Automotive FDS resolution improvement by using the principle of rational approximation

O.Yu.Sergiyenko, Member, IEEE, D. Hernández B., V.V.Tyrsa, P.L.A. Rosas Mendez, W. Hernandez, Member, IEEE, J. I. Nieto Hipolito, O. Starostenko, M. Rivas Lopez

Abstract— In this paper, a novel method of frequency counting of signals coming from automotive sensors is presented. The present method helps to improve fast resolution of output parameters of typical automotive frequency-domain sensors (FDS). Controlling the electromechanical systems in today’s cars is a task that requires a high processing speed. The method proposed here has been tested under computer experiments, and theoretical results have shown that it meets the requirements of speed of response and offset error of the parameters under measurement. Here, both a principle of rational approximation and its application to fast registration of frequency changes in the signal that is proportional to the physical parameter under measurement are shown. Finally, some experimental results are shown as well.

Index Terms—Frequency measurement, rational approximation, frequency domain sensors.

1. Introduction

In today’s cars, one of the most complex parts is the mechatronics, in which sensor networks play a very important role. Most of the sensors embedded in cars are frequency domain sensors (FDS) and, unfortunately, classical methods for frequency measurement [1-3] do not permit fast registration, which is one of the most crucial requirements in automotive applications. Therefore, novel methods of faster frequency measurement are desirable.

In the present paper, a novel method for improving the processing speed of the measurement parameters in frequency domain used in the modern cars is presented.

The general theory of the physical parameter conversion into frequency domain has become of paramount importance in the last decades for researchers and engineers.

This work was supported in part by the Ministry of Science and Innovation (MICINN) of Spain under the research project TEC2007-63121, and the Universidad Politecnica de Madrid.

O.Sergiyenko, D.Hernandez, P.Rosas, M.Rivas, and J.Nieto, are with Autonomous University of Baja California, Mexicali, BC 21280 Mexico (corresponding author to provide phone: 01+(52-686)-566-41-50; fax: 01+(52-686)-566-41-50; e-mail: [e-mail]).

V.V.Tyrsa is with the Mechatronics Faculty, Polytechnic University of Baja California, Mexicali, BC 21376 Mexico (e-mail: [e-mail]).

W. Hernandez is with the EUIT de Telecomunicación at the Universidad Politecnica de Madrid, Spain (e-mail: [e-mail]).

O.Starostenko with UDLA, Puebla, Mexico. ([e-mail])

The measurement method presented here is insensitive to jitter, because of its main property of not searching for the real position of the pulse but for its theoretical position in rigorously periodical processes, thanks to the fundamental laws of Number Theory.

Other industrial applications of frequency measurement techniques and frequency domain analysis of electromechanical systems are presented in [4-10].

For instance, in [4] an overview on the system development of a wireless surface acoustic wave (SAW) temperature measurement with the reader antenna a fast frequency modulated continuous wave (FMCW) which operates in the ISM band of 2.4 GHz and achieves a typical sweep time for data acquisition of 100 μs for application in high-speed high-voltage motors with stand rotation speeds up to 15 000 rpm is introduced. In [5], a single one-port surface acoustic wave (SAW) resonator strain sensor fabricated on 36° (AT) quartz with temperature stability is shown. In [6], quartz-crystal microbalance based on mass conversion into frequency of quartz-crystal self oscillation is presented; and in [7] the wireless sensor interrogator is capable of wireless detection and tracking of the resonant frequency of a passive inductor-capacitor circuit is presented, as well.

In addition, in [8] statistical time-domain techniques are used for the ongoing trends in inertial sensor technology, micro-mechanical gyros and accelerometers. In [9], a generator up-converts low-frequency environmental vibrations to a higher frequency through a mechanical frequency up-converter for most wireless applications is used; and in [10] a method to detect acceleration for seismic prospecting by a silicon-based stress-coupled optical racetrack resonator with a crossbeam mass and resonant wavelength shift is presented.

However, as we can see from [4-10] in all versatility of the papers dedicated to sensors working in frequency domain there is no enough special research of the novel methods which permits fast and accurate at the same time frequency measurement. We will try to present such analysis in this article.

This paper is arranged as follows. Section II is devoted to describe the operating principle of some common automotive FDS. Section III presents some applications of FDS in the automotive industry. Section IV explains the principle of rational approximation and introduces the mathematical formalism of Farey fractions as a tool for it. Section V gives a brief description of the prototype built in this research. Section VI is devoted to present an industrial application of the rational approximation principle to the transducer RPT410 from Druck Incorporated. Finally, Section VII is devoted to the conclusions.