Human–machine redundant braking system for aftermarket low-speed electric vehicle: design and validation

: This paper presents the design and experimental validation of a novel human–machine redundant braking system (HMRBS) for aftermarket low-speed electric vehicles (LSEVs) to realise the backup redundancy ability and improve active safety. First, the HMRBS is designed by connecting the electro-hydraulic braking (EHB) unit oil pipelines in parallel with the manual braking (MB) unit through two three-way shuttle valves. Then, the mathematical model of the EHB subsystem is built, and a master cylinder pressure controller with adaptive fuzzy proportion integration differentiation (PID) and a servo motor speed controller with double-closed-loop proportion integration (PI) are proposed to improve the system response performance. Following this, the co-simulation model of the proposed closed-loop system is established based on AMESim and MATLAB/Simulink to validate the feasibility of the proposed control strategy. Finally, the effectiveness of the HMRBS is also validated by test rig and vehicle experiments. The results imply that the modiﬁed LSEV with the HMRBS meets the requirements of vehicle active braking ability and manual braking redundancy. Furthermore, the proposed controller can signiﬁcantly enhance pressure control accuracy compared to the classical PID controller. The deceleration ﬂuctuation and braking distance in the active braking mode are smaller than those in the manual braking mode, indicating that the proposed system makes the braking effect more stable and safer.


Introduction
Electrification and intelligence are currently emerging as global trends in the vehicle industry.Brake-by-wire technology has been greatly developed and applied to vehicle active braking systems [1][2][3].With the help of the active braking system, intelligent vehicles equipped with advanced driver assistance systems (ADAS), e.g., adaptive cruise control (ACC) and autonomous emergency braking (AEB), can significantly improve driving safety [4][5][6].
Currently, more and more passenger and commercial vehicles are equipped with brake-by-wire systems.However, most LSEVs, such as electric sightseeing vehicles, street sweepers, or light electric logistics vehicles that run on fixed routes or in closed scenes, have not been equipped with brake-by-wire systems due to the low quantity, high development costs, and various customised requirements [7].In addition, the different mechanical structures and vehicle dynamic performance requirements increase the development difficulty.The brake-by-wire systems should be designed, matched, calibrated, and debugged according to different types of vehicles.Therefore, it is necessary to develop an automatic braking system with a simple structure, high reliability, low cost, easy modification, and low debugging difficulty to improve the active braking capability of LSEVs.
Electro-hydraulic braking (EHB) systems are currently the mainstream active braking mode used in intelligent vehicles [8,9].Some EHB products have been successfully developed, such as the MKC1 and iBooster [10,11].Meanwhile, many scholars are also constantly improving and optimising the structure of the EHB system, e.g., a master cylinder based on the speed servo system with an anti-lock function [12], and a dual redundant brake-by-wire for highly automated driving safety [13].A redundancy braking system with EHB has the ability to activate the vehicle's emergency and consistency brake, even if the brakes are not activated due to electrical or mechanical failures or external shocks [14].However, the application object of all the above EHB systems is mass-produced new passenger or commercial vehicles, which makes them unsuitable for use in the aftermarket LSEVs to achieve active braking function.
EHB control strategies play a critical role in braking performance and safety.Recent literature shows increasing interest in EHB control strategies.A double-closed-loop PI feedback control system was proposed to obtain a better position-pressure relationship, where the inner loop and outer loop control the position and pressure, respectively [15].However, the characteristics of the brake oil, the friction, and the large transmission ratio of the transmission mechanism will cause strong nonlinearity, thereby affecting the robustness of the controller [13,16].A fuzzy PI controller for the hydraulic pressure control of the master cylinder was designed to improve the robustness of the PI control method [17][18][19].A sliding mode control method of the electro-hydraulic brake master cylinder pressure was proposed, aiming at the nonlinear problems such as oscillation and low-speed creeping of the master cylinder in the control process [20].However, the position of the master cylinder piston is not considered in the fuzzy PI or sliding mode controller, resulting in low control accuracy.Therefore, it is necessary to design a controller with fast response, high reliability, and low cost to ensure the master cylinder pressure accuracy and stability of the EHB system.
Aiming at these problems, a novel human-machine redundant braking system (HM-RBS) is proposed in this paper, and its innovation points are as follows: 1.
On the premise of retaining the original braking system of LSEV, a low-cost HMRBS is designed by connecting the oil pipelines of the EHB unit in parallel with the manual braking (MB) unit through two three-way shuttle valves.As a result, the HMRBS has two braking modes, active and manual braking modes, thus ensuring the redundancy of braking backup.

2.
The HMRBS mathematical model is established, and the master cylinder pressure controller with adaptive fuzzy PID and the servo motor speed controller with doubleclosed-loop PI are designed.Moreover, a test rig is developed, and an LSEV is modified with the HMRBS.Finally, the effectiveness of the proposed braking system is validated by experiments.
The rest of this paper is organised as follows.Section 2 illustrates the structure design scheme, operating principles, and mathematical model.Section 3 introduces the controller design of the HMRBS.In Section 4, the co-simulation results are given to verify the effectiveness of the proposed scheme.The experiments are carried out on a test rig and modified test LSEV, respectively, in Section 5. Finally, several conclusions are given in Section 6.

Design Scheme
Figure 1 shows the schematic of the human-machine redundant braking system (HMRBS) proposed in this paper.The system mainly comprises the MB unit, the EHB unit, and the wheel cylinder braking (WCB) unit.The EHB unit is connected in parallel to the original vehicle braking system (i.e., MB unit) through two three-way shuttle valves.The MB unit is consistent with the original vehicle system without any changes.It has the advantage of having a simple structure, high reliability, low cost, easy modification, and low debugging, especially for vehicles in the aftermarket.Therefore, the HMRBS has two braking modes: active braking mode and manual braking mode.The HMRBS works as follows: 1.
Active braking mode: First, the EHB subsystem receives the braking pressure request signal via the controller area network (CAN) from upper intelligent driving systems.
Then, the torque output by the brushless DC motor (BLDCM) is increased via the worm gear reducer (WGR).Meanwhile, the rotary motion of the worm gear is converted into the translational motion of the pushrod of the master cylinder 1 (MC1) through the ball screw mechanism (BSM).The high-pressure oil from MC1 enters the two three-way shuttle valves, i.e., SV1 and SV2, and the valve cores of SV1 and SV2 will move to the right.The independent oil circuit system comprises EHB and WCB units in this mode.Finally, the oil enters the brake caliper and increases the braking pressure.

2.
Manual braking mode: In this mode, the oil pressure of the master cylinder 2 (MC2) increases under the action of the foot pedal force, lever mechanism, and vacuum booster (some LSEVs do not have any vacuum booster).Then, the valve cores move to the left so that the MB and WCB units form an independent oil circuit system.The manual braking mode normally works even if the active braking fails.Therefore, the HMRBS can improve vehicle braking safety.

Design Scheme
Figure 1 shows the schematic of the human-machine redundant braking system (HMRBS) proposed in this paper.The system mainly comprises the MB unit, the EHB unit, and the wheel cylinder braking (WCB) unit.The EHB unit is connected in parallel to the original vehicle braking system (i.e., MB unit) through two three-way shuttle valves The MB unit is consistent with the original vehicle system without any changes.It has the advantage of having a simple structure, high reliability, low cost, easy modification, and low debugging, especially for vehicles in the aftermarket.Therefore, the HMRBS has two braking modes: active braking mode and manual braking mode.The HMRBS works as follows: 1. Active braking mode: First, the EHB subsystem receives the braking pressure reques signal via the controller area network (CAN) from upper intelligent driving systems Then, the torque output by the brushless DC motor (BLDCM) is increased via the worm gear reducer (WGR).Meanwhile, the rotary motion of the worm gear is con verted into the translational motion of the pushrod of the master cylinder 1 (MC1 through the ball screw mechanism (BSM).The high-pressure oil from MC1 enters the two three-way shuttle valves, i.e., SV1 and SV2, and the valve cores of SV1 and SV2 will move to the right.The independent oil circuit system comprises EHB and WCB units in this mode.Finally, the oil enters the brake caliper and increases the braking pressure.2. Manual braking mode: In this mode, the oil pressure of the master cylinder 2 (MC2 increases under the action of the foot pedal force, lever mechanism, and vacuum booster (some LSEVs do not have any vacuum booster).Then, the valve cores move to the left so that the MB and WCB units form an independent oil circuit system.The manual braking mode normally works even if the active braking fails.Therefore, the HMRBS can improve vehicle braking safety.

Mathematical Model
A mathematical model of the system is required for the subsequent co-simulation and controller design to validate the feasibility of the design scheme.Therefore, the mathematical models of BLDCM, transmission mechanism, brake master cylinder, wheel cylinder, and brake line are developed in this paper.
The electromagnetic torque of BLDCM can be expressed as [21] where P e stands for electromagnetic power of the motor, T e is electromagnetic torque, and ω is motor angular speed.i a , i b , and i c are the phase currents of three-phase stator windings, respectively.e a , e b , and e c are the back-EMF of three-phase stator windings.
The motor kinematic equation can be obtained by where T e is electromagnetic torque, T L is the additional load torque, and B v is the damping coefficient.
The dynamics model of the master cylinder can be written as ..
where M m1 and M m2 stand for the mass of the front piston and the rear piston, respectively.
x 1 and x 2 stand for the displacement of the front piston and the rear piston, respectively.c m1 and c m2 are the respective spring damping coefficients.k m1 and k m2 are the respective spring stiffness.p m1 and p m2 stand for the pressure of the front and rear chambers, respectively.A is the cross-sectional area of the piston.The continuity equation of hydraulic transmission of the master cylinder can be written as [22] . .
where β is the equivalent volume elastic modulus of the brake oil.V m1 and V m2 are the volumes of chambers after the front and rear pistons are compensated, respectively.d 1 and d 2 are the compensation displacement of the front and rear chambers, respectively.Q m1 and Q m2 are the flow of the front and rear chamber brake lines, respectively.The model of the wheel cylinder can be expressed as [23] M w ..
x w = A w p s − F s − c w .
x w (7) The continuity equation of the hydraulic pressure change of the wheel cylinder can be expressed as .
where M w is the mass of the caliper and x w is the equivalent displacement of the rigid body.A w is the cross-sectional area of the wheel cylinder piston, p s is the oil pressure on the piston, k w is the equivalent stiffness of the spring in the initial state of the piston, c w is the damping coefficient of the wheel cylinder, x q0 is the equivalent preload of spring, x q1 is the equivalent displacement of the rigid body, Q v is the brake oil flow, and L w is the initial liquid width of the wheel cylinder.
The continuity equation of the brake line can be written as where Q p is the flow in the brake line, P p is the actual pressure in the brake line, V p is the volume of the brake hose, and β is the equivalent volumetric elastic modulus of brake oil.The parameters involved in the EHB unit are shown in Table 1.

Controller Design
The HMRBS can realise the independent parallel control of the EHB and MB units.When the vehicle encounters an emergent event, the driver can brake the vehicle by MB unit.If the driver does not notice the emergency, the vehicle can be braked automatically by the EHB unit based on the control strategy.Therefore, the controller of the EHB unit of the HMRBS should be designed to meet braking safety.In the controller design, the master cylinder pressure-tracking performance and control accuracy should be guaranteed [24].
A closed-loop control strategy of the EHB unit is proposed in this paper, including the master cylinder pressure controller with adaptive fuzzy PID and the servo motor speed controller with double-closed-loop PI, shown in Figure 2. k p , k i , and k d are PID control parameters.∆k p , ∆k i , and ∆k d are the variations of the PID control parameters.P tar is target pressure, P act actual pressure, u tar target voltage, u act actual voltage, i tar target current, and i act actual current.

Master Cylinder Pressure Controller Design
In the master cylinder (MC1) pressure controller with adaptive fuzzy PID, the error between the expected pressure and the actual pressure and its change rate are the input signals, and the output is the expected speed of the servo motor.
The The output of the adaptive fuzzy PID controller consists of three correction terms, ∆kp, ∆ki, and ∆kd, which modify the PID control parameters kp, ki, and kd, respectively.The domains and fuzzy subsets for these output terms are defined as follows: the domain of ∆kp is {−6, −4, −2, 0, 2, 4, 6}, the domain of ∆ki is {−3, −2, −1, 0, 1, 2, 3}, and the domain of ∆kd is {−0.6, −0.4,−0.2, 0, 0.2, 0.4, 0.6}.Correspondingly, the fuzzy sets are {NB, NM, NS, ZO, PS, PM, PB}, with a quantification factor of 1 for each term.The membership function type of the input and output variable is mainly triangular, and the membership function is obtained after fuzzification, as shown in Figure 4.The output of the adaptive fuzzy PID controller consists of three correction terms, ∆k p , ∆k i , and ∆k d , which modify the PID control parameters k p , k i , and k d , respectively.The domains and fuzzy subsets for these output terms are defined as follows: the domain of ∆k p is {−6, −4, −2, 0, 2, 4, 6}, the domain of ∆k i is {−3, −2, −1, 0, 1, 2, 3}, and the domain of ∆k d is {−0.6, −0.4,−0.2, 0, 0.2, 0.4, 0.6}.Correspondingly, the fuzzy sets are {NB, NM, NS, ZO, PS, PM, PB}, with a quantification factor of 1 for each term.The membership function type of the input and output variable is mainly triangular, and the membership function is obtained after fuzzification, as shown in Figure 4.  Adaptive fuzzy PID control applies the modern control th of the online controlled object, making the control system adap stantly to achieve better control effects.The formulation of fu the integration of the PID parameter-tuning experience.The and ∆kd, can be set reasonably and dynamically [25].Referenci iables e and ec, adjustments are made to the magnitudes of ∆ initial adjustment phase, the error and the error rate between t sure values are relatively high, so a larger ∆kp is chosen to obtai rate.A smaller ∆kd is selected to prevent differential saturatio somewhat weakened.In the middle stage of adjustment, when ference e and its rate of change ec are moderate, the initial value reduced to control the system with minimal overshoot while sponse rate.To maintain stability, ∆ki, and ∆kd are kept rel changed.In the later stage, to improve the pressure-tracking st propriately, and the integral action is intensified to reduce stea control accuracy.Considering the sensitivity of the system pre in the kd parameter, ∆kd should be reduced to compensate for process caused by the larger ∆kp value during the initial adjus aforementioned parameter adjustment experience, the fuzzy r ble 2.  Adaptive fuzzy PID control applies the modern control theory to set the parameters of the online controlled object, making the control system adapt to the requirements constantly to achieve better control effects.The formulation of fuzzy control rules requires the integration of the PID parameter-tuning experience.The three parameters, ∆k p , ∆k i , and ∆k d , can be set reasonably and dynamically [25].Referencing the values of input variables e and e c , adjustments are made to the magnitudes of ∆k p , ∆k i , and ∆k d .During the initial adjustment phase, the error and the error rate between the actual and desired pressure values are relatively high, so a larger ∆k p is chosen to obtain a higher system response rate.A smaller ∆k d is selected to prevent differential saturation, and the integral effect is somewhat weakened.In the middle stage of adjustment, when the values of pressure difference e and its rate of change e c are moderate, the initial value of ∆k p can be appropriately reduced to control the system with minimal overshoot while ensuring a reasonable response rate.To maintain stability, ∆k i , and ∆k d are kept relatively moderate and unchanged.In the later stage, to improve the pressure-tracking stability, ∆k p is increased appropriately, and the integral action is intensified to reduce steady-state error and enhance control accuracy.Considering the sensitivity of the system pressure controller to changes in the k d parameter, ∆k d should be reduced to compensate for the prolonged adjustment process caused by the larger ∆k p value during the initial adjustment phase.Based on the aforementioned parameter adjustment experience, the fuzzy rules are summarised in Table 2. ∆k p , ∆k i , and ∆k d obtained by fuzzy reasoning are a fuzzy set which cannot calibrate the parameters.Therefore, the fuzzy set should be converted into an actual value that can be recognised by the control system [26].The centroid method is chosen for defuzzification, and can be expressed as where u i is an element of the domain {u 1 , u 2 . . . . . .u i }, and M(u i ) is the value of the membership function when u = u i .

Servo Motor Speed Controller Design
The rapid response and accurate control of the target signal should be accomplished in the servo motor speed controller with double-closed-loop PI.The motor speed loop is set to the outer loop, and the current loop of the motor is set to the interior loop, respectively.
In the outer loop, the input variable is the difference between the expected and actual speed, and the prospective current of the motor is chosen as the output.The difference between the prospective current and the actual motor current obtained by the current sensor is taken as the input variable of the current interior loop PI controller.Subsequently, the output signal is used as the input of the duty ratio of the PWM inverter.Control of PWM can be achieved by adjusting the duty ratio.Finally, the servo motor is driven to forward or reverse motion, and then the master cylinder piston is pushed or pulled by the transmission mechanism to achieve pressure control.
The principle behind pulse width modulation (PWM) is to compare the waveform (modulating wave) synthesised by the required sawtooth/triangular wave (carrier wave) with a reference voltage and determine the polarity of the PWM output.When the sawtooth wave is fed into the inverting input of the comparator and exceeds the reference voltage, the output polarity is the opposite of the sawtooth wave.When the sawtooth wave is fed into the non-inverting input of the comparator and exceeds the reference voltage, the output polarity is the same as the sawtooth wave.

Co-Simulation Model
A co-simulation model of the HMRBS is built with MATLAB/Simulink and AMESim to validate the feasibility of the control algorithm of master cylinder pressure tracking.The EHB unit consists of the controller sub-model and the hydraulic mechanism sub-model.The controller sub-model is developed in MATLAB/Simulink software based on the closedloop control strategy.The hydraulic mechanism sub-model includes the transmission mechanism, brake master cylinder, brake wheel cylinder, and brake pipeline, accomplished in AMEsim software.The exchange of data of the master cylinder pressure and target motor torque is realised in the co-simulation, shown in Figure 5.

Simulation Results
The classical PID and fuzzy PID strategies are compared and analysed in co-simulation.Two signal-inputting simulation conditions are used as follows: (1) a step signal with 6 MPa at 0.5 s; (2) a sine signal with an offset of 3 MPa, an amplitude of 3 MPa, and a frequency of 1 Hz.The results are displayed in Figures 6 and 7.
Figure 6 shows the results of the case with the step signal.The simulation case can evaluate the transient response of rapid pressurisation, rapid decompression, and pressure-holding capacity of the master hydraulic pressure under emergency active braking conditions.The rise time of PID and fuzzy PID is almost the same.The overshoot of PID is 0.26 MPa, and the steady-state error is 0.05 MPa.The overshoot of the fuzzy PID proposed is 0.18 MPa, and the steady-state error is 0.04 MPa, which are reduced by 42% and 20%, respectively.

Simulation Results
The classical PID and fuzzy PID strategies are compared and analysed in co-simulation.Two signal-inputting simulation conditions are used as follows: (1) a step signal with frequency of 1Hz.The results are displayed in Figures 6 and 7.
Figure 6 shows the results of the case with the step signal.The simulation case can evaluate the transient response of rapid pressurisation, rapid decompression, and pressure-holding capacity of the master hydraulic pressure under emergency active braking conditions.The rise time of PID and fuzzy PID is almost the same.The overshoot of PID is 0.26 MPa, and the steady-state error is 0.05 MPa.The overshoot of the fuzzy PID proposed is 0.18 MPa, and the steady-state error is 0.04 MPa, which are reduced by 42% and 20%, respectively.Figure 7 shows the results of the case with the sine signal.The simulation case can validate the dynamic response of the HMRSB under the periodically changing target pressure.The maximum tracking error of PID is 0.65 MPa, while the error of fuzzy PID is 0.62 MPa, which is reduced by 4.6%.
Therefore, the fuzzy PID proposed in this paper is superior to PID in overshoot, steady-state errors, and tracking errors.The results prove the effectiveness and accuracy of the fuzzy PID control strategy.

Test Rig Results
Compared with the simulation analysis, the actual system has uncertainties such as parameter variations, modeling errors, and external disturbances.Therefore, the robust- Figure 7 shows the results of the case with the sine signal.The simulation case can validate the dynamic response of the HMRSB under the periodically changing target pressure.The maximum tracking error of PID is 0.65 MPa, while the error of fuzzy PID is 0.62 MPa, which is reduced by 4.6%.
Therefore, the fuzzy PID proposed in this paper is superior to PID in overshoot, steadystate errors, and tracking errors.The results prove the effectiveness and accuracy of the fuzzy PID control strategy.

Test Rig Results
Compared with the simulation analysis, the actual system has uncertainties such as parameter variations, modeling errors, and external disturbances.Therefore, the robustness of the proposed method can be proved by rig and vehicle experiments.A brake system hardware-in-the-loop (HIL) test rig is built to evaluate the dynamic pressure characteristics of the HMRBS, as shown in Figure 8.The detailed specifications are listed in Table 3.A pressure controller is constructed in MATLAB/Simulink to receive the desired pressure value as input and generate the desired speed for the servo motor.The desired speed of the servo motor is then sent to the motor controller via the CAN Bus analyser.After passing through the motor speed controller and current controller, the motor control torque is outputted to achieve speed control of the motor, thereby driving the master cylinder piston to operate and complete the electro-hydraulic braking.

Name Specifications
Maximum pressure of the master cylinder 8 MPa Rated voltage of the motor 12 V Rated voltage of the oil pressure sensor 5 V Rated voltage range of the controller 9-16 V Baud rate of the CAN Bus analyser 500 kbs Figure 9 shows the time-pressure history results of the step target pressure-tracking test.The pressure value of the master cylinder can coincide well with the target signal with 4 MPa and 6 MPa, respectively.The actual pressure overshoot of the test is kept within 0.6 MPa, and the steady-state error is kept within 0.3 MPa, which meets the basic requirements of the HMRSB for braking efficiency.

Name
Specifications Maximum pressure of the master cylinder 8 MPa Rated voltage of the motor 12 V Rated voltage of the oil pressure sensor 5 V Rated voltage range of the controller 9-16 V Baud rate of the CAN Bus analyser 500 kbs Figure 9 shows the time-pressure history results of the step target pressure-tracking test.The pressure value of the master cylinder can coincide well with the target signal with 4 MPa and 6 MPa, respectively.The actual pressure overshoot of the test is kept within 0.6 MPa, and the steady-state error is kept within 0.3 MPa, which meets the basic requirements of the HMRSB for braking efficiency.The test results of the sine target pressure tracking are provided in Figure 10.Different signal offsets (2 MPa and 3 MPa), amplitude (2 MPa and 3 MPa), and frequency (0.5 Hz and 1 Hz) were set in the test.The results show that the pressure of the master cylinder has high accuracy in tracking the periodic dynamic target pressure.The maximum tracking error between the actual and target values is within 0.7 MPa, which appears in Figure Master cylinder pressure (MPa)  The test results of the sine target pressure tracking are provided in Figure 10.Different signal offsets (2 MPa and 3 MPa), amplitude (2 MPa and 3 MPa), and frequency (0.5 Hz and 1 Hz) were set in the test.The results show that the pressure of the master cylinder has high accuracy in tracking the periodic dynamic target pressure.The maximum tracking error between the actual and target values is within 0.7 MPa, which appears in Figure 10d.However, there are also shortcomings, such as fluctuations of the pressure signal intermittently, which are proportional to the target pressure amplitude and frequency.The fluctuations in all the tests are mainly due to the uncertain frictional characteristics of the actual transmission components, which are not considered in the simulation model.

Test Vehicle Test Results
An LSEV (sightseeing vehicle) was retrofitted with the HMRBS proposed in this paper to verify its braking performance in the road test, shown in Figure 11.A high-precision GPS/IMU system was used to obtain the braking deceleration, vehicle speed, and braking distance.The relevant requirements for road tests mainly refer to GB/T 21268-2014 and GB/T 7258-2017 [27,28].
10d.However, there are also shortcomings, such as fluctuations of the pressure signal intermittently, which are proportional to the target pressure amplitude and frequency.The fluctuations in all the tests are mainly due to the uncertain frictional characteristics of the actual transmission components, which are not considered in the simulation model.

Test Vehicle Test Results
An LSEV (sightseeing vehicle) was retrofitted with the HMRBS proposed in this paper to verify its braking performance in the road test, shown in Figure 11.A high-precision GPS/IMU system was used to obtain the braking deceleration, vehicle speed, and braking distance.The relevant requirements for road tests mainly refer to GB/T 21268-2014 and GB/T 7258-2017 [27,28].Considering that the test vehicle is used in a closed scenario, the maximum braking pressure of the master cylinder is limited to 4 MPa, and it can meet the vehicle braking demand.During the test, the vehicle was accelerated to 30 km/h and then held at a constant speed for a while before the brakes were applied.Emergency and mild brakes with Considering that the test vehicle is used in a closed scenario, the maximum braking pressure of the master cylinder is limited to 4 MPa, and it can meet the vehicle braking demand.During the test, the vehicle was accelerated to 30 km/h and then held at a constant speed for a while before the brakes were applied.Emergency and mild brakes with active and manual braking modes were applied to evaluate the braking performance in different conditions.
The dynamic response of active and manual braking modes in the emergency braking condition is presented in Figure 12.The master cylinder pressure and deceleration generated by the EHB unit increased stably.The speed slowed down linearly, indicating that the EHB unit is reliable and effective in the active braking mode.The manual braking mode has the same deceleration trend as the active braking mode.It indicates that the modification does not affect the manual braking performance.Therefore, the MB unit can be used as a backup of the EHB unit, and the design enables dual braking and independent control.pressure of the master cylinder is limited to 4 MPa, and it can meet the vehicle braking demand.During the test, the vehicle was accelerated to 30 km/h and then held at a constant speed for a while before the brakes were applied.Emergency and mild brakes with active and manual braking modes were applied to evaluate the braking performance in different conditions.
The dynamic response of active and manual braking modes in the emergency braking condition is presented in Figure 12.The master cylinder pressure and deceleration generated by the EHB unit increased stably.The speed slowed down linearly, indicating that the EHB unit is reliable and effective in the active braking mode.The manual braking mode has the same deceleration trend as the active braking mode.It indicates that the modification does not affect the manual braking performance.Therefore, the MB unit can be used as a backup of the EHB unit, and the design enables dual braking and independent control.
Figure 12c illustrates the vehicle speed, acceleration, and braking distance after the HMRBS receives the brake signal.The braking deceleration fluctuates around −0.5 g, and the braking time is about 2.2 s in both braking modes.But the braking distance of the manual and active braking modes is 11.5 m and 10.8 m, respectively.Moreover, the deceleration fluctuation generated by the EHB unit is smaller than that of the MB unit.Therefore, the active braking mode is more stable and effective.The dynamic response of active and manual braking modes in the mild braking condition is presented in Figure 13.The braking distance of the manual and active braking modes is about 20.4 m and 13.6 m, respectively.The braking deceleration fluctuates around −0.2 g and −0.35 g, and the braking time is 4.7 s and 2.9 s, respectively.The EHB unit produces fewer deceleration fluctuations than the MB unit, and the braking force is more stable.Figure 12c illustrates the vehicle speed, acceleration, and braking distance after the HMRBS receives the brake signal.The braking deceleration fluctuates around −0.5 g, and the braking time is about 2.2 s in both braking modes.But the braking distance of the manual and active braking modes is 11.5 m and 10.8 m, respectively.Moreover, the deceleration fluctuation generated by the EHB unit is smaller than that of the MB unit.Therefore, the active braking mode is more stable and effective.
The dynamic response of active and manual braking modes in the mild braking condition is presented in Figure 13.The braking distance of the manual and active braking modes is about 20.4 m and 13.6 m, respectively.The braking deceleration fluctuates around −0.2 g and −0.35 g, and the braking time is 4.7 s and 2.9 s, respectively.The EHB unit produces fewer deceleration fluctuations than the MB unit, and the braking force is more stable.
(c) The dynamic response of active and manual braking modes in the mild braking condition is presented in Figure 13.The braking distance of the manual and active braking modes is about 20.4 m and 13.6 m, respectively.The braking deceleration fluctuates around −0.2 g and −0.35 g, and the braking time is 4.7 s and 2.9 s, respectively.The EHB unit produces fewer deceleration fluctuations than the MB unit, and the braking force is more stable.Therefore, the EHB unit is superior to the MB unit in response speed and braking efficiency in the HMRBS, and the braking effect is more stable.Furthermore, on the premise of retaining the original braking system, the low-cost HMRBS ensures the redundancy of braking backup in case of power failure of the EHB unit.It can meet the braking performance and safety requirements of the LSEV.
An HMRBS with a simple structure, high reliability, low cost, easy modification, and low debugging difficulty for aftermarket LSEVs has been proposed in this paper.The HMRBS retains the original braking system of the LSEV.It can realise the vehicle braking backup redundancy ability and improve active safety.

2.
A master cylinder pressure controller with adaptive fuzzy PID and a servo motor speed controller with double-closed-loop PI have been designed to improve the system response performance.Simulation and test rig experiments have validated the feasibility and pressure-tracking performance.The dynamic pressure-tracking error is less than 0.6 MPa, and the steady-state error is within 0.3 MPa.

3.
An LSEV has been retrofitted with an HMRBS to verify its braking performance in the road test.As a result, the maximum braking deceleration of both manual and active braking modes can reach −0.5 g.Significantly, the deceleration fluctuation and braking distance of the EHB unit are smaller than that of the MB unit, and its braking effect is more stable.

Figure 1 .
Figure 1.The design schematic of the HMRBS.

17 A
closed-loop control strategy of the EHB unit is proposed in this paper, including the master cylinder pressure controller with adaptive fuzzy PID and the servo motor speed controller with double-closed-loop PI, shown in Figure2.kp, ki, and kd are PID control parameters.Δkp, Δki, and Δkd are the variations of the PID control parameters.Ptar is target pressure, Pact actual pressure, utar target voltage, uact actual voltage, itar target current, and iact actual current.

Figure 2 .
Figure 2. Closed-loop control strategy of EHB unit pressure.
initial fuzzy PID parameters are set to kp = 11, ki = 1.5, and kd = 1.1.The deviation between the actual master cylinder pressure value obtained by the pressure sensor and the target pressure value sent by the upper controller can be expressed as e = Pact − Ptar, and its rate of change can be expressed as ec = de/dt.The variables are scaled into the integer discourse domain range of [−6, 6], and both concrete subsets of numbers are {−6, −4, −2, 0, 2, 4, 6}.The fuzzy set corresponding to the basic domain is set to {NB NM NS ZO PS PM PB}.The discourse domain of input variables is divided into seven membership functions: NB (Negative Big), NM (Negative Middle), NS (Negative Small), ZO (Zero), PS (Positive Small), PM (Positive Middle), and PB (Positive Big).Fuzzification of the theoretical domains of e and ec yields a mainly triangular affiliation function, as shown in Figure 3.

Figure 2 .
Figure 2. Closed-loop control strategy of EHB unit pressure.

3. 1 .
Master Cylinder Pressure Controller Design In the master cylinder (MC1) pressure controller with adaptive fuzzy PID, the error between the expected pressure and the actual pressure and its change rate are the input signals, and the output is the expected speed of the servo motor.The initial fuzzy PID parameters are set to k p = 11, k i = 1.5, and k d = 1.1.The deviation between the actual master cylinder pressure value obtained by the pressure sensor and the target pressure value sent by the upper controller can be expressed as e = P act − P tar , and its rate of change can be expressed as e c = d e /d t .The variables are scaled into the integer discourse domain range of [−6, 6], and both concrete subsets of numbers are {−6, −4, −2, 0, 2, 4, 6}.The fuzzy set corresponding to the basic domain is set to {NB NM NS ZO PS PM PB}.The discourse domain of input variables is divided into seven membership functions: NB (Negative Big), NM (Negative Middle), NS (Negative Small), ZO (Zero), PS (Positive Small), PM (Positive Middle), and PB (Positive Big).Fuzzification of the theoretical domains of e and e c yields a mainly triangular affiliation function, as shown in Figure 3.es 2023, 11, x FOR PEER REVIEW

Figure 5 .
Figure 5.The co-simulation model of the EHB unit of HMRBS: (a) the controller sub-model in Matlab/Simulink; and (b) hydraulic mechanism sub-model in AMESim.

Figure 5 .
Figure 5.The co-simulation model of the EHB unit of HMRBS: (a) the controller sub-model in Matlab/Simulink; and (b) hydraulic mechanism sub-model in AMESim.

Figure 6 .
Figure 6.The step target pressure-tracking simulation results: (a) pressure-tracking curve; (b) pressure error curve; (c) electric current curve; and (d) piston displacement curve.

Figure 9 .
Figure 9.The test results of the step target pressure: (a) amplitude 4 MPa; and (b) amplitude 6 MPa.

Figure 9 .
Figure 9.The test results of the step target pressure: (a) amplitude 4 MPa; and (b) amplitude 6 MPa.

Figure 12 .
Figure 12.Emergency braking test: (a) active braking mode; (b) manual braking mode; and (c) comparison of vehicle dynamics characteristics.

Figure 12 .
Figure 12.Emergency braking test: (a) active braking mode; (b) manual braking mode; and (c) comparison of vehicle dynamics characteristics.

Figure 12 .
Figure 12.Emergency braking test: (a) active braking mode; (b) manual braking mode; and (c) comparison of vehicle dynamics characteristics.

Figure 13 .
Figure 13.Mild braking test: (a) active braking mode; (b) manual braking mode; and (c) comparison of vehicle dynamics characteristics.

Figure 13 .
Figure 13.Mild braking test: (a) active braking mode; (b) manual braking mode; and (c) comparison of vehicle dynamics characteristics.

Table 1 .
Parameter in the EHB unit.

Table 2 .
Fuzzy control rule table.

Table 2 .
Fuzzy control rule table.

Table 3 .
The specifications of the test rig.
NameSpecifications Maximum pressure of the master cylinder 8 MPa Rated voltage of the motor 12 V Rated voltage of the oil pressure sensor 5 V Rated voltage range of the controller 9-16 V Baud rate of the CAN Bus analyser 500 kbs

Table 3 .
The specifications of the test rig.

Table 3 .
The specifications of the test rig.