Key Analytical Results Research Articles

Fast and Simple Tuning Rules of Synchronous Reference Frame Proportional-Integral Current Controller

Synchronous reference frame proportional-integral (PI) current controller (CC) is considered the most well-established solution for the current regulation in electrical drives. However, the gain selection of the PI CC is still regarded to be poorly reported, particularly in relation to the effect of the inevitable execution time taken by the controller and inverter. Mostly, tuning process of PI CC is done by trial and error or using simple rules based on pole zero cancelation and pole placement methods which ignore time delays through the controller and inverter. Hence, PI CC delivers significantly different performance compared to the expected one during the digital implementation, especially if high bandwidth or low ratio between the switching and operational frequency are required. Therefore, this paper firstly addresses and analyses the common tuning rules of PI CC which ignore the existence of time delays followed by a rigorous analysis for PI CCs' robustness to the influence of computational and modulation delays. Based on this analysis, generic recommendations have been proposed to select the PI CCs' gains as a function of the electrical drive switching frequency considering the delay effect. A set of simple, generic, and fast tuning rules were derived that guarantee fast dynamic performance with reasonable stability margins. Moreover, the effects of model uncertainties on these developed rules have been analyzed and reported. Comprehensive experimental results are provided to prove the key analytical results of this study and to validate the proposed design recommendations.

Modeling and stability analysis of three- and six-phase asymmetrical grid-connected induction generator

This paper presents the development of linearized model of asymmetrical six-phase grid-connected induction generator (GCIG) for small-signal stability. The developed linearized model has been used to obtain the eigenvalue to evaluate generator stability with respect to parameter variation of the machine in comparison with its three-phase counterpart. During the analysis, suitability of six-phase induction generator for higher output power has been accessed. Instability tendency during low electrical output power can be avoided through closed loop operation of the machine. Hence, the indirect field-oriented control scheme for asymmetrical six-phase GCIG has been proposed for stable operation with higher reliability. The key analytical results have been demonstrated with its experimental validation.

Small signal stability of three-phase and six-phase synchronous motors: A comparative analysis

Small signal stability analysis is conducted for an asymmetrical six-phase synchronous motor in comparison with its equivalent three-phase counterpart. For this purpose, a linearized model of the six-phase synchronous motor is developed using the dq0 approach, which is used in eigenvalue criteria to determine absolute stability in comparison with its equivalent three-phase counterpart. The analysis includes a comparison of the variation in evaluated eigenvalues associated with the stator and rotor sides according to changes in both the three and six-phase machine parameters and working conditions. Key analytical results are experimentally investigated and validated on a test rig.

Transient thermo-mechanical analysis for bimorph soft robot based on thermally responsive liquid crystal elastomers

Thermally responsive liquid crystal elastomers (LCEs) hold great promise in applications of soft robots and actuators because of the induced size and shape change with temperature. Experiments have successfully demonstrated that the LCE based bimorphs can be effective soft robots once integrated with soft sensors and thermal actuators. Here, we present an analytical transient thermo-mechanical model for a bimorph structure based soft robot, which consists of a strip of LCE and a thermal inert polymer actuated by an ultrathin stretchable open-mesh shaped heater to mimic the unique locomotion behaviors of an inchworm. The coupled mechanical and thermal analysis based on the thermo-mechanical theory is carried out to underpin the transient bending behavior, and a systematic understanding is therefore achieved. The key analytical results reveal that the thickness and the modulus ratio of the LCE and the inert polymer layer dominate the transient bending deformation. The analytical results will not only render fundamental understanding of the actuation of bimorph structures, but also facilitate the rational design of soft robotics.

Polygenic adaptation: From sweeps to subtle frequency shifts.

Evolutionary theory has produced two conflicting paradigms for the adaptation of a polygenic trait. While population genetics views adaptation as a sequence of selective sweeps at single loci underlying the trait, quantitative genetics posits a collective response, where phenotypic adaptation results from subtle allele frequency shifts at many loci. Yet, a synthesis of these views is largely missing and the population genetic factors that favor each scenario are not well understood. Here, we study the architecture of adaptation of a binary polygenic trait (such as resistance) with negative epistasis among the loci of its basis. The genetic structure of this trait allows for a full range of potential architectures of adaptation, ranging from sweeps to small frequency shifts. By combining computer simulations and a newly devised analytical framework based on Yule branching processes, we gain a detailed understanding of the adaptation dynamics for this trait. Our key analytical result is an expression for the joint distribution of mutant alleles at the end of the adaptive phase. This distribution characterizes the polygenic pattern of adaptation at the underlying genotype when phenotypic adaptation has been accomplished. We find that a single compound parameter, the population-scaled background mutation rate Θbg, explains the main differences among these patterns. For a focal locus, Θbg measures the mutation rate at all redundant loci in its genetic background that offer alternative ways for adaptation. For adaptation starting from mutation-selection-drift balance, we observe different patterns in three parameter regions. Adaptation proceeds by sweeps for small Θbg ≲ 0.1, while small polygenic allele frequency shifts require large Θbg ≳ 100. In the large intermediate regime, we observe a heterogeneous pattern of partial sweeps at several interacting loci.

Optimal Precoder Design for Distributed Transmit Beamforming Over Frequency-Selective Channels

We consider the problem of optimal precoder design for a multi-input single-output wideband wireless system to maximize two different figures of merit: the total communication capacity and the total received power, subject to individual power constraints on each transmit element. We show that the two optimal precoders satisfy a separation principle that reveals a simple structure for these precoders. We use this separation principle extensively to derive several interesting properties of these two optimal precoders. Some key analytical results are as follows. We show that the power-maximizing precoders must concentrate all their energy in a small number of active channels that cannot exceed the number of input terminals. The capacity-maximizing precoder turns out to be very different from the classical water filling solutions and also very different from the power-maximizing precoders except at asymptotically low SNRs where the power-maximizing precoders also maximize capacity. We also show that the capacity of the wideband system is lower bounded by the sum rate of a multiple-access channel with the same channel gains and power constraints. Finally, the separation principle also yields simple fixed-point algorithms that allow for the efficient numerical computation of the two optimal precoders.

Modeling and analysis of six-phase synchronous motor under fault condition

Multi-phase machines (more than three-phase) are rigorously being investigated for various high power applications due to their increased power to weight ratio, increased frequency and reduced magnitude of torque pulsation, and fault tolerant characteristics. Fault analysis of a system is extremely important, not only to understand its operating characteristic, but it is also required prior to the design of suitable control/protective scheme. Therefore, the aim of this paper is not to devise a new mathematical model and control algorithm, but to investigate the behavior of six-phase synchronous motor (SPSM) under fault conditions caused by open circuit (OC) and short circuit (SC) at its input terminals as that has not been reported so far. Some key analytical results have been experimentally verified.

An Analytical Model of Four-Point Contact Rolling Element Ball Bearings

The purpose of this work is to establish an analytical model and standard way to predict the performance characteristics of a four-point contact, or gothic arch type, rolling element ball bearing. Classical rolling element bearing theory, as developed by Jones, has been extended to include the complex kinematics of the four-point contact bearing; thereby providing complete elementwise attitude and internal load distribution of the bearing under operating conditions. Standard performance parameters, such as element contact stresses, contact angles, inner ring deflections, nonlinear stiffness's, torque, and L10 life, are solved explicitly via standard Newton–Raphson techniques. Race control theory is replaced with a minimum energy state theory to allow both spin and slip to occur at the ball-to-raceway contact. The developed four-point model was programed within the orbis software program. Various test cases are analyzed and key analytical results are compared with the Jones four-point contact ball bearing analysis program, the Wind Turbine Design Guideline, DG03, and traditional two-point (angular contact) analysis codes. Model results for the internal distribution of ball loads and contact angles match the Jones program extremely well for all cases considered. Some differences are found with the DG03 analysis methods, and it is found that modeling a four-point contact bearing by overlaying two opposed angular contact bearings can result in gross errors.

The Importance of Motions that Accompany Those Occurring Along the Reaction Coordinate

The reaction coordinate is a well known quantity used to define the motions critical to chemical reactions, but many other motions always accompany it. These other motions are typically ignored but this is not always possible. Sometimes it is not even clear as to which motions comprise the reaction coordinate: spectral measurements that one may assume are dominated by the reaction coordinate could instead be dominated by the accompanying modes. Examples of different scenarios are considered. The assignment of the visible absorption spectrum of chlorophyll-a was debated for 50 years, with profound consequences for the understanding of how light energy is transported and harvested in natural and artificial solar-energy devices. We recently introduced a new, comprehensive, assignment, the centrepiece of which was determination of the reaction coordinate for an unrecognized photochemical process. The notion that spectroscopy and reactivity are so closely connected comes directly from Hush’s adiabatic theory of electron-transfer reactions. Its basic ideas are reviewed, similarities to traditional chemical theories drawn, key analytical results described, and the importance of the accompanying modes stressed. Also highlighted are recent advances that allow this theory to be applied to general transformations including isomerization processes, hybridization, aromaticity, hydrogen bonding, and understanding why the properties of first-row molecules such as NH3 (bond angle 108°) are so different to those of PH3–BiH3 (bond angles 90–93°). Historically, the question of what is the reaction coordinate and what is just an accompanying motion has not commonly been at the forefront of attention. In our new approach in which all chemical processes are described using the same core theory, this question becomes thrust forward as always being the most important qualitative feature to determine.

Analytical and Semi‐Analytical Tools for the Design of Oscillatory Pumping Tests

Oscillatory pumping tests-in which flow is varied in a periodic fashion-provide a method for understanding aquifer heterogeneity that is complementary to strategies such as slug testing and constant-rate pumping tests. During oscillatory testing, pressure data collected at non-pumping wells can be processed to extract metrics, such as signal amplitude and phase lag, from a time series. These metrics are robust against common sensor problems (including drift and noise) and have been shown to provide information about aquifer heterogeneity. Field implementations of oscillatory pumping tests for characterization, however, are not common and thus there are few guidelines for their design and implementation. Here, we use available analytical solutions from the literature to develop design guidelines for oscillatory pumping tests, while considering practical field constraints. We present two key analytical results for design and analysis of oscillatory pumping tests. First, we provide methods for choosing testing frequencies and flow rates which maximize the signal amplitude that can be expected at a distance from an oscillating pumping well, given design constraints such as maximum/minimum oscillator frequency and maximum volume cycled. Preliminary data from field testing helps to validate the methodology. Second, we develop a semi-analytical method for computing the sensitivity of oscillatory signals to spatially distributed aquifer flow parameters. This method can be quickly applied to understand the "sensed" extent of an aquifer at a given testing frequency. Both results can be applied given only bulk aquifer parameter estimates, and can help to optimize design of oscillatory pumping test campaigns.

Painlevé IV: A numerical study of the fundamental domain and beyond

The six Painlevé equations were introduced over a century ago, motivated by rather theoretical considerations. Over the last several decades, these equations and their solutions, known as the Painlevé transcendents, have been found to play an increasingly central role in numerous areas of mathematical physics. Due to extensive dense pole fields in the complex plane, their numerical evaluation remained challenging until the recent introduction of a fast ‘pole field solver’ (Fornberg and Weideman, 2011). The fourth Painlevé equation has two free parameters in its coefficients, as well as two free initial conditions. After summarizing key analytical results for PIV, the present study applies this new computational tool to the fundamental domain and a surrounding region of the parameter space. We confirm existing analytic and asymptotic knowledge about the equation and also explore solution regimes which have not been described in the previous literature.

LIMERIC: A Linear Adaptive Message Rate Algorithm for DSRC Congestion Control

Wireless vehicle-to-vehicle (V2V) and vehicle-toinfrastructure (V2I) communication holds great promise for significantly reducing the human and financial costs of vehicle collisions. A common characteristic of this communication is the broadcast of a device's core state information at regular intervals (e.g., vehicle speed and location or traffic signal state and timing). Unless controlled, the aggregate of these broadcasts will congest the channel under dense traffic scenarios, reducing the effectiveness of collision avoidance applications that use transmitted information. Active congestion control using distributed techniques is a topic of great interest for establishing the scalability of this technology. This paper defines a new adaptive congestion control algorithm that can be applied to the message rate of devices in this vehicular environment. While other published approaches rely on binary control, the LInear MEssage Rate Integrated Control (LIMERIC) algorithm takes advantage of full-precision control inputs that are available on the wireless channel. The result is provable convergence to fair and efficient channel utilization in the deterministic environment, under simple criteria for setting adaptive parameters. This “perfect” convergence avoids the limit cycle behavior that is inherent to binary control. We also discuss several practical aspects associated with implementing LIMERIC, including guidelines for the choice of system parameters to obtain desired utilization outcomes, a gain saturation technique that maintains robust convergence under all conditions, convergence with asynchronous updates, and using channel load to determine the aggregate message rate that is observable at a receiver. This paper also extends the convergence analysis for two important cases, i.e., measurement noise in the input signal and delay in the update process. This paper illustrates key analytical results using MATLAB numerical results and employs standard NS-2 simulations to demonstrate the performance of LIMERIC in several high-density scenarios.

Targeted delivery of acoustic energy for self-healing

Self-healing materials capable of autonomic crack healing are potentially important in terrestrial and space applications. Where damage-causing forces and healing forces compete, it is of interest to consider ways to increase the healing rate. This article investigates the use of acoustic energy for this purpose. As a means for targeted acoustic energy delivery to the crack site, we study time-reversal mirrors (iterative time reversal and playback) for stress wave focusing at a discontinuity. The article begins with a discussion of the key analytical results. Both pulse propagation and eigenfrequency vibrations are analyzed, and it is argued that if sufficient time is allowed between successive time-reversed playbacks, the focused pulse amplitude grows faster than the eigenfrequency vibrations. Experimental implementations of iterative time-reversed playback on solid circular steel and nylon rods with artificially introduced discontinuities show that even in the one-dimensional propagation studies here, time-reversal mirrors produce satisfactory focusing for a multitone pulse. Based on the significant amplification seen in the steel rods and the more dispersive and dissipative nylon rods, it appears that acoustic energy could be delivered in a targeted manner to a crack using iterative time-reversal mirrors.

Graph Theoretic Foundations of Multibody Dynamics Part II: Analysis and Algorithms.

This second, of a two part paper, uses concepts from graph theory to obtain a deeper understanding of the mathematical foundations of multibody dynamics. The first part [7] established the block-weighted adjacency (BWA) matrix structure of spatial operators associated with serial and tree topology multibody system dynamics, and introduced the notions of spatial kernel operators (SKO) and spatial propagation operators (SPO). This paper builds upon these connections to show that key analytical results and computational algorithms are a direct consequence of these structural properties and require minimal assumptions about the specific nature of the underlying multibody system. We formalize this notion by introducing the notion of SKO models for general tree-topology multibody systems. We show that key analytical results, including mass matrix factorization, inversion, and decomposition hold for all SKO models. It is also shown that key low-order scatter/gather recursive computational algorithms follow directly from these abstract-level analytical results. Application examples to illustrate the concrete application of these general results are provided. The paper also describes a general recipe for developing SKO models. The abstract nature of SKO models allows the application of these techniques to a very broad class of multibody systems.

Graph Theoretic Foundations of Multibody Dynamics Part I: Structural Properties.

This is the first part of two papers that use concepts from graph theory to obtain a deeper understanding of the mathematical foundations of multibody dynamics. The key contribution is the development of a unifying framework that shows that key analytical results and computational algorithms in multibody dynamics are a direct consequence of structural properties and require minimal assumptions about the specific nature of the underlying multibody system. This first part focuses on identifying the abstract graph theoretic structural properties of spatial operator techniques in multibody dynamics. The second part paper exploits these structural properties to develop a broad spectrum of analytical results and computational algorithms.Towards this, we begin with the notion of graph adjacency matrices and generalize it to define block-weighted adjacency (BWA) matrices and their 1-resolvents. Previously developed spatial operators are shown to be special cases of such BWA matrices and their 1-resolvents. These properties are shown to hold broadly for serial and tree topology multibody systems. Specializations of the BWA and 1-resolvent matrices are referred to as spatial kernel operators (SKO) and spatial propagation operators (SPO). These operators and their special properties provide the foundation for the analytical and algorithmic techniques developed in the companion paper.We also use the graph theory concepts to study the topology induced sparsity structure of these operators and the system mass matrix. Similarity transformations of these operators are also studied. While the detailed development is done for the case of rigid-link multibody systems, the extension of these techniques to a broader class of systems (e.g. deformable links) are illustrated.

The international competitiveness of Chinese manufacturing firms and the exit of the renminbi–dollar peg

This paper evaluates the implications of a shift from a pegged to a floating exchange rate regime for the international competitiveness and the economic behavior of Chinese manufacturing firms. Using a conceptual framework that characterizes the relationship between the exchange rate regime and the potential source of a firm's competitive advantage, it yields two key analytical results. First, Chinese manufacturing firms may increase their reliance on a low-margin pricing strategy as the exchange rate regime shifts towards a more flexible one. As a corollary, a low-margin pricing strategy may discourage Chinese manufacturing firms from undertaking costly research and development (R&D) activities, and investments in human capital development. Second, Chinese manufacturing firms have the incentive to employ various wage restraint measures under a floating exchange rate regime at least in the short term. These key analytical results provide insights into a number of policy-relevant issues that may arise at the firm-level. It concludes by providing some general directions on the timing of a complete transition to a floating exchange rate regime.

Closed-form analysis of adjustable-speed drive performance under input-voltage unbalance and sag conditions

Voltage unbalance or sag conditions generated by the line excitation can cause the input rectifier stage of an adjustable-speed drive (ASD) to enter single-phase rectifier operation. This degradation of the input power quality can have a significant negative impact on the induction-machine performance characteristics. This paper provides an approximate closed-form analysis of the impact of line-voltage sags and unbalance on the induction-machine phase voltages, currents, and torque pulsations for a general-purpose ASD consisting of a three-phase diode bridge rectifier, a dc link, and a pulsewidth modulation (PWM) inverter delivering constant volts-per-hertz excitation. Attention is focused on the impact of the dominant second harmonic of the line frequency, which appears in the dc link voltage during the sag/unbalance conditions, neglecting the impact of the other higher order harmonics. In addition to the closed-form analytical results that assume constant rotor speed, both simulation and experimental results are presented, which confirm the key analytical results, including the dominance of the second harmonic in the resulting torque pulsations. The analytical results can be used as a valuable design tool to rapidly evaluate the approximate impact of unbalance/sag conditions on ASD machine performance.

Equilibrium Analysis, Banking, Contagion and Financial Fragility

This paper contains a general equilibrium model of an economy with incomplete markets (GEI) with money and default. The model is a simplified version of the real world consisting of a non-bank private sector, banks, a central bank, a government and a regulator. The model is used to analyse actions by policy-makers and to identify policy relevant empirical work. Key analytical results are: a financially fragile system need not collapse; efficiency can be improved with policy intervention; and a system with heterogeneous banks is more stable than one with homogeneous ones. Existence of monetary equilibria allows for positive default levels in equilibrium. It also characterises contagion and financial fragility as an equilibrium phenomenon. A definition of financial fragility is proposed. Financial fragility occurs when aggregate profitability of the banking sector declines and defaults in the non-bank and banking private sectors increase. Thus, equilibria with financial fragility require financial vulnerability in the banking sector and liquidity shortages in the non-bank private sector. The model will be used as a basis to carry out empirical work on the costs of financial instability, to quantify the effectiveness of particular regulatory tools such as capital requirements, and to identify trade-offs between increasing stability through action by authorities and the efficiency of the financial system.

Analysis of a Multiphase Induction Machine Under Fault Condition in a Phase-Redundant A.C. Drive System

Phase-redundancy is a unique technique for improving the reliability of large variable speed AC drives. This technique, derived from the concept of parallel-redundancy, is based on the capability of a multiphase machine to start and continue running with one or more of its many stator phases open or short circuited with lower performance. Structural unbalance in the machine following loss of excitation is the main source of performance degradation. This paper, therefore, presents a simple generalized approach to analyze the dynamic as well as steady-state behavior of a multiphase induction machine during fault condition in a phase-redundant AC drive system. The key analytical results have been experimentally verified by tests conducted on a laboratory prototype.

Torque Production in Permanent-Magnet Synchronous Motor Drives with Rectangular Current Excitation

Special features of torque production in self-controlled permanent-magnet (PM) synchronous motor drives with rectangular current excitation have been investigated. Addressed issues include the generation of undesired torque pulsations at low speeds and system operating locus limits imposed at high speeds by saturation of the current regulator. Attention is limited to motors in which sources of reluctance torque are suppressed by surface-mounting of the rotor magnets and skewing of the stator slots. Results from the low-speed investigation indicate that the pulsating torque can be minimized by a combination of steps including proper adjustment of the rotor magnet pole atc and effective use of rotor speed feedback compensation. High-speed saturated-regulator performance is significantly influenced by the 120 electrical degree inverter switch conduction intervals inherent with rectangular current excitation. The system torque-speed operating envelope can be expanded by several means, including on-line adjustment of the converter excitation phase angle a, but resulting performance trade-offs require careful scrutiny. A 15-kW prototype PM synchronous motor drive system has been used to confirm key analytical results.