The transition of power grids from systems based on synchronous generators to those integrating increasing shares of renewable energy sources (RES) reduces system inertia and challenges frequency stability, particularly in weak grids. Grid-forming (GFM) control has emerged as a key solution, enabling inverter-based resources to provide synthetic inertia and autonomous grid support. This paper proposes a method for assigning virtual inertia and damping coefficients to multiple GFM inverters in a microgrid or distribution feeder. The objective is to ensure that the aggregated dynamic response at the point of common coupling aligns with target values specified by the grid operator. The proposed method is validated through simulations on an IEEE test network.

Adaptive networks with time-varying connectivity provide a fundamental paradigm to model networks of neurons, whose fingerprint is synaptic plasticity. We employ the stability analysis proposed in a recent paper, based on the formulation of a master stability function, to study cluster synchronization in adaptive networks with neural plasticity. We investigate how adaptation affects multistability in the network, where each stable solution encodes an archetypal pattern for auto-associative memories. This analysis is carried out with respect to the overall coupling strength, the adaptation rule, the number of nodes of the network, and the number of coexisting stable solutions. In particular, the coupling strength can be tuned to determine the maximum cluster size and the variability in the cluster sizes.

This paper presents a black-box method for generating surrogate data from measurements taken on inductors working up to magnetic saturation. The proposed method is based on a sequential neural network architecture, optimized through the Python Tensorflow framework and the Keras API, which accurately predicts the inductor flux dynamics under varying operating conditions. The generated data can be useful to fit existing circuit models to a limited set of physical measurements (easy-to-measure quantities, i.e., inductor voltage and current), complemented by the obtained surrogate data. The proposed black-box model performs well in predicting flux across different frequencies and amplitudes. This research is a first proof of concept (we focus on zero-bias sinusoidal inputs and amorphous-core inductors at fixed temperature); anyway, it highlights the potential of combining deep learning with robust optimization and pre-processing techniques to improve predictive accuracy in circuit models of inductors working up to magnetic saturation. These models can be used for simulating and designing high-power-density switch-mode power supplies.

Digital ΔΣ modulators (DDSM) are used in applications that require a reduction of the wordlength of a digital signal. In the presence of non-idealities, the quantization error of the DDSM can interact with nonlinearities further along the signal chain and generate spurious tones in addition to excess noise. This paper introduces the INIS family of DDSMs that are inherently immune from nonlinearity-induced spurs. Some representative members of the family are analyzed through simulations; one is demonstrated with a hardware implementation. Their performances are compared with those of other well-known DDSM architectures.

In this work, a nonlinear behavioral model is proposed for air-gapped ferrite-core inductors working up to magnetic saturation. The component is represented through the series connection of a nonlinear conservative inductor and a linear resistor, accounting for the instantaneous losses in both the windings and the core. The model is identified and validated through experimental measurements collected on a real buck converter. A very limited set of inductor voltages and currents is used for parameter identification. Some model coefficients depend explicitly on the air-gap length, which is useful for converter design purposes.

In this work, a nonlinear behavioral circuit model is proposed for air-gapped ferrite-core inductors working up to magnetic saturation. The model comprises a nonlinear conservative inductor, with current-dependent inductance, and two linear resistors, accounting for losses in both the winding and the core. Two representations are proposed for the nonlinear inductance, parameterized by both the number of turns and the air-gap length. The model (in both versions) is identified and validated through experimental measurements collected on a real buck converter. Inductor voltages and currents are used for parameter identification. The obtained results exhibit a good match with the experimental measurements used for validation purposes. An example of the application of the model to the design of a buck converter exploiting partially saturating inductors is also proposed.

In this paper, the derivative-free optimization algorithm MADS (mesh adaptive direct search) is adapted for implementation on field programmable gate array (FPGA) with fixed-point data representation. MADS is then exploited to solve constrained nonlinear optimization problems arising from non-linear model predictive control. The application on two examples taken from the literature shows the advantages of the proposed circuit architecture over the existing work, in terms of latency and resource occupation.

With the increasing presence of renewable energy sources in power grids, inertia estimation has become a pivotal problem in ensuring stable energy distribution. Inertia estimation during normal operating conditions of the network is still an open problem, since most algorithms rely on post-fault data or injection of probing signals in the grid. Here we extend a previously proposed algorithm for online inertia estimation to account for the presence of turbine governors in the power grid. The algorithm was tested on the IEEE 14-bus power system and it was successful in tracking the inertia of generators with and without turbine governors.

This paper is concerned with the study of the stability of the cluster-synchronous solution for directed networks of dynamical systems. Two recently proposed methods are compared by using a simple example network, thus evidencing their advantages and disadvantages, potentialities, and limitations.

A novel nonlinear behavioral model is proposed for an amorphous-core inductor working up to magnetic saturation. The model relies only on electrical quantities and represents the component as the series connection of a nonlinear conservative inductor and a nonlinear resistor, which accounts for the instantaneous losses in both the windings and the core. The model is identified and validated through measurements collected on a simple circuit, with applied unbiased sinusoidal voltage at two different frequencies.

The increasing presence of renewable energy sources (RES) in a power grid tends to reduce its inertia constant, which quantifies the grid's ability to contrast the frequency changes due to external disturbances. This led to the development of control strategies that interface the RES to the grid providing synthetic inertia, but these strategies cannot avoid oscillations of the overall system inertia, thus requiring algorithms for the online inertia constant estimation under normal operating conditions of the power grid. In this paper, we consider one of these algorithms, which exploits the data measured online through phasor measurement units, and critically analyze it, in order to efficiently apply it to the estimation of the inertia constant in the IEEE-14-bus power system, also with the addition of a PV power plant. The obtained results point out an increased efficiency of the online estimation of the network inertia.

A nonlinear inductor model has been recently proposed, which takes into account the magnetic saturation and the dependence of the inductance on the temperature. The model depends on seven parameters, which are identified based on experimental measurements of the inductor current in a switch-mode power supply. In this paper we show how the accuracy of each parameter affects the overall modeling accuracy in reproducing the inductor current.

This paper is concerned with the analysis of multi-layer networks consisting of different kinds of oscillators and couplings. In particular, we propose an algorithm for finding equitable clusters in this general class of networks, thus generalizing an existing algorithm specific for networks with identical nodes and one kind of connections. The algorithm is suitable to analyze complex networks of particular interest for the scientific community, such as neuron networks and electrical networks. The algorithm is tested on a random heterogeneous network with 40 oscillators of two different kinds and couplings of two different kinds. The stability of the obtained clusters is checked in a two-dimensional parameter space by using brute-force simulations.

This article is concerned with the design of synthetic central pattern generators (CPGs). Biological CPGs are neural circuits that determine a variety of rhythmic activities, including locomotion, in animals. A synthetic CPG is a network of dynamical elements (here called cells) properly coupled by various synapses to emulate rhythms produced by a biological CPG. We focus on CPGs for locomotion of quadrupeds and present our design approach, based on the principles of nonlinear dynamics, bifurcation theory, and parameter optimization. This approach lets us design the synthetic CPG with a set of desired rhythms and switch between them as the parameter representing the control actions from the brain is varied. The developed four-cell CPG can produce four distinct gaits: walk, trot, gallop, and bound, similar to the mouse locomotion. The robustness and adaptability of the network design principles are verified using different cell and synapse models.

More compact Switched-Mode Power Supplies (SMPSs) satisfying the overall design specifications can be obtained by exploiting ferrite core inductors working in partial saturation. In this case, the inductance is no longer a constant parameter, since it exhibits a sharp drop as the inductor current increases. A behavioral model has been recently proposed, which provides the inductance at steady state. In this paper, a generalization of this model is presented, in order to capture the inductance behavior also during the thermal transient. The model inputs are the the inductor current and the SMPS load current, both measurable quantities. The model fitting to experimental measurements relies on accurate SMPS simulations performed with the envelope analysis method, particularly suitable for fast-slow systems. The simulations are also used to validate the model reliability, through comparisons with the experimental results on a boost converter.

We propose and discuss a digital architecture suitable for hardware implementation of multifunctional neural networks to regulate several gaits for quadruped locomotion. These circuits have a far-reaching application for various bio-inspired robotics and synthetic prosthetics. The circuit is tested by implementing an 8-cell network proposed and analyzed here for the first time, whose robustness is checked with respect to parameter mismatching.

Any Atomic Force Microscope (AFM) scanner based on piezoelectric ceramics is affected by nonlinear distortions, mainly due to rate-independent hysteresis and rate-dependent creep, two different phenomena often referred to, collectively, as rate-dependent hysteresis. To compensate for these distortions, especially in old or cheap instruments, empirical open-loop compensation techniques are frequently adopted. In this paper, a complete hardware/software toolchain is proposed, for data acquisition, identification of hysteresis and creep models, and real-time open-loop compensation of rate-dependent hysteresis in AFM scanners.

Message passing between components of a distributed physical system is non-instantaneous and contributes to determine the time scales of the emerging collective dynamics. In biological neuron networks this is due in part to local synaptic filtering of exchanged spikes, and in part to the distribution of the axonal transmission delays. How differently these two kinds of communication protocols affect the network dynamics is still an open issue due to the difficulties in dealing with the non-Markovian nature of synaptic transmission. Here, we develop a mean-field dimensional reduction yielding to an effective Markovian dynamics of the population density of the neuronal membrane potential, valid under the hypothesis of small fluctuations of the synaptic current. Within this limit, the resulting theory allows us to prove the formal equivalence between the two transmission mechanisms, holding for any synaptic time scale, integrate-and-fire neuron model, spike emission regimes and for different network states even when the neuron number is finite. The equivalence holds even for larger fluctuations of the synaptic input, if white noise currents are incorporated to model other possible biological features such as ionic channel stochasticity.

This paper discusses practical approaches for designing reduced synthetic circuits of central pattern generators (CPGs) for quadruped locomotion using our newly developed bifurcation toolkit. Specifically, two CPGs containing only four elements (cells) are proposed that can reliably generate natural gaits of typical quadrupeds more effectively than large dedicated complex networks do. In addition, we analyze an enhanced locomotion system that incorporates a neuromechanical model for each leg and includes mechanisms of sensory feedback. We demonstrate how the proposed CPGs produce the desired gaits, which remain robust with respect to external perturbations.

This paper describes the MATLAB toolbox HysTool for the identification from experimental measurements and the simulation of four different hysteresis and creep models (Preisach, Prandtl-Ishlinskii, Kuhnen and power-law). The toolbox can automatically generate the inverse models (compensators) and also provide (for three out of four models) the C files for their microcontroller implementation. Tests on two different datasets are provided.

This paper is focused on a new object-oriented toolbox, called CEPAGE, devoted to simulation and analysis of Central Pattern Generators (CPGs). A CPG is a little group of neurons producing periodical patterns, which control rhythmic activities of animals. CEPAGE is conceived to carry out brute-force bifurcation analysis, but can also generate data for subsequent continuation analysis through other widely-used packages, such as AUTO or MATCONT. Two case studies are considered, with three and four neurons, with the twofold purpose of illustrating the main CEPAGE functionalities and provide new analysis results.

Knowing solar irradiance value allows an optimized management of photovoltaic (PV) power plants in terms of produced energy. Unfortunately, although sensing temperature is easy, the measurement of solar irradiance is expensive. In this paper, two circuit architectures for the estimation of the solar irradiance based on simple measurements are proposed. They are thought to be part of a centralized system implemented on field programmable gate array (FPGA) for sensing and monitoring of solar irradiance in a whole PV plant. The FPGA centralized architecture could allow for a real-time irradiance mapping by exploiting information coming from several low-cost measuring circuits suitably allocated on the PV modules. Validations on real irradiance data collected by the U.S. Department of Energy's National Renewable Energy Laboratory are presented.

Hysteresis is a nonlinear phenomenon useful whenever memory is required, but that can become annoying in applications where linearity is desired. In these cases, a possible way to reduce the inconvenience is to compensate the undesired memory effect by pre-processing the input signal through the hysteresis inverse model. In this paper, the inverse of a recently proposed circuit modeling rate-independent hysteretic phenomena is presented and discussed. The inverse circuit model is tested through experimental data measured from a commercial piezoelectric actuator. The obtained results are compared with those obtained by resorting to the well-known Preisach model. All the circuit simulations are performed by using PSPICE.

A circuit architecture modelling rate-independent hysteretic phenomena is presented and discussed. The core of the circuit is a ladder structure with longitudinal nonlinear resistors and transverse linear capacitors. In a separate loop, a linear combination of input and capacitor voltages provides the driving voltage for a resistor with monotonic, piecewise-linear driving-point characteristic. The resistor current represents the output variable. The circuit parameters can be found from experimental data through a standard quadratic programming optimization procedure. The model fitting features are tested by using two experimental data sets. One is the B(H) function of a magnetic material; the other is the deformation of a piezoelectric actuator as a function of the applied voltage. In this last case, an accurate comparison with the predictions of the well-known Preisach model evidences that the circuit model achieves the same accuracy with a much smaller number of parameters. All the circuit simulations are performed by using PSPICE.

The paper provides a framework to save energy and reduce the operative cost of some of today's industrial machinery. Low cost and low power wireless sensor networks is a novel approach to monitoring the tools in order to save energy and keep the tools monitored. Cutting tool wear degrades the product quality in manufacturing processes and also could have implications in health and safety of use. Monitoring tool wear value online is therefore needed to prevent degradation in machine quality. Unfortunately there is no direct way of measuring the tool wear online which is also very low cost. In this work is presented a low power and low cost accelerometer-based system for wear detection of bandsaw blade. The algorithm uses a simple data processing directly on board that can extract features and perform a classification on the state of the blade. Low power design of the node, on board processing and wake up radio capabilities reduce the wireless communication and the power consumption of the node significantly. Experimental results show the high accuracy, up to 100%, of the algorithm and the low power of the proposed approach.

This paper is concerned with the time-domain simulation of circuits including noise sources. In general, when a circuit admits a steady-state solution, small signal analyses are used to determine noise effects. There is a class of circuits (e.g., fractional PLLs based on ΔΣ modulators and forced oscillators) not admitting a steady-state solution with a period reasonable low multiple of the characteristic time scales of the circuit. In commercial analog simulators, time domain noise analyses have been implemented by “extending” linear multi-step integration methods or by introducing sampled versions of noise generators. Through a set of basic benchmark circuits, we show that these extensions are often affected by a relevant numerical noise floor hiding the effects of noise sources and drastically limiting the applicability of time domain noise analysis.

Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically detailed model neurons calls for the availability of fast numerical methods. In fact, exact techniques employ the microscopic simulation of the random opening and closing of individual ion channels, usually based on Markov models, whose computational loads are prohibitive for next generation massive computer models of the brain. In this work, we operatively define a procedure for translating any Markov model describing voltage- or ligand-gated membrane ion-conductances into an effective stochastic version, whose computer simulation is efficient, without compromising accuracy. Our approximation is based on an improved Langevin-like approach, which employs stochastic differential equations and no Montecarlo methods. As opposed to an earlier proposal recently debated in the literature, our approximation reproduces accurately the statistical properties of the exact microscopic simulations, under a variety of conditions, from spontaneous to evoked response features. In addition, our method is not restricted to the Hodgkin-Huxley sodium and potassium currents and is general for a variety of voltage- and ligand-gated ion currents. As a by-product, the analysis of the properties emerging in exact Markov schemes by standard probability calculus enables us for the first time to analytically identify the sources of inaccuracy of the previous proposal, while providing solid ground for its modification and improvement we present here.

In this paper we review and discuss digital circuit architectures implementing piecewise-affine (PWA) functions. These functions are defined over domains that are partitioned (either uniformly or non-uniformly) in polyhedral regions: each PWA function is linear in a polyhedral region. Different solutions, concerning both regular and non-regular domain partitions, are compared in terms of complexity and performances. Measurement results are provided for FPGA implementations. Two examples of control applications are described. On the overall, the goal of this paper is to provide a compact exposition of the state-of-the-art methods for the digital circuit implementation of PWA functions that is accessible to both experts and non-experts.

In this paper we analyze the collective behaviors of networks of Hindmarsh-Rose (HR) neurons and compare them with the behaviors of networks of piecewise-linear (PWL) approximations of the HR neurons. In all cases, the neurons are assumed to be symmetrically and diffusively coupled, with different topologies. The analysis is based on the master stability function (MSF) approach. The obtained results are verified by numerical time domain simulations of networks of 100 neurons. The synchronization properties of the PWL networks turn out to be very similar to those of the HR networks, as well as the dynamical properties of the single neurons (analyzed elsewhere).

In this paper we present a systematic approach to find piecewise-linear approximations of multivariate continuous nonlinear functions, by ensuring a good trade-off between approximation accuracy and model complexity. The proposed (suboptimal) method is based on genetic programming and takes into account the circuit constraints concerning the lower bounds for the size of each domain region (called simplex) where a given nonlinear function is approximated linearly. As a benchmark example, we approximate the well-known Hodgkin-Huxley neuron model.

In this paper we propose an algorithm for real-time vessel segmentation in sequences of RGB images of the human retina. The algorithm is made up of two main blocks providing vessel enhancement and thresholding, respectively. It is implemented on a DSP board for future embedding in ophthalmology equipments. The obtained results (binary images) show a good trade-off between processing speed and accuracy, since the main structure of the vessel network is preserved and the simplicity of the algorithm allows the DSP to process about ten images per second

In this paper we present a mixed-signal integrated circuit in a standard CMOS 0.5 µm technology implementing a piecewise-linear (PWL) function with three inputs, where each input can be either analog or coded with 8 bits. The output of the circuit is a digital word with 8-bit precision, representing the value of the PWL function at the three-dimensional input. The circuit accesses also a 4 kB external memory, which is addressed with a 12-bit word. Experimental results are shown that demonstrate the circuit working up to 50 MHz with a maximum power consumption of 3.7 mW.

The bifurcation analysis of a second-order continuous-time forest-fire impact model is carried out by resorting to a properly defined one-dimensional discrete-time system (map). The map is derived quite directly from the forest-fire model and is exploited to find out the regions of the chosen parameter domain characterized by qualitatively different behaviors. The results are compared with the bifurcation analysis carried out with a different method.

This paper deals with the experimental validation of the bifurcation analysis for a hysteresis circuit oscillator, obtained by means of both a proper circuit implementation and a measurement setup used for the automatic generation of 1D-bifurcation diagrams. The obtained circuit-based results show an excellent qualitative agreement with the numerical results

A property is enounced and proved which gives a criterion for defining the boundary elements of cellular circuits for the minimisation of continuous functionals. The property is illustrated through an example from image processing.