compared with other methods from literature. And also, the method is applied to nonlinear RL electrical circuit model. The results show that the method is effective.

A 3D nonlinear magnetic equivalent circuit model for an axial field flux focusing magnetic gear: Comparison of fixed-point and Newton–Raphson methods

An axial field flux focusing magnetic gear is being modeled in this study utilizing a 3D magnetic equivalent circuit technique that takes into consideration the magnetic saturation of the soft magnetic material. Considering magnetic saturation is a critical feature in modeling magnetic gears, particularly those with flux focusing arrangements where specific regions become highly saturated. However, nonlinear modeling comes with its costs, like increased computation time and resource allocation, so it has always been a hot topic for research and development. The implementation of two nonlinear iterative solvers for the solution of the nonlinear magnetic equivalent circuit was described and a comparison between the two methods was done. The approach presented was chosen to be a good lightweight alternative for 3D finite element method modeling that can be used for early design stages. It provided acceptable nonlinear predictions while requiring less time than a 3D finite element method model and saving memory and resources.

Multiparameter Identification for Active Magnetic Bearing With Uncertainties Based on a Coupled Nonlinear Model

Parameter identification enables active magnetic bearing (AMB) to obtain more state information, which can be used for control optimization, condition monitoring and fault diagnosis for rotating machinery. Due to the limitation of working principle and modeling accuracy, the traditional parameter identification methods show inherent disadvantages in cost, applicability or precision. Thus, this paper proposes an accurate multi-parameter identification method without any instrumentation. This method takes into account the electromagnetic force coupling caused by the asymmetric magnetic circuit, the non-linearity caused by the saturation effect, together with the uncertain parameters caused by machining and assembly errors, temperature, etc. Firstly, the coupled nonlinear magnetic circuit model of the AMB is established by the reluctance network method, and the influence of non-ideal factors on the electromagnetic force is treated. Secondly, a novel experimental method for parameter identification is presented. According to the equilibrium relationship between the electromagnetic force and the supporting load, the force balance equations of the rotor under different working conditions are obtained. Taking the supporting parameters and uncertain geometric parameters as the parameters to be identified, the multi-parameter identification model is established. Finally, the proposed method is validated by the finite element method (FEM) and experiments. The results show that the method can accurately identify the air gap length, rotor origin, static supporting load, and stiffness of the AMB.

Analysis and Compensation of Hysteresis Effect on Electromagnetic Force in Axial Magnetic Bearings

Magnetic bearings (MBs) enable the rotor to run at high speed without lubrication due to no mechanical contact. However, the inherent hysteresis of ferromagnetic materials affects the support characteristics, reducing the design performance and stability margin of MBs, especially for axial MBs using materials with high coercive force. To analyze and compensate for the hysteresis effect on the electromagnetic force in axial MBs, an efficient method is proposed in this paper. Firstly, the hysteresis properties of the ferromagnetic materials are simulated by the Preisach model, and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> relationships under any external magnetic field can be determined. Taking into account the non-ideal factors such as hysteresis and saturation effects, the nonlinear magnetic circuit model of the axial MBs is established. The magnetic flux density working point under different control currents and eccentric displacements can be determined through iterative calculation, and then the air gap flux density distribution and electromagnetic force of the axial MBs are calculated. On this basis, the adverse effects of hysteresis on the bearing capacity and system stability of axial MBs are analyzed. A compensation algorithm is designed based on the inverse model to reduce the hysteresis effect. The inverse model is approximated modeled by the Lissajous curve. Finally, the proposed analysis and control methods are verified by the finite element method (FEM) or experiments. The results show that the proposed analysis method is capable of accomplishing good accuracy and requires less computation time than FEM, it can be applied to arbitrary current variation processes. In addition, the phase lag of the system is effectively improved with the compensation algorithm.

Modeling and Optimal Design of Inductor-Integrated Three-Phase 3-D Wound Core Transformer Under SPWM Excitation

Compared with the laminated core transformer (LCT), the 3D wound core transformer(3D-WCT) has the characteristics of symmetrical magnetic circuit and low vibration. This article focuses on the modeling and optimal design of the 3D-WCT for isolated DC/AC application. Firstly, based on the Jiles-Aterton model, a nonlinear magnetic circuit model of the 3D-WCT is established to calculate the flux density and core loss accurately under SPWM excitation. A thermal network model is presented for the steady-state temperature-rise calculation of the forced-air cooled 3D-WCT. Secondly, the optimal design method is carried out on the basis of the magnetic circuit and thermal network models. Based on the optimized design results, a regression analysis is performed to establish the relationship between the design variables and the performance objectives. Finally, a 75kVA 3D-WCT prototype is manufactured and tested in the actual inverter power supply to verify the established magnetic circuit and thermal network models. The 3D-WCT prototype is applied to the 150kVA inverter power supply, which contributes to achieving high power density and high efficiency of the power supply.

Deep Independent Recurrent Neural Network Technique for Modeling Transient Behavior of Nonlinear Circuits

This paper introduces a novel macromodeling method based on a recurrent neural network called deep independently recurrent neural network (DIRNN). The proposed method applies to time-domain modeling of nonlinear circuits and components, resulting in better training. It overcomes the vanishing and exploding gradient problems encountered with conventional RNNs. In conventional RNNs, all neurons in each layer are involved in recurrent connections that cause unnecessary connections, increasing the model’s complexity over time and making it hard to train for long-time sequences. To solve this problem, the proposed DIRNN’s neurons are independent of each other in recurrent connections, because each neuron only receives connections from its own previous hidden state. The validity of the proposed method is verified by modeling two nonlinear circuit examples, namely, a multi-stage driver terminated by a multi-line interconnect, and an on-chip voltage generator.

Hybrid-Magnet Variable Flux Memory Machine With Improved Field Regulation Capability for Electric Vehicle Applications

This article aims to investigate a novel hybrid-magnet variable flux memory machine (VFMM) with improved field regulation capability for electric vehicle applications. Two sets of permanent magnets (PMs), i.e., high-energy-density neodymium–iron–boron PM and low coercive force (LCF) PM, are arranged in a delta array to improve field regulation capability and torque density. The machine topology, key features, and operating principle of the presented machine are demonstrated. Based on the simplified magnetic circuit model, the underlying design tradeoffs of the presented machine are revealed qualitatively. The nonlinear magnetic circuit model of the presented machine taking saturation and hybrid-magnet leakage flux into consideration is built for machine analysis. Electromagnetic performance comparisons are carried out by finite element analysis between the presented VFMM and the existing VFMM. The results show that the presented machine can achieve significantly improved flux regulation capability while maintaining the high output torque due to the improved arrangement of hybrid magnetic branches and enhanced flux concentration effect. Finally, the investigated VFMM is prototyped. The operating principle and predicted results are verified by experimental results.

Drug Cocktail Formulation via Circuit Design.

Electronic circuits intuitively visualize and quantitatively simulate biological systems with nonlinear differential equations that exhibit complicated dynamics. Drug cocktail therapies are a powerful tool against diseases that exhibit such dynamics. We show that just six key states, which are represented in a feedback circuit, enable drug-cocktail formulation: 1) healthy cell number; 2) infected cell number; 3) extracellular pathogen number; 4) intracellular pathogenic molecule number; 5) innate immune system strength; and 6) adaptive immune system strength. To enable drug cocktail formulation, the model represents the effects of the drugs in the circuit. For example, a nonlinear feedback circuit model fits measured clinical data, represents cytokine storm and adaptive autoimmune behavior, and accounts for age, sex, and variant effects for SARS-CoV-2 with few free parameters. The latter circuit model provided three quantitative insights on the optimal timing and dosage of drug components in a cocktail: 1) antipathogenic drugs should be given early in the infection, but immunosuppressant timing involves a tradeoff between controlling pathogen load and mitigating inflammation; 2) both within and across-class combinations of drugs have synergistic effects; 3) if they are administered sufficiently early in the infection, anti-pathogenic drugs are more effective at mitigating autoimmune behavior than immunosuppressant drugs.

Asynchronous Sampled-Data Controller Design for Switched Markov Jump Systems and Its Applications

This article is dedicated to design asynchronous aperiodic sampled-data controller for a class of Markov jump systems with switching transition rate. The sampling controller corresponding switching transition rate matrix mode is not synchronized with the system corresponding switching transition rate matrix mode due to the possible switching of the transfer rate matrix in the sampling interval. With the help of T–S fuzzy models, the state-space representation of the system is turned into a fuzzy Itô stochastic switched Markov jump systems. By constructing novel Lyapunov functionals, mean square exponential stability criteria, and dissipativity criteria are presented. Furthermore, an asynchronous aperiodic sampled-data controller is designed for fuzzy Itô stochastic Markov jump systems. At last, by fuzzing the nonlinear tunnel diode circuit model and nonlinear mass-spring-damper mechanical model, the effectiveness and lower conservativeness of the proposed method are illustrated.

Extended Kalman Filter-Based SOC Estimation for Lithium Battery Packs

With the continuous reduction of energy and aggravation of environmental damage, the wind and solar complementary power generation system has received wide attention, among which the lithium battery pack is one of the most concerned components of the whole system. Accurate and effective estimation of the state of charge (SOC) of lithium battery pack not only can ensure the rational use of resources and reduce costs, but also ensure the safe and reliable operation of the system. Since the normal operation of Li-ion battery pack has strong nonlinearity, a general nonlinear equivalent circuit model is selected, the charge/discharge multiplier and ambient temperature are fully considered, the Fourier function is used to effectively fit the model parameters, and the extended Kalman filter algorithm (EKF) is used to dynamically estimate the SOC of Li-ion battery pack in combination with the traditional ampere-time integration method, and the simulation is verified by MATLAB software. The results show that the extended Kalman filter algorithm selected in the paper can effectively track the SOC of the lithium battery pack and control the tracking error below 1%.

A data-driven nonlinear frequency response approach based on the Loewner framework: preliminary analysis

We propose a hybrid method based on the combination of computed-aided nonlinear frequency response analysis with the Loewner framework, for the characterization of nonlinear dynamical processes with application in electrochemistry. The method is data-driven, i.e., requiring only samples of the first two generalized transfer functions of the underlying system, given as values of the sampled nonlinear frequency response. Then, the established system fitting and complexity reduction approach (in the frequency domain), known as the Loewner framework, is used to extract the system's invariant quantities. In this analysis, we have used a nonlinear electrical circuit model as a test case, for which the new method provides good results.

Multiobjective Tuning Technique for MPC in Grinding Circuits

We investigate the control challenges in grinding circuits—slow dynamics, long dead times, variable coupling— and the controller tuning challenge, that is, the difficulty in translating operating goals into tuning goals and closed-loop performance. A tuning algorithm for DMC (dynamic matrix control), suitable for the mineral processing industry, is proposed. The tuning problem is posed as a multiobjective optimization problem, in which the tuning goals are directly related to the desired closed-loop performance of process variables. The problem is solved using a compromise optimization, which minimizes the Euclidian distance between a feasible solution and the Utopia solution. Three case studies are presented, which validate the tuning algorithm for DMC in linear and non-linear grinding circuit models. The closed-loop performance obtained with the proposed tuning algorithm is compared to the one obtained through a benchmark tuning technique from the literature. The proposed tuning method has the following features: i) it shapes the closed-loop response according to the goal definitions for linear systems; ii) it requires tailored initial guesses and search spaces to converge to a stabilizing solution in non-linear applications; and iii) it allows the user to specify the desired closed-loop performance behavior in the tuning procedure, allowing the implementation of an adequate controller for each situation.

Modeling and implementation of a novel active voltage balancing circuit using deep recurrent neural network with dropout regularization

SummaryRecurrent neural networks (RNN) emerged as powerful tools to model and analyze the nonlinear behavior of electronic circuits accurately and quickly. Efforts to improve the accuracy of RNN will lead to the design of better‐quality products, which is essential in various fields such as the design of energy harvesting (EH) systems. EH techniques can provide the electrical energy needed for low‐power electronics without the need for a battery or with minimal dependency. Due to the importance of the active voltage balancing circuit in EH systems, we have proposed a new macromodeling method called dropout local‐feedback deep recurrent neural network (Dropout‐LFDRNN) to model and analyze this circuit along with two other nonlinear circuits as examples. This technique is an advance over the LFDRNN macromodeling method, and based on the obtained results from the measurements, we were able to build a fast macromodel for the active balancing circuit, which outperforms conventional deep recurrent neural network modeling method in terms of accuracy without sacrificing speed. It is worth mentioning that this proposed technique in this paper can be considered a viable approach for modeling and analysis of nonlinear electronic components and circuits. In addition to the advantage of generating a more accurate model, the model based on the Dropout‐LFDRNN approach is much faster than the existing transistor‐level models.

Artificial Neural Networks for Microwave Computer-Aided Design: The State of the Art

This article presents an overview of artificial neural network (ANN) techniques for a microwave computer-aided design (CAD). ANN-based techniques are becoming useful for performing forward/inverse modeling for active/passive components to enhance a circuit design. With measured or simulated data of microwave devices, ANNs can be trained to learn relevant microwave relationships, which are, otherwise, computationally expensive or for which efficient analytical formulas are not available. Fundamental concepts of the ANN structure and training, such as feedforward neural networks (FFNNs), recurrent neural networks (RNNs)/dynamic neural networks (DNNs)/time-delay neural networks (TDNNs), deep neural networks, and neural network training and extrapolation, are described. Knowledge-based neural networks (KBNNs) are described for improving the accuracy and reliability of modeling and design optimization. Various advanced ANN techniques, such as neuro-transfer function (neuro-TF) modeling, neural network inverse modeling, and deep neural network modeling, are discussed. The existing and emerging applications of ANN in microwave CAD are identified, such as electromagnetic (EM)/multiphysics modeling, modeling of nonlinear circuits and transistors, filter design, very large-scale integration (VLSI) interconnects, oscillator, transmitter and receiver modeling, and CAD applications in such as gallium nitride (GaN) high electron-mobility transistor (HEMT), wireless power transfer (WPT), microelectromechanical system (MEMS), and substrate-integrated waveguide (SIW).

Comprehensive Analysis of Linear and Nonlinear Equivalent Circuit Model for GaAs-PIN Diode

Comprehensive analysis of small-signal equivalent circuit models for GaAs-based PIN diodes is performed in this article. The analysis provides the equivalent circuit models for PIN diode operation in four different operation modes. A compact nonlinear equivalent circuit model has been developed which takes into account the dc/ac frequency dispersion of the diode dynamic resistance. In order to verify the validity of the proposed circuit model, the comparison between the modeled and measurement data is given, good fitting is obtained for GaAs-based PIN diode.

Design RF Magnetic Devices With Linear and Nonlinear Equivalent Circuit Models: Demystify RF Magnetics With Equivalent Circuit Models

Magnetic materials offer a unique combination of properties for RF applications, such as nonreciprocity, high permeability, broad tunability, strong frequency dispersion, and nonlinearity <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> , <xref ref-type="bibr" rid="ref3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[3]</xref> . In contrast to a dielectric material, where a scalar permittivity constant is often sufficient to represent the property of the material, the permeability of an RF magnetic material is usually a tensor in its linear regime, which is expressed in the form of an asymmetrical matrix; yet each entry in the matrix varies as a function of frequency and biasing field. At high RF power, the magnetic material can be easily driven into a nonlinear regime, which exhibits increased dissipation, drifting of resonant frequency, generation of harmonics, and so on. At a microscale, electromagnetic waves in magnetic materials are often coupled with spin waves that are supported by exchange coupling in quantum mechanics, which adds more complexity to the understanding and applications of the material.

Nonlinear Optimization Strategy for State of Power Estimation of Lithium-Ion Batteries: A Systematical Uncertainty Analysis of Key Impact Parameters

The state of power (SOP) of lithium-ion batteries plays an essential role in power distribution of electric vehicles and energy storage stations. However, due to the highly nonlinear dynamic behaviors and the parameter errors, accurate and reliable SOP estimation is always difficult. This article develops an optimization strategy to estimate SOP, in which the multiple constraints are simultaneously considered and the nonlinear equivalent circuit model (ECM) is directly adopted. On basis of it, the effects of single parameter uncertainty and multiparameter uncertainty are thoroughly investigated. The results show that compared to the conventional method, the proposed method could provide more reliable SOP estimation during the whole operation range. Moreover, different uncertainty sources have different effects on estimation results, not only the estimate values but also the constraint regions. This is the first time to directly employ the nonlinear form of ECM parameters in the SOP estimation and provide a comprehensive investigation of various uncertainty sources.