Research on Pressure Control Algorithm of Regenerative Braking System for Highly Automated Driving Vehicles

Article
Research on Pressure Control Algorithm of Regenerative
Braking System for Highly Automated Driving Vehicles
Liang Chu, Yanwu Xu , Di Zhao * and Cheng Chang

 College of Automotive Engineering, Jilin University, Changchun 130022, China; chuliang@jlu.edu.cn (L.C.);
 xuyanwu95@126.com (Y.X.); changcheng3170@163.com (C.C.)
 * Correspondence: dizhao@jlu.edu.cn

 Abstract: Conclusive evidence has demonstrated the critical importance of highly automated driving
 systems and regenerative braking systems in improving driving safety and economy. However,
 the traditional regenerative braking system cannot be applied to highly automated driving vehicles.
 Therefore, this paper proposes a fully decoupled regenerative braking system for highly automated
 driving vehicles, which has two working modes: conventional braking and redundant braking.
 Aimed at the above two working modes, this paper respectively proposes the pressure control
 algorithm, based on P-V characteristics, and the pressure control algorithm, based on the overflow
 characteristics of the solenoid valve. AMESim is utilized as the simulation platform, and then is co-
 simulated with MATLAB/Simulink, which is embedded with the control algorithm. The simulation
 results show the feasibility and effectiveness of the regenerative braking system and the pressure
 control algorithm.

 


 Keywords: regenerative braking; highly automated driving; pressure control; redundant braking
 


Citation: Chu, L.; Xu, Y.; Zhao, D.;
Chang, C. Research on Pressure
Control Algorithm of Regenerative 1. Introduction
Braking System for Highly With the explosive growth of car ownership, traffic congestion, environmental pollu-
Automated Driving Vehicles. World
 tion, and frequent accidents have become urgent problems to be solved in the current soci-
Electr. Veh. J. 2021, 12, 112. https://
 ety [1,2]. In order to solve the above problems, the development of environment-friendly,
doi.org/10.3390/wevj12030112
 safe, and intelligent vehicles has become the consensus of the automotive industry [3,4].
 Applying the intelligent driving system and regenerative braking system to new
Academic Editor: Xuhui Wen
 energy vehicles can not only improve driving safety, but also further enhance the econ-
 omy [5,6]. As the regenerative braking system is a subsystem of the intelligent driving
Received: 14 July 2021
Accepted: 7 August 2021
 system, it should meet the performance requirements of it. The Society of Automotive Engi-
Published: 10 August 2021
 neering (SAE) divides the intelligent driving system into five levels. Among the five levels,
 level one and level two are called the driving assistance systems, where the driver still
Publisher’s Note: MDPI stays neutral
 needs to participate in driving. Levels three to five are called the highly automated driving
with regard to jurisdictional claims in
 systems, where the driver does not need to be involved in driving. Vehicles equipped
published maps and institutional affil- with level three to five intelligent driving systems are also called highly automated driving
iations. vehicles [7,8]. For the driving assistance system, it requires the regenerative braking system
 to have the functions of brake-by-wire and mechanical backup. For the highly automated
 driving system, it not only requires the regenerative braking system to realize the func-
 tion of brake-by-wire, but also requires it to ensure high reliability, which means that all
Copyright: © 2021 by the authors.
 key functions, including the brake-by-wire, must have redundant backups, rather than a
Licensee MDPI, Basel, Switzerland.
 traditional mechanical backup [9].
This article is an open access article
 Nowadays, many researchers have been working on designing regenerative braking
distributed under the terms and systems for intelligent driving vehicles. The mechanical structure of the regenerative
conditions of the Creative Commons braking system consists of two parts: the motor braking system and the hydraulic braking
Attribution (CC BY) license (https:// system. When the vehicle is braking, the traction motor can work as a generator to
creativecommons.org/licenses/by/ produce regenerative braking torque. At the same point, the kinetic energy of vehicles is
4.0/). converted into electric energy to improve the total energy efficiency of the car. However,

World Electr. Veh. J. 2021, 12, 112. https://doi.org/10.3390/wevj12030112 https://www.mdpi.com/journal/wevj

World Electr. Veh. J. 2021, 12, 112 2 of 18

 the regenerative braking torque produced by the traction motor is influenced by many
 factors, and on some occasions can even be zero; therefore, the regenerative braking system
 needs the hydraulic braking system to produce the friction braking torque, in order to fill
 the difference between the total braking torque and the regenerative braking torque [10,11].
 At present, as the motor technology is mature enough, the research on the regenerative
 braking system mainly focuses on the design of the hydraulic braking system. For example,
 TRW Automotive developed a hydraulic braking system based on a hydraulic booster. By
 controlling the hydraulic booster, this system could decouple the brake pedal and brake
 pressure, so that the brake pressure can be adjusted electronically without pedal input [12].
 Toyota Motor Corporation implemented an electro-hydraulic braking system in the Prius.
 This system mainly consists of a fully by-wire hydraulic control unit and a pedal stroke
 simulator. The hydraulic control unit is used to adjust the cylinder pressure, the pedal
 stroke simulator is used to decouple the brake pedal and brake pressure, as well as simulate
 the pedal feeling [13]. Robert Bosch GmbH developed an electric power braking system
 called iBooster. The working principle of this system is similar to that of the vacuum booster,
 but the power to push the booster piston comes from the movement of the motor, rather
 than the movement of the vacuum booster diaphragm. By controlling the position of the
 booster piston, this system could also decouple the brake pedal and brake pressure, as well
 as control the cylinder pressure by-wire [14]. Honda Motor Corporation installed a novel
 braking system on the Accord Hybrid. This system has two master cylinders, one of which
 is the backup master cylinder and the other is the booster master cylinder. To decouple the
 brake pedal and brake pressure, and control the brake pressure on each axle individually,
 this system is also equipped with a pedal stroke simulator [15,16]. Identical to the layout
 used by Honda, Continental Automotive GmbH designed an electro-hydraulic braking
 system called Mk C1. Compared with Honda, Mk C1 has a similar braking performance,
 but is more integrated [17,18].
 In summary, to adjust the brake pressure independently without pedal input, all the
 above regenerative braking systems decouple the brake pedal and brake pressure, which
 shows that decoupling is a prerequisite for brake-by-wire. However, these systems can only
 remain decoupled in the regular state, once a single point of failure occurs, it will recouple
 the brake pedal and brake pressure. At this point, the driver will participate in driving to
 act as a mechanical backup. As a result, the above systems can only meet the requirements
 of the driver assistance system, and cannot be applied to highly automated driving vehicles.
 For highly automated driving vehicles, even if a single point of failure occurs, the driver is
 still not required to participate in driving, which means that its regenerative braking system
 must remain decoupled to achieve the brake-by-wire function in the event of failure. Since
 the regenerative braking system is critical to the economy and safety of highly automated
 driving vehicles, this paper proposes a fully decoupled regenerative braking system, based
 on the functional requirements of highly automated driving vehicles. This system has two
 working modes: conventional braking and redundant braking. When this system works
 normally, it is in the conventional braking mode; when a single point failure occurs, it
 will enter the redundant braking mode. Regardless of the working mode, this system can
 decouple the brake pedal and brake pressure, thus realizing the brake-by-wire function.
 In order to make new energy vehicles brake safely in both working modes, this paper
 respectively proposes the pressure control algorithm, based on P-V characteristics, and
 the pressure control algorithm, based on the overflow characteristics of the solenoid valve,
 to achieve precise control of wheel cylinder pressure under conventional braking and
 redundant braking.
 The remainder of this paper is organized as follows. Section 2 describes the materials
 and methods. Section 3 presents the results and discussion. Lastly, conclusions are drawn
 in Section 4.

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World Electr. Veh. J. 2021, 12, 112 3 of 18

 2. Materials and Methods
 2. Materials and Methods
 2.1. Regenerative Braking System
 2.1. Regenerative Braking System
 2.1.1. Mechanical Structure of the Regenerative Braking System
 2.1.1. Mechanical Structure of the Regenerative Braking System
 The mechanical structure of the regenerative braking system consists of the motor
 The mechanical structure of the regenerative braking system consists of the motor
 braking system and the hydraulic braking system. The motor braking system is used to
 braking system and the hydraulic braking system. The motor braking system is used to
 generate
 generate regenerative
 regenerative braking
 braking torque.
 torque. IfIf the
 the regenerative
 regenerative braking
 braking torque
 torque cannot
 cannot meet
 meet the
 the
 demand braking torque, the hydraulic braking system will fill the difference
 demand braking torque, the hydraulic braking system will fill the difference between the between the
 demand braking torque and the regenerative braking torque. Shown
 demand braking torque and the regenerative braking torque. Shown in Figure 1 is the in Figure 1 is the
 structure
 structure ofof the
 thehydraulic
 hydraulicbraking
 brakingsystem,
 system, which
 which consists
 consists of the
 of the main
 main brake
 brake unitunit
 (MBU)(MBU)
 and
 and redundant brake unit (RBU). In the MBU, there are three parts: pedal
 redundant brake unit (RBU). In the MBU, there are three parts: pedal simulation unit (PSU), simulation unit
 (PSU),
 power power
 brake unitbrake unit (PBU),
 (PBU), and main andhydraulic
 main hydraulic
 control control unit (MHCU).
 unit (MHCU). The PSU The PSU in-
 includes a
 cludes a brake pedal, a master cylinder, a brake fluid reservoir cup, a pedal
 brake pedal, a master cylinder, a brake fluid reservoir cup, a pedal stroke simulator (PSS), stroke simu-
 lator (PSS),
 and two anddisplacement
 pedal two pedal displacement
 sensors. The sensors. The PBU
 PBU includes includes
 a power a power
 brake brake
 cylinder cylinder
 (PBC) and
 (PBC) and several switching solenoid valves, in which two cavities of the
 several switching solenoid valves, in which two cavities of the PBC have pressure sensors, PBC have pres-
 sure sensors,
 and the and the
 brushless brushless
 motor drivingmotor
 the PBCdriving
 has a the
 rotorPBC has a sensor
 position rotor position sensorsensor.
 and a current and a
 current
 The MHCU sensor. The MHCU
 includes includes
 the inlet the inlet
 and outlet valvesandof outlet valves of each brake.
 each brake.

 Structure of the hydraulic
 Figure 1. Structure
 Figure hydraulic braking
 braking system.
 system. MBU—main brake unit; RBU—redundant
 RBU—redundant
 brake
 brake unit;
 unit; PSU—pedal
 PSU—pedalsimulation
 simulationunit;
 unit;PBU—power
 PBU—power brake
 brakeunit; MHCU—main
 unit; MHCU—main hydraulic
 hydrauliccontrol
 con-
 unit; PSS—pedal
 trol unit; strokestroke
 PSS—pedal simulator; MC—master
 simulator; cylinder;cylinder;
 MC—master SCV—simulator cut-off valve;
 SCV—simulator PBCV—
 cut-off valve;
 power brake cylinder
 PBCV—power cut-off valve;
 brake cylinder cut-offPBC—power brake cylinder;
 valve; PBC—power MSV—mode
 brake cylinder; switchingswitch-
 MSV—mode valve;
 PBIV—power brake cylinder isolation valve; MCIV—master cylinder isolation
 ing valve; PBIV—power brake cylinder isolation valve; MCIV—master cylinder isolation valve;valve; HCV—hy-
 draulic connecting valve; FLIV—inlet valve of left-front wheel cylinder; FLOV—outlet valve of left-
 HCV—hydraulic connecting valve; FLIV—inlet valve of left-front wheel cylinder; FLOV—outlet
 front wheel cylinder; RRIV—inlet valve of right-rear wheel cylinder; RROV—outlet valve of right-
 valve of left-front wheel cylinder; RRIV—inlet valve of right-rear wheel cylinder; RROV—outlet
 rear wheel cylinder; FRIV—inlet valve of right-front wheel cylinder; FROV—outlet valve of right-
 valvewheel
 front of right-rear wheel
 cylinder; cylinder;valve
 RLIV—inlet FRIV—inlet valve
 of left-rear of right-front
 wheel wheel cylinder;
 cylinder; RLOV—outlet FROV—outlet
 valve of left-rear
 valve of right-front wheel cylinder; RLIV—inlet valve of left-rear wheel cylinder;
 wheel cylinder; HSV—high-pressure switching valve; PRV—pressure regulation valve. RLOV—outlet valve
 of left-rear wheel cylinder; HSV—high-pressure switching valve; PRV—pressure regulation valve.
 The pedal stroke simulator (PSS) consists of pistons and elastic elements. When PSS
 works,Theitspedal stroke
 internal simulator
 pressure (PSS)with
 changes consists of pistons
 the volume of and elasticliquid
 the input elements. When PSS
 to simulate the
 works, its internal pressure changes with the volume of the input liquid to simulate
 pedal feel. The PSS is controlled by the simulator cut-off valve (SCV), which is normally the
 apedal feel.
 closed The PSS
 solenoid is controlled
 valve to ensureby thethe
 that simulator
 PSS willcut-off
 remainvalve (SCV),
 closed whenwhich is normally
 the system is not
 a closed solenoid valve to ensure that the PSS will remain closed when the system is not
 powered on. The output interface of the master cylinder is directly connected with the
 powered on. The output interface of the master cylinder is directly connected with the

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 redundant brake unit (RBU). The brake fluid flowing from the master cylinder will pass
 through
 redundant thebrake
 RBU, andunitthe two paths
 (RBU). The brakeof brake
 fluidfluid flowing
 flowing from out of master
 the the RBUcylinder
 will respectively
 will pass
 flow
 through the RBU, and the two paths of brake fluid flowing out of the RBU willthrough
 into two independent hydraulic circuits with an X-shaped arrangement two
 respectively
 master cylinder isolation valves (MCIV1 and MCIV2). Each
 flow into two independent hydraulic circuits with an X-shaped arrangement through independent hydraulic circuit
 directly
 two master drives a brakeisolation
 cylinder of the front
 valves and(MCIV1
 rear axle, andwhich is equipped
 MCIV2). with a normally
 Each independent open
 hydraulic
 solenoid valve drives
 circuit directly as the ainlet
 brakevalve (IV),
 of the andand
 front a normally
 rear axle, closed
 which solenoid
 is equipped valve
 with asathe outlet
 normally
 valve (OV).
 open solenoid valve as the inlet valve (IV), and a normally closed solenoid valve as the
 outletThe high-pressure
 valve (OV). brake fluid in the main brake unit (MBU) comes from the power
 brakeThecylinder
 high-pressure brakein
 (PBC). Shown Figure
 fluid 2 ismain
 in the the structural
 brake unitdiagram(MBU) of the PBC.
 comes fromThe the PBC
 power is
 driven by a brushless motor through the transmission mechanism,
 brake cylinder (PBC). Shown in Figure 2 is the structural diagram of the PBC. The PBC is and the rotary motion
 of the motor
 driven is converted
 by a brushless motor into the linear
 through the reciprocating motion of the
 transmission mechanism, piston,
 and so as motion
 the rotary to realizeof
 the pressure
 the motor adjustment.
 is converted intoThe
 the PBC
 linearisreciprocating
 equipped with six solenoid
 motion of the piston,valves,
 so aswhich are the
 to realize the
 mode
 pressureswitching
 adjustment. valve The
 (MSV),PBCthe is hydraulic
 equipped connecting
 with six solenoidvalve (HCV),
 valves, the power
 which are brake
 the modecyl-
 inder cut-off valves (PBCV1, PBCV2), and the power brake
 switching valve (MSV), the hydraulic connecting valve (HCV), the power brake cylinder cylinder isolation valves
 (PBIV1, PBIV2).(PBCV1,
 cut-off valves The PBIV ensuresand
 PBCV2), that the
 when the system
 power brake is not powered
 cylinder on, valves
 isolation the brake fluid
 (PBIV1,
 will not flow
 PBIV2). The PBIVinto the PBC.that
 ensures The when
 MSV is theused to switch
 system is not the pressure
 powered on, regulation
 the brake fluidmode of not
 will the
 PBC, so that
 flow into thethePBC.cylinder
 The MSV can isincrease
 used toand decrease
 switch pressure
 the pressure in different
 regulation modemovement
 of the PBC,direc-
 so
 tions.
 that theIn cylinder
 addition,can since the PBC
 increase andisdecrease
 not a double cavity
 pressure in structure, it needs to directions.
 different movement use the HCV In
 to make PBC
 addition, sincecontrol
 the PBCtheispressure
 not a doubleof twocavity
 groups of pipelines
 structure, at the
 it needs to same
 use thetime.
 HCV The toPBCV
 make
 is
 PBCused to control
 control the connection
 the pressure of two groupsbetween the PBC at
 of pipelines andthethesamereservoir
 time. Thecup.PBCV
 It canis supple-
 used to
 control the connection between the PBC and the reservoir
 ment the brake fluid for the PBC or discharge the brake fluid from the PBC when cup. It can supplement the brake
 the
 fluid for
 piston the PBC or discharge the brake fluid from the PBC when the piston moves.
 moves.

 Figure 2.
 Figure Structure of
 2. Structure of the
 the power
 power brake
 brake cylinder
 cylinder (excluding motor and transmission mechanism).

 The redundant
 The redundant brake
 brake unit
 unit (RBU)
 (RBU) isis aa simplified
 simplified ESCESC hydraulic control unit,
 hydraulic control unit, which
 which
 omits the inlet valves, the outlet valves, and the low-pressure accumulators, with
 omits the inlet valves, the outlet valves, and the low-pressure accumulators, with only the only the
 hydraulic pumps, high-pressure switching valves (HSV), and pressure
 hydraulic pumps, high-pressure switching valves (HSV), and pressure regulation valves regulation valves
 (PRV) being
 (PRV) being reserved.
 reserved. In
 In the
 the RBU,
 RBU, HSV
 HSV isis the
 the on-off
 on-off solenoid
 solenoid valve,
 valve, which
 which can
 can control
 control the
 the
 opening and closing of the hydraulic pump; PRV is the linear solenoid
 opening and closing of the hydraulic pump; PRV is the linear solenoid valve, which canvalve, which can
 adjust the
 adjust the output
 output pressure
 pressure of
 of the
 the hydraulic
 hydraulic pump.
 pump. Through
 Through the the control
 control of
 of solenoid
 solenoid valves
 valves
 and hydraulic pumps, RBU can achieve accurate brake pressure regulation,
 and hydraulic pumps, RBU can achieve accurate brake pressure regulation, and ensure and ensure
 that the
 that the braking
 brakingsystem
 systemcancanproduce
 produceenough
 enough braking
 brakingforce even
 force if the
 even if main brake
 the main unit fails.
 brake unit
 fails.
 2.1.2. Working Principle of the Regenerative Braking System

 2.1.2.The fully decoupled
 Working Principle ofregenerative braking
 the Regenerative system
 Braking has two working modes: conven-
 System
 tional braking and redundant braking. When the system is in the conventional braking
 mode,Thethe
 fully decoupled
 main regenerative
 brake unit braking
 (MBU) works, the system has two
 regenerative working
 braking modes:
 system conven-
 distributes
 tional braking and redundant braking. When the system is in the conventional
 the motor and hydraulic braking force according to the driver’s braking demand, braking
 motor
 mode, the main brake unit (MBU) works, the regenerative braking system distributes
 battery status, and other information. In order to obtain the target hydraulic braking force, the
 motor and hydraulic braking force according to the driver’s braking demand, motor
 the hardware of the regenerative braking system needs to control the power brake cylinder bat-
 tery
 (PBC)status, and other
 and solenoid information.
 valves. In order
 At this point, to obtain the
 the hydraulic target hydraulic
 connecting braking
 valve (HCV) mustforce,
 open

World Electr. Veh. J. 2021, 12, x 5 of 18

World Electr. Veh. J. 2021, 12, 112 5 of 18

 the hardware of the regenerative braking system needs to control the power brake cylin-
 der (PBC) and solenoid valves. At this point, the hydraulic connecting valve (HCV) must
 to connect two sets of independent hydraulic brake lines together, so that one PBC can
 open to connect two sets of independent hydraulic brake lines together, so that one PBC
 control the pressure of all four brakes.
 can control the pressure of all four brakes.
 During conventional braking, the regenerative braking system has three different pres-
 During conventional braking, the regenerative braking system has three different
 sure regulation modes: high pressure, medium pressure, and low pressure. By controlling
 pressure regulation modes: high pressure, medium pressure, and low pressure. By con-
 the mode switching valve (MSV), power brake cylinder cut-off valves (PBCV1, PBCV2),
 trolling the mode switching valve (MSV), power brake cylinder cut-off valves (PBCV1,
 and power brake cylinder isolation valves (PBIV1, PBIV2), the regenerative braking system
 PBCV2),
 can switch andbetween
 power brake cylinder
 different isolation
 pressure valves (PBIV1,
 regulation modes. PBIV2),
 Shown the regenerative
 in Figures 3–5 arebrak-
 the
 ing
 flowsystem can switch
 directions between
 of brake fluid anddifferent pressure
 the action regulation
 of solenoid modes.
 valves underShown in Figures
 different pressure3–
 5regulation
 are the flow directions of brake fluid and the action of solenoid valves under
 modes. It can be seen that under different pressure regulation modes, the power different
 pressure regulation
 brake cylinder (PBC)modes. It can be
 has different seen that under
 equivalent piston different pressure
 cross-sectional regulation
 areas modes,
 and brake fluid
 the
 displacement, so the pressure regulation rate is also different. This design can reduceand
 power brake cylinder (PBC) has different equivalent piston cross-sectional areas the
 brake fluid displacement,
 performance requirementsso ofthe
 thepressure
 PBC motor regulation rate isthe
 and improve also different.
 pressure This design
 regulation can
 accuracy
 reduce the performance
 under medium and highrequirements
 pressure. of the PBC motor and improve the pressure regu-
 lation accuracy under medium and high pressure.

 Figure 3.
 Figure The flow
 3. The flow direction
 direction of
 of brake
 brake fluid
 fluid and
 and the
 the action
 action of
 of solenoid
 solenoid valves
 valves under
 under low
 low pressure
 pressure
 mode.
 mode.

 Figure
 Figure 4.
 4.The
 Theflow
 flowdirection
 directionof
 ofbrake
 brakefluid
 fluidand
 andthe
 theaction
 actionof
 ofsolenoid
 solenoidvalves
 valvesunder
 under medium
 medium pressure
 pressure
 mode.
 mode.

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 Figure 5. The flow direction of brake fluid and the action of solenoid valves under high pressure
 Figure
 Figure 5. The
 mode. The flow
 flow direction
 direction of
 of brake
 brake fluid
 fluid and the action of solenoid valves under high pressure
 mode.
 mode.
 The equivalent piston cross-sectional area in Figures 3–5 is the cross-sectional area
 The equivalent
 The equivalent piston
 piston cross-sectional
 cross-sectional area
 area in Figures
 Figures 3–5
 3–5 is the cross-sectional area
 subjected to hydraulic pressure, which changes inwith the pressure regulation mode and
 subjected to hydraulic
 subjected hydraulic pressure,
 pressure, which
 which changes
 changeswith
 withthethe
 pressure regulation
 pressure mode
 regulation andand
 mode can
 can be calculated as follows:
 be calculated
 can as follows:
 be calculated as follows:
  low pressure
 pressuremode
  A pis − low
 low pressure mode
 mode
 
 A pbe = = A pis − A medium
 medium pressure mode, , (1)
 (1)
 = − rod medium pressure mode
 pressure mode, (1)
 Arod high pressure mode
 high pressure mode
 high pressure mode
 where 
 where A pbe is the equivalent piston cross-sectional area, mm2;2;; A pisisis
 area, mm isthe
 thepiston
 pistoncross-
 2
 where is
 is the
 the equivalent
 equivalent piston
 piston cross-sectional
 cross-sectional area, mm the piston cross-
 cross-
 sectional
 sectional area,
 area, mm
 mm
 2 ;
 2 ; 
 A is
 is the
 the piston
 piston rod
 rod cross-sectional
 cross-sectional area,
 area, mm
 mm
 2.
 2 .
 sectional
 When mm2; brake
 area, main rod is the(MBU)
 piston roda cross-sectional area, mmredundant
 2.
 Whenthe
 When the main
 the main brakebrakeunit
 unit (MBU)has
 unit (MBU) has aasingle
 has singlepoint
 single pointfailure,
 point failure,the
 failure, redundantbrake
 the redundant
 the brakeunit
 brake unit
 unit
 (RBU)
 (RBU) will
 will replace
 replace the
 the MBU
 MBU to
 to complete
 complete the
 the brake
 brake pressure
 pressure control.
 control. In
 In the
 the redundant
 redundant
 (RBU) will
 braking replace master
 the MBU to complete the brake pressure control. Inwill the redundant
 brakingmode,
 braking mode,two
 mode, two mastercylinder
 two master cylinderisolation
 cylinder isolationvalves
 isolation valves(MCIV1
 valves (MCIV1and
 (MCIV1 andMCIV2)
 and MCIV2) will
 MCIV2) willbebeopened,
 be opened,
 opened,
 and
 and the hydraulic connecting valve (HCV) and power brake cylinder isolation valves
 the hydraulic connecting valve (HCV) and power brake cylinder isolation valves
 and thePBIV2)
 (PBIV1, hydraulic connecting valve (HCV)controland power brake cylinder isolation valves
 (PBIV1, PBIV2)will willbe beclosed.
 closed.TheThepressure
 pressure controlisiscompleted
 completedby bythethehydraulic
 hydraulicpumps,
 pumps,
 (PBIV1, PBIV2)
 high-pressure will be closed. The pressurepressure
 control is completedvalves by the hydraulic pumps,
 high-pressureswitching
 switchingvalves valves(HSV),
 (HSV),and and pressure regulation
 regulation valves (PRV). (PRV).
 high-pressure
 When switching valves (HSV), and pressure regulation valves (PRV). HSV2 will
 Whenthe theregenerative
 regenerativebrakingbrakingsystem
 systemneeds
 needsto tobe
 bepressurized,
 pressurized,HSV1 HSV1and and HSV2 will
 be When the regenerative braking system needs to be pressurized, HSV1 and HSV2 will
 beopened,
 opened,and andPRV1PRV1and andPRV2
 PRV2willwillbebeclosed.
 closed.At Atthis
 thispoint,
 point,the
 thehydraulic
 hydraulicpumps pumpspumppump
 be
 the opened, and PRV1 and PRV2 will be closed. At this point, the hydraulic pumps pump
 thebrake
 brake fluid
 fluid into
 into thethe wheel
 wheelcylinders,
 cylinders,and andthethepressure
 pressure can
 can bebe regulated
 regulated by by adjusting
 adjusting the
 the driving
 the brake fluid
 currentintoofthe wheel
 PRV1 and cylinders,
 PRV2. andprocess,
 This the pressure can be
 including the regulated
 working by adjusting
 condition of
 driving current of PRV1 and PRV2. This process, including the working condition of the
 thesolenoid
 the driving current
 valves of PRV1
 and the anddirection
 flow PRV2. This of process,
 the brake including
 fluid, is the working
 shown in Figure condition
 6. of
 solenoid valves and the flow direction of the brake fluid, is shown in Figure 6.
 the solenoid valves and the flow direction of the brake fluid, is shown in Figure 6.

 Workingstate
 Figure6.6.Working
 Figure stateof
 ofRBU
 RBUduring
 duringactive
 activepressurization.
 pressurization.
 Figure 6. Working state of RBU during active pressurization.

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 When
 When the
 the regenerative
 regenerative braking
 braking system
 system needs
 needs to
 to be
 be depressurized,
 depressurized, PRV1
 PRV1 and PRV2
 and PRV2
 will be opened, HSV1 and HSV2 will be closed, and the brake fluid will flow back to
 will be opened, HSV1 and HSV2 will be closed, and the brake fluid will flow back to the the
 master cylinder to realize the depressurization.
 master cylinder to realize the depressurization.

 2.2. Pressure
 Pressure Control Algorithm
 When the regenerative braking system carries carries out energy recovery, the hydraulic hydraulic
 braking system needs to accurately respond to the target pressure for the vehicle braking
 safety [19,20].
 [19,20].Aiming
 Aimingatat thethe
 two working
 two working modes
 modes of the
 of fully decoupled
 the fully regenerative
 decoupled brak-
 regenerative
 ing system,
 braking this paper
 system, proposes
 this paper the pressure
 proposes control
 the pressure algorithm,
 control based based
 algorithm, on P-Von characteris-
 P-V char-
 tics, and theand
 acteristics, pressure control control
 the pressure algorithm, based onbased
 algorithm, the overflow characteristics
 on the overflow of the sole-
 characteristics of
 noid valve. The
 the solenoid pressure
 valve. control algorithm
 The pressure based onbased
 control algorithm P-V characteristics is suitable
 on P-V characteristics for con-
 is suitable
 ventional brakingbraking
 for conventional mode, and mode,theand
 other thepressure control control
 other pressure algorithm is suitable
 algorithm for redun-
 is suitable for
 redundant
 dant brakingbraking
 mode.mode.
 representation of
 Shown in Figure 7 is the schematic representation of the
 the pressure
 pressure control
 control algorithm.
 algorithm.
 When the regenerative braking system is under conventional braking mode, the required
 volumechange
 fluid volume changeofofthe the
 PBCPBC is calculated
 is calculated firstfirst
 based based onP-V
 on the thecharacteristics
 P-V characteristics
 of wheelof
 wheel cylinders
 cylinders and theand the expansion
 expansion characteristics
 characteristics of the brakeof thehose.
 brake hose.combined
 Then, Then, combined
 with the
 with the pressure
 pressure regulationregulation
 mode, themode, requiredthePBCrequired
 piston PBC piston displacement
 displacement is calculated.is calculated.
 Lastly, ac-
 cording to the required displacement, the drive current of the PBC motor can bemotor
 Lastly, according to the required displacement, the drive current of the PBC can
 obtained.
 be obtained.
 When When thebraking
 the regenerative regenerative
 systembraking
 is undersystem is under
 redundant redundant
 braking mode, it braking mode,
 can calculate
 it can
 the calculate
 drive currenttheofdrive current of
 the pressure the pressure
 regulation valves regulation valveson
 (PRV), based (PRV),
 the PRVbased on the
 overflow
 PRV overflow characteristics.
 characteristics. Meanwhile, the Meanwhile,
 drive signals the of
 drive
 othersignals
 RBU of other RBU
 actuators canactuators
 be obtainedcan ac-
 be
 obtained according to the relationship between the target
 cording to the relationship between the target pressure and actual pressure.pressure and actual pressure.

 Figure
 Figure 7.
 7. Schematic
 Schematic representation of the
 representation of the pressure
 pressure control
 control algorithm.
 algorithm.

 2.2.1.
 2.2.1. The
 The Pressure
 Pressure Control
 Control Algorithm Based on
 Algorithm Based on P-V
 P-V Characteristics
 Characteristics
 The
 The power
 power brake
 brakeunit
 unit(PBU)
 (PBU)isisthe
 themain
 mainpressure
 pressuresource of of
 source thethe
 fully decoupled
 fully re-
 decoupled
 generative braking system. When the main brake unit (MBU) does not fail, all
 regenerative braking system. When the main brake unit (MBU) does not fail, all of the of the high-
 pressure brakebrake
 high-pressure fluid is generated
 fluid by PBU
 is generated byand
 PBU sent
 andtosent
 eachtobrake
 each through solenoid
 brake through valves
 solenoid
 and hydraulic pipelines.
 valves and hydraulic pipelines.

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 World Electr. Veh. J. 2021, 12, 112 8 of 18

 In order
 In order toto generate
 generate the
 the target
 target pressure
 pressure in in the
 the brake,
 brake, it it is
 is necessary
 necessary to to control
 control PBU
 PBU to
 to
 injectInaaorder
 inject certain
 certain volume the
 to generate
 volume of fluid
 of fluid into
 targetinto the brake.
 pressure
 the brake. The required
 in the brake,
 The required braketofluid
 it is necessary
 brake fluid volume
 control can be
 PBU can
 volume be
 obtained
 to inject a by interpolating
 certain volume of the
 fluid P-Vintocharacteristic
 the brake. The curves
 required of the
 brake front and
 fluid
 obtained by interpolating the P-V characteristic curves of the front and rear wheel brakes, rear
 volume wheel
 can be brakes
 obtained
 as shownby ininterpolating the9.P-V
 Figures 88 and
 and characteristic
 If the
 the curves is
 target pressure
 pressure of P,
 thethe
 front and rearvolume
 required wheel brakes,
 of brake
 brake fluid
 fluid
 as shown in Figures 9. If target is P, the required volume of
 as
 for shown
 all fourin Figures
 brakes 8 and
 can be 9. If the
 calculated target
 as pressure
 follows: is P, the required volume of brake fluid
 for all four brakes can be calculated as follows:
 for all four brakes can be calculated as follows:
 
 == 2 
 2 +
 + 2 
 2 ,,
 (2)
 (2)
 Vwc ( P) = 2Vwc1 ( P) + 2Vwc2 ( P), (2)
 where 
 where isis the
 the total
 total required
 required volume
 volume ofof brake
 brake fluid
 fluid at
 at pressure
 pressure P,P, ml;
 ml; is
 is the
 the
 where Vwcvolume
 required ( P) is theoftotal required
 brake fluid volume
 for the of brake
 front fluid brake
 wheel at pressure
 at P, ml; Vwc1
 pressure P, P) isand
 (ml; the 
 required volumeofof brake fluid for front
 the front
 wheelwheel
 brake brake at pressure P, Vml; (and
 P, ml; and 
 required volume brake fluid for the at pressure wc2 P ) is
 is the
 is the required
 required volume
 volume of of brake
 brake fluid
 fluid for the
 the rear
 rear wheel
 wheel brake at at pressure P,P, ml.
 ml.
 the required volume of brake fluid for thefor
 rear wheel brake atbrake
 pressurepressure
 P, ml.

 Figure 8. P-V
 Figure 8.
 Figure 8. P-Vcharacteristic
 P-V characteristic
 characteristic of
 of of front
 front wheel
 wheel
 front brake.
 brake.
 wheel brake.

 Figure 9. P-V
 Figure 9.
 Figure 9. P-Vcharacteristic
 P-V characteristic
 characteristic
 of of
 rear wheel
 rear
 of rear
 brake.
 wheel
 wheel brake.
 brake.

 At aa certain
 At certain time,
 time, if
 if the
 the brake
 brake pressure
 pressure is and
 is and needs
 needs to
 to be
 be adjusted
 adjusted to +
 to + Δ 
 Δ ,,
 the corresponding
 the corresponding fluid
 fluid volume
 volume change
 change in
 in the
 the brake
 brake is:
 is:

World Electr. Veh. J. 2021, 12, 112 9 of 18

 At a certain time, if the brake pressure is Pt0 and needs to be adjusted to ( Pt0 + ∆P),
 the corresponding fluid volume change in the brake is:
 ∆Vwc ( Pt0 , ∆P) = Vwc ( Pt0 + ∆P) − Vwc ( Pt0 ) = 2[Vwc1 ( Pt0 + ∆P) + Vwc2 ( Pt0 + ∆P) − 2Vwc1 ( Pt0 ) + 2Vwc2 ( Pt0 )]. (3)

 When the brake pressure changes from Pt0 to ( Pt0 + ∆P) the volume change of brake
 fluid is also affected by the expansion of brake hose [21], which can be expressed as follows:

 ∆Vhose (∆P) = ωhose ∆P, (4)

 where ∆Vhose (∆P) is the volume change of brake fluid caused by expansion of brake hose,
 ml; and ωhose is the flexibility of the brake hose, ml/MPa.
 According to Formulas (3) and (4), when the brake pressure changes from Pt0 to
 ( Pt0 + ∆P) the volume of brake fluid delivered or inhaled by the power brake cylinder
 (PBC) can be expressed by Formula (5).

 ∆Vpbc ( Pt0 , ∆P) = ∆Vhose (∆P) + ∆Vwc ( Pt0 , ∆P). (5)

 The required piston displacement of PBC can be expressed as follows:

 ∆Vpbc ( Pt0 , ∆P)
 ∆x pbc ( Pt0 , ∆P) = . (6)
 A pbe

 When the PBC is working, the displacement of the PBC piston cannot be controlled
 directly, but it can be indirectly controlled by regulating the motor torque. With the change
 of displacement and cylinder pressure, the hydraulic force and friction on the piston will
 also change, resulting in the change of motor load torque.
 When the PBC is in the pressurized state, the motion equation of the piston can be
 expressed as follows:
 ..
 m pbc x pbc = Fpbr − Fpbh − Ff pb , (7)
 ..
 where m pbc is the piston mass, kg; x pbc is the piston displacement, m; Fpbr is the motor
 thrust on the piston rod, N; Fpbh is the hydraulic force on piston, N; and Ff pb is the friction
 on piston, N.
 When the PBC is in the depressurized state, the motion equation of the piston can be
 expressed as:
 ..
 m pbc x pbc = Fpbr + Fpbh − Ff pb . (8)
 In Formulas (7) and (8), the hydraulic force and friction on the piston change with the
 cylinder pressure and piston displacement [22], which can be expressed as follows:
 (
 Fpbh = A pbe Ppbc
 . , (9)
 Ff pb = Fcpb + f vpb x pbc

 where Ppbc is the pressure of PBC, MPa; Fcpb is the coulomb friction, N; and f vpb is the
 coefficient of viscous friction, N/(m/s).
 When the period of system control ∆t is small enough, the change in pressure can
 be regarded as linear. If the pressure in the power brake cylinder (PBC) changes from Pt0
 to ( Pt0 + ∆P) within ∆t, the hydraulic force on the piston at any time within ∆t can be
 expressed as:
 ∆P
  
 Fpbh (t) = A pbe Pt0 + t . (10)
 ∆t

World Electr. Veh. J. 2021, 12, 112 10 of 18

 Similarly, when ∆t is small enough, the change in piston speed can also be regarded
 .
 as linear. Assuming that the current piston speed is x pbc0 , then at any time within ∆t, the
 friction on the piston can be expressed as:

 . 2∆x pbc ( Pt0 , ∆P)
 Ff pb (t) = Fcpb + f vpb x pbc0 + t. (11)
 ∆t2

 Combined with Formulas (7), (10) and (11), when PBC is in the pressurized state, the
 acceleration of piston at any time in ∆t can be expressed as:

 .. Fpbr − Fpbh (t) − Ff pb (t)
 x pbc (t) = . (12)
 m pbc

 Combined with Formulas (8), (10) and (11), when PBC is in the depressurized state,
 the acceleration of piston at any time in ∆t can be expressed as:

 .. Fpbr + Fpbh (t) − Ff pb (t)
 x pbc (t) = . (13)
 m pbc

 Since the piston needs to move ∆x pbc ( Pt0 , ∆P) within ∆t, we can obtain the following
 relationships: ( . . R t ..
 x pbc (t) = x pbc0 + 0 x pbc (t)dt
 R ∆t . . (14)
 ∆x pbc = 0 x pbc (t)dt
 By substituting Formula (12) into Formula (14), it can be obtained that the motor thrust
 on the piston rod in the pressurized state is:
 .
 2m∆x pbc 2mx pbc0 . 2∆x pbc A pbe ∆P
 Fpbr = − + f vpb x pbc0 + + Fcpb + + A pbe Pt0 . (15)
 ∆t2 ∆t 3∆t 3

 By substituting Formula (13) into Formula (14), it can be obtained that the motor thrust
 on the piston rod in the depressurized state is:
 .
 2m∆x pbc 2mx pbc0 . 2∆x pbc A pbe ∆P
 Fpbr = − + f vpb x pbc0 + + Fcpb − − A pbe Pt0 . (16)
 ∆t2 ∆t 3∆t 3

 The brushless motor transforms the rotating motion into linear motion through the
 transmission mechanism, and the torque of the motor is transformed into the thrust of the
 piston rod at the same time. The power brake cylinder (PBC) described in this paper adopts
 two stages of transmission, the first stage is gear transmission, and the second stage is ball
 screw transmission. Therefore, the required motor torque can be expressed as follows:

 Fpbr I pbs
 Tpbm = , (17)
 2πη pbs i pb0

 where η pbs is the ball screw efficiency; Tpbm is the required motor torque, N·m; i pb0 is the
 transmission ratio of the first stage gear; and I pbs is the ball screw lead, m.
 According to Formula (17), the required motor torque can be obtained. The motor
 driver can output the target torque by controlling the stator current. If the output torque
 is maintained unchanged in the control period ∆t, the pressure will change to ( Pt0 + ∆P)
 after ∆t.

 2.2.2. The Pressure Control Algorithm Based on Overflow Characteristics of the Solenoid
 Valve
 The highly automated driving system should have the ability to realize brake-by-wire
 control even when the regenerative braking system has a single point of failure, which

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World Electr. Veh. J. 2021, 12, 112 11 of 18

 which means that the regenerative braking system should have a second component to
 means brake-by-wire.
 realize that the regenerative braking system should have a second component to realize
 brake-by-wire.
 The second braking component in the fully decoupled regenerative braking system
 is theThe second braking
 redundant brake unit component in the fully
 (RBU). According to decoupled regenerative
 the description brakingthe
 of RBU above, system
 RBU
 is the redundant brake unit (RBU). According to the description
 has two pressure regulation valves (PRV), which are linear, normally open solenoid of RBU above, the RBU
 has two pressure regulation valves (PRV), which are linear, normally open
 valves. After the coil is energized, the moving iron and the fixed iron of the solenoid valve solenoid valves.
 After the coil is energized, the moving iron and the fixed iron of the solenoid valve will
 will generate electromagnetic force due to magnetization. The electromagnetic force
 generate electromagnetic force due to magnetization. The electromagnetic force pushes the
 pushes the moving iron and the spool to overcome the hydraulic force and spring force,
 moving iron and the spool to overcome the hydraulic force and spring force, to close the
 to close the solenoid valve [23]. The spool motion equation of the linear, normally open
 solenoid valve [23]. The spool motion equation of the linear, normally open solenoid valve
 solenoid valve can be expressed as follows:
 can be expressed as follows:
 .. = − − , (18)
 mcpv x cpv = Fmpv − Fhpv − Fspv , (18)
 where is the mass of the moving iron, kg; is the displacement of the moving
 ..
 where
 iron, m;m cpv is is
 thethemass of the moving
 electromagnetic iron,
 force, x cpvis is
 N;kg; thethe displacement
 hydraulic force, of
 N; the is
 andmoving
 iron,
 the m; Fmpv
 spring N. electromagnetic force, N; Fhpv is the hydraulic force, N; and Fspv is the
 is the
 force,
 spring force, the
 Among N. above three forces, the electromagnetic force is related to the position of
 the spool and theabove
 Among the three forces,
 coil current the electromagnetic
 [24], which can be calculated forcebyisFormula
 related to(19).
 the The
 position of
 spring
 the spool and the coil current [24], which can be calculated by Formula
 force is related to spring stiffness, preload, and displacement, while the hydraulic force is (19). The spring
 force is to
 related related
 spoolto spring
 stress stiffness,
 area preload,pressure.
 and hydraulic and displacement,
 These two while
 forcesthe
 canhydraulic forceby
 be calculated is
 related
 the to spool
 AMESim stress area
 simulation and hydraulic pressure. These two forces can be calculated by
 model.
 the AMESim simulation model.
 
 = A µ N 2i 2 , (19)
 pv 0 −c c
 Fmpv = 2 
2 , (19)
 2 xcpv0 − xcpv
 where is the area of working air gap, m2; is the vacuum permeability, N/(A2); 
 is the coil
 where is the area
 A pv turn; is of
 theworking
 coil current, A;m
 air gap, 2 ; µ is theisvacuum
 and 0 the initial working air
 permeability, N/(Agap2 );ofNthe
 c is
 spool, m.
 the coil turn; ic is the coil current, A; and xcpv0 is the initial working air gap of the spool, m.
 As
 As shown
 shownin inFigure
 Figure10,
 10,ononthe basis
 the of of
 basis thethemodeling
 modeling method
 methoddescribed in reference
 described in refer-
 [25,26], this paper
 ence [25,26], establishes
 this paper the simulation
 establishes model of
 the simulation the normally
 model open linear
 of the normally opensolenoid
 linear
 valve in AMESim.
 solenoid In the AMESim
 valve in AMESim. In themodel,
 AMESim the model,
 electromagnetic force and coil
 the electromagnetic inductance
 force and coil
 of the solenoid
 inductance valve
 of the are obtained
 solenoid valve areby obtained
 looking up bythe table.up
 looking The
 thecoil model
 table. Theiscoil
 represented
 model is
 by an RL series
 represented by ancircuit, and circuit,
 RL series the powerand supply
 the poweris DC power
 supply andpower
 is DC is controlled by PWM
 and is controlled
 by PWM signals.
 signals.

 Figure
 Figure 10.
 10. The
 The AMESim
 AMESim model
 model of
 of the
 the solenoid
 solenoid valve.
 valve.

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 x 12 of
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 For the connection of the hydraulic components, the inlet port of the solenoid valve
 For the connection of the hydraulic components, the inlet port of the solenoid valve is
 is connected to a constant pressure source and the outlet port is connected to the brake.
 connected to a constant pressure source and the outlet port is connected to the brake. By
 By applying
 applying different
 different driving
 driving currents
 currents to the
 to the solenoid
 solenoid valve,
 valve, the pressure
 the pressure response
 response curve
 curve can
 can be obtained, as shown in Figure 11. It can be seen that in a certain range of driving
 be obtained, as shown in Figure 11. It can be seen that in a certain range of driving current,
 current,
 the linearthenormally
 linear normally open solenoid
 open solenoid valve ashows
 valve shows a proportional
 proportional overflowoverflow charac-
 characteristic,
 teristic, whichthe
 which means means
 finalthe final steady-state
 steady-state overflow overflow
 pressurepressure can be adjusted
 can be adjusted by control-
 by controlling the
 ling the driving
 driving current. current.

 Figure 11. The overflow characteristic curve of the solenoid valve.

 In the
 In the redundant
 redundant brake
 brake unit
 unit (RBU),
 (RBU), the
 the overflow
 overflow pressure
 pressure of
 of the
 the pressure
 pressure regulation
 regulation
 valve (PRV)
 valve (PRV) is
 is approximately
 approximately equal
 equal to
 to the
 the wheel
 wheel cylinder
 cylinder pressure,
 pressure, so
 so the
 the wheel
 wheel cylinder
 cylinder
 pressure can be adjusted by controlling the coil current. The relationship between wheel
 pressure can be adjusted by controlling the coil current. The relationship between wheel
 cylinder pressure
 cylinder pressure and
 and coil
 coil current
 current can
 can be
 be expressed
 expressed as
 as follows:
 follows:
 Pwc − Pmc ==K PRV ic,,
 − (20)

 PRV is the proportional coefficient between overflow pressure and coil current,
 where K
 ml/Mpa; 
 ml/Mpa; Pwc is the
 the wheel
 wheelcylinder
 cylinderpressure,
 pressure,Mpa;
 Mpa; and
 and is the
 PMc is the master
 master cylinder
 cylinder pres-
 pressure,
 sure,
 Mpa. Mpa.

 3. Results
 3. Results and
 and Discussion
 Discussion
 The brushless
 The brushless motor
 motor model
 model and
 and pressure
 pressure control
 control model
 model are
 are built
 built in
 in Matlab/Simulink,
 Matlab/Simulink,
 and the hydraulic braking system model is built in AMESim. The
 and the hydraulic braking system model is built in AMESim. The mainmain parameters used
 parameters in
 used
 the simulations are set in Table 1.
 in the simulations are set in Table 1.
 3.1. Results
 Table 1. Mainand Discussion
 parameters of Conventional
 used Braking Mode
 in the simulations.
 In order to verify the pressure regulation performance of the power brake cylinder
 Parameter
 (PBC), the pressurization test of PBC was carried out. In theValue
 pressurization test, Units
 the piston
 of PBCCross-sectional
 moves at a fixed area of PBC
 speed, andpiston 329 brake unit (PBU)mm
 the controller of the power 2
 switches
 Cross-sectional
 the pressure areamode
 regulation of PBCbypiston rod the solenoid valves.
 adjusting 119 After switching themmmode,
 2

 Diameter
 the piston changesof front wheel cylinder
 the direction of movement, but the speed57.15remains unchanged. mm The
 simulation resultsofare
 Diameter shown
 rear wheel incylinder
 Figures 12–15. 37.68 mm
 Diameter of master cylinder 20.5 mm
 Peak power of PBC motor 450 W
 Peak torque of PBC motor 2.2 N∙m
 Rated speed of PBC motor 4000 r/min

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 18

 Table 1. Main parameters
 Flexibility
 Flexibility of used
 ofthe
 the in the
 brake
 brake simulations.
 hose
 hose 6.25
 6.25××10
 −3
 10−3 ml/MPa
 ml/MPa
 Ball
 Ballscrew
 screwlead
 lead 0.005
 0.005 m
 Parameter Value Units m
 Transmission
 Transmissionratio
 ratioofofthe
 thefirst
 firststage
 stagegear
 gear 1.8
 1.8 //
 Cross-sectional area of PBC piston 329 mm2
 Ball screw
 Ballarea
 screw efficiency
 efficiency 0.96
 0.96 /
 Cross-sectional of PBC piston rod 119 mm2 /
 Proportional
 Proportional coefficient
 coefficient
 Diameter of front wheel cylinder of
 ofPRV
 PRV 57.1519.8
 19.8 mmMPa/A
 MPa/A
 Diameter ofDiameter
 rear wheelof
 Diameter of PSS PSS
 cylinder 37.68 15
 15 mm mmmm
 Stiffness
 Stiffnessof
 Diameter PSS
 PSSspring(1st
 ofmaster cylinder stage)
 spring(1st stage) 20.59.03
 9.03 mmN/mm
 N/mm
 Peak power
 Stiffness of PBC motor 450 W N/mm
 StiffnessofofPSS
 PSSspring(2nd
 spring(2ndstage)
 Peak torque of PBC motor
 stage) 42.16
 42.16
 2.2
 N/mm
 N·m
 Rated speed of PBC motor 4000 r/min
 3.1.
 3.1.Results
 Results and
 andDiscussion
 Flexibility Discussion
 of the brake ofofConventional
 ConventionalBraking
 hose Braking Mode
 × 10−3
 Mode
 6.25 ml/MPa
 In Ball screw
 verify lead
 the pressure regulation 0.005
 In order to verify the pressure regulation performance of the power brake
 order to performance of the power m cylinder
 brake cylinder
 Transmission
 (PBC), ratio of the first stage gear 1.8In the pressurization test,
 /
 (PBC), the pressurization test of PBC was carried out. In the pressurization test,the
 the pressurization test of PBC was carried out. thepiston
 piston
 Ball screw efficiency 0.96 /
 of
 ofPBC
 PBC moves
 moves at
 at aafixed
 fixed speed,
 speed, and
 and the
 the controller
 controller of
 of the
 the power
 power brake
 brake unit
 unit (PBU)
 (PBU) switches
 switches
 Proportional coefficient of PRV 19.8 MPa/A
 the
 thepressure
 pressureregulation
 regulation
 Diameter of mode
 modeby
 PSS byadjusting
 adjustingthethesolenoid
 15 valves.
 solenoid valves.After
 Afterswitching
 mm the
 switching themode,
 mode,
 the
 the piston changes the direction of movement, but the speed remains unchanged. The
 piston changes
 Stiffness of PSS the direction
 spring(1st stage)of movement, but
 9.03the speed remains unchanged.
 N/mm The
 simulation results
 Stiffness
 simulation of PSSare
 results shown
 shownin
 spring(2nd
 are inFigures
 Figures12–15.
 stage) 12–15. 42.16 N/mm

 Figure
 Figure12.
 Figure 12.Pressure
 12. Pressure curve
 Pressure curveof
 curve ofPBC.
 of PBC.
 PBC.

 Figure
 Figure13.
 Figure 13.Piston
 13. Pistondisplacement
 Piston displacementcurve
 displacement curveof
 curve ofPBC.
 of PBC.
 PBC.

World
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 2021, 12, 14
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 of18
 18

 Figure
 Figure 14.
 Figure14. Push
 14.Push rod
 Pushrod force
 rodforce curve
 forcecurve of
 curveof PBC.
 ofPBC.
 PBC.

 Figure15.
 Figure
 Figure 15. Pressureregulation
 15.Pressure
 Pressure regulationmode
 regulation modecurve
 mode curveof
 curve ofPBC.
 of PBC.
 PBC.

 Accordingtotothe
 According theabove
 above simulation
 simulation results,
 results, withwith the gradual
 the gradual
 gradual increase
 increase of pressure,
 of pressure,
 pressure, PBC
 According to the above simulation results, with the increase of PBC
 PBC
 will will
 switch switch
 the the
 pressure pressure
 regulationregulation
 mode mode
 from low from low
 pressure pressure
 to medium to medium
 pressure pressure
 and high
 will switch the pressure regulation mode from low pressure to medium pressure and high
 and high by
 pressure, pressure,
 changing by the
 changing
 pistonthe piston displacement
 displacement and equivalentand equivalent
 equivalent cross-sectional
 cross-sectional area. Alt-
 Alt-
 pressure, by changing the piston displacement and cross-sectional area.
 area. Although
 hough the the pressure the pressure
 pressure regulation regulation
 regulation mode mode
 mode changes, changes,
 changes, the the brake the brake
 brake pressure pressure
 pressure doesdoes notdoes not
 not change change
 change sud-sud-
 hough
 suddenly and keeps at a steady growth. If we look closely at the changing trend of
 denly and
 denly and keeps
 keeps at at aa steady
 steady growth.
 growth. If If we
 we look
 look closely
 closely at at the
 the changing
 changing trend trend ofof the
 the pres-
 pres-
 the pressure, we can see that the pressurization rate gradually decreases as the pressure
 sure, we
 sure, we can
 can see
 see that
 that thethe pressurization
 pressurization rate rate gradually
 gradually decreases
 decreases asas the
 the pressure
 pressure regulation
 regulation
 regulation mode switches from low to medium and high pressure. This is because the
 mode switches from low to medium and high pressure.
 mode switches from low to medium and high pressure. This is because the equivalent This is because the equivalent
 equivalent piston cross-sectional area in medium and high pressure modes is smaller than
 piston cross-sectional
 piston cross-sectional area area in
 in medium
 medium and and high
 high pressure
 pressure modes
 modes is is smaller
 smaller than
 than that
 that in
 in the
 the
 that in the low pressure mode. As the PBC piston moves at a fixed speed, the fluid volume
 low pressure
 low pressure mode.
 mode. As As the PBC PBC piston
 piston moves
 moves at a fixed speed, speed, the the fluid
 fluid volume
 volume dis-dis-
 discharged from the PBCthe is smaller too, resultingatinaafixedlower pressurization rate.
 charged from
 charged from the
 the PBCPBC is is smaller
 smaller too,
 too, resulting
 resulting in in aa lower
 lower pressurization
 pressurization rate.rate.
 In addition, although the pressure changes greatly, the absolute value of push rod
 In addition,
 addition, although
 although the the pressure
 pressure changes
 changes greatly,
 greatly, the
 the absolute
 absolute valuevalue of push
 push rodrod
 forceInchanges little. In detail, the absolute value of the push rod force does of not increase
 force
 force changes little.
 changesaslittle. In detail, the absolute
 In detail,increases.
 the absolute value
 value of of the push rod force does not increase
 significantly the pressure Compared tothe
 the push
 mediumrod pressure
 force does not increase
 mode, the push
 significantly as
 significantly as the
 the pressure
 pressure increases.
 increases. Compared
 Compared to to the
 the medium
 medium pressure
 pressure mode,
 mode, thethe push
 push
 rod force is even reduced in high pressure mode. This is because the high-pressure mode
 rod force
 rod force isis even
 even reduced
 reduced in high high pressure
 pressure mode.
 mode. This
 This isis because
 because thethe high-pressure
 high-pressure mode
 has the smaller equivalentinpiston cross-sectional area. A benefit from this is that the mode
 piston
 has
 has the
 the smaller
 smaller equivalent
 equivalent piston
 piston cross-sectional
 cross-sectional area.
 area.
 can generate a higher pressure with the same push rod force. As a result, AA benefit
 benefit from
 from this
 this is that
 is that the
 the
 this piston
 piston
 variable
 can generate
 can generate aa higher
 higher pressure
 pressure withwith the
 the same
 same push
 push rodrod force.
 force. As
 As aa result,
 result, this
 this variable
 variable

World Electr. Veh. J. 2021, 12, x 15 of 18
World Electr. Veh. J. 2021, 12, 112
 x 15 of 18

 piston cross-sectional area control method can reduce the output torque range of the mo-
 piston
 tor, andcross-sectional
 piston area control
 reduce the performance
 cross-sectional area control methodcan
 requirements
 method canreduce
 reduce
 of theoutput
 the PBC
 the outputtorque
 motor. torquerange
 rangeofof the
 the mo-
 motor,
 tor, and
 and reduce reduce
 In order the the performance
 toperformance requirements
 requirements
 verify the pressure control of the
 of accuracy PBC
 the PBC motor. motor.
 of the pressure control algorithm
 basedInInonorder
 order
 P-V totoverify
 verifythe
 thepressure
 characteristics, pressure control
 control
 a random accuracy
 accuracy
 pressure of pressure
 of the
 following the
 testpressure control
 control
 is carried algorithm
 algorithm
 out. The based
 simula-
 based
 on P-V
 tion oncharacteristics,
 results P-Varecharacteristics, a random
 shown ina Figures
 random andpressure
 16pressure following
 17. following test
 test is is carried
 carried out.out.
 TheThe simula-
 simulation
 tion results
 results are shown
 are shown in Figures
 in Figures 16 17.
 16 and and 17.

 Figure 16. Pressure control effects.
 Figure 16.
 Figure Pressure control
 16. Pressure control effects.
 effects.

 Figure 17.
 Figure Pressure control
 17. Pressure control error.
 error.
 Figure 17. Pressure control error.
 From the above simulation results, it can be seen that the proposed pressure control
 From the above simulation results, it can be seen that the proposed pressure control
 algorithm,
 From the based
 aboveon simulation
 P-V characteristics, it can
 results, can can accurately
 be seen that follow
 thethethe target
 proposed pressure,
 pressure and
 control
 algorithm, based on P-V characteristics, accurately follow target pressure, and the
 the control
 algorithm, error
 based is within
 on P-V 0.5 MPa, which
 characteristics, can
 canmeet meet
 accuratelythe safety
 follow requirements of
 the target pressure,the highly
 and au-
 the
 control
 automatederror is within
 driving 0.5MPa,
 system. which can the safety requirements of the highly
 control error is within
 tomated driving system. 0.5MPa, which can meet the safety requirements of the highly au-
 tomated driving system.
 3.2. Results and Discussion of Redundant Braking Mode
 3.2. Results and Discussion of Redundant Braking Mode
 In the and
 3.2. Results redundant
 Discussion braking mode, the
 of Redundant redundant
 Braking Mode brake unit (RBU) realizes accurate
 In the redundant braking mode, the redundant
 pressure control by adjusting the coil current of the pressure brake unit (RBU) realizes
 regulation accurate
 valve (PRV). In
 In the
 pressure redundant
 control by brakingthe
 adjusting mode,
 coil the redundant
 current of the brake unit
 pressure (RBU) realizes
 regulation valve accurate
 (PRV). In
 order to verify the control effects of the RBU pressure control algorithm, a random pressure
 pressure
 order control
 to verify bycontrol
 adjusting the of
 coil
 thecurrent of the pressure regulation valve (PRV). In
 following test isthe
 carried effects
 out. The simulationRBUresults
 pressure
 are control
 shown inalgorithm, a random
 Figures 18 pres-
 and 19, and it
 order
 sure
 can be to verify
 following the
 seen thattest control
 theisRBU effects
 carried of
 out. The
 pressure the RBU
 simulation
 control pressure control
 results
 algorithm can are algorithm,
 alsoshown a random
 in Figures
 accurately follow18 and
 the pres-
 19,
 target
 sure following
 pressure, which test is carried
 means out. The simulation
 the proposed regenerative results are shown
 braking system in Figures
 can 18 and
 maintain 19,
 a high