SlideShare a Scribd company logo
1 of 1
SLIDING-MODE CONTROL FOR A THREE-PHASE UNITY POWER FACTOR
RECTIFIER OPERATING AT FIXED SWITCHING FREQUENCY
ABSTRACT
This paper presents an improved variable hysteresis band current-control in natural frame
for a three-phase unity power rectifier. The proposed control algorithm is based on three
decoupled sliding-mode controllers combined with three independent Kalman filters. The use of
Kalman filters instead of a non-adaptive state observer improves the quality of the estimated
signals in presence of noise, increasing the immunity of the control loop in noisy environments.
To reduce drastically the computational load in the Kalman algorithm, a reduced bilinear model
is derived which allows to use a Kalman filter algorithm instead of an extended Kalman filter. A
fast output-voltage control is also presented which avoids output-voltage variations when a
sudden change in the load or a voltage sag appears. Moreover, a fixed switching frequency
algorithm is proposed which uses a variable hysteresis-band in combination with a switching
decision algorithm, ensuring a switching spectrum concentrated around the desired switching
frequency. The overall control proposal has been fully integrated into a digital signal processor.
Selected experimental results are introduced to validate the theoretical contributions of this
paper.

More Related Content

What's hot

Adaptive dead times compensation for grid-connected pwm inverters of single s...
Adaptive dead times compensation for grid-connected pwm inverters of single s...Adaptive dead times compensation for grid-connected pwm inverters of single s...
Adaptive dead times compensation for grid-connected pwm inverters of single s...
Ecwaytech
 
Adaptive dead times compensation for grid-connected pwm inverters of single s...
Adaptive dead times compensation for grid-connected pwm inverters of single s...Adaptive dead times compensation for grid-connected pwm inverters of single s...
Adaptive dead times compensation for grid-connected pwm inverters of single s...
Ecwayt
 
Performance analysis of three phase shunt hybrid active power filter
Performance analysis of three phase shunt hybrid active power filterPerformance analysis of three phase shunt hybrid active power filter
Performance analysis of three phase shunt hybrid active power filter
eSAT Journals
 
Instantaneous Reactive Power Theory And Its Applications
Instantaneous Reactive Power Theory And Its ApplicationsInstantaneous Reactive Power Theory And Its Applications
Instantaneous Reactive Power Theory And Its Applications
arunj89
 
Shunt active power filter
Shunt active power filterShunt active power filter
Shunt active power filter
Ranganath
 
Ge generator and ups problems
Ge generator and ups problemsGe generator and ups problems
Ge generator and ups problems
michaeljmack
 
Precise accelerated torque control for small inductance brushless dc motor
Precise accelerated torque control for small inductance brushless dc motorPrecise accelerated torque control for small inductance brushless dc motor
Precise accelerated torque control for small inductance brushless dc motor
Ecwaytech
 

What's hot (17)

Consumption analysis method for optimizing reactive compensation at MV
Consumption analysis method for optimizing reactive compensation at MVConsumption analysis method for optimizing reactive compensation at MV
Consumption analysis method for optimizing reactive compensation at MV
 
Adaptive dead times compensation for grid-connected pwm inverters of single s...
Adaptive dead times compensation for grid-connected pwm inverters of single s...Adaptive dead times compensation for grid-connected pwm inverters of single s...
Adaptive dead times compensation for grid-connected pwm inverters of single s...
 
Adaptive dead times compensation for grid-connected pwm inverters of single s...
Adaptive dead times compensation for grid-connected pwm inverters of single s...Adaptive dead times compensation for grid-connected pwm inverters of single s...
Adaptive dead times compensation for grid-connected pwm inverters of single s...
 
Performance analysis of three phase shunt hybrid active power filter
Performance analysis of three phase shunt hybrid active power filterPerformance analysis of three phase shunt hybrid active power filter
Performance analysis of three phase shunt hybrid active power filter
 
Instantaneous Reactive Power Theory And Its Applications
Instantaneous Reactive Power Theory And Its ApplicationsInstantaneous Reactive Power Theory And Its Applications
Instantaneous Reactive Power Theory And Its Applications
 
Contingency analysis
Contingency analysisContingency analysis
Contingency analysis
 
Shunt active power filter
Shunt active power filterShunt active power filter
Shunt active power filter
 
Power Quality Improvement in Distribution System using ANN Based Shunt Active...
Power Quality Improvement in Distribution System using ANN Based Shunt Active...Power Quality Improvement in Distribution System using ANN Based Shunt Active...
Power Quality Improvement in Distribution System using ANN Based Shunt Active...
 
Chapter#4
Chapter#4Chapter#4
Chapter#4
 
Performance enhancement of shunt active power filter with fuzzy and hysteresi...
Performance enhancement of shunt active power filter with fuzzy and hysteresi...Performance enhancement of shunt active power filter with fuzzy and hysteresi...
Performance enhancement of shunt active power filter with fuzzy and hysteresi...
 
Ge generator and ups problems
Ge generator and ups problemsGe generator and ups problems
Ge generator and ups problems
 
Precise accelerated torque control for small inductance brushless dc motor
Precise accelerated torque control for small inductance brushless dc motorPrecise accelerated torque control for small inductance brushless dc motor
Precise accelerated torque control for small inductance brushless dc motor
 
EE-524 Project report
EE-524 Project reportEE-524 Project report
EE-524 Project report
 
Enhancement of Power System Dynamics Using a Novel Series Compensation Scheme
Enhancement of Power System Dynamics Using a Novel Series Compensation SchemeEnhancement of Power System Dynamics Using a Novel Series Compensation Scheme
Enhancement of Power System Dynamics Using a Novel Series Compensation Scheme
 
Reactive power consumption in modern power system
Reactive power consumption in modern power systemReactive power consumption in modern power system
Reactive power consumption in modern power system
 
Optimal voltage control
Optimal voltage controlOptimal voltage control
Optimal voltage control
 
Generation shift factor and line outage factor
Generation shift factor and line outage factorGeneration shift factor and line outage factor
Generation shift factor and line outage factor
 

Similar to Sliding mode control for a three-phase unity power factor rectifier operating at fixed switching frequency

A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
Ecway2004
 
A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
Ecwaytechnoz
 
A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
Ecwaytech
 
A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
Ecwaytechnoz
 
A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
Ecwaytech
 
A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
Ecwayt
 
Control Structure for Single-Phase Stand -Alone Wind Based Energy Sources
Control Structure for Single-Phase Stand -Alone Wind Based Energy SourcesControl Structure for Single-Phase Stand -Alone Wind Based Energy Sources
Control Structure for Single-Phase Stand -Alone Wind Based Energy Sources
Shiva Kumar
 

Similar to Sliding mode control for a three-phase unity power factor rectifier operating at fixed switching frequency (20)

Optimized Aircraft Electric Control System Based on Adaptive Tabu Search Algo...
Optimized Aircraft Electric Control System Based on Adaptive Tabu Search Algo...Optimized Aircraft Electric Control System Based on Adaptive Tabu Search Algo...
Optimized Aircraft Electric Control System Based on Adaptive Tabu Search Algo...
 
Design Of Hybrid Series Active Filters for Harmonic Reduction in Single Phase...
Design Of Hybrid Series Active Filters for Harmonic Reduction in Single Phase...Design Of Hybrid Series Active Filters for Harmonic Reduction in Single Phase...
Design Of Hybrid Series Active Filters for Harmonic Reduction in Single Phase...
 
A Shunt Active Power Filter for 12 Pulse Converter Using Source Current Detec...
A Shunt Active Power Filter for 12 Pulse Converter Using Source Current Detec...A Shunt Active Power Filter for 12 Pulse Converter Using Source Current Detec...
A Shunt Active Power Filter for 12 Pulse Converter Using Source Current Detec...
 
G010334953
G010334953G010334953
G010334953
 
Summary Presentation on PMU Based Transmission Line Protection Scheme
Summary Presentation on PMU Based Transmission Line Protection Scheme Summary Presentation on PMU Based Transmission Line Protection Scheme
Summary Presentation on PMU Based Transmission Line Protection Scheme
 
Hysteresis current controller for single phase three level vsi
Hysteresis current controller for single phase three level vsiHysteresis current controller for single phase three level vsi
Hysteresis current controller for single phase three level vsi
 
Methods for Voltage Stability Enhancement
Methods for Voltage Stability EnhancementMethods for Voltage Stability Enhancement
Methods for Voltage Stability Enhancement
 
A Novel Approach of Harmonic Reduction with Transformer Connected 3-Phase Mul...
A Novel Approach of Harmonic Reduction with Transformer Connected 3-Phase Mul...A Novel Approach of Harmonic Reduction with Transformer Connected 3-Phase Mul...
A Novel Approach of Harmonic Reduction with Transformer Connected 3-Phase Mul...
 
A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
 
A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
 
A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
 
A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
 
A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
 
A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...A high performance spwm controller for three-phase ups systems operating unde...
A high performance spwm controller for three-phase ups systems operating unde...
 
ICICCE0324
ICICCE0324ICICCE0324
ICICCE0324
 
International Journal of Computational Engineering Research(IJCER)
International Journal of Computational Engineering Research(IJCER)International Journal of Computational Engineering Research(IJCER)
International Journal of Computational Engineering Research(IJCER)
 
International Journal of Engineering Research and Development
International Journal of Engineering Research and DevelopmentInternational Journal of Engineering Research and Development
International Journal of Engineering Research and Development
 
Unit Power Factor Servo Drive Control System
Unit Power Factor Servo Drive Control SystemUnit Power Factor Servo Drive Control System
Unit Power Factor Servo Drive Control System
 
New three dimensional space vector based switching signal generation techniqu...
New three dimensional space vector based switching signal generation techniqu...New three dimensional space vector based switching signal generation techniqu...
New three dimensional space vector based switching signal generation techniqu...
 
Control Structure for Single-Phase Stand -Alone Wind Based Energy Sources
Control Structure for Single-Phase Stand -Alone Wind Based Energy SourcesControl Structure for Single-Phase Stand -Alone Wind Based Energy Sources
Control Structure for Single-Phase Stand -Alone Wind Based Energy Sources
 

More from I3E Technologies

More from I3E Technologies (20)

Add
AddAdd
Add
 
Design of a low voltage low-dropout regulator
Design of a low voltage low-dropout regulatorDesign of a low voltage low-dropout regulator
Design of a low voltage low-dropout regulator
 
An efficient constant multiplier architecture based on vertical horizontal bi...
An efficient constant multiplier architecture based on vertical horizontal bi...An efficient constant multiplier architecture based on vertical horizontal bi...
An efficient constant multiplier architecture based on vertical horizontal bi...
 
Aging aware reliable multiplier design with adaptive hold logic
Aging aware reliable multiplier design with adaptive hold logicAging aware reliable multiplier design with adaptive hold logic
Aging aware reliable multiplier design with adaptive hold logic
 
A high performance fir filter architecture for fixed and reconfigurable appli...
A high performance fir filter architecture for fixed and reconfigurable appli...A high performance fir filter architecture for fixed and reconfigurable appli...
A high performance fir filter architecture for fixed and reconfigurable appli...
 
A generalized algorithm and reconfigurable architecture for efficient and sca...
A generalized algorithm and reconfigurable architecture for efficient and sca...A generalized algorithm and reconfigurable architecture for efficient and sca...
A generalized algorithm and reconfigurable architecture for efficient and sca...
 
A combined sdc sdf architecture for normal i o pipelined radix-2 fft
A combined sdc sdf architecture for normal i o pipelined radix-2 fftA combined sdc sdf architecture for normal i o pipelined radix-2 fft
A combined sdc sdf architecture for normal i o pipelined radix-2 fft
 
Reverse converter design via parallel prefix adders novel components, method...
Reverse converter design via parallel prefix adders  novel components, method...Reverse converter design via parallel prefix adders  novel components, method...
Reverse converter design via parallel prefix adders novel components, method...
 
Pre encoded multipliers based on non-redundant radix-4 signed-digit encoding
Pre encoded multipliers based on non-redundant radix-4 signed-digit encodingPre encoded multipliers based on non-redundant radix-4 signed-digit encoding
Pre encoded multipliers based on non-redundant radix-4 signed-digit encoding
 
Energy optimized subthreshold vlsi logic family with unbalanced pull up down ...
Energy optimized subthreshold vlsi logic family with unbalanced pull up down ...Energy optimized subthreshold vlsi logic family with unbalanced pull up down ...
Energy optimized subthreshold vlsi logic family with unbalanced pull up down ...
 
Variable form carrier-based pwm for boost-voltage motor driver with a charge-...
Variable form carrier-based pwm for boost-voltage motor driver with a charge-...Variable form carrier-based pwm for boost-voltage motor driver with a charge-...
Variable form carrier-based pwm for boost-voltage motor driver with a charge-...
 
Ultrasparse ac link converters
Ultrasparse ac link convertersUltrasparse ac link converters
Ultrasparse ac link converters
 
Single inductor dual-output buck–boost power factor correction converter
Single inductor dual-output buck–boost power factor correction converterSingle inductor dual-output buck–boost power factor correction converter
Single inductor dual-output buck–boost power factor correction converter
 
Ripple minimization through harmonic elimination in asymmetric interleaved mu...
Ripple minimization through harmonic elimination in asymmetric interleaved mu...Ripple minimization through harmonic elimination in asymmetric interleaved mu...
Ripple minimization through harmonic elimination in asymmetric interleaved mu...
 
Resonance analysis and soft switching design of isolated boost converter with...
Resonance analysis and soft switching design of isolated boost converter with...Resonance analysis and soft switching design of isolated boost converter with...
Resonance analysis and soft switching design of isolated boost converter with...
 
Reliability evaluation of conventional and interleaved dc–dc boost converters
Reliability evaluation of conventional and interleaved dc–dc boost convertersReliability evaluation of conventional and interleaved dc–dc boost converters
Reliability evaluation of conventional and interleaved dc–dc boost converters
 
Power factor corrected zeta converter based improved power quality switched m...
Power factor corrected zeta converter based improved power quality switched m...Power factor corrected zeta converter based improved power quality switched m...
Power factor corrected zeta converter based improved power quality switched m...
 
Pfc cuk converter fed bldc motor drive
Pfc cuk converter fed bldc motor drivePfc cuk converter fed bldc motor drive
Pfc cuk converter fed bldc motor drive
 
Optimized operation of current fed dual active bridge dc dc converter for pv ...
Optimized operation of current fed dual active bridge dc dc converter for pv ...Optimized operation of current fed dual active bridge dc dc converter for pv ...
Optimized operation of current fed dual active bridge dc dc converter for pv ...
 
Online variable topology type photovoltaic grid-connected inverter
Online variable topology type photovoltaic grid-connected inverterOnline variable topology type photovoltaic grid-connected inverter
Online variable topology type photovoltaic grid-connected inverter
 

Recently uploaded

Query optimization and processing for advanced database systems
Query optimization and processing for advanced database systemsQuery optimization and processing for advanced database systems
Query optimization and processing for advanced database systems
meharikiros2
 
Kuwait City MTP kit ((+919101817206)) Buy Abortion Pills Kuwait
Kuwait City MTP kit ((+919101817206)) Buy Abortion Pills KuwaitKuwait City MTP kit ((+919101817206)) Buy Abortion Pills Kuwait
Kuwait City MTP kit ((+919101817206)) Buy Abortion Pills Kuwait
jaanualu31
 
"Lesotho Leaps Forward: A Chronicle of Transformative Developments"
"Lesotho Leaps Forward: A Chronicle of Transformative Developments""Lesotho Leaps Forward: A Chronicle of Transformative Developments"
"Lesotho Leaps Forward: A Chronicle of Transformative Developments"
mphochane1998
 
1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
AldoGarca30
 
Introduction to Robotics in Mechanical Engineering.pptx
Introduction to Robotics in Mechanical Engineering.pptxIntroduction to Robotics in Mechanical Engineering.pptx
Introduction to Robotics in Mechanical Engineering.pptx
hublikarsn
 
Digital Communication Essentials: DPCM, DM, and ADM .pptx
Digital Communication Essentials: DPCM, DM, and ADM .pptxDigital Communication Essentials: DPCM, DM, and ADM .pptx
Digital Communication Essentials: DPCM, DM, and ADM .pptx
pritamlangde
 

Recently uploaded (20)

Query optimization and processing for advanced database systems
Query optimization and processing for advanced database systemsQuery optimization and processing for advanced database systems
Query optimization and processing for advanced database systems
 
Post office management system project ..pdf
Post office management system project ..pdfPost office management system project ..pdf
Post office management system project ..pdf
 
Design For Accessibility: Getting it right from the start
Design For Accessibility: Getting it right from the startDesign For Accessibility: Getting it right from the start
Design For Accessibility: Getting it right from the start
 
Kuwait City MTP kit ((+919101817206)) Buy Abortion Pills Kuwait
Kuwait City MTP kit ((+919101817206)) Buy Abortion Pills KuwaitKuwait City MTP kit ((+919101817206)) Buy Abortion Pills Kuwait
Kuwait City MTP kit ((+919101817206)) Buy Abortion Pills Kuwait
 
"Lesotho Leaps Forward: A Chronicle of Transformative Developments"
"Lesotho Leaps Forward: A Chronicle of Transformative Developments""Lesotho Leaps Forward: A Chronicle of Transformative Developments"
"Lesotho Leaps Forward: A Chronicle of Transformative Developments"
 
Ground Improvement Technique: Earth Reinforcement
Ground Improvement Technique: Earth ReinforcementGround Improvement Technique: Earth Reinforcement
Ground Improvement Technique: Earth Reinforcement
 
Online electricity billing project report..pdf
Online electricity billing project report..pdfOnline electricity billing project report..pdf
Online electricity billing project report..pdf
 
Max. shear stress theory-Maximum Shear Stress Theory ​ Maximum Distortional ...
Max. shear stress theory-Maximum Shear Stress Theory ​  Maximum Distortional ...Max. shear stress theory-Maximum Shear Stress Theory ​  Maximum Distortional ...
Max. shear stress theory-Maximum Shear Stress Theory ​ Maximum Distortional ...
 
UNIT 4 PTRP final Convergence in probability.pptx
UNIT 4 PTRP final Convergence in probability.pptxUNIT 4 PTRP final Convergence in probability.pptx
UNIT 4 PTRP final Convergence in probability.pptx
 
fitting shop and tools used in fitting shop .ppt
fitting shop and tools used in fitting shop .pptfitting shop and tools used in fitting shop .ppt
fitting shop and tools used in fitting shop .ppt
 
8086 Microprocessor Architecture: 16-bit microprocessor
8086 Microprocessor Architecture: 16-bit microprocessor8086 Microprocessor Architecture: 16-bit microprocessor
8086 Microprocessor Architecture: 16-bit microprocessor
 
Theory of Time 2024 (Universal Theory for Everything)
Theory of Time 2024 (Universal Theory for Everything)Theory of Time 2024 (Universal Theory for Everything)
Theory of Time 2024 (Universal Theory for Everything)
 
1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
 
COST-EFFETIVE and Energy Efficient BUILDINGS ptx
COST-EFFETIVE  and Energy Efficient BUILDINGS ptxCOST-EFFETIVE  and Energy Efficient BUILDINGS ptx
COST-EFFETIVE and Energy Efficient BUILDINGS ptx
 
AIRCANVAS[1].pdf mini project for btech students
AIRCANVAS[1].pdf mini project for btech studentsAIRCANVAS[1].pdf mini project for btech students
AIRCANVAS[1].pdf mini project for btech students
 
Linux Systems Programming: Inter Process Communication (IPC) using Pipes
Linux Systems Programming: Inter Process Communication (IPC) using PipesLinux Systems Programming: Inter Process Communication (IPC) using Pipes
Linux Systems Programming: Inter Process Communication (IPC) using Pipes
 
Electromagnetic relays used for power system .pptx
Electromagnetic relays used for power system .pptxElectromagnetic relays used for power system .pptx
Electromagnetic relays used for power system .pptx
 
Introduction to Robotics in Mechanical Engineering.pptx
Introduction to Robotics in Mechanical Engineering.pptxIntroduction to Robotics in Mechanical Engineering.pptx
Introduction to Robotics in Mechanical Engineering.pptx
 
PE 459 LECTURE 2- natural gas basic concepts and properties
PE 459 LECTURE 2- natural gas basic concepts and propertiesPE 459 LECTURE 2- natural gas basic concepts and properties
PE 459 LECTURE 2- natural gas basic concepts and properties
 
Digital Communication Essentials: DPCM, DM, and ADM .pptx
Digital Communication Essentials: DPCM, DM, and ADM .pptxDigital Communication Essentials: DPCM, DM, and ADM .pptx
Digital Communication Essentials: DPCM, DM, and ADM .pptx
 

Sliding mode control for a three-phase unity power factor rectifier operating at fixed switching frequency

  • 1. SLIDING-MODE CONTROL FOR A THREE-PHASE UNITY POWER FACTOR RECTIFIER OPERATING AT FIXED SWITCHING FREQUENCY ABSTRACT This paper presents an improved variable hysteresis band current-control in natural frame for a three-phase unity power rectifier. The proposed control algorithm is based on three decoupled sliding-mode controllers combined with three independent Kalman filters. The use of Kalman filters instead of a non-adaptive state observer improves the quality of the estimated signals in presence of noise, increasing the immunity of the control loop in noisy environments. To reduce drastically the computational load in the Kalman algorithm, a reduced bilinear model is derived which allows to use a Kalman filter algorithm instead of an extended Kalman filter. A fast output-voltage control is also presented which avoids output-voltage variations when a sudden change in the load or a voltage sag appears. Moreover, a fixed switching frequency algorithm is proposed which uses a variable hysteresis-band in combination with a switching decision algorithm, ensuring a switching spectrum concentrated around the desired switching frequency. The overall control proposal has been fully integrated into a digital signal processor. Selected experimental results are introduced to validate the theoretical contributions of this paper.