Analysis of the aliasing effect caused in hardware-in-the-loop when reading PWM inputs of power converters

Hardware-in-the-loop (HIL) systems are commonly used to debug controllers in closed-loop operation. Therefore, the frequency response of the emulated subsystem is of special relevance. Undesirable oscillations can appear as a consequence of digitally sampling the switch control signals in power converter HIL models. These oscillations at relatively low frequencies, below the switching frequency, may confound the closed-loop operation and, therefore, the appropriate debugging of the controller. This paper shows that the lost information when an HIL model reads a PWM signal may create some output offset error or steady-state fluctuations, especially when the switching period and the sampling step get closer. The aliasing frequencies produced by the input sampling are calculated, and the small-signal analysis explains the relation between the output oscillation and the input PWM sub-harmonics. The output error spectrum proves that the main error sub-harmonics have the same aliasing frequency components. Both captured oscilloscope results obtained by an NI myRIO device and MATLAB simulations verify that significant distortions can be seen in the output inductor current if there is a low aliasing frequency in the digital version of the input PWM signal read by the HIL mode

Identification and Restoration of a Class of Aliased Signals

A fundamental theorem of Digital Signal Processing is Shannon's sampling theorem, whichdictates the minimum rate (called the Nyquist rate") at which a continuous-time signalmust be sampled in order to faithfully reproduce the signal from its samples. If a signalcan be reproduced from its samples, then clearly no information about the original signalhas been lost in the sampling process. However, when a signal is sampled at a rate lowerthan the Nyquist Rate, the true spectral content of the original signal is distorted due toaliasing," wherein frequencies in the original signal greater than the sampling frequencyappear as lower frequencies in the sampled signal. This distortion is generally held to beirrecoverable, i.e., whenever aliasing occurs, information is considered to be inevitably lost.This research challenges this notion and presents a technique for identifying aliasingand recovering an unaliased version of a signal from its aliased samples. The method isapplicable to frequency-modulated (FM) signals with a continuous instantaneous frequency(IF), and utilizes analysis of the IF of the aliased signal to 1) determine whether the signalhas potentially been aliased and, if so, 2) compensate for the aliasing by reconstructingan estimate of the true IF of the signal. Time-frequency methods are used to analyzethe potentially aliased signal and estimate the IF, together with modulation, re-samplingand interpolation stages to reconstruct an estimate of the unaliased signal. The proposedtechnique can yield excellent reconstruction of FM signals given ideal estimates of the IF

Harmonic analysis in finite phase space

Cataloged from PDF version of article.The Wigner distribution and linear canonical transforms are important tools for optics, signal processing, quantum mechanics, and mathematics. In this thesis, we study the discrete versions of Wigner distributions and linear canonical transforms. In the definition of a discrete entity we focus on two aspects: structural analogy and continuum approximation and/or limits. Based on this framework, the tradeoffs are analyzed and a compromise for a discrete Wigner distribution that meets both objectives to a high degree is presented by consolidating sampling theory and the algebraic approach. Such a compromise is necessary since it is impossible to meet the conditions to the highest possible degree. The differences between discrete and continuous time-frequency analysis are also discussed in a group theoretical perspective. In the second part of the thesis, the discrete versions of linear canonical transforms are reviewed and their connections to the continuous theory is established. As a special case the discrete fractional Fourier transform is defined and its properties are derived.Korkmaz, SayitM.S

Determination of the resonance response in an engine cylinder with a bowl-in-piston geometry by the finite element method for inferring the trapped mass

[EN] Cylinder resonance phenomenon in reciprocating engines consists of high-frequency pressure oscillations excited by the combustion. The frequency of these oscillations is proportional to the speed of sound on pent-roof combustion chambers and henceforth the resonance frequency can be used to estimate the trapped mass, but in bowl-in-piston chambers a geometrical factor must be added in order to deal with the bowl disturbance. This paper applies the finite element method (FEM) to provide a resonance calibration for new design combustion chambers, which are commonly dominated by the bowl geometry near the top dead centre. The resonance calibration does not need any sensor information when it is solved by a FEM procedure, and consequently, is free from measurement errors. The calibration is proven to be independent of the chamber conditions and the results obtained are compared with experimental data by using spectral techniques and measuring precisely the trapped mass.[EN]This research has been partially supported by the European Union in framework of the POWERFUL project, seventh framework program FP7/2007-2013, theme 7, sustainable surface transport (grant agreement number SCP8-GA-2009-234032).Broatch Jacobi, JA.; Guardiola, C.; Bares-Moreno, P.; Denia Guzmán, FD. (2016). Determination of the resonance response in an engine cylinder with a bowl-in-piston geometry by the finite element method for inferring the trapped mass. International Journal of Engine Research. 17(5):534-542. https://doi.org/10.1177/1468087415589701S534542175Powell, J. D. (1993). Engine Control Using Cylinder Pressure: Past, Present, and Future. Journal of Dynamic Systems, Measurement, and Control, 115(2B), 343-350. doi:10.1115/1.2899074Desantes, J. M., Galindo, J., Guardiola, C., & Dolz, V. (2010). Air mass flow estimation in turbocharged diesel engines from in-cylinder pressure measurement. Experimental Thermal and Fluid Science, 34(1), 37-47. doi:10.1016/j.expthermflusci.2009.08.009Finol, C. A., & Robinson, K. (2006). Thermal modelling of modern engines: A review of empirical correlations to estimate the in-cylinder heat transfer coefficient. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 220(12), 1765-1781. doi:10.1243/09544070jauto202Torregrosa, A. J., Broatch, A., Martín, J., & Monelletta, L. (2007). Combustion noise level assessment in direct injection Diesel engines by means of in-cylinder pressure components. Measurement Science and Technology, 18(7), 2131-2142. doi:10.1088/0957-0233/18/7/045Luján, J. M., Bermúdez, V., Guardiola, C., & Abbad, A. (2010). A methodology for combustion detection in diesel engines through in-cylinder pressure derivative signal. Mechanical Systems and Signal Processing, 24(7), 2261-2275. doi:10.1016/j.ymssp.2009.12.012Payri, F., Broatch, A., Tormos, B., & Marant, V. (2005). New methodology for in-cylinder pressure analysis in direct injection diesel engines—application to combustion noise. Measurement Science and Technology, 16(2), 540-547. doi:10.1088/0957-0233/16/2/029Zhen, X., Wang, Y., Xu, S., Zhu, Y., Tao, C., Xu, T., & Song, M. (2012). The engine knock analysis – An overview. Applied Energy, 92, 628-636. doi:10.1016/j.apenergy.2011.11.079Draper C. S. The physical effects of detonation in a closed cylindrical chamber. Technical report, National Advisory Committee for Aeronautics, 1938.Payri, F., Olmeda, P., Guardiola, C., & Martín, J. (2011). Adaptive determination of cut-off frequencies for filtering the in-cylinder pressure in diesel engines combustion analysis. Applied Thermal Engineering, 31(14-15), 2869-2876. doi:10.1016/j.applthermaleng.2011.05.012Hickling, R., Feldmaier, D. A., Chen, F. H. K., & Morel, J. S. (1983). Cavity resonances in engine combustion chambers and some applications. The Journal of the Acoustical Society of America, 73(4), 1170-1178. doi:10.1121/1.389261Bodisco, T., Reeves, R., Situ, R., & Brown, R. (2012). Bayesian models for the determination of resonant frequencies in a DI diesel engine. Mechanical Systems and Signal Processing, 26, 305-314. doi:10.1016/j.ymssp.2011.06.014Guardiola, C., Pla, B., Blanco-Rodriguez, D., & Bares, P. (2014). Cycle by Cycle Trapped Mass Estimation for Diagnosis and Control. SAE International Journal of Engines, 7(3), 1523-1531. doi:10.4271/2014-01-1702Torregrosa, A. J., Broatch, A., Margot, X., Marant, V., & Beauge, Y. (2004). Combustion chamber resonances in direct injection automotive diesel engines: A numerical approach. International Journal of Engine Research, 5(1), 83-91. doi:10.1243/146808704772914264Broatch, A., Margot, X., Gil, A., & Christian Donayre, (José). (2007). Computational study of the sensitivity to ignition characteristics of the resonance in DI diesel engine combustion chambers. Engineering Computations, 24(1), 77-96. doi:10.1108/02644400710718583Payri, F., Molina, S., Martín, J., & Armas, O. (2006). Influence of measurement errors and estimated parameters on combustion diagnosis. Applied Thermal Engineering, 26(2-3), 226-236. doi:10.1016/j.applthermaleng.2005.05.006Mechel, F. P. (Ed.). (2008). Formulas of Acoustics. doi:10.1007/978-3-540-76833-3Samimy, B., & Rizzoni, G. (1996). Mechanical signature analysis using time-frequency signal processing: application to internal combustion engine knock detection. Proceedings of the IEEE, 84(9), 1330-1343. doi:10.1109/5.535251Lapuerta, M., Armas, O., & Hernández, J. J. (1999). Diagnosis of DI Diesel combustion from in-cylinder pressure signal by estimation of mean thermodynamic properties of the gas. Applied Thermal Engineering, 19(5), 513-529. doi:10.1016/s1359-4311(98)00075-1FUENMAYOR, F. J., DENIA, F. D., ALBELDA, J., & GINER, E. (2002). H -ADAPTIVE REFINEMENT STRATEGY FOR ACOUSTIC PROBLEMS WITH A SET OF NATURAL FREQUENCIES. Journal of Sound and Vibration, 255(3), 457-479. doi:10.1006/jsvi.2001.4165Benajes, J., Molina, S., García, A., Belarte, E., & Vanvolsem, M. (2014). An investigation on RCCI combustion in a heavy duty diesel engine using in-cylinder blending of diesel and gasoline fuels. Applied Thermal Engineering, 63(1), 66-76. doi:10.1016/j.applthermaleng.2013.10.052Chen, A., & Dai, X. (2010). Internal combustion engine vibration analysis with short-term Fourier-transform. 2010 3rd International Congress on Image and Signal Processing. doi:10.1109/cisp.2010.5646222Stanković, Lj., & Böhme, J. F. (1999). Time–frequency analysis of multiple resonances in combustion engine signals. Signal Processing, 79(1), 15-28. doi:10.1016/s0165-1684(99)00077-8Costa, A. H., & Boudreaux-Bartels, G. F. (1999). An overview of aliasing errors in discrete-time formulations of time-frequency representations. IEEE Transactions on Signal Processing, 47(5), 1463-1474. doi:10.1109/78.75724

An overview of aliasing errors in discrete-time formulations of time-frequency representations

Initial algorithms for computing the Wigner distribution and other time-frequency representations belonging to Cohen\u27s fixed kernel class required that the input signal be 1) oversampled by at least a factor of two; 2) analytic; 3) explicitly or implicitly interpolated by at least a factor of two in order to avoid aliasing errors. Recently proposed algorithms claim that they provide alias-free results for signals sampled at or near the Nyquist rate without requiring oversampling. In this paper, we demonstrate that most of these claims are invalid. Since the Wigner distribution can be directly used to obtain any other time-frequency representation belonging to Cohen\u27s fixed kernel class, we first evaluate several recently proposed discrete Wigner distribution formulations that claim to be alias-free, and then, we proceed to identify classes of signals that will always give aliasing errors for each of the investigated discrete Wigner distribution formulations, even when the signal has been oversampled by at least a factor of two. Finally, we state the necessary conditions for each of the advertised alias-free methods to produce truly alias-free time-frequency representations. ©1997 IEEE