The VDM plays an essential role in studying and analysing the braking system and other ACAS. Since this work considers only normal and emergency straightline braking, a 3-DOFs EV model provides sufficient information on vehicle motion and brake dynamics for RABS validation. Figure 2 shows a schematic diagram of the VDM describing longitudinal, lateral, and yaw motions with wheel rotations. However, the suspension in this model is considered rigid where pitch and roll motions are neglected, and only the front wheels can be steered. The equations of motion are given as follows [52] :

m ( V ˙ x − γ V y ) = ( F f l x + F f r x ) cos δ f − ( F f l y + F f r y ) sin δ f + ( F r l x + F r r x ) (1)

m ( V ˙ y + γ V x ) = ( F f l y + F f r y ) cos δ f + ( F f l x + F f r x ) sin δ f + ( F r l y + F r r y ) − m γ V x (2)

I z γ ˙ = l f ( F f l y + F f r y ) cos δ f + l f ( F f l x + F f r x ) sin δ f − l r ( F r l y + F r r y ) + M z (3)

M z = T f 2 [ ( F f l x + F f r x ) cos δ f + ( F f l y − F f r y ) sin δ f ] − T r 2 ( F r l x − F r r x ) (4)

where: m denotes vehicle total mass, V ˙ x ( V x ) vehicle CG longitudinal acceleration (velocity), V ˙ y ( V y ) vehicle CG lateral acceleration (velocity), γ ˙ ( γ ) vehicle CG yaw rate (angle), I z vehicle yaw moment of inertia, δ f front wheels steering angle, F i x ( F i y ) wheel i-th longitudinal (lateral) force, M z wheels yaw moment, l f ( l r ) CG distance from the front (rear) axle. Subscripts fl (fr) and rl (rr) indicate the front-left (right) and rear-left (right) wheels, respectively, T f ( T r ) represents the track width of the front (rear) wheels.

Finally, the vehicle sideslip angle β is defined as the angle between the vehicle’s longitudinal axis and the direction of its travel concerning the CG.

β = tan − 1 = V y V x (5)

The wheels are the only elements in direct contact with the ground and considerably influence the vehicle’s behaviour. Therefore, the tire model should provide accurate longitudinal and lateral dynamics calculations. Various tire models have been widely investigated in the literature, e.g., the magic formula (MF) and the brush model. This work considers a nonlinear MF model due to its simplicity and low calculation requirements. The model uses empirical parameters to describe the tire-road interaction at the contact point. Braking and cornering forces are calculated as functions of slip ratio κ and slip angle α. Empirical parameters can be specified based on the wheels’ vertical loads and camber angle. The equation describing the MF tire is given as follows [53] :

y = D sin [ C arctan { B x − E ( B x − arctan ( B x ) ) } ] (6)

To make the model output curve symmetric concerning the coordinate origin, horizontal and vertical displacements are defined as follows [53] :

Y = y + S v (7)

x = X + S h (8)

where: y is the model output ( F x , F y ) , Y is the model output after vertical displacement S v , x is the model input (κ or α), and X is the input with a horizontal displacement S h . B, C, D, and E are the stiffness, the shape, the peak, and the curvature coefficients, respectively. The tire behaviour depends on these coefficients, and they vary from one road to another [28] . The wheels slip ratio (driving/braking) is given as follows:

κ = − v x − r ω w v x (9)

The tires slip angle α f / α r can be calculated based on geometric derivation using wheel velocity vectors as follows [54] :

α f l = − δ f + tan − 1 ( v y + ϒ l f v x − ϒ T f 2 ) (10)

α f r = − δ f + tan − 1 ( v y + ϒ l f v x + ϒ T f 2 ) (11)

α r l = tan − 1 ( v y − ϒ r v x − ϒ T r 2 ) (12)

α r r = tan − 1 ( v y − ϒ l r v x + ϒ T r 2 ) (13)

The rotational dynamics for each wheel is the sum of driving, braking, and wheel-road torques acting around the wheel’s spin axis, as shown in Figure 2. The wheel rotational behaviour can be expressed according to the following torque balance equation [55] :

I w ω ˙ w = T d − T b − r F x (14)

where: vx (vy) is the vehicle longitudinal (lateral) velocity, I w denotes the wheel inertia, ω ˙ w is the wheel angular velocity derivative, T d is the driving torque, T b is the wheel braking torque, and r is the wheel’s effective radius.

Vertical load at each wheel, taking into account the load transfer due to the longitudinal and lateral accelerations, can be calculated as follows [56] :

F f l x = g m l r 2 ( l r + l f ) − m V ˙ x h c g 2 ( l r + l f ) − m V ˙ y h c g 2 ( l r + l f ) T f (15)

F f r x = g m l r 2 ( l r + l f ) − m V ˙ x h c g 2 ( l r + l f ) + m V ˙ y h c g 2 ( l r + l f ) T f (16)

F r l x = g m l r 2 ( l r + l f ) + m V ˙ x h c g 2 ( l r + l f ) − m V ˙ y h c g 2 ( l r + l f ) T r (17)

F r r x = g m l r 2 ( l r + l f ) + m V ˙ x h c g 2 ( l r + l f ) + m V ˙ y h c g 2 ( l r + l f ) T r (18)

Generally, regenerative torque is insufficient to brake the vehicle under specific conditions [16] . Also, RBS cannot be activated in various situations, for example, when the battery SOC is high, or the vehicle speed is below the limit of torque production. With these considerations, using a ceaseless frictional braking system (FBS) with RBS is expected to cover the remaining torque. The integration between FBS and RBS is essential and requires a braking strategy to control both [59] . Depending on the integration strategy, the resulting brakes can be classified into two types: a blended RBS (also series or superimposed) and a cooperative RBS (also parallel or non-blended) [29] . The integrated braking system has three main modes of operation: pure regenerative braking, pure frictional braking, and blended regenerative-frictional braking.

Both RBS and FBS always work simultaneously in cooperative braking, as shown in Figure 3(a). The brake command is distributed between the two systems based on a constant ratio [58] . The FBS is permanently connected to the brake pedal and boosted all the time by RBS [29] . The driver’s experience with the amount of brake pedal depressing and travel must remain similar to in conventional brake. This can be achieved by adjusting the brake pressure produced at a given pedal’s input. Thus, RBS can only contribute to a limited braking torque

[58] . However, cooperative braking has the advantages of simple control and high reliability owing to maintaining the hydraulic brake structure unchanged, providing the total braking torque alone when RBS is deactivated.

Blended braking is based on proper blending between RBS and FBS brake torques [29] [47] . When the demand is within EMs capacity, only RBS operates to meet this demand [47] [58] . However, if the brake demand is higher than the RBS torque capacity, FBS provides the remaining portion that is not covered by RBS [58] . In this strategy, the braking priority is maintained by RBS, where EMs operate at max power providing a significant braking torque [60] . The brake control must ensure that the vehicle’s deceleration is independent of its speed for pedal input [58] .

RBS takes precedence over FBS, especially at slow braking or low deceleration. When the brake pedal is depressed too fast (hard), the brake control provides more braking torque through the FBS for faster deceleration. Here, the brake pedal is separated from the friction brake callipers, enabling real electronic brakes, also called BBW. Control of blended braking is more complex but demonstrates improved performance and higher energy recovery than the cooperative system [45] . Figure 3(b) shows a schematic representation of the blended RBS.

In acceleration-based, the wheel slip is controlled by monitoring and maintaining the wheel acceleration within a given window. The acceleration is estimated using the wheel angular velocity measurement and used as control feedback. The ECU continuously reads wheel speed sensor information to calculate the vehicle speed and wheel slip ratio and sends control signals to the hydraulic brake actuators. Hydraulic actuators are switched on and off based on ECU control signals to reduce, maintain, or increase pressure, ensuring the wheel slip ratio is always within the ABS stable range (10% - 30%). Thus wheels never lock up, and maximum force transfer is realized [62] [63] . Below this range, the wheel behaviour tends to be more slippery (whole spinning at κ = 0%), and above this range, it tends to be more skidding (full skidding at κ = 100%). ECU switches between the three modes continuously when ABS is enabled [6] . However, with the on-off operation of the actuators, undesired vibrations appear on the pedal, which makes an uncomfortable feeling for the driver, and the brake performance is considerably decreased [19] .

ABS can also be implemented electronically based on wheel slip, where wheel slip is directly controlled by a non-logic control method. Fortunately, monitoring and controlling wheel slip instead of acceleration in the hydraulic ABS allow for realizing a slip-based ABS, also regenerative ABS (hereafter referred to as RABS). Wheel slip is more efficient in controlling brake force and eliminating the vibration on the brake pedal [7] . The continuous slip regulation can be achieved via RBS, where EMs produce constant braking torque. The slip ratio target at which the force transfer is maintained maximum is in the range of 10% - 20% [64] [65] . RABS highly fits the layout and packaging requirements of future EVs. However, RABS must be robust enough, comparable to acceleration-based ABS, to handle the uncertainties generated by the rapid changes in the road surface [43] .

The function of the braking system is to decelerate the vehicle quickly and safely while maintaining its direction under control. During the braking, the vehicle load is shifted between the front and rear axles resulting in an unbalanced distribution of the braking forces, and the stopping distance is considerably increased [66] . A correct distribution of braking torques between the front and rear axles and left and right wheels have a crucial impact on brake performance and vehicle behaviour. The front-to-rear distribution should be calculated from a vehicle stability standpoint, considering that rear wheels must never lock up before the front ones [50] . Maximum braking efficiency corresponding to the shortest stopping distance is obtained through employing correct distribution strategies of braking torques, e.g. wheels load [58] . An effective distribution method widely used is based on the ideal-curve distribution between front and rear axles. Braking with a ratio below the curve means most braking is provided by the front axle, while values above the curve cause a significant contribution by the rear axle [58] [66] . The brake force required for a constant vehicle deceleration is given in the following equation:

F b = m v α x ( g ) = F b f + F b r (19)

The coefficient of proportionality of the ideal allocation between the front and rear axle is given by the wheels’ vertical loads ratio:

P = F b f / F b r = F z f / F z r (20)

Thus, the ideal braking force portion of the front and rear axles can be calculated in terms of the wheels’ vertical loads proportionality as follows:

F b f = P m v α x / ( 1 + P ) = P F b / ( 1 + P ) (21)

F b r = m v α x / ( 1 + P ) = F b / ( 1 + P ) (22)

where: F b is the total braking force for a given vehicle deceleration, F b f ( F b r ) the ideal front (rear) axle braking force. P front and rear axles brake force ratio based on I-curve distribution.

For RABS based on wheel slip control feasibility, a relationship between IWMs torques and the wheel slip must exist. This relationship can be obtained by working out the time derivative of the wheel slip ratio and further fixing it according to:

T b c m d = ( J w ( κ + 1 ) L r m / ( L f + L r ) + r ) F x − J w r ( V x κ ˙ ) (23)

The braking torque reference obtained from the wheel slip control is compared with the driver’s brake request to realize vehicle deceleration in response to the driver’s command. Coordinate control is responsible for braking torque distribution between the IWMs and EWBs based on the blended braking method. The torque distribution unit continuously reads the braking torque required and compares it with the IWMs speed-torque map to determine the brake torque portion that IWMs can provide. Then the confined reference is weighted by the vehicle speed and the battery SOC limiting factors, having a value between 0 - 1. The IWMs torque is estimated and subtracted from the total brake torque demand at each wheel to calculate the torque portion of EWBs. EWBs intervene and deliver the appropriate braking torque part, which IWMs cannot cover (e.g., working in constant power area or flux weakening mode) to meet the driver’s demand (800 Nm), as shown in Figure 5. Thus there are three operation modes defined by toque allocation control as follows:

• Pure regenerative braking: when the total brake torque demand is within the IWMs power capacity, given that the battery SOC and the vehicle speed allow for energy recovery, IWMs are only used to generate a pure regenerative torque, and the energy recovery is maximum.

• Blended regenerative-frictional braking: when the required braking torque is out of the IWMs power capacity, given that the SOC and vehicle speed factors allow for energy recovery, then both IWMS and EWBs work and generate a mixed brake torque, and the energy recuperation is SOC-dependent.

• Pure frictional braking: when the required braking torque is within (out) the power capacity of IWMs, given that the SOC state and (or) the vehicle speed does not allow any energy recovery, then EWBs are only used to generate a pure frictional torque, and the energy recovery is zero.

In this manoeuvre, two braking scenarios are carried out, a regular emergency braking with brakes partially and fully applied, respectively.

• Regular braking Scenario (1A)

Figure 6(1a) shows the working areas of both IWMs and EWBs to meet the torque demand under braking manoeuvre 1A with ABS enabled/disabled. It can be seen that the ABS activation period starts with brake application at 3.5 s and lasts until the vehicle speed becomes less than 7 km/h at 5.2 s, where ABS is disabled by the control system automatically. When ABS is enabled, the RABS control switches between modes: firstly from pure regenerative braking (3.5 s - 5.06 s), then blended braking (5.06 s - 5.2 s), and lastly, pure frictional braking (5.2 s to 6.25 s) at which vehicle comes to a standstill. Similarly, when ABS is disabled (over the whole brake period), the RABS control switches between modes: initially from pure regenerative (3.5 s to 8.6 s), then blended (8.6 s - 9 s), and finally to pure frictional (9 s - 10 s) until vehicle’s full stop. Figure 7(1a) shows the vehicle speed and the front-right wheel speed. It can be noted that the time required to reach a vehicle’s complete halt is relatively short (2.75 s) with ABS enabled, while it takes almost two times the previous period (6.5 s) with ABS disabled. In other words, the stopping distance with ABS is much shorter. Figure 8(1a) shows the regenerative and frictional torques of the front-right wheel with both ABS enabled/disabled. When ABS is active, the IWM works at the highest performance, providing maximum pure regenerative torque (−800 Nm), which swiftly brakes the vehicle. EWB intervened only for a brief period at the end of the braking and provided a small braking torque. When ABS is idle, the

IWM generates a constant regenerative torque (−200 Nm) much lower than that with ABS active, increasing the stopping distance significantly. Similarly, EWB starts at the end of braking, providing a small portion (blended torque) which increases until the point IWM quits, while EWB keeps working alone, generating pure frictional torque (−200 Nm) until the vehicle comes to a full stop. Figure 9(1a) shows the slip ratio of the front (rear)-right wheels with both ABS enabled/disabled. It is noted that with ABS, the slip ratio is regulated at an optimum value of κ ≈ 0.18, at which maximum μ_road is maintained, allowing a maximum gripping force. Figure 10(1a) shows the brake forces generated by the front (rear)-right wheels with different ratios due to ideal distribution. Figure 11(1a) shows the SOC for battery packs BP1 and BP3 when ABS is enabled/ disabled. It is evident that when ABS is enabled, the energy recovery is much higher than when ABS is disabled, and battery packs are recharged faster in this case.

• Emergency braking Scenario (1B)

Figure 6(1b) shows the working areas of both IWMs and EWBs to meet the braking demand in emergency braking manoeuvres with ABS enabled/disabled. The ABS is enabled on the brake pedal, hitting at 3.5 s until the vehicle decelerates to a speed below 7 km/h at 5.2 s. ABS is automatically disabled, and standard frictional braking begins until the vehicle’s full stop at 5.5 s. Both IWMs and EWBs work together when ABS is enabled to generate a blended torque commanded by the wheel slip controller until the vehicle reaches the standstill at

5.25 s. When ABS is disabled, a blending braking mode is held, and both IWMs and EWBs collaborate to decelerate the vehicle to a complete stop at 5.7 s. Figure 7(1b) shows the vehicle and the front-right wheel speeds. In this scenario, there is a slight difference in vehicle stopping time (around 0.2 s) between the two modes of ABS. This difference can be related to the fact that the required torque (by wheel slip controller) is the same as the driver demand (full depression) in both cases. However, when ABS is enabled, the front-right wheel speed decreases gradually with the vehicle speed (owing to slip control). However, it drops steeply to zero after around 0.2 s from brake application with ABS disabled, indicating a locked wheel. Figure 8(1b) shows the regenerative and frictional torques of the front-right wheel with ABS enabled/disabled. When ABS is enabled, the IWM works below its max power providing pure regenerative torque (−650 Nm), while EWB delivers the remaining portion that IWM does not cover. When ABS is disabled, the driver demands the highest braking torque where IWM works at its maximum power generating constant torque (−800 Nm), and the EWB generates the top-up portion. Figure 9(1b) shows the slip ratio of the front (rear)-right wheels when ABS is enabled/disabled. ABS carries on wheel slip regulation at the ideal value κ ≈ 0.18, corresponding to the highest available and the highest grip force as shown in Figure 10(1b). However, when ABS is disabled, the wheels’ slip limit is reached, leading to a significant decrease in power transfer. Figure 11(1b) shows the SOC for battery packs BP1/BP3 when ABS is enabled/disabled. In this scenario, energy recuperation with ABS disabled is greater than that with ABS enabled. This can be explained in the same way as in the torque discussion, where maximum regenerative torque is demanded as the brake pedal is fully depressed.

In this manoeuvre, also two braking scenarios are carried out, the regular braking with brakes partially and the emergency braking with brakes fully applied, both with the ABS enabled and disabled.

• Regular braking Scenario (2A)

For high-speed regular braking manoeuvre 2A, the same discussion of manoeuvre 1A is feasible with the only difference in initial speed and brake period. Figure 12(2a) showcases the operational regions of IWMs and EWBs to satisfy torque requisites during braking manoeuvre 2A under varying conditions of ABS activation. Notably, ABS becomes active upon initial brake application at 12 s,

ceasing when the vehicle velocity drops below 7 km/h at 18 s, a point at which the control system autonomously disables ABS. When ABS is engaged, the RABS seamlessly transitions between distinct modes: commencing with the exclusive employment of pure regenerative braking (12 s - 18 s), followed by blended braking (18 s - 18.5 s), then pure frictional braking (18.5 s - 19 s) until the vehicle achieves a complete halt. Conversely, in the absence of ABS, RABS dynamically shifts between modes: initially employing pure regenerative braking (12 s - 27.6 s), subsequently transitioning to blended braking (27.6 s - 28.1 s), and ultimately resorting to pure frictional braking (28.1 s - 29 s) until the vehicle reaches a state of rest. Figure 13(2a) illustrates the vehicle speed and front-right wheel speed. Remarkably, the duration necessary to bring the vehicle to a complete standstill is substantially shorter (7 s) when ABS is enabled, whereas, in the absence of ABS, it is nearly 2.5 times the previous value (17 s). Thus, the implementation of ABS considerably reduces the vehicle’s stopping distance. Figure 14(2a) elucidates the evolutions of regenerative and frictional torques exerted on the front-right wheel with and without ABS activation. Under active ABS, the IWM operates at peak capacity, supplying maximum pure regenerative torque (−800 Nm) to effectuate rapid deceleration. The intervention of EWB is confined to a brief interval towards the conclusion of braking, imparting a minor braking torque. Conversely, in the idle state of ABS, the IWM generates a sustained

regenerative torque (−200 Nm), significantly inferior to its ABS-enabled counterpart, thereby substantially elongating the stopping distance. Similarly, EWB commences its influence towards the terminal phase of braking, initially contributing a blended torque that progressively ascends until the point of IWM disengagement, subsequently persisting independently developing a pure frictional torque (−200 Nm) until the vehicle attains a complete stop. Figure 15(2a) exhibits the slip ratio of the front (rear)-right wheels with ABS enabled/disabled. It is evident that ABS effectively regulates the slip ratio to an optimum reference value, enabling the maintenance of maximum road adhesion coefficient and hence maximum gripping force. Figure 16(2a) displays the brake forces exerted by the front (rear)-right wheels, indicating different ratios due to ideal distribution. Figure 17(2a) showcases the SOC for battery packs BP1 and BP3 when ABS is enabled or disabled. The results clearly demonstrate that ABS enhances energy recovery, leading to faster recharging of battery packs compared to when ABS is disabled.

• Emergency braking Scenario (2B)

Similarly, high-speed emergency braking manoeuvre 2B can be investigated in the same way that manoeuvres 1B is discussed with the difference in the vehicle’s initial speed and brake period. Figure 12(2b) illustrates the operational boundaries of both IWMs and EWBs for effectively addressing the exigent braking

requirements during emergency manoeuvres with varying states of ABS activation. ABS engagement is initiated at 12 s upon brake pedal actuation and ceases when the vehicle decelerates below 7 km/h at 18 s. Subsequently, ABS is automatically disabled, enabling standard frictional braking to govern the vehicle’s deceleration until it reaches a complete halt at 18.2 s. With ABS active, both IWMs and EWBs synergistically collaborate to generate a blended torque until 18 s the point at which IWMs disengage and EWBs continue delivering the remained braking torque required to bring the vehicle to a standstill at 18.2 s. Conversely, in the absence of ABS, a blending braking mode is upheld, wherein both IWMs and EWBs harmoniously cooperate producing blended braking torque over the period 12 s to 18.2 s and followed by only frictional brake by EWBs over the short final phase 18.2 s bringing the vehicle to a complete stop by 18.4 s. Figure 13(2b) depicts the velocity profiles of the vehicle and the front-right wheel. Within this specific context, a subtle disparity in the duration of vehicle deceleration (approximately 0.2 s) becomes evident when comparing the two ABS modes. This discrepancy can be attributed to the synchronization between the torque demanded by the wheel slip controller and the driver’s full depression of the brake pedal, which remains consistent across both scenarios.

However, with ABS enabled, the front-right wheel speed experiences a gradual reduction with respect to the vehicle speed, owing to slip control mechanisms. Conversely, in the absence of ABS, the front-right wheel speed precipitously plunges to zero within approximately 0.2 s from the initiation of brake application, indicative of wheel lockup. Figure 14(2b) showcases the variations of regenerative and frictional torques exerted on the front-right wheel under ABS-enabled and ABS-disabled configurations. With ABS active, the IWM operates below its peak power capacity, delivering pure regenerative torque (−650 Nm), while the EWB supplies the complementary torque to compensate for the portion not covered by the IWM. In contrast, when ABS is disabled, the driver demands maximum braking torque, prompting the IWMs to operate at maximum power, providing a constant torque (−800 Nm), with the EWB supplementing the residual torque requirement. Figure 15(2b) illustrates the wheel slip ratios observed in the front (rear)-right wheels during both ABS-enabled and ABS-disabled conditions. ABS consistently modulates the wheel slip ratio to achieve an optimal value of κ ≈ 0.18, maintaining high adhesion with the road and, consequently, maximizing the gripping force, as validated in Figure 16(2b). Conversely, when ABS is deactivated, the wheels approach their slip limits, resulting in a significant reduction in power transfer efficacy. Figure 17(2b) reveals the SOC profiles for battery packs BP1 and BP3 upon the activation and deactivation of ABS. In this particular configuration, energy recuperation with ABS disabled surpasses that achieved with ABS enabled. This can be explained analogously to the torque discourse, where the maximal regenerative torque is demanded in response to full depression of the brake pedal.