Variable Boundary Layer Research Articles

Stability of Compressible Mixing Layers Modified by Wakes and Jets

Binary free shear layers are frequently used as a model to study the stability of flows relevant in propulsion devices. The stability behaviour of binary, compressible mixing layer have been investigated and reported in the literature by many research groups and detailed description of the stability characteristics and flow topology have been published. The stability of more complex free shear layers, such as mixing layers modified by jets and wakes, has received less attention and a smaller number of references report on the stability characteristics of such flows. The availability of advanced numerical techniques as well as computational power nowadays allow the study of complex flows by direct numerical simulation. The present investigation is an extension of previous work on the stability of complex free shear flows where besides growth rates, wave numbers and frequencies, the flow topology resulting from the interaction of mixing layers, jets and wakes are investigated. The results show that, depending on the jet or wake strength relative to the mixing layer fast and slow stream velocities, the characteristic Kelvin-Helmholtz vortices may be enhanced and a more complex vortex distribution topology results. These vorticity distributions have a significant effect on the mixture between different species on the upper and lower stream and the mixing layer to jet species ratio. The effect of three-dimensional disturbances with spanwise wavenumber β * 0 are also considered and the most amplified modes are determined for a low convective mach number condition. Different combinations of hydrogen and oxygen on the mixing layer and jets are considered. For that study the base flow is determined from a parabolic, variable properties boundary layer code. The results show that oblique disturbances are more stable than two-dimensional disturbances but with different strength depending on the particular binary free shear layer considered.

A Simple Analytical Model of the Nocturnal Low-Level Jet over the Great Plains of the United States

Abstract A simple analytical model including both diurnal thermal forcing over sloping terrain (the “Holton” mechanism) and diurnally varying boundary layer friction (the “Blackadar” mechanism) is developed to account for the observed amplitude and phase of the low-level jet (LLJ) over the Great Plains and to understand better the role of each mechanism. The present model indicates that, for the pure Holton mechanism (time-independent friction coefficient), the maximum southerly wind speed occurs (depending on the assumed friction coefficient) between sunset and midnight local standard time, which is earlier than the observed after-midnight maximum. For the pure Blackadar mechanism (time-independent thermal forcing), the present model shows that generally occurs later (closer to sunrise) than observed and has a strong latitudinal dependence. For both mechanisms combined, the present model indicates that occurs near to the observed time, which lies between the time obtained in the pure Holton mechanism and the time obtained in the pure Blackadar mechanism; furthermore, is larger (and closer to that observed) than in each one considered individually. The amplitude and phase of the LLJ as a function of latitude can be obtained by the combined model by allowing for the observed latitude-dependent mean and diurnally varying thermal forcing.

Seasonal and diurnal variation in particulate matter (PM10 and PM2.5) at an urban site of Beijing: analyses from a 9-year study.

Air pollution has become a top environmental concern in China. In the present study, 9 years of PM10 and PM2.5 data from an urban monitoring station in Beijing was analyzed relative to other gaseous pollutants and several meteorological parameters. The levels and characteristics of particulate matters as well as the sources and factors affecting them were provided in the present study. During the 9-year observation period, PM10 and PM2.5 showed high levels, with annual mean values of 138.5 ± 92.9 and 72.3 ± 54.4 μg/m(3), respectively. Slight decreasing trends of annual mean PM10 and PM2.5 were observed; autumn was the main season that contributed to the decrease in annual mean PM10 and PM2.5. Higher values for both PM fractions were generally observed in the spring and summer months, respectively, whereas lower values were found in the summer and spring months, respectively. Pronounced diurnal variations were found for PM10 and PM2.5, which both displayed a bimodal pattern with peaks between 7:00 and 8:00 a.m. as well as 7:00 and 11:00 p.m.; a minimum generally appeared at approximately noon. The seasonal and diurnal variations in particulate concentration are mostly dominated by the seasonal and diurnal variability of boundary layer and source emissions. A principal components analysis revealed that both the traffic-related emissions and combustion sources were major contributions to the particles; their contributions ranged between 35.5-75.1%. Furthermore, a directional analysis shows a stronger association between particles and the southerly winds, the PM derived from sources south of Beijing, most likely secondary PM, significantly affects concentrations at the sampling site. To improve air quality in Beijing, mitigation measures including phasing out high energy-consuming industries and prioritize the use of clean energy sources should be designed to reduce emissions from both local and regional sources.

Sensorless Control of PMSM Based on Sliding Mode Observer

A novel sliding mode observer(SMO) of PMSM(permanent magnetic synchronous motor) was presented, which estimated the rotor position and angular velocity accurately.The proposed SMO substitutes a sigmoid function for the conventional signum function with a variable boundary layer which is changed according to the rotational velocity.The dependence to motor parameters and chattering effects that is commonly found in signum function using for the switching function were overcome.By combining the model of PMSM under d-q coordinate,the convergence condition of observer was deduced.The convergence was verified by the Lyapunov theory.Simulation results show that the rotor position and velocity can be observed accurately,and also has good dynamic performance and robustness.

Sensored Field Oriented Control of a Robust Induction Motor Drive Using a Novel Boundary Layer Fuzzy Controller

Physical sensors have a key role in implementation of real-time vector control for an induction motor (IM) drive. This paper presents a novel boundary layer fuzzy controller (NBLFC) based on the boundary layer approach for speed control of an indirect field-oriented control (IFOC) of an induction motor (IM) drive using physical sensors. The boundary layer approach leads to a trade-off between control performances and chattering elimination. For the NBLFC, a fuzzy system is used to adjust the boundary layer thickness to improve the tracking performance and eliminate the chattering problem under small uncertainties. Also, to eliminate the chattering under the possibility of large uncertainties, the integral filter is proposed inside the variable boundary layer. In addition, the stability of the system is analyzed through the Lyapunov stability theorem. The proposed NBLFC based IM drive is implemented in real-time using digital signal processor (DSP) board TI TMS320F28335. The experimental and simulation results show the effectiveness of the proposed NBLFC based IM drive at different operating conditions.

Sliding Mode Speed Control for Induction Motor Drives with State-Dependent Gain Method

The main obstacle of conventional sliding mode control is caused by discontinuous function of high control activity which is known as chattering phenomenon. In this research, the chattering phenomenon is significantly reduced by a newly developed algorithm. A fast sigmoid function with varying boundary layer algorithm is designed as a state-dependent to replace the discontinuous function in conventional sliding mode control. It is known that the switching gain of sliding mode control is proportional to the chattering level, and normally a large switching gain is applied to handle the uncertainties. This research proposes a state-dependent sliding mode control which is the switching gain and boundary layer is proportional to the sigmoid function of the sliding mode controller. As a result, the boundary layer and the switching gain will change depend on uncertainties of the motor drives system. The induction motor is controlled by vector control strategy, using indirect field orientation and Space Vector Pulse Width Modulation technique. Experimental result have proved that the proposed state-dependent sliding mode control able to deal with external load disturbances as well as effectively free from chattering phenomenon compared to conventional sliding mode control. The proposed algorithm and the vector control strategy are developed in digital signal processing board. The results have confirmed that the state-dependent sliding mode control is superior with regard to external load disturbances and variation in the reference speed setting when compared to conventional sliding mode control and fixed boundary layer sliding mode control.

A puff model using a three-dimensional analytical solution for the pollutant diffusion process

A new model for the dispersion of passive puffs is presented (puff model). The model is based on the GILTT (Generalized Integral Laplace Transform Technique) approach, a general technique for solving the advection–diffusion equation. It is a well-known hybrid method that had solved a wide class of direct and inverse problems mainly in the area of Heat Transfer and Fluid Mechanics and the solution is given in series form. It is used a boundary layer parameterization that allows the model to be applied routinely using as input simple ground-level meteorological data. A preliminary performance evaluation is shown in the case of continuous emission from an elevated source in a variable boundary layer (with a time resolution of 10min).

Spatial variability of the wave bottom boundary layer over movable rippled beds

[1] Observations of the spatially dependent velocity field over movable bed forms subjected to slightly skewed and asymmetric regular wave forcing were collected. The dynamics between the ripple elements is dominated by coherent vortices, characterized by the swirling strength, and evidenced in the temporal and spectral characterization. Within the boundary layer, spectral energy in the second harmonic (3f0) is amplified at the ripple slopes and is consistent with the location of the expected strongest pressure gradients. First-moment and second-moment velocity statistics were used to address the spatial variability of the intra-ripple hydrodynamics. Estimates of displacement and momentum thicknesses (δ* and δmom) are smaller than suggested by the higher harmonics, but consistently highlight areas of adverse and favorable pressure gradients. Shear stress and roughness estimates were inferred by fitting a logarithmic model to first-moment and second-moment statistics of the velocity field. The maximum Shields parameter was observed to peak at the stoss slope of asymmetric ripples during the strongest and shorter half-wave period (onshore). First-moment roughness estimates are similar in magnitude to bed load parameterizations provided by Li et al. (1997), and about a factor of 3 larger than second-moment estimates. Assessment of the vertical transfer of horizontal momentum derived using a Reynolds decomposition suggests that stresses inferred from the logarithmic law using first-moment velocity statistics appropriately reproduce the mean momentum transfer for the longer and weaker offshore half-wave period.

Estimating surface NO2 and SO2 mixing ratios from fast-response total column observations and potential application to geostationary missions.

Total-column nitrogen dioxide (NO2) data collected by a ground-based sun-tracking spectrometer system (Pandora) and an photolytic-converter-based in-situ instrument collocated at NASA’s Langley Research Center in Hampton, Virginia were analyzed to study the relationship between total-column and surface NO2 measurements. The measurements span more than a year and cover all seasons. Surface mixing ratios are estimated via application of a planetary boundary-layer (PBL) height correction factor. This PBL correction factor effectively corrects for boundary-layer variability throughout the day, and accounts for up to ≈75 % of the variability between the NO2 data sets. Previous studies have made monthly and seasonal comparisons of column/surface data, which has shown generally good agreement over these long average times. In the current analysis comparisons of column densities averaged over 90 s and 1 h are made. Applicability of this technique to sulfur dioxide (SO2) is briefly explored. The SO2 correlation is improved by excluding conditions where surface levels are considered background. The analysis is extended to data from the July 2011 DISCOVER-AQ mission over the greater Baltimore, MD area to examine the method’s performance in more-polluted urban conditions where NO2 concentrations are typically much higher.

Sensorless control of high‐power interior permanent‐magnet synchronous motor drives at very low speed

A novel sensorless control scheme is proposed for an interior permanent-magnet synchronous motor drives at very low speed based on sliding-mode observer (SMO) in this study, which substitutes a sigmoid function for the sign or saturation function with a variable boundary layer, overcomes the time delay caused by the low-pass filter and the chattering problem used in the conventional SMO. In this study, an adaptive SMO is employed to estimate the rotor speed and extended electromotive force, a three-phase soft phase-locked loop technology is used to estimate rotor position because of its strong robustness since under voltage phase unbalance or polluted and variable-frequency environment. The global asymptotic stability of the proposed adaptive SMO is verified using Lyapunov stability analysis with considering motor parameter variations. Experimental results are presented to verify the principles and to demonstrate the effectiveness of the proposed method at very low speed from 2 to 17 r/min.

Effectiveness Assessment of Tactical Laser Engagement Scenarios in the Lower Atmosphere

This study quantifies the effectiveness of proposed high-energy tactical laser missions, such as the Advanced Tactical Laser Advanced Concept Technical Demonstration and the Electric Laser on a Large Aircraft program, with consideration of simulated engagement scenarios in the lower atmosphere or troposphere, and establishes the need for a high-energy laser tactical decision aid. The simulations can be varied by geographic location and recent/ current atmospheric weather conditions. The atmospheric effects are defined through the Air Force Institute of Technology Center for Directed Energy high-energy laser end-to-end operational simulation model. This model enables the creation of vertical profiles of temperature, pressure, water vapor content, optical turbulence, and atmospheric particulates and hydrometeors as they relate to line-by-line layer extinction coefficient magnitude at wavelengths from the ultraviolet to the radio frequency. The expected propagation performance is assessed at the wavelength of 1:315 m in tactical laser engagement scenarios at a representative midlatitude site. Seasonal and boundary-layer variations (summer and winter) and time-of-day variations for a range of relative humidity percentile conditions are considered to determine optimum efficiency in a specific environment. Each atmospheric particulate/hydrometeor is evaluated based on its wavelength-dependent forward and off-axis scattering characteristics and absorption effects on the propagating environment. In addition to realistic vertical profiles of molecular and aerosol absorption and scattering, correlated optical turbulence profiles in probabilistic (percentile) format are used. The physically correct atmospheric characterizations used in a high-energy laser end-to-end operational simulation demonstrate the usefulness of implementing an engineering performancemodel with current meteorological conditions to a mission plan and optimize potential tactical high-energy laser combat engagements.

A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM), is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

A New Fuzzy Sliding Mode Controller with Auto-adjustable Saturation Boundary Layers Implemented on Vehicle Suspension

This study develops a fuzzy sliding mode controller (FSMC) based on a variable boundary layer. A fuzzy inference mechanism is used to on-line tune the thickness of the boundary layers of the controller. Minimum rule base has been used for the fuzzy inference system which results in low calculation effort. The aim of this paper is to design a controller which will eliminate the chattering of FSMC while maintains the robustness of the controller. To prove the effectiveness of this method, an experiment has been done using MATLAB/SIMULINK. In this experiment, the results of FSMC with auto-adjustable boundary layers are compared with the results of FSMC with fixed boundary layers and the results of FSMC with sign function. The results of the experiment confirm that the performance of fuzzy sliding mode controller based on auto-adjustable boundary layer method is superior to the fixed boundary layer method.

Thermal and viscous boundary layers in turbulent Rayleigh–Bénard convection

AbstractWe present the results from numerical simulations of turbulent Rayleigh–Bénard convection for an aspect ratio (diameter/height) of 1.0, Prandtl numbers of 0.4 and 0.7, and Rayleigh numbers from $1\ensuremath{\times} 1{0}^{5} $ to $1\ensuremath{\times} 1{0}^{9} $. Detailed measurements of the thermal and viscous boundary layer profiles are made and compared to experimental and theoretical (Prandtl–Blasius) results. We find that the thermal boundary layer profiles disagree by more than 10 % when scaled with the similarity variable (boundary layer thickness) and likewise disagree with the Prandtl–Blasius results. In contrast, the viscous boundary profiles collapse well and do agree (within 10 %) with the Prandtl–Blasius profile, but with worsening agreement as the Rayleigh number increases. We have also investigated the scaling of the boundary layer thicknesses with Rayleigh number, and again compare to experiments and theory. We find that the scaling laws are very robust with respect to method of analysis and they mostly agree with the Grossmann–Lohse predictions coupled with laminar boundary layer theory within our numerical uncertainty.

Satellite Attitude Maneuver using Sliding Mode Control under Body Angular Velocity Constraints

paper presents a robust sliding-mode control technique to be applied to quaternion-based attitude control for rest-to-rest maneuvers with external disturbances. A sliding mode controller has been designed to force the state variables of the closed loop system to converge to the desired values. A control strategy is designed based on a novel mathematical rule that computes the discontinuous feedback gains. The proposed approach is defined in such a way that the selected controller parameters can drive the state to hit the sliding surface fast and then keep the state sliding along the surface with less and tracking error. Moreover, the control parameters are adjusted to avoid the body angular velocity reached the upper limit during the maneuver. A simulation model of the controlled spacecraft system was developed in MATLAB-SIMULINK software. The phase portraits and the state plots prove the control technique power. The chattering problem of the sliding mode control has been adopted using variable thickness boundary layer technique. The second method of Lyapunov is used to guarantee the system stability under the proposed control laws action. Simulations have been carried out to demonstrate and verify the developed controller performance. Keywordsicrosatellite, attitude control, sliding mode control,

Boundary layer versus free tropospheric CO budget and variability over the United States during summertime

The regional Weather Research and Forecasting Model with Chemistry (WRF‐Chem) version 3.2 is used to analyze the carbon monoxide (CO) budget and spatiotemporal variability over the United States in summer 2008. CO tracers for different emission sources are used to separate the modeled CO fields into the contributions from individual sources (pollution inflow to the model domain, chemical production within the model domain, and local emissions by type). The implementation of tagged CO tracers into WRF‐Chem constitutes an innovative aspect of this work. We evaluate WRF‐Chem CO concentrations using aircraft, satellite, and surface observations. The model reproduces fairly well the observed CO concentrations for the entire altitude range but tends to underestimate fire emissions and overestimate anthropogenic sources and CO from pollution inflow. Evaluation results also show that the model gives a good representation of background CO mixing ratios with mean biases better than ∼15 ppbv in the free troposphere (FT) and less than 20 ppbv toward the surface. The analysis of the CO budget over the contiguous United States shows that at the surface, CO from inflow is the dominant source, with a mean relative contribution of 63 ± 19%. Anthropogenic and photochemically produced CO contribute to surface CO to a lesser extent (18 ± 14% and 14 ± 8%, respectively). The average contribution from fire emissions to surface CO during the period examined is small (2 ± 5%) but can have a large impact in certain regions and times. Similar trends are found in the planetary boundary layer (PBL). In the FT, the average CO relative contributions are estimated as 84 ± 12% for CO from inflow, 5 ± 4% for anthropogenic CO, 9 ± 7% for photochemically produced CO, and 1 ± 5% for CO from fires. Using WRF‐Chem simulations, we also examine the representation of surface and PBL CO concentration variability that would be captured by current near infrared (NIR) and thermal infrared (TIR) satellite observations. We find that CO total columns are impacted by variability in the lowermost troposphere (LMT) at the ∼10% level, indicating limited sensitivity for air quality applications. The same is generally true for the FT CO column obtained from TIR measurements, although this does provide a good measure for capturing the pollution inflow variability and is therefore valuable in providing initial and boundary conditions to constrain regional models. We further analyze the situations under which the LMT concentrations obtained from recently demonstrated multispectral (NIR + TIR) observations capture the surface CO variability.

Integration of an atmospheric dispersion model with a dynamic multimedia fate model: Development and illustration

Growing attention is devoted to understand the influence of the short-term variations in air concentrations on the environmental fate of semivolatile organic compounds (SVOCs) such as polycyclic aromatic hydrocarbons (PAHs). These variations are ascribable to factors such as temperature-mediated air-surface exchange and variability of planetary boundary layer (PBL) height and structure. But when investigating the fate of SVOCs at a local scale, further variability can derive from specific point source contributions. In this context, a new modeling approach (AirPlus) which integrates a previously developed model (AirFug) with an air dispersion model (AERMOD) is presented. The integrated model is illustrated for two PAHs in a Northern Italy scenario. Results show how chemical contributions deriving from background advective inflows, local emissions and a point source interact in an hourly-varying meteorological scenario to determine air concentration rapid changes and the consequent response of the soil compartment.

Evaluation of cloud fraction and its radiative effect simulated by IPCC AR4 global models against ARM surface observations

Abstract. Cloud Fraction (CF) is the dominant modulator of radiative fluxes. In this study, we evaluate CF simulated in the IPCC AR4 GCMs against ARM long-term ground-based measurements, with a focus on the vertical structure, total amount of cloud and its effect on cloud shortwave transmissivity. Comparisons are performed for three climate regimes as represented by the Department of Energy Atmospheric Radiation Measurement (ARM) sites: Southern Great Plains (SGP), Manus, Papua New Guinea and North Slope of Alaska (NSA). Our intercomparisons of three independent measurements of CF or sky-cover reveal that the relative differences are usually less than 10% (5%) for multi-year monthly (annual) mean values, while daily differences are quite significant. The total sky imager (TSI) produces smaller total cloud fraction (TCF) compared to a radar/lidar dataset for highly cloudy days (CF > 0.8), but produces a larger TCF value than the radar/lidar for less cloudy conditions (CF < 0.3). The compensating errors in lower and higher CF days result in small biases of TCF between the vertically pointing radar/lidar dataset and the hemispheric TSI measurements as multi-year data is averaged. The unique radar/lidar CF measurements enable us to evaluate seasonal variation of cloud vertical structures in the GCMs. Both inter-model deviation and model bias against observation are investigated in this study. Another unique aspect of this study is that we use simultaneous measurements of CF and surface radiative fluxes to diagnose potential discrepancies among the GCMs in representing other cloud optical properties than TCF. The results show that the model-observation and inter-model deviations have similar magnitudes for the TCF and the normalized cloud effect, and these deviations are larger than those in surface downward solar radiation and cloud transmissivity. This implies that other dimensions of cloud in addition to cloud amount, such as cloud optical thickness and/or cloud height, have a similar magnitude of disparity as TCF within the GCMs, and suggests that the better agreement among GCMs in solar radiative fluxes could be a result of compensating effects from errors in cloud vertical structure, overlap assumption, cloud optical depth and/or cloud fraction. The internal variability of CF simulated in ensemble runs with the same model is minimal. Similar deviation patterns between inter-model and model-measurement comparisons suggest that the climate models tend to generate larger biases against observations for those variables with larger inter-model deviation. The GCM performance in simulating the probability distribution, transmissivity and vertical profiles of cloud are comprehensively evaluated over the three ARM sites. The GCMs perform better at SGP than at the other two sites in simulating the seasonal variation and probability distribution of TCF. However, the models remarkably underpredict the TCF at SGP and cloud transmissivity is less susceptible to the change of TCF than observed. In the tropics, most of the GCMs tend to underpredict CF and fail to capture the seasonal variation of CF at middle and low levels. The high-level CF is much larger in the GCMs than the observations and the inter-model variability of CF also reaches a maximum at high levels in the tropics, indicating discrepancies in the representation of ice cloud associated with convection in the models. While the GCMs generally capture the maximum CF in the boundary layer and vertical variability, the inter-model deviation is largest near the surface over the Arctic.

Observations of the boundary layer, cloud, and aerosol variability in the southeast Pacific near-coastal marine stratocumulus during VOCALS-REx

Abstract. Aircraft observations made off the coast of northern Chile in the Southeastern Pacific (20° S, 72° W; named Point Alpha) from 16 October to 13 November 2008 during the VAMOS Ocean-Cloud- Atmosphere-Land Study-Regional Experiment (VOCALS-REx), combined with meteorological reanalysis, satellite measurements, and radiosonde data, are used to investigate the boundary layer (BL) and aerosol-cloud-drizzle variations in this region. On days without predominately synoptic and meso-scale influences, the BL at Point Alpha was typical of a non-drizzling stratocumulus-topped BL. Entrainment rates calculated from the near cloud-top fluxes and turbulence in the BL at Point Alpha appeared to be weaker than those in the BL over the open ocean west of Point Alpha and the BL near the coast of the northeast Pacific. The cloud liquid water path (LWP) varied between 15 g m−2 and 160 g m−2. The BL had a depth of 1140 ± 120 m, was generally well-mixed and capped by a sharp inversion without predominately synoptic and meso-scale influences. The wind direction generally switched from southerly within the BL to northerly above the inversion. On days when a synoptic system and related mesoscale costal circulations affected conditions at Point Alpha (29 October–4 November), a moist layer above the inversion moved over Point Alpha, and the total-water mixing ratio above the inversion was larger than that within the BL. The accumulation mode aerosol varied from 250 to 700 cm−3 within the BL, and CCN at 0.2 % supersaturation within the BL ranged between 150 and 550 cm−3. The main aerosol source at Point Alpha was horizontal advection within the BL from south. The average cloud droplet number concentration ranged between 80 and 400 cm−3. While the mean LWP retrieved from GOES was in good agreement with the in situ measurements, the GOES-derived cloud droplet effective radius tended to be larger than that from the aircraft in situ observations near cloud top. The aerosol and cloud LWP relationship reveals that during the typical well-mixed BL days the cloud LWP increased with the CCN concentrations. On the other hand, meteorological factors and the decoupling processes have large influences on the cloud LWP variation as well.

A High-Speed Sliding-Mode Observer for the Sensorless Speed Control of a PMSM

This paper proposes a sensorless speed control strategy for a permanent-magnet synchronous motor (PMSM) based on a new sliding-mode observer (SMO), which substitutes a sigmoid function for the signum function with a variable boundary layer. In order to apply a sensorless PMSM control which is robust against parameter fluctuations and disturbances, a high-speed SMO is proposed, which estimates the rotor position and the angular velocity from the back EMF. In the conventional SMO, a low-pass filter and an additional position compensation of the rotor are used to reduce the chattering problem that is commonly found in the SMO using the signum function. In order to overcome the time delay caused by the low-pass filter, in this research, a sigmoid function is used for the switching function instead of the signum function. Also, the variation in the stator resistance is estimated to improve the steady-state performance of the SMO. The stability of the proposed SMO was verified using the Lyapunov second method to determine the observer gain. The validity of the proposed high-speed PMSM sensorless velocity control has been demonstrated with simulations and real experiments.