Contractive projections in Paley-Wiener spaces

Let $S_1$ and $S_2$ be disjoint finite unions of parallelepipeds. We describe necessary and sufficient conditions on the sets $S_1,S_2$ and exponents $p$ such that the canonical projection $P$ from $PW_{S_1\cup S_2}^p$ to $PW_{S_1}^p$ is a contraction

Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials

Let $\Gamma$ be a subset of $\{0,1,2,...\}$. We show that if $\Gamma$ has `gaps' then the completeness and frame properties of the system $\{t^ke^{2\pi i nt}: n\in\mathbb{Z},k\in\Gamma\}$ differ from those of the classical exponential systems. This phenomenon is closely connected with the existence of certain uniqueness sets for lacunary polynomials.Comment: 16 pages, 1 figur

Component-in-the-Loop Testing of Automotive Powertrains Featuring All-Wheel-Drive

The article is dedicated to the methodology of designing component-in-the-loop (CiL) testing systems for automotive powertrains featuring several drivelines, including variants with individually driven axles or wheels. The methodical part begins with descriptions of operating and control loops of CiL systems having various simulating functionality—from a “lumped” vehicle for driving cycle tests to vehicles with independently rotating drivelines for simulating dynamic maneuvers. The sequel contains an analysis that eliminates a lack of clarity observed in the existing literature regarding the principles of building a “virtual inertia” and synchronization of loading regimes between individual drivelines of the tested powertrain. In addition, a contribution to the CiL methodology is offered by analyzing the options of simulating tire slip taking into account a limited accuracy of measurement equipment and a limited performance of actuating devices. The methodical part concludes with two examples of mathematical models that can be employed in CiL systems to simulate vehicle dynamics. The first one describes linear motion of a “lumped” vehicle, while the second one simulates vehicle’s trajectory motion taking into account tire slip in both the longitudinal and lateral directions. The practical part of the article presents a case study showing an implementation of the CiL design principles in a laboratory testing facility intended for an all-wheel-drive hybrid powertrain of a heavy-duty vehicle. The CiL system description is followed by the test results simulating the hybrid powertrain operation in a driving cycle and in trajectory maneuvering. The results prove the validity of the proposed methodical principles, as well as their suitability for practical implementations

Transverse-momentum ptp_t correlations on (η,ϕ)(\eta,\phi) from mean-ptp_{t} fluctuations in Au-Au collisions at sNN=\sqrt{s_{NN}} = 200 GeV

We present first measurements of the pseudorapidity and azimuth $(\eta,\phi)$ bin-size dependence of event-wise mean transverse momentum $$ fluctuations for Au-Au collisions at $\sqrt{s_{NN}} = 200$ GeV. We invert that dependence to obtain $p_t$ autocorrelations on differences $(\eta_\Delta,\phi_\Delta)$ interpreted to represent velocity/temperature distributions on ($\eta,\phi$). The general form of the autocorrelations suggests that the basic correlation mechanism is parton fragmentation. The autocorrelations vary strongly with collision centrality, which suggests that fragmentation is strongly modified by a dissipative medium in the more central Au-Au collisions relative to peripheral or p-p collisions. \\Comment: 7 pages, 3 figure

Comparative Study of Powertrain Hybridization for Heavy-Duty Vehicles Equipped with Diesel and Gas Engines

This article describes a study that aimed to estimate the fuel-saving potential possessed by the hybridization of conventional powertrains intended for heavy-duty vehicles based on diesel and natural gas fueled engines. The tools used for this analysis constitute mathematical models of vehicle dynamics and the powertrain, including its components, i.e., the engine, electric drive, transmission, and energy storage system (ESS). The model of the latter, accompanied by experimental data, allowed for an analysis of employing a supercapacitor regarding the selection of its energy content and the interface between the traction electric drive and the ESS (in light of the wide voltage operating range of supercapacitors). The results revealed the influence of these factors on both the supercapacitor efficiency (during its operation within a powertrain) and the vehicle fuel economy. After implementation of the optimized ESS design within the experimentally validated vehicle model, simulations were conducted in several driving cycles. The results allowed us to compare the fuel economy provided by the hybridization for diesel and gas powertrains in different driving conditions, with different vehicle masses, taking into account the onboard auxiliary power consumption

Model Analysis of Electrically Driven Vehicles by Means of Unknown Input Observers

The article describes a method to analyze the powertrain operation of electrically driven vehicles in cases of insufficient information (i.e., unknown control algorithms, no torque measurements during vehicle tests). The method implies mathematical modeling with involvement of so-called unknown input observers. A variant of such an observer is proposed. Using that observer, studies of a hybrid vehicle and a pure electric vehicle are performed. The models with torque observers simulated tests of said vehicles conducted on a chassis dynamometer and on roads. For the hybrid vehicle, operating regimes of main powertrain components were identified. For the electric vehicle, the identification revealed a coordinated operation of regenerative braking and mechanical braking. Adequacy of the modeling, including identification of the unmeasured torques, was verified through a comparison with experimental data

Performance Analysis of the Sliding Mode Control for Automated Vehicle Path Tracking at Low Adhesion Surfaces

The article analyses prospects of using a type of robust controllers called relay regulators for automation of vehicle lateral motion. The operation of these regulators in so-called sliding modes is considered along with the “chattering” problem caused by deviations from the “ideal” sliding mode inevitable in actual implementations. For the analysis of vehicle motion, a mathematical model was elaborated, which calculates vehicle dynamics taking into account non-linear tire-road adhesion characteristics. In the conducted study, emphasis was put on low adhesion surfaces, which can be considered as the most difficult case for automatic lateral control of a vehicle. In order to implement automated path tracking within the model, two relay regulators were elaborated differing from one another in the order of dynamics. A comparative study of these regulators was conducted by means of simulations. The regulator that had shown best performance was then tested for robustness by means of modeling, in which maneuvers on snow, ice and a mixed surface were simulated

X-in-the-Loop Testing of a Thermal Management System Intended for an Electric Vehicle with In-Wheel Motors

The article describes an elaboration of the X-in-the-loop (XiL) testing environment for a thermal management system (TMS) intended for the traction electric drive of an electric vehicle, which has each of its wheels driven by an in-wheel motor. The TMS features the individual thermal regulation of each electric drive using a hydraulic layout with parallel pipelines and electrohydraulic pumps embedded into them. The XiL system is intended as a tool for studying and developing the TMS design and controls. It consists of the virtual part and the physical part. The former simulates the vehicle operating in a driving cycle with the heat power dissipated by the electric drive components, which entails the change in their temperature regimes. The physical part includes the TMS itself consisting of a radiator, pipelines, and pumps. The physical part also features devices intended for simulation of the electric drive components in terms of their thermal and hydraulic behaviors, as well as devices that simulate airflow induced by the vehicle motion. Bilateral, real-time interactions are established between the two said parts combining them into a cohesive system, which models the studied electric vehicle and its components. The article gives a description of a laboratory setup, which implements the XiL environment including the mathematical models, hardware devices, as well as the control loops that establish the interaction of those components. An example of using this system in a driving cycle test shows the interaction between its parts and operation of the TMS in conditions simulated in both virtual and physical domains. The results constitute calculated and measured quantities including vehicle speed, operating parameters of the electric drives, coolant and air flow rates, and temperatures of the system components