Zero Vector Research Articles

Saddle-to-saddle dynamics in diagonal linear networks*

Abstract In this paper we fully describe the trajectory of gradient flow over two-layer diagonal linear networks for the regression setting in the limit of vanishing initialisation. We show that the limiting flow successively jumps from a saddle of the training loss to another until reaching the minimum ℓ 1 -norm solution. We explicitly characterise the visited saddles as well as the jump times through a recursive algorithm reminiscent of the LARS algorithm used for computing the Lasso path. Starting from the zero vector, coordinates are successively activated until the minimum ℓ 1 -norm solution is recovered, revealing an incremental learning. Our proof leverages a convenient arc-length time-reparametrisation which enables to keep track of the transitions between the jumps. Our analysis requires negligible assumptions on the data, applies to both under and overparametrised settings and covers complex cases where there is no monotonicity of the number of active coordinates. We provide numerical experiments to support our findings.

ENHANCED MODEL-FREE PREDICTIVE CONTROL FOR VOLTAGE SOURCE INVERTERS USING AN ADAPTIVE OBSERVER

In this paper, a free model predictive control based on the active vector execution time (AVET-MFPC) using an adaptive observer is proposed for two-level voltage source inverters. The traditional model-free predictive control (MFPC) uses the sampling period to select one voltage vector for all candidate vectors according to the minimizing cost function principle. With the proposed control, two vectors are selected at one sampling period. The first vector is an active vector that uses the execution time of the active vector to select it, while the second one is a zero vector as it is applied after the active vector. The execution time is calculated using the ultra-local model (ULM) equation. In the traditional MFPC, the factor in the ULM is chosen with approximate values ranging between ±50 % of the nominal value. This paper proposes an adaptive sliding mode observer (ASMO) with an improved design to observe the variation of this factor, especially in case of mismatch parameters and during a step change in the reference signal. Combining the proposed ASMO observer and the AVET-MFPC controller gives faster system response, good tracking results, and less computational burden. Finally, the effectiveness of the proposed control model is approved and confirmed under various conditions, as well as the simulations carried out and the results obtained.

A Novel Battery Temperature-Locking Method Based on Self-Heating Implemented with an Original Driving Circuit While Electric Vehicle Driving: A Numerical Investigation

In extremely cold environments, when battery electric vehicles (BEVs) are navigating urban roads at low speeds, the limited heating capacity of the on-board heat pump system and positive temperature coefficient (PTC) device can lead to an inevitable decline in battery temperature, potentially falling below its permissible operating range. This situation can subsequently result in vehicle malfunctions and, in severe cases, traffic accidents. Henceforth, a novel battery self-heating method during driving is proposed to maintain battery temperature. This approach is ingeniously embedded within the heating mechanism within the motor driving system without any necessity to alter or modify the existing driving circuitry. In the meantime, the battery voltage can be regulated to prevent it from surpassing the limit, thereby ensuring the battery’s safety. This method introduces the dead zone into the space vector pulse width modulation (SVPWM) algorithm to form the newly proposed dSVPWM algorithm, which successfully changes the direction of the bus current in a PWM period and forms AC, and the amplitude of the battery alternating current (AC) can also be controlled by adjusting the heating intensity defined by the ratio of the dead zone and the compensation vector to the original zero vector. Through the Simulink model of the motor driving system, the temperature hysteresis locking strategy, grounded in the field-oriented control (FOC) method and employing the dSVPWM algorithm, has been confirmed to provide controllable and sufficiently stable motor speed regulation. During the low-speed phase of the China Light Vehicle Test Cycle (CLTC), the battery temperature fluctuation is meticulously maintained within a range of ±0.2 °C. The battery’s minimum temperature has been successfully locked at around −10 °C. In contrast, the battery temperature would decrease by a significant 1.44 °C per minute without the implementation of the temperature-locking strategy. The voltage of the battery pack is always regulated within the range of 255~378 V. It remains within the specified upper and lower thresholds. The battery voltage overrun can be effectively avoided.

Wind Finslerian Structures: From Zermelo’s Navigation to the Causality of Spacetimes

The notion of wind Finslerian structure Σ \Sigma is developed; this is a generalization of Finsler metrics (and Kropina ones) where the indicatrices at the tangent spaces may not contain the zero vector. In the particular case that these indicatrices are ellipsoids, called here wind Riemannian structures, they admit a double interpretation which provides: (a) a model for classical Zermelo’s navigation problem even when the trajectories of the moving objects (planes, ships) are influenced by strong winds or streams, and (b) a natural description of the causal structure of relativistic spacetimes endowed with a non-vanishing Killing vector field K K (SSTK splittings), in terms of Finslerian elements. These elements can be regarded as conformally invariant Killing initial data on a partial Cauchy hypersurface. The links between both interpretations as well as the possibility to improve the results on one of them using the other viewpoint are stressed. The wind Finslerian structure Σ \Sigma is described in terms of two (conic, pseudo) Finsler metrics, F F and F l F_l , the former with a convex indicatrix and the latter with a concave one. Notions such as balls and geodesics are extended to Σ \Sigma . Among the applications, we obtain the solution of Zermelo’s navigation with arbitrary time-independent wind, metric-type properties for Σ \Sigma (distance-type arrival function, completeness, existence of minimizing, maximizing or closed geodesics), as well as description of spacetime elements (Cauchy developments, black hole horizons) in terms of Finslerian elements in Killing initial data. A general Fermat’s principle of independent interest for arbitrary spacetimes, as well as its applications to SSTK\xspace spacetimes and Zermelo’s navigation, are also provided.

New asymptotic stability theory for real order systems and applications

Metzler asymptotic stability of real order systems gives hidden paths of nontrivial solutions to geometric constant solutions as time tends to ∞ in positive and negative orthants of Euclidean space when associated with random initial-time. Suppose that there is a governing law that describes the flow of geometric variables described by a real-order system in Euclidean space and a geometric solution zero vector that satisfies such a system. We introduce the concepts of orthant Metzler asymptotic stability that give rise to the notion of so-called new L-asymptotic stability. We prove that there exist order-dependent conditions that give a new L-asymptotic stability. The main results of this paper are comparison theorems that give L-asymptotic stability, which is essential in finding convergence of non-negative and non-positive solutions to geometric constant solutions. We establish upper and lower theoretical α-order Mittag-Leffler bounds of the Euclidean norm measure of non-trivial solutions to such systems, which characterize the Mittag-Leffler rate of decay. As applications of some theoretical results, we provide three examples that include a feedback method to control cancer in a cancer chemotherapy model to illustrate the effectiveness.

Attosecond and nano-Coulomb electron bunches via the Zero Vector Potential mechanism

The commissioning of multi-petawatt class laser facilities around the world is gathering pace. One of the primary motivations for these investments is the acceleration of high-quality, low-emittance electron bunches. Here we explore the interaction of a high-intensity femtosecond laser pulse with a mass-limited dense target to produce MeV attosecond electron bunches in transmission and confirm with three-dimensional simulation that such bunches have low emittance and nano-Coulomb charge. We then perform a large parameter scan from non-relativistic laser intensities to the laser-QED regime and from the critical plasma density to beyond solid density to demonstrate that the electron bunch energies and the laser pulse energy absorption into the plasma can be quantitatively described via the Zero Vector Potential mechanism. These results have wide-ranging implications for future particle accelerator science and associated technologies.

Current-Prediction-Controlled Quasi-Z-Source Cascaded Multilevel Photovoltaic Inverter

To address problems that traditional two-stage inverters suffer such as high cost, low efficiency, and complex control, this study adopts a quasi-Z-source cascaded multilevel inverter. Firstly, the quasi-Z-source inverter utilizes a unique impedance network to achieve single-stage boost and inversion without requiring a dead zone setting. Additionally, its cascaded multilevel structure enables independent control of each power unit structure without capacitor voltage sharing problems. Secondly, this study proposes a current-predictive control strategy to reduce current harmonics on the grid side. Moreover, the feedback model of current and system state is established, and the fast control of grid-connected current is realized with the deadbeat control weighted by the predicted current deviation. And a grid-side inductance parameter identification is added to improve control accuracy. Also, an improved multi-carrier phase-shifted sinusoidal PWM method is adopted to address the issue of switching frequency doubling, which is caused by the shoot-through zero vector in quasi-Z-source inverters. Finally, the problems of switching frequency doubling and high harmonics on the grid side are solved by the improved deadbeat control strategy with an improved MPSPWM method. And a seven-level simulation model is built in MATLAB (2022b) to verify the correctness and superiority of the above theory.

Co-operative Current Ripple Reduction Strategy for Three-Phase Inverter With Flexible Zero Vector Redistribution

Co-operative Current Ripple Reduction Strategy for Three-Phase Inverter With Flexible Zero Vector Redistribution

Harmonic signed trees

A signed graph G˙ is defined to be harmonic if its net-degree vector d±(G˙) is a zero vector or an eigenvector of adjacency matrix A(G˙) corresponding to an eigenvalue λ. In this paper, we demonstrate the existence of λ-harmonic signed trees with arbitrary diameter and the nonexistence of finite 0-harmonic signed trees. And we determine all harmonic signed trees with diameter at most 5. Moreover, we give some general properties of finite harmonic signed trees. In particular, a 1-harmonic signed tree must be 1 net-regular.

Model predictive control for Vienna rectifier with constant frequency based on inductance parameters online identification

When the finite control set model predictive control (FCS-MPC) is applied to the three-level converter, there are problems such as large current harmonics, high requirements for the computing efficiency of the microcontroller, complex multi-objective optimization and limited output vector switching. In addition,the mismatch of inductance parameter may directly affect the observation accuracy of FCS-MPC. To solve the above problem,a double vector model predictive control strategy with constant frequency strategy based on the inductance parameters on-line identification is presented.First, a single objective cost function based on the direct power is constructed by optimizing the redundant vector which is selected to balance the neutral-point potential, the design of weighting factor is avoided.At the same time, in order to effectively reduce the grid current ripple under single vector modulation, space vector pulse width modulation (SVPWM) is realized by combining with zero vector control mode. And, a parameter identification method based on model reference adaptive system(MARS) is proposed to overcome the effect of model parameter mismatch.Finally, the results show that the proposed F-MPCCF has good steady-state and dynamic performance from the static, transient and neutral-point potential control.

Relegated Thrust Ripples for Linear Induction Motors Based-Four Voltage Vectors Finite-Set Predictive Control and Model Reference Adaptive System

—These days, there are extensive signifies to the evolution of newfound control procedures like model predictive control. The finite-state predictive thrust control (FSPTC) for LIMs is still not deftly addressed by scholars and limited research was acted to exploit the FSPTC for LIM drive systems. Therefore, the current study proposes a novel finite-state predictive thrust control (NFSPTC) for linear induction motors (LIMs) with reduced numbers of voltage vectors (VVs) in the prediction phase. The NFSPTC utilizes the conventional direct thrust control (DTC) concept to reduce the required VVs from eight to only four which consist of two active vectors and two zero vectors. Decreasing the number of predicted VVs leads to a significant reduction in computational time. Moreover, the weighting factor is removed to reduce the effort in selecting the best weighting factor. Since the LIM drive system can be succeeded by developing a sensorless speed estimation, the linear speed is estimated depending on the model reference adaptive system (MRAS) before using actual sensors; thus, low cost can be attained. The suggested control approach is validated by simulation proofs based on a 3-kW arc machine. The gained findings clarified the effectiveness of the proposed four VVs control over the eight VVs procedure in dipping the thrust ripple. Besides, using the four VVs control under variable speed and fixed thrust load, the execution time was decreased by 50%. Furthermore, the proposed control procedures ensued in maintaining the primary flux linkage constant alongside succeeding a glowing-tracking speed profile throughout the tackled speed and thrust load variations.”

On an analogue of a property of singular M-matrices for the Lyapunov and Stein operators

A well-known result for a singular irreducible M-matrix A is that the only nonnegative vector that belongs to the range space of A is the zero vector. In this paper, we prove an analogue of this result for the Lyapunov and Stein transformations, which act on the inner product space of real symmetric matrices.

Mitigation of common mode voltage in ultra sparse matrix converters using auxiliary shoot‐through switches for wind energy systems

SummaryThis paper targets to minimize the peak common mode voltage (CMV) in ultra sparse matrix converters (USMC) by applying new zero vectors for the space vector modulation technique (SVM). Conventional zero vectors in the SVM raise the peak CMV by 42.23%. An increased magnitude of CMV is associated with the occurrence of leakage current, hence resulting in insulation degradation. So, the reduction of peak CMV is necessary for USMC. The proposed method offers suitable switching arrangements using auxiliary shoot through (AST) switches to minimize the peak‐to‐peak CMV. This proposed method holds the advantages of the conventional method, like a wide range of modulation index and zero current switching at the rectifier side, and also reduces the CMV problem. This paper also provides a comparative analysis of the existing reported methods and the proposed method. The effectiveness of the proposed method is validated through both simulation and experimental results.

Ladder operators with no vacuum, their coherent states, and an application to graphene

In literature ladder operators of different nature exist. The most famous are those obeying canonical (anti-) commutation relations, but they are not the only ones. In our knowledge, all ladder operators have a common feature: the lowering operators annihilate a non zero vector, the vacuum. This is connected to the fact that operators of these kind are often used in factorizing some positive operators, or some operators which are bounded from below. This is the case, of course, of the harmonic oscillator, but not only. In this paper we discuss what happens when considering lowering operators with no vacua. In particular, after a general analysis of this situation, we propose a possible construction of coherent states, and we apply our construction to graphene.

A Computationally Efficient Model Predictive Control Method for Dual Three-Phase PMSM of Electric Vehicle With Fixed Switching Frequency

Aiming at the problems of large harmonic current, unfixed switching frequency and heavy calculation burden in the model predictive current control (MPCC) methods of dual three-phase permanent magnet synchronous motor (DT-PMSM). This paper presents a computationally efficient MPCC method with a fixed switching frequency. Firstly, the virtual voltage vectors (V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s) are synthesized by two large vectors and two medium-small vectors. The V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s effectively reduce the harmonic currents, and the goal of the synthetic V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> is that the harmonic current in the x-y subspace is zero. Therefore, the weighting factor of the harmonic term is eliminated in the cost function. Secondly, an optimal voltage vector selection method is designed to reduce the candidate voltage vectors in the control set and relieves the calculation burden. In addition, to further reduce ripple current and torque ripple, the duty cycle modulation method is introduced to calculate the dwell time of the V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . The zero vector is inserted in the middle and both sides of the V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s to achieve the purpose of fixing the switching frequency. Finally, the effectiveness of the proposed method is verified by experiments.

A Low-Complexity Double Vector Model Predictive Current Control for Permanent Magnet Synchronous Motors

Compared to the conventional finite control set model predictive control (FCS-MPC), the double vector model predictive current control (DVMPCC) for permanent magnet synchronous motors (PMSMs) has a better steady-state performance without significantly increasing the switching frequency. However, determining optimal vectors with their dwell times requires a high computational burden. A low-complexity DVMPCC in the steady state was proposed in this study to address this problem. Firstly, the operating state of the motor was judged according to the speed error. During steady-state operation, the first optimal active vector was selected from three candidate vectors adjacent or identical to the active vector applied in the previous control period, reducing the number of comparisons by half. Next, the second optimal vector was selected from the other two active vectors, and the zero vector, the second optimal vector with the duty cycle, was determined according to the deadbeat condition of the q-axis current and cost function minimization. Finally, simulation and experimental results proved that the proposed low-complexity DVMPCC for surface-mounted permanent magnet synchronous motors is practical and feasible.

Modelling, Simulation and Implementation on dSpace 1103 of the Direct Power Control in a Three-Phase Shunt Active Power Filter System

This article describes a control method called "direct power control" designed specifically for parallel active power filters. The purpose of this method is to attenuate harmonics in the supply current and offset reactive power problems. The main goal is to bring the active power and reactive power back to the reference values through hysteresis control. The output of the hysteresis controller is combined with the switching table to regulate active and reactive power in real time by determining the optimal switching configuration of the inverter. This study proposes a novel switching table design based on analyzing the impact of the inverter switching vector on the instantaneous reactive and active power derivatives. The goal is to reduce the number of commutations by eliminating zero vectors while maintaining the required DC bus voltage using anti-windup techniques based on PI controllers.

STRUCTURES OF THE SETS OF BOREL AND PICARD EXCEPTIONAL VECTORS OF ANALYTIC CURVES

Previously, we have described the structure of the sets of Picard and Borel exceptional vectors for a transcendental p-dimensional integer curve with linearly independent components without common zeros. It was proved that the set of Borel exceptional vectors together with the zero vector is a finite union of subspaces of dimension not higher than p-1 of a p-dimensional complex Euclidean space. In addition, the sum of the dimensions of all these subspaces does not exceed p and any pairwise intersection of these subspaces contains only the zero vector. The set of Picard exceptional vectors has the same structure. For an integer curve of non-integer or zero order, the set of Borel exceptional vectors together with the zero vector is a single subspace of dimension no higher than p-1, which is not the case for the set of Picard exceptional vectors of an integer curve of non-integer order. The sufficiency of these results is confirmed to some extent by the corresponding examples. In this paper, we show that the above results on the structure of the set of Borel and Picard exceptional vectors for integer curves can be transferred to the case of analytic curves in the circle. We have also constructed an analytic curve in the circle, which confirms, to some extent, the sufficiency of the results. However, it was not possible to find out whether the corresponding result is transferred to the case of analytic curves of non-integer or zero order.

Low‐computation‐burden model predictive current control for the grid‐tied quasi‐Z‐source inverter

AbstractThe appealing design known as the quasi‐Z‐source inverter (qZSI) can function in both buck and boost modes. In the meantime, model predictive control (MPC) for power transformers has attracted a lot of interest. In order to improve performance and solve the shortcomings of the current MPC, this paper suggests a low‐computation‐burden model predictive current control (LCB‐MPCC) for the grid‐tied qZSI. Two active vectors, one zero vector, and one shoot‐through (ST) vector are used in the production of the output voltage. To get around the weighting factor, a modified sliding‐mode control technique is suggested for instantly controlling the inductor current and capacitor voltage to their regulating spots. The duty cycle of the ST vector is acquired by the dead‐beat control to restrict the inductor current and significantly reduce the inductor current ripple. Additionally, an effective and quick optimal sector selection strategy is provided that uses a look‐up table to pick the optimal sector rather than a number of intricate calculations. Therefore, the proposed LCB‐MPCC greatly reduces the computational burden. To demonstrate the efficacy and benefits of the suggested technique, simulation and experimental results are presented.

Enhanced Low-Speed Characteristics With Constant Switching Torque-Controller-Based DTC Technique of Five-Phase Induction Motor Drive With FOPI Control

The Classical hysteresis controller-based DTC (C-DTC) of an induction motor is a simple control scheme with better dynamics and steady-state characteristics when compared with the flux-oriented control (FOC) scheme. The major drawbacks of the C-DTC scheme are variable switching frequency and high average torque ripple under different rotor speeds. In this paper, the two-level five-leg inverter-controlled five-phase induction motor drive with constant switching torque controller-based DTC (PI-CST-DTC) scheme is introduced to improve the steady-state performance with constant switching frequency under various operating speeds. However, the proposed PI-CST-DTC exhibits slower torque and slower speed dynamics w.r.t C-DTC which is due to the periodic occurrence of zero vectors under transients. These slower dynamics are improved with the help of the proposed fractional order PI (FOPI) constant switching torque controller-based DTC (FOPI-CST-DTC) method. With the help of the hardware results, it has been verified that the proposed FOPI-based CST-DTC exhibits improved low-speed steady-state and dynamic performance of the five-phase induction motor drive. The proposed CST-DTC techniques with PI and FOPI controllers are compared with C-DTC for torque ripple reduction and %THD analysis and dynamics through hardware results.