AdaptiveCruiseControlStrategyDesignwithOptimizedActive ...In this paper, Carsim software is used to build vehicle dynamics model for collaborative simulation. e vehicles are four-wheel

Research ArticleAdaptive Cruise Control Strategy Design with Optimized ActiveBraking Control Algorithm

Wenguang Wu 12 Debiao Zou3 Jian Ou1 and Lin Hu 12

1School of Automotive amp Mechanical Engineering Changsha University of Science amp Technology Changsha 410114 China2Hunan Key Laboratory of Smart Roadway and Cooperative Vehicle-Infrastructure Systems Changsha 410114 China3Mechanical and Vehicle Engineering Hunan University Changsha 410006 China

Correspondence should be addressed to Lin Hu hulincsusteducn

Received 8 June 2020 Accepted 26 June 2020 Published 21 July 2020

Guest Editor Yong Chen

Copyright copy 2020WenguangWu et alampis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

ampe braking quality is considered as the most important performance of the adaptive control system that influences the vehiclesafety and ride comfort remarkably ampis research is aimed at designing an adaptive cruise control (ACC) system based on activebraking algorithm using hierarchical control Taking into account the vehicle with safety and comfort the upper decision-makingcontroller is designed based on model predictive control algorithm amprottle controller and braking controller are designed withfeedforward and feedback algorithms as the bottom controller where the braking controller is designed based on the hydraulicbraking model ampe whole model is simulated collaboratively with Amesim Carsim and Simulink By comparison with the fulldeceleration model the results show that the proposed algorithm can not only make the vehicle maintain a safe distance under thepremise of following the target vehicle ahead effectively but also provide favorable driving comfort

1 Introduction

In recent years one of the most important goals in theautomotive industry has been to offer passengers the highestlevel of safety comfort and efficiency by partially orcompletely removing driving duties from humans Ad-vanced Driver Assistant System (ADAS) has become a re-search hotspot in the field of intelligent transportation it notonly improves the road capacity [1] but also ensures thesafety of drivers and vulnerable road users to some extent[2 3] Studies have shown that the active safety systemssuch as adaptive cruise control electronic stability controlor lane keeping assistant which are already on the auto-motive market can improve safety by decreasing thenumber of traffic accidents among which the ACC helpsa lot to reduce the driverrsquos work intensity an ACCequipped vehicle uses radar or other sensors that detectthe distance and speed to other preceding vehicles(downstream vehicles) on the highway In the absence ofpreceding vehicles the ACC vehicle travels at a driver-setspeed If a preceding vehicle is detected on the highway by

the vehiclersquos radar the ACC system determines to controlthe throttle and braking system so as to maintain anexpected distance and acceleration from the precedingvehicle [4]

ampe planning and decision-making modules are theldquobrainrdquo of the vehicle and have a high degree of intelligenceAll response actions of the vehicle are performed accordingto the instructions issued by the module By processing andcalculating the real-time state information and environ-mental information of the vehicle this module can plan themost reasonable vehicle movement state and send it to theexecution control module [5] ampe most critical parts for theACC the planning and decision-making module need todecide the optimal control target according to the relativemotion state between the host vehicle and the target vehicleexpected longitudinal acceleration or distance [6] So far thedecision algorithms of the ACC mainly have the followingforms PID feedback control model predictive control fuzzylogic control and optimal control [7ndash10]

Longitudinal control is the basic function of ACC systemwhere the control technology is used to achieve constant

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 8382734 10 pageshttpsdoiorg10115520208382734

speed driving of the vehicle maintaining the distance be-tween vehicles or the time between vehicles to follow theleading vehicle identifying and tracking the curve of thevehicle ahead automatic braking and other functions ampequality of the longitudinal control effect has a direct impacton the safety and comfort of ACC system ampe executivecontrol module mainly achieves rapid response to the in-structions issued by the planning and decision module andprecise tracking of the expected goal through the precisecontrol of the driving system and the braking system ACCsystem in accordance with the working conditions can bedivided into cruise mode following mode and overtakingmode [11] the research scope of this article is car-followingmodel whose function is to keep an appropriate distanceand speed with the leading vehicle In order to furtherimprove the effect of vehicle longitudinal control dynamicmodel has become one of the key links in the field of vehiclelongitudinal control Among them Zhan established alongitudinal dynamic model and braking system model forACC system [12] ampe researchers adopted longitudinalcontrol method based on vehicle longitudinal inverse modeland used vehicle inverse model to control electronic throttleand braking pressure [13 14]

With the development of ACC system more and moreworking conditions involve speeds of 30 kmh and below sothe vehicle longitudinal control has experienced the de-velopment process from single throttle control to combinedthrottle-braking control [15] Due to strong robustness lowaccuracy requirements for controlled objects and no needfor accurate modeling classical control methods representedby PID control and numerical look-up tables are widelyused In addition many researchers use the modified form ofPID controller to study longitudinal control of vehicles andtry to improve longitudinal control effect by improving PIDcontroller [16 17]

Adaptive Neural Network scheme has been used in aplatoon in order to solve the traffic stability problem [18]PID algorithm is used to directly control the acceleratorpedal and the brake pedal to control the acceleration anddeceleration of the vehicle to maintain the distance from thepreceding vehicle [19 20] ampe fuzzy logic-based ACCcontroller is used to make one vehicle follow another vehiclestably having no shock during the process of the acceleratorand brake switching [21 22] ampe fuzzy ACC system withspeed sign detection capability and synovial control is usedfor adaptive control system [23 24] ampe change of signallight is also considered to control the driving of vehicles atintersections [25] ampe prospective velocity of the precedingvehicle is estimated by a prediction model based on themeasured intervehicle distance and the I2V communicationto enable an anticipatory driving behavior for the controlledvehicle [26]

One can conclude from the research that the previousactive braking functions of adaptive cruise-following systemalso did not fully consider the ride comfort and hydraulichysteresis problem ampis research is aimed at designing anACC considering the vehicle ride and proposing an analysismodel based on active braking algorithm using hierarchicalcontrol

In this paper considering the safety comfort and thephysical characteristics of hydraulic braking system byswitching on and off the valve and motor start-stopadjusting the hydraulic cylinder pressure a new ACCcontrol strategy based on active braking is proposed Bycomparison with the full deceleration model the proposedmethod can improve the braking ride comfort obviouslyampe remainder of this paper is structured as follows Section2 modeling Section 3 control algorithm research Section 4simulation and discussion Section 5 conclusions

2 Modeling

ampis paper is aimed at designing a control scheme that couldguarantee safety considering the vehicle characteristic andensure braking comfort at all times As shown in Figure 1the vehicle longitudinal dynamics model the hydraulicbraking system and the control mechanism are included inthe proposed researchmodelampemain idea of the controllermodel is as follows

(1) ampe real-time safety distance according to the vehiclespeed and the actual distance and relative speedbetween leader vehicle and follower vehicle areobtained as the controller input

(2) ampe limitation of the acceleration and relative dis-tance of the follower vehicle is calculated by thelongitudinal dynamics model

(3) ampe expected acceleration of the follower vehicle iscalculated and the optimized brake pressure istransmitted to the executive agency including activebrake controller and active throttle controller

(4) ampe braking pressure is produced by the hydraulicbraking system and the vehicle speed slows down Inthis process the brake pressure information is alsotransmitted to the longitudinal dynamics model

21 Vehicle DynamicsModel In this paper Carsim softwareis used to build vehicle dynamics model for collaborativesimulation ampe vehicles are four-wheel drive B-classhatchback with the engine power of 125 kW and with thehydraulic ABS braking system ampe vehicle model includes 7subsystems the body aerodynamics input transmissionsystem braking system steering system suspension systemand the tire ampe parameters of the vehicles are shown inTable 1 ampe output of the model includes the longitudinalvelocity v acceleration a engine speed ωe and position S

22 Vehicle Reverse Longitudinal Dynamics Model In theACC system the control command from the host controlleris a desired vehicle acceleration that needs to be shifted to thedesired throttle opening and brake pressure by the vehiclereverse longitudinal dynamic model which then transmittedto the vehicle longitudinal dynamics model to control thevehicle acceleration deceleration or uniform motion inorder to achieve the function of the car adaptive cruisesystem [27 28]

2 Mathematical Problems in Engineering

221 Mode Switch To the vehicle dynamics system ac-celeration and braking are separate movements Whenbraking the car should first release the accelerator pedalusing engine drag wind resistance and rolling resistanceand other ways to brake If the above action still cannot meetthe needs of vehicle deceleration then depress the brakepedal applying brake force to increase vehicle decelerationBesides taking into account the driving comfort and thereliability of the corresponding parts of the vehicle thedesigning process should avoid frequent switching betweenacceleration control and braking control

It is easy to directly measure the maximum decelerationvalue amax at different speeds in Carsim software as shownin Figure 2 In order to improve the driving comfort of thevehicle the width of the transition area is set on the upper

and lower sides of the switching curve which is generallytaken from experience

ampe expected acceleration of the vehicle is defined asafdes According to the switching curve when afdes ge amax thecar switches to acceleration control On the contrary whenafdes le amax the car switches to braking control

222 Acceleration Control If the vehicle switches to ac-celeration control mode it is necessary to do as the expectedacceleration requires ampe expected torque is calculated from

Leading vehicle

Radar

Driverrsquos setting

Acceleration evaluation model

Mode switcher

Reverse longitudinal dynamics model ACC control

mechanism

Upper decision controller

Controller input

Active braking controller

Active throttle controller

Hydraulic braking system

Braking pressure

The model is built in SimulinkThe model is built in CarsimThe model is built in Amesim

Deceleration evaluation model

Bottom executive controller

Acceleration system

Engine torque

Figure 1 Scheme of the proposed ACC control model

Table 1 Parameters of the vehicles

Parameters Symbol ValueSprung mass (kg) M 1111Distance between CM and front axle (m) a 104Distance between CM and rear axle (m) b 156Air density (kgm3) ρ 1206Rolling resistance coefficient f 002Track (m) d 1695Centroid height (m) H 054Gear ratio of main gear i0 41Transmission gear N 6Gear ratio of transmission ig 1Tire rolling radius (m) r 0311Air resistance coefficient CD 0342Frontal area (m2) A 16ampe efficiency of the drive system η 09 0 5 10 15 20 25 30 35

ndash06

ndash04

ndash02

00

Lower limitationUpper limitation

Acc

eler

atio

n (m

s2 )

Velocity (ms)

2Δh

Figure 2 Acceleration controlbraking control switching curve

Mathematical Problems in Engineering 3

the expected acceleration and then the desired throttleopening can be checked through the engine mapping

Without considering the conversion quality of rotatingparts the longitudinal dynamic analysis of the vehicle isanalyzed and the vehicle longitudinal dynamics model is asfollows

mafdes Ft minus Fxb minus 1113936 F(v)

1113936 F(v) 12

CDAρv2

+ mgf

(1)

where afdes is the expected acceleration m is the vehiclemass Ft is the driving force Fxb is the braking force 1113936 F(v)

is the sum of the resistances CD is the air resistance coef-ficient A is the frontal area ρ is the air density v is the carspeed g is the gravitational acceleration and f is the rollingresistance coefficient

Regardless of the elastic deformation of the transmissionsystem the driving force can be calculated as follows

Ft ητ ωtωe( 1113857igi0

rTe KdTe (2)

where η is the mechanical efficiency Te is the engine torqueωt is the torque converter turbine speed ωe is the enginespeed ig is the transmission gear ratio i0 is the main gearratio τ(ωtωe) is a torque converter characteristic functionr is the wheel rolling radius and Kd is a variable that can beobserved in real time

Kd ητ ωtωe( 1113857RgRm

rητ vRgRm1113872 1113873 rωe( 11138571113872 1113873RgRm

r (3)

When the vehicle is accelerating Fxb 0 And the ex-pected engine output torque can be obtained according tothe transmission gear ratio and speed ratio

Tdes ma + 1113936 F(v)

Kd (4)

It is easy to get the throttle opening of the engine fromthe mapping by taking the throttle opening required tooutput different torques at different speeds ampe values areexpressed as follows

αdes f Tdesωe( 1113857 (5)

223 Braking Control If the car switches to braking controlmode it is necessary to do as the expected decelerationrequires ampe desired braking force can be calculatedaccording to the desired acceleration and the brakingpressure can be obtained through the braking reverse model[29]

In this case the engine output torque is terminatedTe 0 according to equation (2) it can be seen that Ft 0the vehicle longitudinal force can be shown as

mafdes minus Fxb minus 1113936 F(v) (6)

ampe braking force and braking pressure can be ap-proximated as a linear relationship as follows

Fbdes KbPdes (7)

where Kb is a constantIt is not hard to calculate the braking pressure from

equations (6) and (7)

Pdes minus mafdes minus 05CDAρv2 minus mgf

11138681113868111386811138681113868111386811138681113868

Kb (8)

23 Active Braking Hydraulic System Model ampe expectedacceleration got from upper-level decision controller istransformed by the inverse vertical dynamic model into thedesired braking pressure or desired throttle opening to theunderlying accelerator and brake actuator Active brakingobjective is archived by controlling the plunger pump andvalves to start or stop to achieve the object hydraulic oilpressure thereby controlling the brake calipers

231 Designing of the Active Braking Principle ampe sim-plified hydraulic structure of active braking system is shownin Figure 3 ampe working principle is as follows If the systemswitches into the active braking mode there are three activemodes booster packing and decompression When pres-sure increases high-pressure directional valve 6 and di-rectional valve 5 are opened and the pump motor is startedBrake fluid flows through high-pressure valve 6 and motorpump and then through the inlet valve 12 into the wheelcylinder then pushing the piston of wheel cylinder to slowdown the wheel rotate speed When braking force reaches acertain intensity active braking system switches into thepressure hold-on mode directional valve 5 is opened pumpmotor and high-pressure valve 6 are closed and wheelcylinder pressure keeps constant at this state When pressuredecreases the high-pressure valve 6 is opened directionalvalve 5 and the motor are closed and the braking fluid flowsinto the low-pressure accumulator 9 increasing the brakingfluid storage of the accumulator In the process of the newpressure increase case plunger pump 8 works and thebraking fluid flows out of the low-pressure accumulator 9and then through inlet valve 12 to the wheel cylinder

232 Modeling of the Hydraulic Braking System

(1) Accumulator modelampe pressure and volume of the accumulator followthe idea gas law ampe mathematical model is asfollows

PAVnA P1V

n1 P2V

n2 (9)

where PA and VA are the inflation pressure andaccumulator capacity respectively P1 and P2 are thehighest and the lowest pressure values of the accu-mulator and V1 and V2 are the highest and thelowest volume values of the accumulator Consid-ering that the braking process could be seen as


adiabatic n 14 Apart from these PA should meetthe requirement that 025P1＜PA＜09P2

(2) Motor pump modelampe motor starts to work when the accumulatorpressure is below the lower limit and stops when theaccumulator pressure reaches the upper limit ampemathematical model is as follows [30]

Qb VcωE

E αPin +(1 minus α)Pout1113858 1113859 (10)

(i) where Qb is the oil pump flow rate Vc is the pumpdisplacement ω is the motor speed Pout and Pin arethe output and input of pump pressure respectivelyE is the bulk modulus of braking fluid and α is thepump pressure factor

(3) High-speed switch solenoid switch modelFor the on-off action of the solenoid switch that iscontrolled by the input voltage there will be a certaindelay phenomenon In addition inertia of the spoolcan also cause delay ampe mathematical model of thehigh-speed on-off valve with the second-order delayis as follows

G(s) K1ω

s2 + 2ξωs + ω2 (11)

whereK1 is the current gainω is the valve frequencyand ξ is the equivalent damping ratio of the valve

(4) Restrictor model

ampe restrictor controls the flow rate by the order ofsystem pressure and the mathematical model is asfollows

q a tanh2χ

((2Δp)ρ)

1113968

]Re1113888 1113889

qmax (12)

where q is the hydraulic medium flow A is the ef-fective circulation area of valves χ is the hydraulicdiameter ρ is the fluid density Δp is the valversquospressure difference ] is the sports viscosity and Re isthe critical Reynolds number

(5) Braking modelampe braking model is as follows

md2bdt2

minus PS + Ceqdb

dt+ Km b0 + b( 1113857

bS 1113938t

0 Qdt

(13)

where m is the brake caliper mass b is the brake caliperdisplacement P is the hydraulic cylinder brakingpressure Ceq is the equivalent damping Km is thespring stiffness x0 is the spring initial position and S isthe area of hydraulic cylinder cross section

3 Control Algorithms

Due to the complex conditions of the vehicle following theformer researches have shown that the ACC system should

1

2

3

56

78

7 9

1010

4 45 6

3

8 7

79

1010

Rear le piston Rear right piston Front right piston Front le piston

Secondary piston

Input

Primary piston

Figure 3 Schematic of the active hydraulic braking system (1) Master cylinder (2) hydraulic unit (3) hydraulic circuit (4) check valve (5)directional valve (6) high pressure directional valve (7) pressure-increasing valve (8) oil returning pump (9) low pressure accumulator(10) pressure-reducing valve


both control the vehicle speed and adapt to external in-terference such as the leading vehiclersquos velocity [31 32]Independent hierarchical control method is used in theproposed ACC model And the control method is dividedinto the upper controller (decision-making controller)module and the bottom controller (underlying executivemodule controller)

ampe upper controller determines the expected acceler-ation afdes based on the driving information provided by thesensors and the driverrsquos settings at this time Based on theoutput from the upper controller the bottom controllermakes the vehicle dynamics system to achieve the desiredacceleration

31 Upper Controller Design

311 Establishment of the Follower Model Car-followingmodel is built based on the driver desired distance and thevehicle dynamic characteristic Equation (14) describes thedriver desired distance [33] and equation (15) shows therelationship of the vehicle dynamic

ddes Thvf + d0 (14)

where ddes is the expect distanceTh is the time headway vf isthe velocity of the following vehicle and d0 is the minimumsafe distance when the two vehicles stop

It is clear that the distance error and the velocity dif-ference can be as follows

Δ d ddes minus d

Δv vl minus vf 1113896 (15)

where d is the factual distance Δ d is the distance error vl isthe velocity of the leading vehicle and Δv is the velocitydifference

A simulation system is built to analyze the vehicle dy-namic relationship ampe frequency response method isadopted to identify the system input and output charac-teristics and finally the transfer function is obtained asequation (18)

af K

Ts + 1afdes (16)

where K is the gain and T is the time delayCombining equations (16)ndash(19) the car-following model

can be as follows

_x Aprimex + Bprimeu + Gprimev (17)

where x [Δ dΔv af ]T u afdes λ ap

Aprime 0 1 minus Th0 0 minus 10 0 minus (1T)

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ Bprime

00

KT

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ and Gprime 0 1 01113858 1113859

T

x is the system status variable u is the system input λ isthe disturbance of the input which is the preceding vehiclersquosacceleration ap here Aprime Bprime and Gprime are the coefficient matrixof the input

312 Performance Index Design

(1) Following performance indexampe ACC system needs to control the vehicle fol-lowing the leading vehicle steadily and the followingperformance is manifested in the performance indexof speed and the safety index [34ndash36]ampe square sum of the speed error Δv(k) and thedistance error Δ d(k) is taken as the following per-formance index

lt(k) wΔd(Δ d(k))2 + wΔv(Δv(k))2 (18)

where Δ d(k) sf(k) minus sl(k) minus ddes(vl(k)) Δv(k)

vh(k) minus vf(k)wΔd and wΔv are the distance errorweight and speed error weight sf is the displacement ofthe front car and sh is the distance of the car traveledampe following performance index in the forecast timedomain is as follows

Lt(k) 1113936 lt(k)

k1P

(19)

(2) Safety indexampe vehicle should keep a safe distance to avoidcollision Meanwhile the distance between the twovehicles should avoid being too large to avoid ac-cidental vehicle insertion ampe vehicle should alsokeep an appropriate speed difference to ensure safetyand to increase traffic efficiency And the velocityerror between two vehicles should not be too largeampe optimization problem is solved subject to de-sired intervehicle distance and acceleration limita-tion which are incorporated as constraintsamperefore the constraints of the vehicle distanceerror and speed error are as follows

0leΔd(k)leΔdmax

Δvmin leΔv(k)leΔvmax1113896 (20)

(3) System prediction optimizationBased on the index functions and constraintsestablished before the integrated index for the op-timization problem is established as follows

L 1113936P

i1Δ d(k + i + 1 | k)2wΔ d

+ 1113936P

i1Δv(k + i + 1 | k)2wΔv

(21)

where P is the length of the predictive sample timeSystem constraints are as follows

xmin lex(k + i | k)lexmax

ymin ley(k + i | k)leymax1113896 i 0 P minus 1 (22)

From the above analysis the objective optimizationproblem of the system can be described as follows


mini0 Pminus 1

L (23)

subject to0leΔ d(k)leΔdmax

Δvmin leΔv(k)leΔvmax

xmin lex(k + i | k)le xmax

ymin ley(k + i | k)leymax

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)

32 Bottom Controller Design ampe bottom controller is thesystem that ensures the vehicle response is constant with theexpected value calculated by the upper controller as much aspossible ampe desired acceleration from the upper controlleris translated into the desired braking pressure or throttleopening to the braking controller and the throttle controllervia the inverse longitudinal braking model

321 rottle Controller ampe PID algorithm is adopted inthe throttle controller to ensure the system is working inrobust and reliable condition ampe algorithm takes the linearcombination of the errorrsquos proportion (P) integral (I) anddifferential (D) as control variables and controlling object

ampe PID control law is as follows

Δy Kp ε +1TI

1113946t

0εdt + TD

dεdt

1113890 1113891 (25)

where ε is the difference between the expected accelerationades and the actual car acceleration a Kp is the proportionalgain TI is the integration time constant and TD is thederivative time constant

ampe conversion to transfer function is as follows

(s) U(s)

E(s) Kp 1 +

1TIs

+ TDs1113888 1113889 (26)

322 Braking Controller ampe purpose of the brakingpressure controller is to make the real braking pressure andthe expected as close as possible so as to follow up the desiredacceleration Due to inertial links (mechanical system in-ertia electrical system inertia and control system inertia) ofthe active braking control system real-time control valuecannot act on the control system timely Even if the pa-rameters of the classical discrete PID algorithm are opti-mized the control result still has serious lag and overshootwhich cannot meet the control requirements ampe ideas forsolving these problems will be given in the next paragraph

By using proportional feedback control it is easy todouble the interference noise in feedback accelerationwhich is not conducive to the stability Feedback controlstructure is used tomake the actual pressure follow the targetpressure And the feedforward control structure is used toimprove the controller execution response to recuperate thetime lag of the feedback controller ampe cooperation of thefeedback and feedforward controller is used to eliminate thestatic error and improve the accuracy of acceleration control

ampe overall structure of the braking controller is shown inFigure 4

Feedforward compensator uses the look-up tablemethod According to the pressure difference between theactual pressure and the ideal pressure of the hydrauliccylinder the system controls the duty cycle signal of theincreasing and reducing valve so as to control the pressurechange rate of the hydraulic cylinder precisely controllingthe hydraulic cylinder pressure

When the pressure difference is active the system willselect a larger duty cycle in order to quickly increase or reducehydraulic cylinder pressure When the pressure difference ispositive the system will choose a smaller duty cycle to ac-curately track the ideal pressure and to improve the wheelpressure accuracy and robustness [37 38] specifically as listedin Table 2 where X is the pressure difference Y1 is the valveduty signal of the booster valve and Y2 is the duty cycle of thevalve control signal of the pressure reducing valve

Similar to the throttle controller the PID algorithm isused in the braking controller ampe difference between theexpected braking pressure and the actual braking pressure istaken as the target control variable From the design processone can conclude that the designs of the feedforwardcompensator and the feedback compensator do not affecteach other and can be performed independently

4 Simulation and Discussion

A collaborative simulation model is built by MatlabSimulink Carsim and Amesim to validate the proposedalgorithm ampe simulation parameters and restrictions aredefined as shown in Table 3

Simulation conditions are as follows at 0ndash15 s theleading vehicle drives at 20ms at 15ndash25 s the leadingvehicle accelerates to 30ms with acceleration 1ms2 at25ndash35 s the leading vehicle drives at 30ms at 35ndash42 s theleading vehicle slows down to 18ms with decelerationminus 17ms2 ampe initial distance between two vehicles is 50mand the initial speed of the follower vehicle is 25ms ampesimulation results are shown in Figures 5ndash8 ampe followprocess includes 3 stages shown as follows

Feedforwardcompensator

Lower controlobject

Feedbackcompensator

+

++

+

+

ndash

acon

ades e

wd

xfmiddotmiddot

Figure 4 Structure of the braking controller

Table 2 Duty ratio of high-pressure valve and directional valveunder different pressure differencesX (MPa) minus 6 minus 4 minus 3 minus 2 minus 1 minus 05 minus 03 minus 01Y1 () 100 40 35 30 25 20 15 10Y2 () 0 0 0 0 0 0 0 0X (MPa) 0 01 03 05 1 2 3 4 6Y1 () 0 0 0 0 0 0 0 0 0Y2 () 0 10 20 20 25 30 40 40 100


41 S-1 FollowDistanceAdjustment During the time 0 minus 5 sthe actual distance between the two vehicles is greater thanthe desired distance the system judges the condition is safeampe upper controller instructs the bottom controller toaccelerate to shorten the distance to improve the trafficefficiency ampe braking controller is on the standby modeand the throttle is in a small opening As the velocity in-creases the expected distance also increases

42 S-2 Follow Velocity Adjustment As the velocity of thefollower vehicle increases the expected distance increasesalsoampe actual distance is shortened as the velocity differenceincreases the system judges the condition is in danger ampeupper controller instructs the bottom controller to decelerateto lengthen the distance to improve the safety ampe throttlecontroller is on the standby mode the braking controlleropens valves 5 and 6 and starts the brake pump (Figure 3) andthe braking pressure is increased And then the vehicle de-celeration increases and the velocity of the follower vehicledecreases near the velocity of the leading vehicle

Table 3 ampe simulation parameters

Items ts(s) th(s) τ(s) d0(m) dc(m) vmin(ms) vmax(ms)Value 02 15 07 7 5 0 36Items aumin(ms2) aumax(ms2) R N P RValue minus 3 2 1 5 10 diag 2 10 0

0 10 20 30 40 50 6016

20

24

28

32

Vel

ocity

(ms

)

Time (s)

FollowerLeading

S-1S-2

S-3

Figure 5 ampe vehicle velocity of the two vehicles

0 10 20 30 40 50 6025

30

35

40

45

50

55

Actual distanceExpected distance

Dist

ance

(m)

Time (s)

S-1S-2

S-3

Figure 6 Distance between the two vehicles

0 10 20 30 40 50 60Time (s)

ndash2

ndash1

0

1

2 S-2

Acc

eler

atio

n (m

s2 )

S-1

S-3

Figure 7 Acceleration of the follower vehicle

Expected braking pressureActual braking pressure

0 10 20 30 40 50 60Time (s)

00

04

08

12

16

20

Brak

ing

pres

sure

(MPa

)

S-3

S-2

S-1

Figure 8 Braking pressure of the follower vehicle


43 S-3 Follow with the Leading Vehicle As the leadingvehicle accelerates during 15ndash25 s and decelerates during35ndash42 s the follower vehicle changes the throttle openingand braking pressure keeping the desired distance andspeed As can be seen from Figure 7 although the accel-eration of the vehicle has slight fluctuation the accelerationfalls in a narrow range of minus 3 to 2ms2 which ensures the ridecomfort As can be seen in Figure 8 the target pressurefollows the change of the desired acceleration responsequickly and steadily with less hysteresis

To illustrate purposes and evaluate results convenientlya comparison with a state-of-the-art ACC used in the au-tomotive industry research is analyzed [39] In this paperthe safety and comfort are evaluated and provided directlyampe full declaration method is used in the mode whichpresents detailed simulation results for one consideredscenario ampe results show that the velocity of the leadingvehicle accelerates from 10msndash15ms and the accelerationof follower vehicle falls in a width range of minus 10 minus 5ms2ampejerk caused by application of full braking results in un-comfortable driving

By comparison the proposed strategy results show thatthe acceleration of the vehicle has slight fluctuation and fastresponse which implies comfortable driving without jerkymaneuvers ampe ability of keeping intervehicle distance asclose as possible to safe distance shows good trackingperformance In this way both safety and comfort areachieved by utilizing the proposed model based on opti-mization of active braking strategy

5 Conclusions

ampis research is aimed at proposing an ACC strategy con-sidering the safety and comfort based on the active brakingwhere the system hysteresis problem is included For thispurpose vehicle dynamics model vehicle reverse longitu-dinal dynamics model and active hydraulic braking systemmodel are proposed And the models are simulated inCarsim MATLABSimulink and Amesim collaborativelyampe control algorithm is proposed and optimized to improvethe ride comfort From the results it can be seen that thevelocity and distance values are preserved in the specifiedcomfortable range although the vehicle velocity changesobviously

(1) ampe control algorithm based on the model predictivecontrol algorithm can be optimized by consideringthe multivariable constraints simultaneously that isto say the cruise-following control safety can beensured and the ride comfort can be satisfied

(2) ampe proposed algorithm is evaluated by comparisonwith using full deceleration simulation and it showsactive performance on position and velocity track-ing ampus we can conclude that the proposed ap-proach guarantees safety and comfort for ACC-equipped vehicles in low velocity conditions

ampis study only focuses on the occupant kinematicsduring the pre-crash period the occupant kinematics and

injury indexes within the in-crash phase of such typicalscenario require subsequent study

Data Availability

All data included in this study are available upon request tothe corresponding author

Conflicts of Interest

ampe authors declare no conflicts of interest

Acknowledgments

ampis research was funded by the National Natural ScienceFoundation of China under Grant nos 51775178 51875049and 51705035 and Hunan Science Foundation for Distin-guished Young Scholars of China under Grant no2019JJ20017

References

[1] L Hu J Ou J Huang Y Chen and D Cao ldquoA review ofresearch on traffic conflicts based on intelligent vehiclesrdquoIEEE Access vol 8 pp 24471ndash24483 2020

[2] L Hu X Hu J Wan M Lin and J Huang ldquoampe injuryepidemiology of adult riders in vehicle-two-wheeler crashes inChina Ningbo 2011-2015rdquo Journal of Safety Research vol 72pp 21ndash28 2020

[3] Y Peng C Fan L Hu et al ldquoTunnel driving occupationalenvironment and hearing loss in train drivers in ChinardquoOccupational and Environmental Medicine vol 76 no 2pp 97ndash104 2019

[4] R Rajamani Adaptive Cruise Control Vehicle Dynamics andControl pp 141ndash170 Springer US Boston MA USA 2012

[5] A Weiszligmann D Gorges and X Lin ldquoEnergy-optimaladaptive cruise control combining model predictive controland dynamic programmingrdquo Control Engineering Practicevol 72 pp 125ndash137 2018

[6] F Schrodel P Herrmann and N Schwarz ldquoAn improvedmulti-object adaptive cruise control approachrdquo IFAC-PapersOnLine vol 52 no 8 pp 176ndash181 2019

[7] Y He B Ciuffo Q Zhou et al ldquoAdaptive cruise controlstrategies implemented on experimental vehicles a reviewrdquoIFAC-PapersOnLine vol 52 no 5 pp 21ndash27 2019

[8] M Li Y Chen and C-C Lim ldquoStability analysis of complexNetwork control system with dynamical topology and delaysrdquoIEEE Transactions on Systems Man and Cybernetics Systemspp 1ndash10 2020

[9] L Yang Y Chen Z Liu K Chen and Z Zhang ldquoAdaptivefuzzy control for teleoperation system with uncertain kine-matics and dynamicsrdquo International Journal of ControlAutomation and Systems vol 17 no 5 pp 1158ndash1166 2019

[10] B Guo and Y Chen ldquoRobust adaptive fault-tolerant controlof four-wheel independently actuated electric vehiclesrdquo IEEETransactions on Industrial Informatics vol 16 no 5pp 2882ndash2894 2018

[11] B Gontildei-Ros W J Schakel A E Papacharalampous et alldquoUsing advanced adaptive cruise control systems to reducecongestion at sags an evaluation based on microscopic trafficsimulationrdquo Transportation Research Part C EmergingTechnologies vol 102 pp 411ndash426 2019


[12] J Zhan ldquoSetup of vehicle longitudinal dynamic model foradaptive cruise controlrdquo Journal of Jilin University (Engi-neering) vol 36 no 2 pp 157ndash160 2006

[13] S Huang andW Ren ldquoAutonomous intelligent cruise controlwith actuator delaysrdquo Journal of Intelligent and RoboticSystems vol 23 no 1 pp 27ndash43 1998

[14] A S A Rachman A F Idriz S Li and S Baldi ldquoReal-timeperformance and safety validation of an integrated vehicledynamic control strategyrdquo IFAC-PapersOnLine vol 50 no 1pp 13854ndash13859 2017

[15] J E Naranjo C Gonzalez R Garcia and T DePedroldquoACC+StopampGo maneuvers with throttle and brake fuzzycontrolrdquo IEEE Transactions on Intelligent TransportationSystems vol 7 no 2 pp 213ndash225 2006

[16] P Shakouri A Ordys D S Laila and M Askari ldquoAdaptivecruise control system comparing gain-scheduling PI and LQcontrollersrdquo IFAC Proceedings Volumes vol 44 no 1pp 12964ndash12969 2011

[17] P Ioannou Z Xu S Eckert D Clemons and T SiejaldquoIntelligent cruise control theory and experimentrdquo in Pro-ceedings of 32nd IEEE Conference on Decision and Controlpp 1885ndash1890 San Antonio TX USA December 1993

[18] S Kitazono and H Ohmori ldquoSemi-Autonomous adaptivecruise control in mixed trafficrdquo Proceedings of 2006 SICE-CASE International Joint Conferencepp 3240ndash3245 BusanSouth Korea October 2006

[19] M H Lee H G Park S H Lee K S Yoon and K S LeeldquoAn adaptive cruise control system for autonomous vehi-clesrdquo International Journal of Precision Engineering andManufacturing vol 14 no 3 pp 373ndash380 2013

[20] X Wu G Qin H Yu S Gao L Liu and Y Xue ldquoUsingimproved chaotic ant swarm to tune PID controller on co-operative adaptive cruise controlrdquo Optik vol 127 no 6pp 3445ndash3450 2016

[21] N C Basjaruddin K Kuspriyanto D Saefudin et al ldquoDe-veloping adaptive cruise control based on fuzzy logic usinghardware simulationrdquo International Journal of Electrical ampComputer Engineering vol 4 no 6 2014

[22] G Prabhakar S Selvaperumal and P N Pugazhenthi ldquoFuzzyPD plus I control-based adaptive cruise control system insimulation and real-time environmentrdquo IETE Journal ofResearch vol 65 no 1 pp 69ndash79 2019

[23] R Rizvi S Kalra C Gosalia et al ldquoFuzzy Adaptive CruiseControl system with speed sign detection capabilityrdquo inProceedings of 2014 IEEE International Conference on FuzzySystems pp 968ndash976 IEEE Beijing China July 2014

[24] B Ganji A Z Kouzani S Y Khoo and M Shams-ZahraeildquoAdaptive cruise control of a HEV using sliding mode controlrdquoExpert Systems with Applications vol 41 no 2 pp 607ndash615 2014

[25] L Hu Y Zhong W Hao et al ldquoOptimal route algorithmconsidering traffic light and energy consumptionrdquo IEEEAccess vol 6 pp 59695ndash59704 2018

[26] K Gao F Han P Dong N Xiong and R Du ldquoConnectedvehicle as a mobile sensor for real time queue length atsignalized intersectionsrdquo Sensors vol 19 no 9 p 2059 2019

[27] D Hou Study on Vehicle Forward Collision Avoidance SystemTsinghua University Beijing China 2004

[28] Y Liu J Che and C Cao ldquoAdvanced autonomous under-water vehicles attitude control with L 1 backstepping adaptivecontrol strategyrdquo Sensors vol 19 no 22 p 4848 2019

[29] H Zheng and M Zhao ldquoDevelopment a HIL test bench forelectrically controlled steering systemrdquo Proceedings of SAETechnical Paper Series SAE International April 2016

[30] X Qi J Song et al ldquoModeling and analysis of vehicle ESPhydraulic control device using AMESimrdquo Machine Tools andHydraulic vol 8 pp 115-116 2005

[31] S Moon I Moon and K Yi ldquoDesign tuning and evaluationof a full-range adaptive cruise control system with collisionavoidancerdquo Control Engineering Practice vol 17 no 4pp 442ndash455 2009

[32] D H Han K S Yi J K Lee B S Kim and S Yi ldquoDesign andevaluation of inteligent vehicle cruise control systems using avehicle simulatorrdquo International Journal of AutomotiveTechnology vol 7 no 3 pp 377ndash383 2006

[33] D Yanakiev and I Kanellakopoulos ldquoLongitudinal control ofheavy-duty vehicles for automated highway systemsrdquo Pro-ceedings of the 1995 American Control Conference SeattleWA USA June 1995

[34] M Guocheng Research on the Adaptive Cruise ControlTracking System Applied for Motor Vehicle Beijing Institute ofTechnology Beijing China 2014

[35] Z Zhang D Luo Y Rasim et al ldquoA vehicle active safetymodel vehicle speed control based on driver vigilance de-tection using wearable EEG and sparse representationrdquoSensors vol 16 no 2 p 242 2016

[36] R Du G Qiu K Gao L Hu and L Liu ldquoAbnormal roadsurface recognition based on smartphone acceleration sen-sorrdquo Sensors vol 20 no 2 p 451 2020

[37] L Hu X Hu Y Che et al ldquoReliable state of charge estimationof battery packs using fuzzy adaptive federated filteringrdquoApplied Energy vol 262 2020

[38] Z Zhang L Zhang L Hu C Huang et al ldquoActive cellbalancing of lithium-ion battery pack based on average stateof chargerdquo International Journal of Energy Research vol 44no 4 pp 2535ndash2548 2020

[39] S Magdici and M Althoff ldquoAdaptive cruise control withsafety guarantees for autonomous vehiclesrdquo IFAC-Paper-sOnLine vol 50 no 1 pp 5774ndash5781 2017


speed driving of the vehicle maintaining the distance be-tween vehicles or the time between vehicles to follow theleading vehicle identifying and tracking the curve of thevehicle ahead automatic braking and other functions ampequality of the longitudinal control effect has a direct impacton the safety and comfort of ACC system ampe executivecontrol module mainly achieves rapid response to the in-structions issued by the planning and decision module andprecise tracking of the expected goal through the precisecontrol of the driving system and the braking system ACCsystem in accordance with the working conditions can bedivided into cruise mode following mode and overtakingmode [11] the research scope of this article is car-followingmodel whose function is to keep an appropriate distanceand speed with the leading vehicle In order to furtherimprove the effect of vehicle longitudinal control dynamicmodel has become one of the key links in the field of vehiclelongitudinal control Among them Zhan established alongitudinal dynamic model and braking system model forACC system [12] ampe researchers adopted longitudinalcontrol method based on vehicle longitudinal inverse modeland used vehicle inverse model to control electronic throttleand braking pressure [13 14]

With the development of ACC system more and moreworking conditions involve speeds of 30 kmh and below sothe vehicle longitudinal control has experienced the de-velopment process from single throttle control to combinedthrottle-braking control [15] Due to strong robustness lowaccuracy requirements for controlled objects and no needfor accurate modeling classical control methods representedby PID control and numerical look-up tables are widelyused In addition many researchers use the modified form ofPID controller to study longitudinal control of vehicles andtry to improve longitudinal control effect by improving PIDcontroller [16 17]

Adaptive Neural Network scheme has been used in aplatoon in order to solve the traffic stability problem [18]PID algorithm is used to directly control the acceleratorpedal and the brake pedal to control the acceleration anddeceleration of the vehicle to maintain the distance from thepreceding vehicle [19 20] ampe fuzzy logic-based ACCcontroller is used to make one vehicle follow another vehiclestably having no shock during the process of the acceleratorand brake switching [21 22] ampe fuzzy ACC system withspeed sign detection capability and synovial control is usedfor adaptive control system [23 24] ampe change of signallight is also considered to control the driving of vehicles atintersections [25] ampe prospective velocity of the precedingvehicle is estimated by a prediction model based on themeasured intervehicle distance and the I2V communicationto enable an anticipatory driving behavior for the controlledvehicle [26]

One can conclude from the research that the previousactive braking functions of adaptive cruise-following systemalso did not fully consider the ride comfort and hydraulichysteresis problem ampis research is aimed at designing anACC considering the vehicle ride and proposing an analysismodel based on active braking algorithm using hierarchicalcontrol

In this paper considering the safety comfort and thephysical characteristics of hydraulic braking system byswitching on and off the valve and motor start-stopadjusting the hydraulic cylinder pressure a new ACCcontrol strategy based on active braking is proposed Bycomparison with the full deceleration model the proposedmethod can improve the braking ride comfort obviouslyampe remainder of this paper is structured as follows Section2 modeling Section 3 control algorithm research Section 4simulation and discussion Section 5 conclusions

2 Modeling

ampis paper is aimed at designing a control scheme that couldguarantee safety considering the vehicle characteristic andensure braking comfort at all times As shown in Figure 1the vehicle longitudinal dynamics model the hydraulicbraking system and the control mechanism are included inthe proposed researchmodelampemain idea of the controllermodel is as follows

(1) ampe real-time safety distance according to the vehiclespeed and the actual distance and relative speedbetween leader vehicle and follower vehicle areobtained as the controller input

(2) ampe limitation of the acceleration and relative dis-tance of the follower vehicle is calculated by thelongitudinal dynamics model

(3) ampe expected acceleration of the follower vehicle iscalculated and the optimized brake pressure istransmitted to the executive agency including activebrake controller and active throttle controller

(4) ampe braking pressure is produced by the hydraulicbraking system and the vehicle speed slows down Inthis process the brake pressure information is alsotransmitted to the longitudinal dynamics model

21 Vehicle DynamicsModel In this paper Carsim softwareis used to build vehicle dynamics model for collaborativesimulation ampe vehicles are four-wheel drive B-classhatchback with the engine power of 125 kW and with thehydraulic ABS braking system ampe vehicle model includes 7subsystems the body aerodynamics input transmissionsystem braking system steering system suspension systemand the tire ampe parameters of the vehicles are shown inTable 1 ampe output of the model includes the longitudinalvelocity v acceleration a engine speed ωe and position S

22 Vehicle Reverse Longitudinal Dynamics Model In theACC system the control command from the host controlleris a desired vehicle acceleration that needs to be shifted to thedesired throttle opening and brake pressure by the vehiclereverse longitudinal dynamic model which then transmittedto the vehicle longitudinal dynamics model to control thevehicle acceleration deceleration or uniform motion inorder to achieve the function of the car adaptive cruisesystem [27 28]







Leading vehicle

Radar



Mode switcher


mechanism


Controller input




Braking pressure




Acceleration system

Engine torque




ndash06

ndash04

ndash02

00


Acc

eler

atio

n (m

s2 )

Velocity (ms)

2Δh






1113936 F(v) 12

CDAρv2

+ mgf

(1)





rTe KdTe (2)




r (3)


Tdes ma + 1113936 F(v)

Kd (4)







Fbdes KbPdes (7)




11138681113868111386811138681113868111386811138681113868

Kb (8)





PAVnA P1V

n1 P2V

n2 (9)





Qb VcωE




G(s) K1ω

s2 + 2ξωs + ω2 (11)




q a tanh2χ

((2Δp)ρ)

1113968

]Re1113888 1113889

qmax (12)



md2bdt2

minus PS + Ceqdb

dt+ Km b0 + b( 1113857

bS 1113938t

0 Qdt

(13)




1

2

3

56

78

7 9

1010

4 45 6

3

8 7

79

1010


Secondary piston

Input

Primary piston







ddes Thvf + d0 (14)



Δ d ddes minus d




af K

Ts + 1afdes (16)


can be as follows




⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ Bprime

00

KT

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ and Gprime 0 1 01113858 1113859

T







Lt(k) 1113936 lt(k)

k1P

(19)


0leΔd(k)leΔdmax



L 1113936P

i1Δ d(k + i + 1 | k)2wΔ d

+ 1113936P

i1Δv(k + i + 1 | k)2wΔv

(21)






mini0 Pminus 1

L (23)





⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)




Δy Kp ε +1TI

1113946t

0εdt + TD

dεdt

1113890 1113891 (25)



(s) U(s)

E(s) Kp 1 +

1TIs

+ TDs1113888 1113889 (26)











Lower controlobject

Feedbackcompensator

+

++

+

+

ndash

acon

ades e

wd

xfmiddotmiddot








0 10 20 30 40 50 6016

20

24

28

32

Vel

ocity

(ms

)

Time (s)

FollowerLeading

S-1S-2

S-3


0 10 20 30 40 50 6025

30

35

40

45

50

55


Dist

ance

(m)

Time (s)

S-1S-2

S-3


0 10 20 30 40 50 60Time (s)

ndash2

ndash1

0

1

2 S-2

Acc

eler

atio

n (m

s2 )

S-1

S-3



0 10 20 30 40 50 60Time (s)

00

04

08

12

16

20

Brak

ing

pres

sure

(MPa

)

S-3

S-2

S-1






5 Conclusions






Data Availability




Acknowledgments


References















































Leading vehicle

Radar



Mode switcher


mechanism


Controller input




Braking pressure




Acceleration system

Engine torque




ndash06

ndash04

ndash02

00


Acc

eler

atio

n (m

s2 )

Velocity (ms)

2Δh






1113936 F(v) 12

CDAρv2

+ mgf

(1)





rTe KdTe (2)




r (3)


Tdes ma + 1113936 F(v)

Kd (4)







Fbdes KbPdes (7)




11138681113868111386811138681113868111386811138681113868

Kb (8)





PAVnA P1V

n1 P2V

n2 (9)





Qb VcωE




G(s) K1ω

s2 + 2ξωs + ω2 (11)




q a tanh2χ

((2Δp)ρ)

1113968

]Re1113888 1113889

qmax (12)



md2bdt2

minus PS + Ceqdb

dt+ Km b0 + b( 1113857

bS 1113938t

0 Qdt

(13)




1

2

3

56

78

7 9

1010

4 45 6

3

8 7

79

1010


Secondary piston

Input

Primary piston







ddes Thvf + d0 (14)



Δ d ddes minus d




af K

Ts + 1afdes (16)


can be as follows




⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ Bprime

00

KT

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ and Gprime 0 1 01113858 1113859

T







Lt(k) 1113936 lt(k)

k1P

(19)


0leΔd(k)leΔdmax



L 1113936P

i1Δ d(k + i + 1 | k)2wΔ d

+ 1113936P

i1Δv(k + i + 1 | k)2wΔv

(21)






mini0 Pminus 1

L (23)





⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)




Δy Kp ε +1TI

1113946t

0εdt + TD

dεdt

1113890 1113891 (25)



(s) U(s)

E(s) Kp 1 +

1TIs

+ TDs1113888 1113889 (26)











Lower controlobject

Feedbackcompensator

+

++

+

+

ndash

acon

ades e

wd

xfmiddotmiddot








0 10 20 30 40 50 6016

20

24

28

32

Vel

ocity

(ms

)

Time (s)

FollowerLeading

S-1S-2

S-3


0 10 20 30 40 50 6025

30

35

40

45

50

55


Dist

ance

(m)

Time (s)

S-1S-2

S-3


0 10 20 30 40 50 60Time (s)

ndash2

ndash1

0

1

2 S-2

Acc

eler

atio

n (m

s2 )

S-1

S-3



0 10 20 30 40 50 60Time (s)

00

04

08

12

16

20

Brak

ing

pres

sure

(MPa

)

S-3

S-2

S-1






5 Conclusions






Data Availability




Acknowledgments


References













































1113936 F(v) 12

CDAρv2

+ mgf

(1)





rTe KdTe (2)




r (3)


Tdes ma + 1113936 F(v)

Kd (4)







Fbdes KbPdes (7)




11138681113868111386811138681113868111386811138681113868

Kb (8)





PAVnA P1V

n1 P2V

n2 (9)





Qb VcωE




G(s) K1ω

s2 + 2ξωs + ω2 (11)




q a tanh2χ

((2Δp)ρ)

1113968

]Re1113888 1113889

qmax (12)



md2bdt2

minus PS + Ceqdb

dt+ Km b0 + b( 1113857

bS 1113938t

0 Qdt

(13)




1

2

3

56

78

7 9

1010

4 45 6

3

8 7

79

1010


Secondary piston

Input

Primary piston







ddes Thvf + d0 (14)



Δ d ddes minus d




af K

Ts + 1afdes (16)


can be as follows




⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ Bprime

00

KT

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ and Gprime 0 1 01113858 1113859

T







Lt(k) 1113936 lt(k)

k1P

(19)


0leΔd(k)leΔdmax



L 1113936P

i1Δ d(k + i + 1 | k)2wΔ d

+ 1113936P

i1Δv(k + i + 1 | k)2wΔv

(21)






mini0 Pminus 1

L (23)





⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)




Δy Kp ε +1TI

1113946t

0εdt + TD

dεdt

1113890 1113891 (25)



(s) U(s)

E(s) Kp 1 +

1TIs

+ TDs1113888 1113889 (26)











Lower controlobject

Feedbackcompensator

+

++

+

+

ndash

acon

ades e

wd

xfmiddotmiddot








0 10 20 30 40 50 6016

20

24

28

32

Vel

ocity

(ms

)

Time (s)

FollowerLeading

S-1S-2

S-3


0 10 20 30 40 50 6025

30

35

40

45

50

55


Dist

ance

(m)

Time (s)

S-1S-2

S-3


0 10 20 30 40 50 60Time (s)

ndash2

ndash1

0

1

2 S-2

Acc

eler

atio

n (m

s2 )

S-1

S-3



0 10 20 30 40 50 60Time (s)

00

04

08

12

16

20

Brak

ing

pres

sure

(MPa

)

S-3

S-2

S-1






5 Conclusions






Data Availability




Acknowledgments


References












































Qb VcωE




G(s) K1ω

s2 + 2ξωs + ω2 (11)




q a tanh2χ

((2Δp)ρ)

1113968

]Re1113888 1113889

qmax (12)



md2bdt2

minus PS + Ceqdb

dt+ Km b0 + b( 1113857

bS 1113938t

0 Qdt

(13)




1

2

3

56

78

7 9

1010

4 45 6

3

8 7

79

1010


Secondary piston

Input

Primary piston







ddes Thvf + d0 (14)



Δ d ddes minus d




af K

Ts + 1afdes (16)


can be as follows




⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ Bprime

00

KT

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ and Gprime 0 1 01113858 1113859

T







Lt(k) 1113936 lt(k)

k1P

(19)


0leΔd(k)leΔdmax



L 1113936P

i1Δ d(k + i + 1 | k)2wΔ d

+ 1113936P

i1Δv(k + i + 1 | k)2wΔv

(21)






mini0 Pminus 1

L (23)





⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)




Δy Kp ε +1TI

1113946t

0εdt + TD

dεdt

1113890 1113891 (25)



(s) U(s)

E(s) Kp 1 +

1TIs

+ TDs1113888 1113889 (26)











Lower controlobject

Feedbackcompensator

+

++

+

+

ndash

acon

ades e

wd

xfmiddotmiddot








0 10 20 30 40 50 6016

20

24

28

32

Vel

ocity

(ms

)

Time (s)

FollowerLeading

S-1S-2

S-3


0 10 20 30 40 50 6025

30

35

40

45

50

55


Dist

ance

(m)

Time (s)

S-1S-2

S-3


0 10 20 30 40 50 60Time (s)

ndash2

ndash1

0

1

2 S-2

Acc

eler

atio

n (m

s2 )

S-1

S-3



0 10 20 30 40 50 60Time (s)

00

04

08

12

16

20

Brak

ing

pres

sure

(MPa

)

S-3

S-2

S-1






5 Conclusions






Data Availability




Acknowledgments


References














































ddes Thvf + d0 (14)



Δ d ddes minus d




af K

Ts + 1afdes (16)


can be as follows




⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ Bprime

00

KT

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ and Gprime 0 1 01113858 1113859

T







Lt(k) 1113936 lt(k)

k1P

(19)


0leΔd(k)leΔdmax



L 1113936P

i1Δ d(k + i + 1 | k)2wΔ d

+ 1113936P

i1Δv(k + i + 1 | k)2wΔv

(21)






mini0 Pminus 1

L (23)





⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)




Δy Kp ε +1TI

1113946t

0εdt + TD

dεdt

1113890 1113891 (25)



(s) U(s)

E(s) Kp 1 +

1TIs

+ TDs1113888 1113889 (26)











Lower controlobject

Feedbackcompensator

+

++

+

+

ndash

acon

ades e

wd

xfmiddotmiddot








0 10 20 30 40 50 6016

20

24

28

32

Vel

ocity

(ms

)

Time (s)

FollowerLeading

S-1S-2

S-3


0 10 20 30 40 50 6025

30

35

40

45

50

55


Dist

ance

(m)

Time (s)

S-1S-2

S-3


0 10 20 30 40 50 60Time (s)

ndash2

ndash1

0

1

2 S-2

Acc

eler

atio

n (m

s2 )

S-1

S-3



0 10 20 30 40 50 60Time (s)

00

04

08

12

16

20

Brak

ing

pres

sure

(MPa

)

S-3

S-2

S-1






5 Conclusions






Data Availability




Acknowledgments


References










































mini0 Pminus 1

L (23)





⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)




Δy Kp ε +1TI

1113946t

0εdt + TD

dεdt

1113890 1113891 (25)



(s) U(s)

E(s) Kp 1 +

1TIs

+ TDs1113888 1113889 (26)











Lower controlobject

Feedbackcompensator

+

++

+

+

ndash

acon

ades e

wd

xfmiddotmiddot








0 10 20 30 40 50 6016

20

24

28

32

Vel

ocity

(ms

)

Time (s)

FollowerLeading

S-1S-2

S-3


0 10 20 30 40 50 6025

30

35

40

45

50

55


Dist

ance

(m)

Time (s)

S-1S-2

S-3


0 10 20 30 40 50 60Time (s)

ndash2

ndash1

0

1

2 S-2

Acc

eler

atio

n (m

s2 )

S-1

S-3



0 10 20 30 40 50 60Time (s)

00

04

08

12

16

20

Brak

ing

pres

sure

(MPa

)

S-3

S-2

S-1






5 Conclusions






Data Availability




Acknowledgments


References














































0 10 20 30 40 50 6016

20

24

28

32

Vel

ocity

(ms

)

Time (s)

FollowerLeading

S-1S-2

S-3


0 10 20 30 40 50 6025

30

35

40

45

50

55


Dist

ance

(m)

Time (s)

S-1S-2

S-3


0 10 20 30 40 50 60Time (s)

ndash2

ndash1

0

1

2 S-2

Acc

eler

atio

n (m

s2 )

S-1

S-3



0 10 20 30 40 50 60Time (s)

00

04

08

12

16

20

Brak

ing

pres

sure

(MPa

)

S-3

S-2

S-1






5 Conclusions






Data Availability




Acknowledgments


References













































5 Conclusions






Data Availability




Acknowledgments


References







































































Documents

AdaptiveCruiseControlStrategyDesignwithOptimizedActive ...In this paper, Carsim software is used to build vehicle dynamics model for collaborative simulation. e vehicles are four-wheel