Vector control schemes have recently been used to drive linear induction motors(LIM)in high-performance applications.This trend promotes the development of precise and efficient control schemes for individual motors.T...Vector control schemes have recently been used to drive linear induction motors(LIM)in high-performance applications.This trend promotes the development of precise and efficient control schemes for individual motors.This research aims to present a novel framework for speed and thrust force control of LIM using space vector pulse width modulation(SVPWM)inverters.The framework under consideration is developed in four stages.To begin,MATLAB Simulink was used to develop a detailed mathematical and electromechanical dynamicmodel.The research presents a modified SVPWM inverter control scheme.By tuning the proportional-integral(PI)controller with a transfer function,optimized values for the PI controller are derived.All the subsystems mentioned above are integrated to create a robust simulation of the LIM’s precise speed and thrust force control scheme.The reference speed values were chosen to evaluate the performance of the respective system,and the developed system’s response was verified using various data sets.For the low-speed range,a reference value of 10m/s is used,while a reference value of 100 m/s is used for the high-speed range.The speed output response indicates that themotor reached reference speed in amatter of seconds,as the delay time is between 8 and 10 s.The maximum amplitude of thrust achieved is less than 400N,demonstrating the controller’s capability to control a high-speed LIM with minimal thrust ripple.Due to the controlled speed range,the developed system is highly recommended for low-speed and high-speed and heavy-duty traction applications.展开更多
In order to compensate for the deficiency of Sine Pulse Width Modulation(SPWM), on the base of analyzing the principle of space w tot pulse width modulation and being compared with SPWM, the method of solving workin...In order to compensate for the deficiency of Sine Pulse Width Modulation(SPWM), on the base of analyzing the principle of space w tot pulse width modulation and being compared with SPWM, the method of solving working time of adjacent vector and the method of generate space voltage vector were introduced. The experiment to the inverter which consists of IGBT proves that SVPWM centrol algorithm can reduce harmonic effectively, it is beneficial to enhancing the utilization rate of voltage source inverter direct current power supply.展开更多
Ⅰ. INTRODUCTION MULTILEVEL inverters are increasingly being used in high-power medium voltage applications due to their superior performance compared to two-level inverters, such as lower common-mode voltage, lower d...Ⅰ. INTRODUCTION MULTILEVEL inverters are increasingly being used in high-power medium voltage applications due to their superior performance compared to two-level inverters, such as lower common-mode voltage, lower dv/dt, lower harmonics in output voltage and current, and reduced voltage on the power switches.展开更多
This paper presents frequency domain method for harmonic analysis of space vector based STATCOM. Space Vector Pulse Width Modulation (SVPWM) method is an advanced PWM method. It is a best method among all the PWM tech...This paper presents frequency domain method for harmonic analysis of space vector based STATCOM. Space Vector Pulse Width Modulation (SVPWM) method is an advanced PWM method. It is a best method among all the PWM techniques. It provides a freedom in a switching cycle for placement space vector. In this paper, the SVPWM is used for switching of STATCOM. The harmonic (or frequency) domain is a steady-state form of harmonic analysis method, which represents converters to their harmonic spectra. This paper presents harmonic analysis by means of harmonic domain for space vector based Static shunt converter (STATCOM). Performance of the STATCOM is evaluated in harmonic domain simulation studies in MATLAB environment.展开更多
This paper presents analytical frequency domain method for harmonic modeling and evaluation of Space Vector Pulse Width Modulation (SVPWM) based static synchronous series converter (SSSC). SVPWM is the best among all ...This paper presents analytical frequency domain method for harmonic modeling and evaluation of Space Vector Pulse Width Modulation (SVPWM) based static synchronous series converter (SSSC). SVPWM is the best among all the PWM techniques. It gives a degree of freedom of space vector placement in a switching cycle. Dynamic modeling technique is used for space vector modulation (SVM) based voltage source converter that is adapted as a static synchronous series converter (SSSC) for harmonic analysis using dynamic harmonic domain. Performance of the SSSC is evaluated in dynamic harmonic domain simulation studies in MATLAB environment. The switching function spectra are necessary for harmonic transfer matrix which is calculated using Fourier series. This paper presents the analysis of harmonics for space vector based SSSC during steady state and dynamic condition.展开更多
Direct torque control (DTC) of Switched reluctance motor is known straightforward control structure with similar execution to that of field situated control strategies. In any case, the part of ideal determination of ...Direct torque control (DTC) of Switched reluctance motor is known straightforward control structure with similar execution to that of field situated control strategies. In any case, the part of ideal determination of the voltage space vector is one of the weakest focuses in a routine DTC drive because of adjustable switching frequency and high torque ripple. In this paper, ideal choice of voltage space vectors is accomplished utilizing ANFIS (Adaptive Neuro Fuzzy Inference System) with space vector Modulation. SVM-DTC gives consistent switching frequency and the proposed ANFIS controller’s structure manages the torque and stator flux error signals through the fuzzy deduction to get a yield that takes the type of space voltage vector. Simulation results accept the proposed evolutionary system with quick torque and flux reaction with minimized torque ripple and flux ripple.展开更多
In this paper, an improved hybrid space vector pulse width modulation (HSVPWM) technique is proposed for IM (induction motor) drives. The basic principle involved in the proposed random pulse width modulation (RPWM) c...In this paper, an improved hybrid space vector pulse width modulation (HSVPWM) technique is proposed for IM (induction motor) drives. The basic principle involved in the proposed random pulse width modulation (RPWM) cuddled SVPWM is amalgamating the pre-calculated switching timings for various sections of hexagonal space vector boundary and the random selection of carrier between two triangular signals, in order to disband acoustic switching noise spectrum with improved fundamental component. The arbitrary selection between triangular carriers, which is decided by digital signal states (Low or High) of the linear feedback shift register (LFSR) based pseudo random binary sequence (PRBS) generator. The SVPWM offers a control degree of freedom in terms of positioning of vectors inside every sampling interval and hence it has six possible variants of the voltage vectors arrangements in each sector. The developed HSVPWM is thoroughly analyzed in using the MATLAB? based simulation for all SVPWM variants. From the simulation and experimental results viz. harmonic spectrum, harmonic spread factor (HSF), total harmonic distortion (THD) etc., and the superiority of the proposed scheme such as better utilization of DC bus and the randomization of the harmonic power are evidenced. For the practical implementation, Xilinx XC3S500E FPGA device has been used.展开更多
This study introduces the Orbit Weighting Scheme(OWS),a novel approach aimed at enhancing the precision and efficiency of Vector Space information retrieval(IR)models,which have traditionally relied on weighting schem...This study introduces the Orbit Weighting Scheme(OWS),a novel approach aimed at enhancing the precision and efficiency of Vector Space information retrieval(IR)models,which have traditionally relied on weighting schemes like tf-idf and BM25.These conventional methods often struggle with accurately capturing document relevance,leading to inefficiencies in both retrieval performance and index size management.OWS proposes a dynamic weighting mechanism that evaluates the significance of terms based on their orbital position within the vector space,emphasizing term relationships and distribution patterns overlooked by existing models.Our research focuses on evaluating OWS’s impact on model accuracy using Information Retrieval metrics like Recall,Precision,InterpolatedAverage Precision(IAP),andMeanAverage Precision(MAP).Additionally,we assessOWS’s effectiveness in reducing the inverted index size,crucial for model efficiency.We compare OWS-based retrieval models against others using different schemes,including tf-idf variations and BM25Delta.Results reveal OWS’s superiority,achieving a 54%Recall and 81%MAP,and a notable 38%reduction in the inverted index size.This highlights OWS’s potential in optimizing retrieval processes and underscores the need for further research in this underrepresented area to fully leverage OWS’s capabilities in information retrieval methodologies.展开更多
The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we ...The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.展开更多
Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of ...Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.展开更多
This paper investigates a Luenberger flux observer with speed adaptation for a direct field oriented control of an induction motor. An improved method of speed estimation that operates on the principle of speed adapti...This paper investigates a Luenberger flux observer with speed adaptation for a direct field oriented control of an induction motor. An improved method of speed estimation that operates on the principle of speed adaptive flux and current observer has been proposed. An observer is basically an estimator that uses a plant model and a feedback loop with measured stator voltage and current. Simulation results show that the proposed direct field oriented control with the proposed observer provides good performance dynamic characteristics. The induction motor is fed by an indirect power electronics converter. This indirect converter is controlled by a sliding mode technique that enables minimization of harmonics introduced by the line converter, as well as the control of the power factor and DC-link voltage. The robustness of the overall system is studied using simulation for different operating modes and varied parameters.展开更多
Analysis of a four-dimensional displacement vector on the fabric of space-time in the special or general case into two Four-dimensional vectors, according to specific conditions leads to the splitting of the total fab...Analysis of a four-dimensional displacement vector on the fabric of space-time in the special or general case into two Four-dimensional vectors, according to specific conditions leads to the splitting of the total fabric of space-time into a positive subspace-time that represents the space of causality and a negative subspace-time which represents a space without causality, thus, in the special case, we have new transformations for the coordinates of space and time modified from Lorentz transformations specific to each subspace, where the contraction of length disappears and the speed of light is no longer a universal constant. In the general case, we have new types of matric tensor, one for positive subspace-time and the other for negative subspace-time. We also find that the speed of the photon decreases in positive subspace-time until it reaches zero and increases in negative subspace-time until it reaches the speed of light when the photon reaches the Schwarzschild radius.展开更多
This paper proposes a dual-frequency discontinuous space vector pulse width modulation(DFDSVPWM)for a five-phase voltage source inverter with harmonic injection.In this modulation,for dual-frequency voltage output and...This paper proposes a dual-frequency discontinuous space vector pulse width modulation(DFDSVPWM)for a five-phase voltage source inverter with harmonic injection.In this modulation,for dual-frequency voltage output and reduction of switching losses,two different zero-vector-inserted modes are flexibly employed by alternatively using two types of zero vectors.Based on the comparison with continuous SVPWM,the idea and principle of the proposed DFDSVPWM are analyzed and an example of PWM signals for one bridge is also presented.For switching losses analysis,the impact factors and the calculation method are investigated and the corresponding implementation is given as well.The simulation and experimental results from a prototype verify the correctness and effectiveness of the proposed modulation and it has the advantages of outputting dual-frequency voltage and reducing switching losses.展开更多
This paper is concerned with two popular and powerful methods in electrical drive applications:fieldoriented control(FOC)and space vector modulation(SVM).The proposed FOC-SVM method is incorporated with a predictive c...This paper is concerned with two popular and powerful methods in electrical drive applications:fieldoriented control(FOC)and space vector modulation(SVM).The proposed FOC-SVM method is incorporated with a predictive current control(PCC)-based technique.The suggested method estimates the desirable electrical torque to track mechanical torque at a fixed speed operation of permanent magnet synchronous motor(PMSM).The estimated torque is used to calculate the reference current based on FOC.In order to improve the performance of the traditional SVM,a PCC method is established as a switching pattern modifier.Therefore,PCC-based SVM is employed to further minimize the torque ripples and transient response.The performance of the controller is evaluated in terms of torque and current ripple and transient response to step variations of the torque command.The proposed method has been verified with MATLAB-Simulink model.Simulation results confirm the ability of this technique in minimizing the torque and speed ripples and fixing switching frequency,simultaneously.However,it is sensitive to parameter changes.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
A vector space secret sharing scheme based on certificates is proposed in this paper. The difficulties of solving discrete logarithm assure confidential information's security, and the use of each participant's cert...A vector space secret sharing scheme based on certificates is proposed in this paper. The difficulties of solving discrete logarithm assure confidential information's security, and the use of each participant's certificate makes the dealer have no need to transfer secret information to the participants. The proposed scheme is dynamic. It can effectively check cheaters and does not have secure channel requirements.展开更多
This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from t...This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from the known Poincare estimates. The main ingredients of the proofs rely on the fractional maximal functions. These results evidently have applications to the regularity of subelliptic PDE.展开更多
基金The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Large Groups Project under grant number(RGP.2/111/43).
文摘Vector control schemes have recently been used to drive linear induction motors(LIM)in high-performance applications.This trend promotes the development of precise and efficient control schemes for individual motors.This research aims to present a novel framework for speed and thrust force control of LIM using space vector pulse width modulation(SVPWM)inverters.The framework under consideration is developed in four stages.To begin,MATLAB Simulink was used to develop a detailed mathematical and electromechanical dynamicmodel.The research presents a modified SVPWM inverter control scheme.By tuning the proportional-integral(PI)controller with a transfer function,optimized values for the PI controller are derived.All the subsystems mentioned above are integrated to create a robust simulation of the LIM’s precise speed and thrust force control scheme.The reference speed values were chosen to evaluate the performance of the respective system,and the developed system’s response was verified using various data sets.For the low-speed range,a reference value of 10m/s is used,while a reference value of 100 m/s is used for the high-speed range.The speed output response indicates that themotor reached reference speed in amatter of seconds,as the delay time is between 8 and 10 s.The maximum amplitude of thrust achieved is less than 400N,demonstrating the controller’s capability to control a high-speed LIM with minimal thrust ripple.Due to the controlled speed range,the developed system is highly recommended for low-speed and high-speed and heavy-duty traction applications.
文摘In order to compensate for the deficiency of Sine Pulse Width Modulation(SPWM), on the base of analyzing the principle of space w tot pulse width modulation and being compared with SPWM, the method of solving working time of adjacent vector and the method of generate space voltage vector were introduced. The experiment to the inverter which consists of IGBT proves that SVPWM centrol algorithm can reduce harmonic effectively, it is beneficial to enhancing the utilization rate of voltage source inverter direct current power supply.
文摘Ⅰ. INTRODUCTION MULTILEVEL inverters are increasingly being used in high-power medium voltage applications due to their superior performance compared to two-level inverters, such as lower common-mode voltage, lower dv/dt, lower harmonics in output voltage and current, and reduced voltage on the power switches.
文摘This paper presents frequency domain method for harmonic analysis of space vector based STATCOM. Space Vector Pulse Width Modulation (SVPWM) method is an advanced PWM method. It is a best method among all the PWM techniques. It provides a freedom in a switching cycle for placement space vector. In this paper, the SVPWM is used for switching of STATCOM. The harmonic (or frequency) domain is a steady-state form of harmonic analysis method, which represents converters to their harmonic spectra. This paper presents harmonic analysis by means of harmonic domain for space vector based Static shunt converter (STATCOM). Performance of the STATCOM is evaluated in harmonic domain simulation studies in MATLAB environment.
文摘This paper presents analytical frequency domain method for harmonic modeling and evaluation of Space Vector Pulse Width Modulation (SVPWM) based static synchronous series converter (SSSC). SVPWM is the best among all the PWM techniques. It gives a degree of freedom of space vector placement in a switching cycle. Dynamic modeling technique is used for space vector modulation (SVM) based voltage source converter that is adapted as a static synchronous series converter (SSSC) for harmonic analysis using dynamic harmonic domain. Performance of the SSSC is evaluated in dynamic harmonic domain simulation studies in MATLAB environment. The switching function spectra are necessary for harmonic transfer matrix which is calculated using Fourier series. This paper presents the analysis of harmonics for space vector based SSSC during steady state and dynamic condition.
文摘Direct torque control (DTC) of Switched reluctance motor is known straightforward control structure with similar execution to that of field situated control strategies. In any case, the part of ideal determination of the voltage space vector is one of the weakest focuses in a routine DTC drive because of adjustable switching frequency and high torque ripple. In this paper, ideal choice of voltage space vectors is accomplished utilizing ANFIS (Adaptive Neuro Fuzzy Inference System) with space vector Modulation. SVM-DTC gives consistent switching frequency and the proposed ANFIS controller’s structure manages the torque and stator flux error signals through the fuzzy deduction to get a yield that takes the type of space voltage vector. Simulation results accept the proposed evolutionary system with quick torque and flux reaction with minimized torque ripple and flux ripple.
文摘In this paper, an improved hybrid space vector pulse width modulation (HSVPWM) technique is proposed for IM (induction motor) drives. The basic principle involved in the proposed random pulse width modulation (RPWM) cuddled SVPWM is amalgamating the pre-calculated switching timings for various sections of hexagonal space vector boundary and the random selection of carrier between two triangular signals, in order to disband acoustic switching noise spectrum with improved fundamental component. The arbitrary selection between triangular carriers, which is decided by digital signal states (Low or High) of the linear feedback shift register (LFSR) based pseudo random binary sequence (PRBS) generator. The SVPWM offers a control degree of freedom in terms of positioning of vectors inside every sampling interval and hence it has six possible variants of the voltage vectors arrangements in each sector. The developed HSVPWM is thoroughly analyzed in using the MATLAB? based simulation for all SVPWM variants. From the simulation and experimental results viz. harmonic spectrum, harmonic spread factor (HSF), total harmonic distortion (THD) etc., and the superiority of the proposed scheme such as better utilization of DC bus and the randomization of the harmonic power are evidenced. For the practical implementation, Xilinx XC3S500E FPGA device has been used.
文摘This study introduces the Orbit Weighting Scheme(OWS),a novel approach aimed at enhancing the precision and efficiency of Vector Space information retrieval(IR)models,which have traditionally relied on weighting schemes like tf-idf and BM25.These conventional methods often struggle with accurately capturing document relevance,leading to inefficiencies in both retrieval performance and index size management.OWS proposes a dynamic weighting mechanism that evaluates the significance of terms based on their orbital position within the vector space,emphasizing term relationships and distribution patterns overlooked by existing models.Our research focuses on evaluating OWS’s impact on model accuracy using Information Retrieval metrics like Recall,Precision,InterpolatedAverage Precision(IAP),andMeanAverage Precision(MAP).Additionally,we assessOWS’s effectiveness in reducing the inverted index size,crucial for model efficiency.We compare OWS-based retrieval models against others using different schemes,including tf-idf variations and BM25Delta.Results reveal OWS’s superiority,achieving a 54%Recall and 81%MAP,and a notable 38%reduction in the inverted index size.This highlights OWS’s potential in optimizing retrieval processes and underscores the need for further research in this underrepresented area to fully leverage OWS’s capabilities in information retrieval methodologies.
文摘The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.
文摘Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.
文摘This paper investigates a Luenberger flux observer with speed adaptation for a direct field oriented control of an induction motor. An improved method of speed estimation that operates on the principle of speed adaptive flux and current observer has been proposed. An observer is basically an estimator that uses a plant model and a feedback loop with measured stator voltage and current. Simulation results show that the proposed direct field oriented control with the proposed observer provides good performance dynamic characteristics. The induction motor is fed by an indirect power electronics converter. This indirect converter is controlled by a sliding mode technique that enables minimization of harmonics introduced by the line converter, as well as the control of the power factor and DC-link voltage. The robustness of the overall system is studied using simulation for different operating modes and varied parameters.
文摘Analysis of a four-dimensional displacement vector on the fabric of space-time in the special or general case into two Four-dimensional vectors, according to specific conditions leads to the splitting of the total fabric of space-time into a positive subspace-time that represents the space of causality and a negative subspace-time which represents a space without causality, thus, in the special case, we have new transformations for the coordinates of space and time modified from Lorentz transformations specific to each subspace, where the contraction of length disappears and the speed of light is no longer a universal constant. In the general case, we have new types of matric tensor, one for positive subspace-time and the other for negative subspace-time. We also find that the speed of the photon decreases in positive subspace-time until it reaches zero and increases in negative subspace-time until it reaches the speed of light when the photon reaches the Schwarzschild radius.
基金This work was supported in part by the National Natural Science Foundation of China(51507079)the China Postdoctoral Science Foundation Funded Project(2014M560421,2016T90454)the Fundamental Research Funds for the Central Universities(NJ20160046,NS2018025).
文摘This paper proposes a dual-frequency discontinuous space vector pulse width modulation(DFDSVPWM)for a five-phase voltage source inverter with harmonic injection.In this modulation,for dual-frequency voltage output and reduction of switching losses,two different zero-vector-inserted modes are flexibly employed by alternatively using two types of zero vectors.Based on the comparison with continuous SVPWM,the idea and principle of the proposed DFDSVPWM are analyzed and an example of PWM signals for one bridge is also presented.For switching losses analysis,the impact factors and the calculation method are investigated and the corresponding implementation is given as well.The simulation and experimental results from a prototype verify the correctness and effectiveness of the proposed modulation and it has the advantages of outputting dual-frequency voltage and reducing switching losses.
文摘This paper is concerned with two popular and powerful methods in electrical drive applications:fieldoriented control(FOC)and space vector modulation(SVM).The proposed FOC-SVM method is incorporated with a predictive current control(PCC)-based technique.The suggested method estimates the desirable electrical torque to track mechanical torque at a fixed speed operation of permanent magnet synchronous motor(PMSM).The estimated torque is used to calculate the reference current based on FOC.In order to improve the performance of the traditional SVM,a PCC method is established as a switching pattern modifier.Therefore,PCC-based SVM is employed to further minimize the torque ripples and transient response.The performance of the controller is evaluated in terms of torque and current ripple and transient response to step variations of the torque command.The proposed method has been verified with MATLAB-Simulink model.Simulation results confirm the ability of this technique in minimizing the torque and speed ripples and fixing switching frequency,simultaneously.However,it is sensitive to parameter changes.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金Supported by the National Natural Science Foun-dation of China(60573129) the Opening Foundation of State Key La-boratory of Information Security and the Opening Foundation of KeyLaboratory of Computer Network and Information Security, Ministryof Education of PRC.
文摘A vector space secret sharing scheme based on certificates is proposed in this paper. The difficulties of solving discrete logarithm assure confidential information's security, and the use of each participant's certificate makes the dealer have no need to transfer secret information to the participants. The proposed scheme is dynamic. It can effectively check cheaters and does not have secure channel requirements.
基金Research supported in part by he National Sience Foundation Grant # DMS93-15963
文摘This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from the known Poincare estimates. The main ingredients of the proofs rely on the fractional maximal functions. These results evidently have applications to the regularity of subelliptic PDE.