Linear System Model Research Articles

Fiscal- and Space-Constrained Energy Optimization Model for Hybrid Grid-Tied Solar Nanogrids

Due to rising fossil fuel costs, electricity tariffs are also increasing. This is motivating users to install nanogrid systems to reduce their electricity bills using solar power. However, the two main constraints for a solar system installation are the initial financial investment cost and the availability of space for the installation of solar panels. Achieving greater electricity savings requires more panels and a larger energy storage system (ESS). However, a larger ESS also increases the electricity bill and reduces the available solar power due to higher charging power requirements. The increase in solar power leads to the need for more space for solar panel installation. Therefore, achieving the maximum electricity savings for a consumer unit requires an optimized number of solar panels and ESS size within the available financial budget and the available physical space. Thus, this study presents a fiscal- and space-constrained mixed-integer linear programming-based nanogrid system model (FS-MILP) designed to compute the optimal number of solar panels and ESS requirements, and the daily electricity unit consumption and savings. The proposed model is also validated through an OMNET++-based simulation using real-time solar irradiance and residential load values of one year for the city of Karachi, Pakistan. The investigation results show that a maximum of 1050 electricity units can be saved and exported to the main power grid within the maximum financial budget of PKR 1,000,000/-.

Design of a Hydrogen Production System Considering Energy Consumption, Water Consumption, CO2 Emissions and Cost

CO2 emissions associated with hydrogen production can be reduced replacing steam methane reforming with electrolysis using renewable electricity with a trade-off of increasing energy consumption, water consumption and cost. In this research, a linear programming optimization model of a hydrogen production system that considers simultaneously energy consumption, water consumption, CO2 emissions and cost on a cradle-to-gate basis was developed. The model was used to evaluate the impact of CO2 intensity on the optimum design of a hydrogen production system for Japan considering different stakeholders’ priorities. Hydrogen is produced using steam methane reforming and electrolysis. Electricity sources include grid, wind, solar photovoltaic, geothermal and hydro. Independent of the stakeholders’ priorities, steam methane reforming dominates hydrogen production for cradle-to-gate CO2 intensities larger than 9 kg CO2/kg H2, while electrolysis using renewable electricity dominates for lower cradle-to-gate CO2 intensities. Reducing the cradle-to-gate CO2 intensity increases energy consumption, water consumption and specific cost of hydrogen production. For a cradle-to-gate CO2 intensity of 0 kg CO2/kg H2, the specific cost of hydrogen production varies between 8.81 and 13.6 USD/kg H2; higher than the specific cost of hydrogen production targeted by the Japanese government in 2030 of 30 JPY/Nm3, 3.19 USD/kg H2.

On the amplitude truncation effect in electromagnetic energy harvesters: Modeling and experimental validation

Energy harvesters based on a piecewise linear system make it possible to extract more energy from environment vibrations. The amplitude truncation effect is a phenomenon of an energy harvester with a piecewise linear system. It shows a wider energy harvesting bandwidth and a lower voltage response than the purely linear counterpart. This work investigates the influence of spring length on the amplitude truncation effect and power density of electromagnetic energy harvesters. We first establish an analytical model of the piecewise linear system. Then, we apply the averaging method to explore the voltage responses in the frequency domain and compare the influence of various parameters. Later, we conduct a finite element simulation to analyze the voltage response at a constant frequency. The results obtained by the finite element simulation and averaging method match well with the experimental measurements. The experimental results demonstrate that the amplitude truncation effect is more visible at the shorter spring. Spring length plays a key role in the power density of an electromagnetic energy harvester. The case of 40 mm yields a maximum average power of 45.13 mW. The case of 30 mm displays a maximum power density of 2.35 mW/cm 3.

Balance Control of a Configurable Inverted Pendulum on an Omni-Directional Wheeled Mobile Robot

This paper considers the balance control problems of a configurable inverted pendulum with an omni-directional wheeled mobile robot. The system consists of two parts. One is an inverted pendulum, and another one is an omni-directional wheeled mobile robot. The system can be configured as a rotary inverted pendulum or a spherical inverted pendulum. The objective is to control the omni-directional wheeled mobile robot to provide translational force on the plane to balance the spherical inverted pendulum and to provide the moment to balance the rotary inverted pendulum. Detailed dynamic models of these two systems are derived for the control strategy design and simulation studies. Stabilizing controllers based on the second-order sliding mode control are designed for both systems. The closed-loop stability is proved based on the passivity properties. The proposed control schemes can guarantee semi-globally asymptotical stability over the upper-half plane. In addition, the conventional sliding mode controllers proposed in our previous work and Linear-Quadratic Regulator (LQR) controllers based on the linearized system models about its upright equilibrium point are also used for performance comparison. The effectiveness of the control strategies is investigated and verified using simulation and experimental studies. In the simulation studies, different sources of uncertainty and disturbance are investigated. It is shown that the second-order sliding mode control outperforms the conventional sliding mode control and LQR control without any uncertainty and disturbance. For robustness to the matched disturbance, the simulation results show that the second-order sliding mode controller has a less significant steady-state oscillation in the pendulum’s angular displacement than other controllers. The simulation results also show that only the second-order sliding mode controller can stabilize the system with a significant initial deviation from the pendulum’s upright position. Finally, the experimental results demonstrate that second-order sliding mode control outperforms conventional sliding mode control and LQR control.

Rolling stability analysis of high-static-low-dynamic stiffness floating raft vibration isolation systems

Floating raft vibration isolation (FRVI) systems employing isolators with high-static-low-dynamic stiffness (HSLDS) characteristics offer excellent large-scale and multidirectional vibration attenuation performance ideally suited to stealth applications in ocean faring vessels. However, the rolling motions of vessels in heavy seas can produce large displacements and induce instability in HSLDS-FRVI systems, and our present state of understanding of these systems is insufficient to facilitate the design of more stable systems. The present work addresses this issue by establishing an accurate analytical model of a double-layer FRVI system with 12 degrees of freedom to facilitate detailed rolling stability analyses when adopting HSLDS isolators. This model is also adapted to obtain a simplified single-layer HSLDS-FRVI system model and a corresponding single-layer equivalent linear system (ELS) model for investigating the factors contributing to FRVI system stability. The results demonstrate that the single-layer HSLDS-FRVI system obtains increasingly superior rolling stability compared to that of the corresponding ELS as the system loading increases. Also, good rolling stability can be maintained by applying proper mounting locations for the isolators. Additional factors contributing to FRVI system stability are deduced by comparing the results obtained for double-layer HSLDS-HSLDS, HSLDS-ELS, ELS-HSLDS, and ELS-ELS systems. The results demonstrate that the use of isolators with HSLDS characteristics is most beneficial for improving the rolling stability of double-layer FRVI systems when applied between the ground and bottom layers, and maximum rolling stability is obtained when the mass of the lower level is close to that of the upper level.

General Unit Hydrograph from Chow’s Linear Theory of Hydrologic Systems and Its Applications

This research solves Chow’s linear hydrologic systems equations thoroughly to result in a theoretical instantaneous unit hydrograph (UH), which is a superposition of many (M) negative exponential functions. This implies that the instantaneous UH can be imagined as a superposition of many linear reservoirs in parallel. Mathematically, at M→∞, the theoretical UH (in terms of Taylor series) converges to the writer’s general UH that is a simple analytic expression derived inductively from empiricism. Therefore, this research turns the recent conceptual general UH to a theoretical law that approximates real-world watershed processes as a time-invariant linear hydrologic system. Specifically, we first review Chow’s linear hydrologic systems model and apply it to a conceptual watershed with an instantaneous storm, which results in a theoretical instantaneous UH and an S-hydrograph in the superposition of many negative exponential functions. The resulting S-hydrograph then is shown mathematically to be identical to the writer’s general UH at M→∞. Finally, the general theoretical UH is applied to 10 real-world watersheds for 19 rainfall-runoff simulations. It is noteworthy that the proposed method has two advantages: (1) it is general for storms with different rainfall durations, and (2) it does not require to define excess rainfall and direct runoff in advance because rainfall losses and baseflow can be a part of the solution process. It is expected that this research provides a deeper understanding of the general UH and thus helps promote its applications in practice.

Privacy-Preserving Sliding Mode Control for Voltage Restoration of AC Microgrids Based on Output Mask Approach

Although privacy-preserving is often considered in energy management and energy scheduling of microgrids (MGs), to the best of authors’ knowledge, there are almost no literatures on distributed secondary control of MGs with privacy-preserving. To fill this gap, this article investigates the privacy-preserving problem for voltage restoration of an ac MG. First, the model of the MG is transformed into a linear multiagent system model by feedback linearization. Furthermore, output mask approach, which avoids divulging the initial condition by inserting a dynamic mask on the exchanged state information, is adopted to make the distributed generator agents exactly converge to the reference value rather than the value with a preset certain convergence error by differential private. Meanwhile, the sliding mode control scheme with simple structure is adopted to accelerate the convergence speed of the masked system. However, it is difficult to design the controller directly because of the strong nonlinearity brought by the mask function. To solve this problem, we first implement the controller for the original system, and then extend it to the masked system. After that, we carry out the consensus analysis of the controlled masked system. Finally, the effectiveness of the proposed control scheme is validated in the MATLAB/Simulink environment.

Artificial neural network and dataset optimization for implementation of linear system models in resource‐constrained embedded systems

AbstractOn‐board training of artificial neural network (ANN) is important in instances where real time data are required for model training. Provision of on‐board intelligence enables the developed systems to self‐recalibrate and enhances their efficiencies. In this work, investigations have been performed to determine optimized parameters of ANN model for linear systems. The performance parameters that is, model parameters, memory requirements, accuracy and processing time are chosen by considering the model to be installed on commercially available microcontrollers that have very limited on‐board memory. Minimum data requirements for training ANN models of linear systems are also explored for better performance. All dataset ranges are normalized in order to exclude the effects of range differences. It is shown that for linear systems, 1–3–1 architecture produces best results against ≤100 data points when Bayesian Regularization (BR) training function is used along with Log Sigmoid Activation function. Simulations for 1–3–1 architecture are then performed for datasets having 10, 25, 50 and 100 data points. The results show that training with 25 data points produces over‐all better performance than other datasets. A large dataset utilizes more training time and memory whereas a smaller dataset produces relatively lesser accuracy. The effects of clustered data and uniformly distributed data are also explored. It is found that total epochs in case of clustered data are significantly higher than uniformly distributed data. The combination of these optimized parameters that is, 1–3–1 architecture, with BR and Log function, for ≤100 data points can be used for the development and implementation of linear components or systems in resource‐constrained embedded systems.

Data-Driven Identification of Dissipative Linear Models for Nonlinear Systems

We consider the problem of identifying a dissipative linear model of an unknown nonlinear system that is known to be dissipative, from time-domain input–output data. We first learn an approximate linear model of the nonlinear system using standard system identification techniques and then perturb the system matrices of the linear model to enforce dissipativity, while closely approximating the dynamical behavior of the nonlinear system. Further, we provide an analytical relationship between the size of the perturbation and the radius in which the dissipativity of the linear model guarantees local dissipativity of the unknown nonlinear system. We demonstrate the application of this identification technique through two examples.

Regional differences in urban residents' consumption behaviour in China: from the perspective of the habit formation time effect

This study constructs a panel extended linear expenditure system (ELES) model that includes the theory of internal habit formation and expands the theoretical connotation of the original model. It also decomposes the dynamic evolution characteristics of Chinese urban residents' psychological and physiological needs among various consumption expenditures. It explains the partial causes of the time effect in the panel ELES model from consumer behaviour. We have obtained the following innovative conclusions after the empirical analysis of urban residents’ consumption behaviour in different regions of China. First, urban residents have habit formation effects on seven types of consumption expenditure. Second, the timeliness of the psychological needs of various commodity expenditures differs between the eastern and mid-western region of China, and this difference has expanded since 2013. The COVID-19 pandemic has reduced the psychological needs for various commodity expenditures while having little impact on physiological needs. Finally, the study puts forward some policy recommendations, such as tapping the potential of commodity consumption with psychological needs growth, further enhance the cultivation of low-income people's consumption in the mid-western region, and implementing more detailed consumption supports with different regions' consumption preferences.

Controllability analysis of Flyback converter with constant power load based on switched linear systems

A converter cascaded system is usually used for power conversion. However, due to the increase of the number of converters in the cascaded system, the amount of power switches and circuit elements also increases accordingly, which makes it difficult to analyze the dynamic characteristics and design control strategy. To understand the control theoretical characteristics of converter cascaded system and provide a theoretical basis for circuit parameters analysis and manipulation strategy design, taking the Flyback converter cascaded system as an example, this paper establishes an accurate switching linear systems model, discusses the control theoretical characteristics of the system in detail by using the controllability theorems. The simulations and experimental results prove the correctness of the analysis.

Error model for linear DoFP imaging systems perturbed by spatially varying polarization states.

Division of focal plane (DoFP) polarization sensors can perform linear polarimetric imaging in one shot. However, since they use several neighboring pixels to estimate the polarization state, fast spatial variations of the scene may lead to estimation errors. We investigate the influence of the spatial variations of the three polarimetric parameters of interest (intensity, degree of linear polarization, and angle of polarization) on these errors. Using theoretical derivations and imaging experiments, we demonstrate that the spatial variations of intensity are the main source of estimation errors, much more than variations in the polarization state. Building on this analysis, we show that compensating the intensity variations within a superpixel is sufficient to reach the estimation performance of state-of-the-art demosaicing methods.

Probing the Relationship Between Latent Linear Dynamical Systems and Low-Rank Recurrent Neural Network Models

A large body of work has suggested that neural populations exhibit low-dimensional dynamics during behavior. However, there are a variety of different approaches for modeling low-dimensional neural population activity. One approach involves latent linear dynamical system (LDS) models, in which population activity is described by a projection of low-dimensional latent variables with linear dynamics. A second approach involves low-rank recurrent neural networks (RNNs), in which population activity arises directly from a low-dimensional projection of past activity. Although these two modeling approaches have strong similarities, they arise in different contexts and tend to have different domains of application. Here we examine the precise relationship between latent LDS models and linear low-rank RNNs. When can one model class be converted to the other, and vice versa? We show that latent LDS models can only be converted to RNNs in specific limit cases, due to the non-Markovian property of latent LDS models. Conversely, we show that linear RNNs can be mapped onto LDS models, with latent dimensionality at most twice the rank of the RNN. A surprising consequence of our results is that a partially observed RNN is better represented by an LDS model than by an RNN consisting of only observed units.

Deontic-doxastic belief revision and linear system model.

Deontic-doxastic belief revision and linear system model.

Incremental adaptive optimal control for nonlinear systems with disturbance and input time-delay

In this paper, a model-free incremental adaptive optimal control scheme is proposed for nonlinear systems in presence of disturbance and input time-delay. The linear time-varying approximate model of the nonlinear system is obtained by incremental method, in which the relevant matrix parameters are identified by recursive least squares (RLS) estimation. A time-delay matrix function is constructed by neural network (NN) to eliminate the input time-delay, and the external disturbance of nonlinear system is dealt with by [Formula: see text] optimal control; incremental adaptive dynamic programming (IADP) algorithm is used to get the control law by solving Hamilton–Jacobi–Isaacs (HJI) equation. Convergence analysis of the proposed control scheme is provided. Simulations are given to verify the effectiveness of the proposed control scheme.

Characterization and correction of diffusion gradient-induced eddy currents in second-order motion-compensated echo-planar and spiral cardiac DTI.

Very high gradient amplitudes played out over extended time intervals as required for second-order motion-compensated cardiac DTI may violate the assumption of a linear time-invariant gradient system model. The aim of this work was to characterize diffusion gradient-related system nonlinearity and propose a correction approach for echo-planar and spiral spin-echo motion-compensated cardiac DTI. Diffusion gradient-induced eddy currents of 9 diffusion directions were characterized at b values of 150 s/mm2 and 450 s/mm2 for a 1.5Tesla system and used to correct phantom, ex vivo, and in vivo motion-compensated cardiac DTI data acquired with echo-planar and spiral trajectories. Predicted trajectories were calculated using gradient impulse response function and diffusion gradient strength- and direction-dependent zeroth- and first-order eddy current responses. A reconstruction method was implemented using the predicted -space trajectories to additionally include off-resonances and concomitant fields. Resulting images were compared to a reference reconstruction omitting diffusion gradient-induced eddy current correction. Diffusion gradient-induced eddy currents exhibited nonlinear effects when scaling up the gradient amplitude and could not be described by a 3D basis alone. This indicates that a gradient impulse response function does not suffice to describe diffusion gradient-induced eddy currents. Zeroth- and first-order diffusion gradient-induced eddy current effects of up to -1.7rad and -16 to +12 rad/m, respectively, were identified. Zeroth- and first-order diffusion gradient-induced eddy current correction yielded improved image quality upon image reconstruction. The proposed approach offers correction of diffusion gradient-induced zeroth- and first-order eddy currents, reducing image distortions to promote improvements of second-order motion-compensated spin-echo cardiac DTI.

Linear System Order Reduction Model Using Stability Equation Method and Factor Division Algorithm for MIMO Systems

Abstract: A New mixed method is proposed which combines the advantages of Stability Equation method and factor division algorithm in deriving the reduced order models for higher-order linear dynamic systems. The denominator of the reduced order model is obtained by the stability equation method and the numerator values are calculated using factor division algorithm. The reduced order models retain the steady-state value and guarantees stability of the original system. The proposed algorithm has also been extended for the design of PID controller for MIMO systems. The numerical examples are solved in literature to show the flexibility and effectiveness over other existing methods

A generalized proportional Caputo fractional model of multi-agent linear dynamic systems via impulsive control protocol

This paper deals with multi-agent systems that, due to using the generalized proportional Caputo fractional derivative, possess memories. The information exchange between agents does not occur continuously but only at fixed given update times, and the lower limit of the fractional derivative changes according to the update times. Two types of multi-agent systems are studied, namely systems without a leader and systems with a leader. For a generalized proportional Caputo fractional model of multi-agent linear dynamic systems, sufficient conditions for exponential stability via impulsive control are obtained. In the case of the presence of a leader in the multi-agent system, we derive sufficient conditions for the leader-following consensus via impulsive control based on the leader’s influence. Simulation results are provided to verify the essential role of the generalized proportional Caputo fractional derivative and impulsive control in realizing the consensus of multi-agent systems.

Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation-Dissipation Inequalities.

Thermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR quantifies the minimal energetic cost of achieving a certain precision in determining a nonequilibrium current. In this initial stage of our research program, our goal is to provide the quantum theoretical basis of TURs using microphysics models of linear open quantum systems where it is possible to obtain exact solutions. In paper [Dong et al., Entropy 2022, 24, 870], we show how TURs are rooted in the quantum uncertainty principles and the fluctuation–dissipation inequalities (FDI) under fully nonequilibrium conditions. In this paper, we shift our attention from the quantum basis to the thermal manifests. Using a microscopic model for the bath’s spectral density in quantum Brownian motion studies, we formulate a “thermal” FDI in the quantum nonequilibrium dynamics which is valid at high temperatures. This brings the quantum TURs we derive here to the classical domain and can thus be compared with some popular forms of TURs. In the thermal-energy-dominated regimes, our FDIs provide better estimates on the uncertainty of thermodynamic quantities. Our treatment includes full back-action from the environment onto the system. As a concrete example of the generalized current, we examine the energy flux or power entering the Brownian particle and find an exact expression of the corresponding current–current correlations. In so doing, we show that the statistical properties of the bath and the causality of the system+bath interaction both enter into the TURs obeyed by the thermodynamic quantities.

Modal analysis of viscoelastic three-dimensional rotating beam with generic tip mass

In this paper, the nonlinear dynamic modelling, free vibration and nonlinear analysis of three-dimensional viscoelastic Euler-Bernoulli beam undergoing hub motion incorporating substantial tip mass is accomplished. The kinetic, and potential energy of the system are derived in terms of velocities of general point on the link and center of gravity of the tip mass expressed in multi-floating co-ordinate systems. Hamilton's principle is used to obtain the governing equations of motion and linearly coupled boundary conditions. The material of the beam is considered as viscoelastic constituted of Kelvin-Voigt rheological model. The mass attached at the terminal end of the beam is assumed to have eccentricity in axial, lateral, as well as transverse directions. Free vibration analysis is performed on the linearized system model to obtain the transcendental eigenfrequency equation. Further, the dynamic equations of motion of beam are discretized using the obtained mode shapes and the response of system under rotary motion of hub is investigated. The steady state solutions and frequency response curves exhibiting bi-stable and tri-stable regions are obtained using method of multiple scales. The bifurcation diagrams of the system are studied for resonance conditions when the frequency of the rotary motion becomes equal or nearly equal to the normalized beam frequencies. The saddle node and pitchfork bifurcations exhibiting multiple solutions and jump phenomena are observed and investigated to avoid catastrophic failure of the system. The numerical simulations of modal parameters of the system, nonlinear characteristics, and their parametric dependency is discussed thoroughly.