An active trailer braking controller to improve the lateral stability of car-trailer systems is presented. The special and complex structures of these types of vehicles exhibit unique unstable motion behavior, such as...An active trailer braking controller to improve the lateral stability of car-trailer systems is presented. The special and complex structures of these types of vehicles exhibit unique unstable motion behavior, such as the trailer swing, jack-knifing and rollover. These unstable motion modes may lead to fatal accidents. The effects of passive mechanical parameters on the stability of car-trailer systems have been thoroughly investigated. Some of the passive parameters, such as the center of gravity of the trailer, may be drastically varied during various operating conditions. Even for an optimal design of a car-trailer system, based on a specific passive parameter set, the lateral stability cannot be guaranteed. In order to improve the lateral stability of car-trailer systems, an active trailer braking controller is designed using the Linear Quadratic Regular (LQR) technique. To derive the controller, a vehicle model with 3 Degrees Of Freedom (DOF) is developed to represent the car-trailer system. A single lane-change maneuver has been simulated to examine the performance of the controller and the numerical results are compared with those of the baseline design. The benchmark investigation indicates that the optimal controller based on the LQR technique can effectively improve the high-speed lateral stability of the car-trailer system.展开更多
The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fat...The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov's direct method is proposed in this paper.After decoupling the six degree-of-freedom(DOF)motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.展开更多
The control problems associated with vehicle height adjustment of electronically controlled air suspension (ECAS) still pose theoretical challenges for researchers, which manifest themselves in the publications on t...The control problems associated with vehicle height adjustment of electronically controlled air suspension (ECAS) still pose theoretical challenges for researchers, which manifest themselves in the publications on this subject over the last years. This paper deals with modeling and control of a vehicle height adjustment system for ECAS, which is an example of a hybrid dynamical system due to the coexistence and coupling of continuous variables and discrete events. A mixed logical dynamical (MLD) modeling approach is chosen for capturing enough details of the vehicle height adjustment process. The hybrid dynamic model is constructed on the basis of some assumptions and piecewise linear approximation for components nonlinearities. Then, the on-off statuses of solenoid valves and the piecewise approximation process are described by propositional logic, and the hybrid system is transformed into the set of linear mixed-integer equalities and inequalities, denoted as MLD model, automatically by HYSDEL. Using this model, a hybrid model predictive controller (HMPC) is tuned based on online mixed-integer quadratic optimization (MIQP). Two different scenarios are considered in the simulation, whose results verify the height adjustment effectiveness of the proposed approach. Explicit solutions of the controller are computed to control the vehicle height adjustment system in realtime using an offline multi-parametric programming technology (MPT), thus convert the controller into an equivalent explicit piecewise affine form. Finally, bench experiments for vehicle height lifting, holding and lowering procedures are conducted, which demonstrate that the HMPC can adjust the vehicle height by controlling the on-off statuses of solenoid valves directly. This research proposes a new modeling and control method for vehicle height adjustment of ECAS, which leads to a closed-loop system with favorable dynamical properties.展开更多
This paper presents a simple sliding mode control strategy used for an electronic differential system for electric vehicle with two independent wheel drives. When a vehicle drives along a curved road lane, the speed o...This paper presents a simple sliding mode control strategy used for an electronic differential system for electric vehicle with two independent wheel drives. When a vehicle drives along a curved road lane, the speed of the inner wheel has to be different from that of the outer wheel in order to prevent the vehicle from vibrating and travelling an unsteady path. Because each wheel of this electrical vehicle has independent driving force, an electrical differential system is required to replace a gear differential system. However, it is difficult to analyse the nonlinear behaviour of the differential system in relation to the speed and steering angle, as well as vehicle structure. The proposed propulsion system consists of two permanent magnet synchronous machines that ensure the drive of the two back driving wheels. The proposed control structure called independent machines for speed control allows the achievement of an electronic differential which ensures the control of the vehicle behaviour on the road. It also allows to control, independently, every driving wheel to turn at different speeds in any curve. Analysis and simulation results of the proposed system are presented in this paper.展开更多
With penetration growing of renewable energy sources which integrated into power system have caused problems on grid stability. Electric Vehicles (EV) are one of the renewable energy sources that can bring significant...With penetration growing of renewable energy sources which integrated into power system have caused problems on grid stability. Electric Vehicles (EV) are one of the renewable energy sources that can bring significant impacts to power system during their charging and discharging operations. This article established a model of single machine infinite bus (SMIB) power system considering EV as a case study of load disturbance for power system oscillation. The objective of this research is to enhance stability and overcome the drawbacks of traditional control algorithms such as power system stabilizer (PSS), PID controller and fuzzy logic controller (FLC). The implementation’s effect of FLC parallel with PID controller (Fuzzy-PID) has been shown in this paper. The speed deviation (?ω) and electrical power (Pe) are the important factors to be taken into consideration without EV (only change in mechanical torque), EV with change in the mechanical torque and sudden plug-in EV. The obtained result by nonlinear simulation using Matlab/Simulink of a SMIB power system with EV has shown the effectiveness of using (Fuzzy-PID) against all disturbances.展开更多
Electrical system of military vehicle is a typical parameterized nonlinear system where complicated bifurcations may exist and threaten its safe and stable operation. An algebraic criterion for Hopf bifurcation is pre...Electrical system of military vehicle is a typical parameterized nonlinear system where complicated bifurcations may exist and threaten its safe and stable operation. An algebraic criterion for Hopf bifurcation is presented briefly and applied to find Hopf bifurcation point of the electrical system with automatic voltage regulator(AVR) dynamics in military vehicle. Hopf bifurcation controllers are designed for this electrical system by using wash-out filter,linear feedback,nonlinear feedback and their combination. The linear feedback control makes the system bring Hopf bifurcation at preferable parameter,the nonlinear feedback control modifies the type of the bifurcation,and the wash-out filter enhances the system damping,thus,the Hopf bifurcation is eliminated and the electrical system stability is ensured. Simulation results show the controller's validity.展开更多
Nowadays validation of anti-lock braking systems(ABS) relies mainly on a large amount of road tests.An alternative means with higher efficiency is employing the hardware-in-the-loop simulation(HILS) system to subs...Nowadays validation of anti-lock braking systems(ABS) relies mainly on a large amount of road tests.An alternative means with higher efficiency is employing the hardware-in-the-loop simulation(HILS) system to substitute part of road tests for designing,testing,and tuning electronic control units(ECUs) of ABS.Most HILS systems for ABS use expensive digital signal processor hardware and special purpose software,and some fail-safe functions with regard to wheel speeds cannot be evaluated since artificial wheel speed signals are usually provided.In this paper,a low-cost ABS HILS test bench is developed and used for validating the anti-lock braking performance and tuning control parameters of ABS controllers.Another important merit of the proposed test bench is that it can comprehensively evaluate the fail-safe functions with regard to wheel speed signals since real tone rings and sensors are integrated in the bench.A 5-DOF vehicle model with consideration of longitudinal load transfer is used to calculate tire forces,wheel speeds and vehicle speed.Each of the four real-time wheel speed signal generators consists of a servo motor plus a ring gear,which has sufficient dynamic response ability to emulate the rapid changes of the wheel speeds under strict braking conditions of very slippery roads.The simulation of braking tests under different road adhesion coefficients using the HILS test bench is run,and results show that it can evaluate the anti-lock braking performance of ABS and partly the fail-safe functions.This HILS system can also be used in such applications as durability test,benchmarking and comparison between different ECUs.The test bench developed not only has a relatively low cost,but also can be used to validate the wheel speed-related ECU design and all its fail-safe functions,and a rapid testing and proving platform with a high efficiency for research and development of the automotive ABS is therefore provided.展开更多
The control problem of trajectory based path following for passenger vehicles is studied. Comprehensive nonlinear vehicle model is utilized for simulation vehicle response during various maneuvers in MATLAB/Simulink. ...The control problem of trajectory based path following for passenger vehicles is studied. Comprehensive nonlinear vehicle model is utilized for simulation vehicle response during various maneuvers in MATLAB/Simulink. In order to follow desired path, a driver model is developed to enhance closed loop driver/vehicle model. Then, linear quadratic regulator(LQR) controller is developed which regulates direct yaw moment and corrective steering angle on wheels. Particle swam optimization(PSO) method is utilized to optimize the LQR controller for various dynamic conditions. Simulation results indicate that, over various maneuvers, side slip angle and lateral acceleration can be reduced by 10% and 15%, respectively, which sustain the vehicle stable. Also, anti-lock brake system is designed for longitudinal dynamics of vehicle to achieve desired slip during braking and accelerating. Proposed comprehensive controller demonstrates that vehicle steerability can increase by about 15% during severe braking by preventing wheel from locking and reducing stopping distance.展开更多
This work studies the stabilization of a class of control systems that use communication networks as signal transmission medium. The lateral motion of independently actuated four-wheel vehicle is modeled as an uncerta...This work studies the stabilization of a class of control systems that use communication networks as signal transmission medium. The lateral motion of independently actuated four-wheel vehicle is modeled as an uncertain-linear system. Time delay and quantization density are modeled as Markov chains.The networked control systems(NCSs) with plants being lateral motion are first transformed to switched linear systems with uncertain parameters. Sufficient and necessary conditions for the stochastic stability of closed-loop networked control systems are then established. By solving the matrix inequalities, this work presents an output-feedback controller that depends on the modes of time delay and quantization density. The controller performance is illustrated via a vehicular lateral motion system.展开更多
Since the aerodynamic center moving backward sharply in hypersonic flight,the stability margin of the hypersonic vehicle increases largely while the maneuverability decreases.We proposed a novel method to solve this c...Since the aerodynamic center moving backward sharply in hypersonic flight,the stability margin of the hypersonic vehicle increases largely while the maneuverability decreases.We proposed a novel method to solve this contradiction.We used relaxed static stability(RSS)to improve the maneuverability in hypersonic flight,and designed the stability augmentation system(SAS)to ensure the stability in subsonic flight.Therefore,the relationship between static stability and maneuverability was quantitatively analyzed in the first step,and the numerical value of RSS was obtained on the premise of good maneuverability.Secondly,the relationship between static stability and aerodynamic parameters was quantitatively analyzed.We properly adjusted aerodynamic parameters based on the quantitative relationship to achieve the specific static stability set in the first step,and therefore provided the engineering realization methods.The vehicle will be statically unstable in subsonic flight with the specific static stability.Lastly,SAS was needed to ensure the stability of the vehicle in subsonic flight.Simulation studies were conducted by comparing the linear SAS to the nonlinear SAS,and the results showed that the nonlinear dynamicinversion controller can synthesize with proportional-integrall-derivative(PID)controller robustly and stabilize the hypersonic vehicle.展开更多
For the constant distance spacing policy,the existing researches of the string stability focus on the single-predecessor information framework(SPIF) and predecessor-successor information framework(PSIF).The resear...For the constant distance spacing policy,the existing researches of the string stability focus on the single-predecessor information framework(SPIF) and predecessor-successor information framework(PSIF).The research results demonstrated that the string stability could not be guaranteed with the SPIF,and then the PSIF was proposed to resolve this string instability.But the issue,whether the string stability can be guaranteed when applying the PSIF,is still controversial.Meanwhile,most of the previous researches on the string stability were conducted without consideration of the parasitic time delays and lags.In this paper,the practical longitudinal vehicle dynamics model is built with consideration of the parasitic time delays and lags existing in the actuators,sensors or the communication systems.Secondly,the detailed theoretical analysis of string stability in frequency domain is conducted to demonstrate that the classical linear control laws can not ensure the string stability when applying both the symmetrical PSIF(SPSIF) and asymmetrical PSIF(APSIF).Thirdly,a control law,which adds the position and velocity information of the leading vehicle,is proposed to guarantee string stability for small/medium platoon,and the other control law,which adds the acceleration information of the controlled vehicle,is proposed to guarantee string stability for large platoon as well as small/medium platoon.Finally,the comparative simulation is conducted to confirm the conducted analysis and the proposed control laws.The conducted research completes the means to analyze the string stability in frequency domain,provides the parameters' reference for the design and implementation of the practical automatic following controllers,and improves the reliability and stability of the platoon of automatic vehicles.展开更多
文摘An active trailer braking controller to improve the lateral stability of car-trailer systems is presented. The special and complex structures of these types of vehicles exhibit unique unstable motion behavior, such as the trailer swing, jack-knifing and rollover. These unstable motion modes may lead to fatal accidents. The effects of passive mechanical parameters on the stability of car-trailer systems have been thoroughly investigated. Some of the passive parameters, such as the center of gravity of the trailer, may be drastically varied during various operating conditions. Even for an optimal design of a car-trailer system, based on a specific passive parameter set, the lateral stability cannot be guaranteed. In order to improve the lateral stability of car-trailer systems, an active trailer braking controller is designed using the Linear Quadratic Regular (LQR) technique. To derive the controller, a vehicle model with 3 Degrees Of Freedom (DOF) is developed to represent the car-trailer system. A single lane-change maneuver has been simulated to examine the performance of the controller and the numerical results are compared with those of the baseline design. The benchmark investigation indicates that the optimal controller based on the LQR technique can effectively improve the high-speed lateral stability of the car-trailer system.
基金supported by the National High Technology Development Program of China(863Program,Grant No.2008AA092301)the Fundamental Research Foundation of Harbin Engineering University(Grant No.HEUFT08001)the Postdoctoral Science Foundation of China(Grant No.20080440838)
文摘The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov's direct method is proposed in this paper.After decoupling the six degree-of-freedom(DOF)motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.
基金Supported by National Natural Science Foundation of China(Grant No.51375212)Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institutions of China+1 种基金Research Fund for the Doctoral Program of Higher Education of China(Grant No.20133227130001)China Postdoctoral Science Foundation(Grant No.2014M551518)
文摘The control problems associated with vehicle height adjustment of electronically controlled air suspension (ECAS) still pose theoretical challenges for researchers, which manifest themselves in the publications on this subject over the last years. This paper deals with modeling and control of a vehicle height adjustment system for ECAS, which is an example of a hybrid dynamical system due to the coexistence and coupling of continuous variables and discrete events. A mixed logical dynamical (MLD) modeling approach is chosen for capturing enough details of the vehicle height adjustment process. The hybrid dynamic model is constructed on the basis of some assumptions and piecewise linear approximation for components nonlinearities. Then, the on-off statuses of solenoid valves and the piecewise approximation process are described by propositional logic, and the hybrid system is transformed into the set of linear mixed-integer equalities and inequalities, denoted as MLD model, automatically by HYSDEL. Using this model, a hybrid model predictive controller (HMPC) is tuned based on online mixed-integer quadratic optimization (MIQP). Two different scenarios are considered in the simulation, whose results verify the height adjustment effectiveness of the proposed approach. Explicit solutions of the controller are computed to control the vehicle height adjustment system in realtime using an offline multi-parametric programming technology (MPT), thus convert the controller into an equivalent explicit piecewise affine form. Finally, bench experiments for vehicle height lifting, holding and lowering procedures are conducted, which demonstrate that the HMPC can adjust the vehicle height by controlling the on-off statuses of solenoid valves directly. This research proposes a new modeling and control method for vehicle height adjustment of ECAS, which leads to a closed-loop system with favorable dynamical properties.
文摘This paper presents a simple sliding mode control strategy used for an electronic differential system for electric vehicle with two independent wheel drives. When a vehicle drives along a curved road lane, the speed of the inner wheel has to be different from that of the outer wheel in order to prevent the vehicle from vibrating and travelling an unsteady path. Because each wheel of this electrical vehicle has independent driving force, an electrical differential system is required to replace a gear differential system. However, it is difficult to analyse the nonlinear behaviour of the differential system in relation to the speed and steering angle, as well as vehicle structure. The proposed propulsion system consists of two permanent magnet synchronous machines that ensure the drive of the two back driving wheels. The proposed control structure called independent machines for speed control allows the achievement of an electronic differential which ensures the control of the vehicle behaviour on the road. It also allows to control, independently, every driving wheel to turn at different speeds in any curve. Analysis and simulation results of the proposed system are presented in this paper.
文摘With penetration growing of renewable energy sources which integrated into power system have caused problems on grid stability. Electric Vehicles (EV) are one of the renewable energy sources that can bring significant impacts to power system during their charging and discharging operations. This article established a model of single machine infinite bus (SMIB) power system considering EV as a case study of load disturbance for power system oscillation. The objective of this research is to enhance stability and overcome the drawbacks of traditional control algorithms such as power system stabilizer (PSS), PID controller and fuzzy logic controller (FLC). The implementation’s effect of FLC parallel with PID controller (Fuzzy-PID) has been shown in this paper. The speed deviation (?ω) and electrical power (Pe) are the important factors to be taken into consideration without EV (only change in mechanical torque), EV with change in the mechanical torque and sudden plug-in EV. The obtained result by nonlinear simulation using Matlab/Simulink of a SMIB power system with EV has shown the effectiveness of using (Fuzzy-PID) against all disturbances.
基金Sponsored by Foundation for Science Research Development of Nanjing University of Science and Technology
文摘Electrical system of military vehicle is a typical parameterized nonlinear system where complicated bifurcations may exist and threaten its safe and stable operation. An algebraic criterion for Hopf bifurcation is presented briefly and applied to find Hopf bifurcation point of the electrical system with automatic voltage regulator(AVR) dynamics in military vehicle. Hopf bifurcation controllers are designed for this electrical system by using wash-out filter,linear feedback,nonlinear feedback and their combination. The linear feedback control makes the system bring Hopf bifurcation at preferable parameter,the nonlinear feedback control modifies the type of the bifurcation,and the wash-out filter enhances the system damping,thus,the Hopf bifurcation is eliminated and the electrical system stability is ensured. Simulation results show the controller's validity.
基金supported by National Natural Science Foundation of China(Grant No.50908008)National Hi-tech Research and Development Program of China(863Program,Grant No.2009AA11Z216)
文摘Nowadays validation of anti-lock braking systems(ABS) relies mainly on a large amount of road tests.An alternative means with higher efficiency is employing the hardware-in-the-loop simulation(HILS) system to substitute part of road tests for designing,testing,and tuning electronic control units(ECUs) of ABS.Most HILS systems for ABS use expensive digital signal processor hardware and special purpose software,and some fail-safe functions with regard to wheel speeds cannot be evaluated since artificial wheel speed signals are usually provided.In this paper,a low-cost ABS HILS test bench is developed and used for validating the anti-lock braking performance and tuning control parameters of ABS controllers.Another important merit of the proposed test bench is that it can comprehensively evaluate the fail-safe functions with regard to wheel speed signals since real tone rings and sensors are integrated in the bench.A 5-DOF vehicle model with consideration of longitudinal load transfer is used to calculate tire forces,wheel speeds and vehicle speed.Each of the four real-time wheel speed signal generators consists of a servo motor plus a ring gear,which has sufficient dynamic response ability to emulate the rapid changes of the wheel speeds under strict braking conditions of very slippery roads.The simulation of braking tests under different road adhesion coefficients using the HILS test bench is run,and results show that it can evaluate the anti-lock braking performance of ABS and partly the fail-safe functions.This HILS system can also be used in such applications as durability test,benchmarking and comparison between different ECUs.The test bench developed not only has a relatively low cost,but also can be used to validate the wheel speed-related ECU design and all its fail-safe functions,and a rapid testing and proving platform with a high efficiency for research and development of the automotive ABS is therefore provided.
文摘The control problem of trajectory based path following for passenger vehicles is studied. Comprehensive nonlinear vehicle model is utilized for simulation vehicle response during various maneuvers in MATLAB/Simulink. In order to follow desired path, a driver model is developed to enhance closed loop driver/vehicle model. Then, linear quadratic regulator(LQR) controller is developed which regulates direct yaw moment and corrective steering angle on wheels. Particle swam optimization(PSO) method is utilized to optimize the LQR controller for various dynamic conditions. Simulation results indicate that, over various maneuvers, side slip angle and lateral acceleration can be reduced by 10% and 15%, respectively, which sustain the vehicle stable. Also, anti-lock brake system is designed for longitudinal dynamics of vehicle to achieve desired slip during braking and accelerating. Proposed comprehensive controller demonstrates that vehicle steerability can increase by about 15% during severe braking by preventing wheel from locking and reducing stopping distance.
基金supported by Humanities and Social Sciences Youth Foundation of the Ministry of Education(17YJC630093)
文摘This work studies the stabilization of a class of control systems that use communication networks as signal transmission medium. The lateral motion of independently actuated four-wheel vehicle is modeled as an uncertain-linear system. Time delay and quantization density are modeled as Markov chains.The networked control systems(NCSs) with plants being lateral motion are first transformed to switched linear systems with uncertain parameters. Sufficient and necessary conditions for the stochastic stability of closed-loop networked control systems are then established. By solving the matrix inequalities, this work presents an output-feedback controller that depends on the modes of time delay and quantization density. The controller performance is illustrated via a vehicular lateral motion system.
基金supported in part by the National Natural Science Foundation of China(Nos.61673209,61741313)the Funding of Jiangsu Innovation Program for Graduate Education(No.CXZZ13_0170)+3 种基金the Funding for Outstanding Doctoral Dissertation in NUAA(No.BCXJ13-06)the Jiangsu Six Peak of Talents Program(No.KTHY-027)the Funding of China Launch Vehicle Technology Innovation Program of University and Institute(No.CALT201503)the Aeronautical Science Foundation(No.2016ZA52009)
文摘Since the aerodynamic center moving backward sharply in hypersonic flight,the stability margin of the hypersonic vehicle increases largely while the maneuverability decreases.We proposed a novel method to solve this contradiction.We used relaxed static stability(RSS)to improve the maneuverability in hypersonic flight,and designed the stability augmentation system(SAS)to ensure the stability in subsonic flight.Therefore,the relationship between static stability and maneuverability was quantitatively analyzed in the first step,and the numerical value of RSS was obtained on the premise of good maneuverability.Secondly,the relationship between static stability and aerodynamic parameters was quantitatively analyzed.We properly adjusted aerodynamic parameters based on the quantitative relationship to achieve the specific static stability set in the first step,and therefore provided the engineering realization methods.The vehicle will be statically unstable in subsonic flight with the specific static stability.Lastly,SAS was needed to ensure the stability of the vehicle in subsonic flight.Simulation studies were conducted by comparing the linear SAS to the nonlinear SAS,and the results showed that the nonlinear dynamicinversion controller can synthesize with proportional-integrall-derivative(PID)controller robustly and stabilize the hypersonic vehicle.
基金supported by Doctoral Foundation of Ministry of Education of China (Grant No.20070006011)
文摘For the constant distance spacing policy,the existing researches of the string stability focus on the single-predecessor information framework(SPIF) and predecessor-successor information framework(PSIF).The research results demonstrated that the string stability could not be guaranteed with the SPIF,and then the PSIF was proposed to resolve this string instability.But the issue,whether the string stability can be guaranteed when applying the PSIF,is still controversial.Meanwhile,most of the previous researches on the string stability were conducted without consideration of the parasitic time delays and lags.In this paper,the practical longitudinal vehicle dynamics model is built with consideration of the parasitic time delays and lags existing in the actuators,sensors or the communication systems.Secondly,the detailed theoretical analysis of string stability in frequency domain is conducted to demonstrate that the classical linear control laws can not ensure the string stability when applying both the symmetrical PSIF(SPSIF) and asymmetrical PSIF(APSIF).Thirdly,a control law,which adds the position and velocity information of the leading vehicle,is proposed to guarantee string stability for small/medium platoon,and the other control law,which adds the acceleration information of the controlled vehicle,is proposed to guarantee string stability for large platoon as well as small/medium platoon.Finally,the comparative simulation is conducted to confirm the conducted analysis and the proposed control laws.The conducted research completes the means to analyze the string stability in frequency domain,provides the parameters' reference for the design and implementation of the practical automatic following controllers,and improves the reliability and stability of the platoon of automatic vehicles.