Search Results (602)

For the splitting iterative scheme to solve the system of linear equations, an equivalent form in terms of descent and residual vectors is formulated. We propose an extrapolation technique using the new formulation, such that a new splitting iterative scheme (NSIS) can be simply generated from the original one by inserting an acceleration parameter preceding the descent vector. The spectral radius of the NSIS is proven to be smaller than the original one, and so has a faster convergence speed. The orthogonality of consecutive residual vectors is coined into the second NSIS, from which a stepwise varying orthogonalization factor can be derived explicitly. Multiplying the descent vector by the factor, the second NSIS is proven to be absolutely convergent. The modification is based on the maximal reduction of residual vector norm. Two-parameter and three-parameter NSIS are investigated, wherein the optimal value of one parameter is obtained by using the maximization technique. The splitting iterative schemes are unified to have the same iterative form, but endowed with different governing equations for the descent vector. Some examples are examined to exhibit the performance of the proposed extrapolation techniques used in the NSIS. Full article

Bilinear systems can be developed from the point of view of time-varying linear differential equations or from the symmetry of Lie theory, in particular Lie algebras, Lie groups, and Lie semigroups. For bilinear control systems with bounded control range, we analyze when a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists, for the induced system on projective space. We use the system semigroup by considering piecewise constant controls and use spectral properties to extend the result to bilinear systems in ${\mathbb{R}}^d$. The contribution of this paper highlights the relationship between all the existent control sets. We show that the controllability property of a bilinear system is equivalent to the existence and uniqueness of a control set of the projective system. Full article

Oncological hyperthermia (HT) is a medical technique aimed at heating a specific region of the human body containing a tumour. The heat makes the tumour cells more sensitive to the cytotoxic effects of radiotherapy and chemotherapy. Electromagnetic (EM) HT devices radiate a single-frequency EM field that induces a temperature increase in the treated region of the body. The typical radiative HT frequencies are between 60 and 150 MHz for deep HT applications, while 434 MHz and 915 MHz are used for superficial HT. The input EM power can reach up to 2000 W in deep HT and 250 W in superficial applications, and the E-field should be linearly polarized. This study proposes the development and use of E-field sensors to measure the distribution and evaluate the polarization of the E-field radiated by HT devices inside equivalent phantoms. This information is fundamental for the validation and assessment of HT systems. The sensor is constituted by three mutually orthogonal probes. Each probe is composed of a dipole, a diode, and a high-impedance transmission line. The fundamental difference in the operability of this sensor with respect to the standard E-field square-law detectors lies in the high-power values of the considered EM sources. Numerical analyses were performed to optimize the design of the E-field sensor in the whole radiative HT frequency range and to characterize the sensor behaviour at the power levels of HT. Then the sensor was realized, and measurements were carried out to evaluate the E-field radiated by commercial HT systems. The results show the suitability of the developed sensor to measure the E-field radiated by HT applicators. Additionally, in the measured devices, the linear polarization is evidenced. Accordingly, the work shows that in these devices, a single probe can be used to completely characterize the field distribution. Full article

This paper establishes some links between Sturm–Liouville problems and the well-known controllability property in linear dynamic systems, together with a control law design that allows any prefixed arbitrary final state finite value to be reached via feedback from any given finite initial conditions. The scheduled second-order dynamic systems are equivalent to the stated second-order differential equations, and they are used for analysis purposes. In the first study, a control law is synthesized for a forced time-invariant nominal version of the current time-varying one so that their respective two-point boundary values are coincident. Afterward, the parameter that fixes the set of eigenvalues of the Sturm–Liouville system is replaced by a time-varying parameter that is a control function to be synthesized without performing, in this case, any comparison with a nominal time-invariant version of the system. Such a control law is designed in such a way that, for given arbitrary and finite initial conditions of the differential system, prescribed final conditions along a time interval of finite length are matched by the state trajectory solution. As a result, the solution of the dynamic system, and thus that of its differential equation counterpart, is subject to prefixed two-point boundary values at the initial and at the final time instants of the time interval of finite length under study. Also, some algebraic constraints between the eigenvalues of the Sturm–Liouville system and their evolution operators are formulated later on. Those constraints are based on the fact that the solutions corresponding to each of the eigenvalues match the same two-point boundary values. Full article

We investigate the bridge problem for stochastic processes, that is, we analyze the statistical properties of trajectories constrained to begin and terminate at a fixed position within a time interval $\tau$. Our primary focus is the time-reversal symmetry of these trajectories: under which conditions do the statistical properties remain invariant under the transformation $t\to \tau -t$? To address this question, we compare the stochastic differential equation describing the bridge, derived equivalently via Doob’s transform or stochastic optimal control, with the corresponding equation for the time-reversed bridge. We aim to provide a concise overview of these well-established derivation techniques and subsequently obtain a local condition for the time-reversal asymmetry that is specifically valid for the bridge. We are specifically interested in cases in which detailed balance is not satisfied and aim to eventually quantify the bridge asymmetry and understand how to use it to derive useful information about the underlying out-of-equilibrium dynamics. To this end, we derived a necessary condition for time-reversal symmetry, expressed in terms of the current velocity of the original stochastic process and a quantity linked to detailed balance. As expected, this formulation demonstrates that the bridge is symmetric when detailed balance holds, a sufficient condition that was already known. However, it also suggests that a bridge can exhibit symmetry even when the underlying process violates detailed balance. While we did not identify a specific instance of complete symmetry under broken detailed balance, we present an example of partial symmetry. In this case, some, but not all, components of the bridge display time-reversal symmetry. This example is drawn from a minimal non-equilibrium model, namely Brownian Gyrators, that are linear stochastic processes. We examined non-equilibrium systems driven by a "mechanical” force, specifically those in which the linear drift cannot be expressed as the gradient of a potential. While Gaussian processes like Brownian Gyrators offer valuable insights, it is known that they can be overly simplistic, even in their time-reversal properties. Therefore, we transformed the model into polar coordinates, obtaining a non-Gaussian process representing the squared modulus of the original process. Despite this increased complexity and the violation of detailed balance in the full process, we demonstrate through exact calculations that the bridge of the squared modulus in the isotropic case, constrained to start and end at the origin, exhibits perfect time-reversal symmetry. Full article

This paper addresses the issues of sensor failures and actuator faults in mining tracked mobile vehicles (TMVs) operating in harsh environments by proposing a global fixed-time fault-tolerant control strategy based on a hierarchical unknown input observer structure. First, a kinematic and dynamic model of the TMV is established considering side slip and track slip, and its linear parameter-varying (LPV) model is constructed through parameter-dependent linearization. Then, a distributed structure consisting of four collaborating low-dimensional observers is designed, including a state observer, a disturbance observer, a position sensor fault observer, and a wheel speed sensor fault observer, and the fixed-time convergence of the closed-loop system is proven. Additionally, by equivalently treating actuator faults as power losses, an observer capable of identifying and compensating for motor efficiency losses is designed. Finally, an adaptive fault-tolerant control law is proposed by combining nominal control, disturbance compensation, and sliding mode switching terms, achieving global fixed-time stability and fault tolerance. Experimental results demonstrate that the proposed control system maintains excellent trajectory tracking performance even in the presence of sensor faults and actuator power losses, with tracking errors less than 0.1 m. Full article

This paper presents an algorithm for the implementation of a model that calculates shunt currents in redox flow batteries. The formation patterns of the equivalent electrical circuit that models shunt currents in redox flow batteries are analyzed in such a way that the proposed algorithm is applicable for batteries with any number of cell stacks and any number of cells per stack. Linear algebra is applied to solve the equation system related to the equivalent electric circuit. The solution of such a system of equations is obtained by performing the inverse of a matrix and premultiplying that matrix on both sides of the equation system. This being rather trivial, the real problem lies in automating the generation of the matrices relative to the system of equations. For this reason, it is analyzed how to generate the matrixes in order to facilitate the implementation of their generation. Finally, the most important parts of the implementation of the resolution algorithm are shown. Full article

The radial magnetic bearing system is an open-loop, unstable, strong nonlinear system with a high rotor speed, predisposition to jitter, and poor interference immunity. The system is subjected to the main interference generated by gravity, and rotor imbalance and sensor runout seriously affect the system’s rotor position control performance. A plug-in repetitive control method based on equivalent-input-disturbance (EID) is presented to address the issue of decreased control accuracy of the magnetic bearing system caused by disturbances from gravity, rotor imbalance, and sensor runout. First, a linearized model of the magnetic bearing rotor containing parameter fluctuations due to the eddy current effect and temperature rise effect is established, and a plug-in repetitive controller (PRC) is designed to enhance the rejection effect of periodic disturbances. Next, an EID system is introduced, and a Luenberger observer is used to estimate the state variables and disturbances of the system. The estimates of the EID are then used for feedforward compensation to address the issue of large overshoot in the system. Finally, simulations are conducted for comparison with the PID control method and PRC control method. The plug-in repetitive controller method assessed in this paper improves control performance by an average of 87.9% and 57.7% and reduces the amount of over-shooting by an average of 66.5% under various classes of disturbances, which proves the efficiency of the control method combining a plug-in repetitive controller with the EID theory. Full article

Asymmetry in the supply voltage in three-phase circuits disrupts the flow of currents. This worsens the efficiency of the distribution system and increases the problems in determining the mathematical model of the energy system. Among many power theories, the most accurate is the Currents’ Physical Components (CPC) power theory, which tries to justify the physical essence of each component. Such knowledge can be used to improve efficiency and reduce transmission losses in the power system. This article discusses the method of mathematical decomposition of current components in the case of a three-wire line connecting an asymmetric power source with linear time-invariant (LTI) loads. Special cases where irregularities appear in the results of calculations according to the CPC theory are discussed. The problem of equivalent conductance in the case of a non-zero value of the constant voltage component is discussed. The method of determining symmetrical components for periodic non-sinusoidal waveforms is also discussed. These considerations are supported by numerical examples. Full article

This paper investigates a multi-sensor system for the state estimation of a maneuvering target, wherein the process noise of the target dynamics and the measurement noise of the sensor network are mutually correlated, and the measurement noises across different sensors are also cross-correlated. Under such conditions, we propose a globally optimal sequential least squares fusion estimation algorithm within the framework of linear minimum mean square error (LMMSE) estimation. This method is specifically designed to preserve structural symmetry and to accommodate the time-ordered arrival of sensor observations transmitted over a network. Rigorous theoretical analysis establishes the performance equivalence between the proposed sequential fusion estimator and the centralized Kalman filter. Numerical simulations further demonstrate the algorithm’s superior estimation accuracy and stability under symmetry constraints, particularly when the noise statistics exhibit spatial or temporal symmetry. Full article

The propulsion system is a critical component of medium–low-speed maglev trains and the single-sided linear induction motor (SLIM) has been adopted to generate thrust. However, the SLIM operates periodically in maglev trains. The temperature of the secondary plate of the SLIM rises significantly due to eddy currents when the train enters and leaves the station, where large slip occurs. Subsequently, the temperature decreases through natural cooling during the shift interval time. This periodic operating condition is rarely addressed in the existing literature and warrants attention, as the temperature accumulates over successive periods, potentially resulting in thermal damage and thrust variation. Furthermore, the conductivity of plate varies significantly in the process, which affects the losses and thrust, requiring a coupled analysis. To investigate the temperature variation patterns, this paper proposes a coupled model integrating the lumped parameter thermal network (LPTN) and the equivalent circuit (EC) of the SLIM. Given the unique structure of the F-shaped rail, the LPTN mesh is well designed to account for the skin effect. Three experiments and a finite element method (FEM)-based analysis were conducted to validate the proposed model. Finally, optimizations were performed with respect to different shift interval time, plate materials, and carriage numbers. The impact of temperature on thrust is also discussed. The results indicate that the minimum shift interval time and maximum carriage number are 70.7 s and 9, respectively, with thrust increasing by 22.0% and 22.0%. Furthermore, the use of copper as the plate material can reduce the maximum temperature by 22.01% while decreasing propulsion thrust by 26.1%. Full article

Incremental capacity analysis (ICA), where incremental charge (Q) movements associated with changes in potential are tracked, and cyclic voltammetry (CV), where current response to a linear voltage sweep is recorded, are used to investigate the properties of electrochemical systems. Electrochemical impedance spectroscopy (EIS), on the other hand, is a powerful, non-destructive technique that can be used to determine small-signal AC impedance over a wide frequency range. It is frequently used to design battery equivalent-circuit models. This manuscript explores the relationships between ICA, CV and EIS and demonstrates how sweep rate in CV is related to charging (C) rate in ICA. In addition, it shows the connection between observations linked to rate of charge movement in CV and ICA and intermittent, irregular behavior seen in EIS when performed on a battery. It also explains the use of an additional DC stimulus during EIS to ensure reliability of battery impedance data and to facilitate equivalent-circuit modeling, and suggests a method for obtaining data analogous to CV from a whole battery without risking its destruction. Full article

This article aims to clarify the applicability of He’s two-scale fractal dimension transform by replacing $t^{\mathsf{\alpha }}$ with $\mathsf{\tau }$. It demonstrates the potential to capture the influence of the fractal parameter on the system’s damping frequency, particularly when the viscoelastic term (damping) does not equal half of the fractional inertia force term. The analysis examines the elastomer materials’ dynamic fractal amplitude–time response, considering the viscohyperelastic effects related to the material’s energy dissipation capacity. To determine the amplitude of oscillations for the nonlinear equation of motion of a body supported by a viscohyperelastic elastomer subjected to uniaxial stretching, the harmonic balance perturbation method, combined with the two-scale fractal dimension transform and Ross’s formula, is employed. Numerical calculations demonstrate the effectiveness of He’s two-scale fractal transformation in capturing fractal phenomena associated with the fractional time derivative of deformation. This is due to a correlation between the fractional rate of viscoelasticity and the fractal structure of media in elastomer materials, which is reflected in the oscillation amplitude decay. Furthermore, the approach introduced by El-Dib to replace the original fractional equation of motion with an equivalent linear oscillator with integer derivatives is used to further assess the qualitative and quantitative performance of our derived solution. The proposed approach elucidates the applicability of He’s two-scale fractal calculus for determining the amplitude of oscillations in viscohyperelastic systems, where the fractal derivative order of the inertia and damping terms varies. Full article

At present, photovoltaic power generation is becoming increasingly popular, and one of its major drawbacks is the low photoelectric conversion efficiency of photovoltaic cells. In order to improve power generation efficiency, an equivalent circuit model of photovoltaic cells and a simulation structure of photovoltaic power generation systems have been established. The working principle and MPPT (Maximum Power Point Tracking) control process of the improved Fibonacci linear search algorithm have been analyzed to achieve the goal of improving power generation efficiency. The improved Fibonacci linear search algorithm is applied in the MPPT technology of photovoltaic power generation system, and simulation experiments are conducted. Through analysis and simulation, MPPT can quickly track the maximum power point when the external lighting conditions change and has good tracking effect. Full article

The behavior of long-span concrete-filled steel tube (CFST) arch bridges during the pouring stage is complex. The coupling effect of the time-varying hydration heat and the evolution of the elastic modulus is crucial for the linear control of the structure. Most of the existing models focus on static self-weight analysis but generally ignore the above-mentioned dynamic heat–force interaction, resulting in significant prediction deviations. In response to this limitation, this paper proposes an analysis method for the injection stage considering the time-varying heat of hydration and elastic modulus of concrete inside the pipe. Firstly, based on the composite index model of the hydration heat and through the reduction of the participating materials, the heat source function of the hydration heat of the arch rib was obtained, and its accuracy was verified by using two test components. Secondly, the equivalent application method of the hydration heat temperature field of the bar system model was proposed. Combined with the modified time-varying model of the elastic modulus at the initial age, the analysis method for the pouring stage of concrete-filled steel tube arch bridges was established. Finally, the accuracy of the proposed method was verified by analysis and calculation combined with engineering examples and comparison with the measured results. The results show that the time-varying heat of hydration and the time-varying elastic modulus during the concrete pouring stage inside the pipe can lead to residual deflection after the arch rib is poured. The calculated value of the example reaches 154 mm, while the influence of the lateral displacement is relatively small and recoverable. The proposed method improves the calculation accuracy by 44.19% compared with the traditional method, which is of great significance for the actual engineering construction control. Full article