Coordinated control strategy of electro-hydraulic braking for energy regeneration

Control Engineering Practice 96 (2020) 104324

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Control Engineering Practice journal homepage: www.elsevier.com/locate/conengprac

Coordinated control strategy of electro-hydraulic braking for energy regeneration Pei Xiaofei a ,∗, Pan Hao a , Chen Zhenfu b , Guo Xuexun a , Yang Bo a a b

Hubei Key Laboratory of Advanced Technology of Automotive Components, Wuhan, China Hubei Collaborative Innovation Center of Automotive Components Technology, Wuhan, China

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Keywords: Electro-hydraulic braking Coordinated control Braking intention Genetic algorithm Simulation test

ABSTRACT This paper presents a coordinated control strategy of electro-hydraulic braking for distributed electric vehicles. To meet braking regulations requirements in conjunction with the characteristic of the in-wheel motor and power battery, the feasible region of the maximum regenerative braking torque and the evaluation indexes of the electro-hydraulic braking are proposed. In order to realize the optimal objective of energy regeneration and braking stability, the coordinated control of electro-hydraulic braking can be taken as a global distribution problem of two braking torques — hydraulic and regenerative. The optimal distribution coefficients are achieved by the genetic algorithm (GA) under different braking conditions. Moreover, the braking intention of the driver is integrated into the weight coefficients to achieve a dynamic distribution. The results of simulation show that the proposed strategy not only has better performance of energy regeneration and braking stability than I curve distribution, but also satisfies the characteristics of the driver’s braking behavior under corresponding situations.

1. Introduction Electro-hydraulic braking is composed of traditional hydraulic braking and regenerative motor braking. It is a key technology to increase the range of electric vehicles and reduce brake wear (Chiara & Canova, 2013; Lv, Zhang, Li, et al., 2015a; Rauh & Ammon, 2011). Since regenerative braking is insufficient to meet the entire braking requirements, how to coordinate hydraulic and regenerative braking is a key problem of electro-hydraulic braking. However, it is difficult to simultaneously ensure the braking stability and the optimum energy recovery. The ideal braking force distribution curve (called the I curve), is a traditional mechanism which ensures wheel lock on both the front axle and rear axle simultaneously. Although the I curve realizes a better braking performance, the energy recovery efficiency may be greatly limited (Gao & Ehsani, 2001; Guo, He, & Sun, 2013). In addition, many limiting factors associated with regenerative braking should be taken into account when determining the braking distribution. These include the characteristics of motor and battery, pedal feeling, transmission and brake by wire system, road adhesion (Gong, Chang, Jiang, et al., 2016; Lv, Zhang, Li, et al., 2015b; Meng, Zechang, Guirong, et al., 2012; Paul, Velenis, Cao, et al., 2017; Sangtarash, Esfahanian, Nehzati, et al., 2008; Zhang, Li, Lv, et al., 2014; Zhang, Yu, Pan, et al., 2015; zhou & Miaohua, 2018). In order to achieve both braking stability and optimal energy recovered under various constraints of regenerative braking, many control

strategies have been proposed including fuzzy logic, optimal control, model predictive control (Maia, Silva, Araújo, et al., 2015; Wu, Wang, Li, et al., 2018; Xiao, Lu, Wang, et al., 2017; Xu, Zhao, Ren, et al., 2016). Moreover, Sun, Liu, He, et al. (2016) considered the uncertainty effect of the system and adopted the six-sigma method to improve the reliability of the distribution algorithm. However, the driver’s braking intention also has an influence on the priority of the electro-hydraulic braking distribution. The driver’s braking intention is rarely considered when dynamically tuning the control weight between energy regeneration and braking stability. Recently, distributed electric vehicle control has become an important issue which is very suitable for electro-hydraulic braking. More control freedom and regenerative energy could be achieved since regenerative braking is used for each wheel. However, electro-hydraulic braking requires brake-by-wire. Due to the reduction of mechanical connection and the decoupling of pedal feeling by brake-by-wire systems, this results in an increase in the difficulty of distribution problem. For regenerative braking of distributed electric vehicles, optimizationbased algorithms are widely used including nonlinear programming, control allocation, collaborative optimization, multi-objective evolutionary algorithm (Pennycott, De Novellis, Gruber, et al., 2014; Wang, Zhao, Li, et al., 2019; Yu, Chen, & Peng, 2016). In addition, genetic algorithms (GA) are a good candidate for solving the global

∗ Corresponding author. E-mail address: [email protected] (X. Pei).

https://doi.org/10.1016/j.conengprac.2020.104324 Received 26 March 2019; Received in revised form 3 January 2020; Accepted 23 January 2020 Available online xxxx 0967-0661/© 2020 Elsevier Ltd. All rights reserved.

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Control Engineering Practice 96 (2020) 104324

Then, the maximum charging power is converted to the regenerative braking torque as Eq. (3), ( ) min 𝑃𝑐ℎ𝑔_𝐼 max , 𝑃𝑐ℎ𝑔_𝑈 max 𝜂𝑏 𝑇max _𝑏𝑎𝑡 = 9550 (3) 𝑛 ⋅ 𝜂𝑚

optimal problem. GA algorithms have already been adopted to energy management of hybrid vehicles (Lee, Tsang, Chi, et al., 2015; McGehee & Yoon, 2015). In this paper, the coordinated control of electro-hydraulic braking is converted to finding the optimal solution of distribution coefficients by GA algorithm. The contributions of the proposed regenerative braking strategy lie in the following three aspects: (1) The driver’s braking intention based on Hidden Markov Model (HMM) is incorporated into the electro-hydraulic braking distribution. Hence, the control weight between the energy regeneration and braking stability could be adjusted dynamically. Braking stability is more important when the driver requests heavy braking. Conversely, more energy regeneration could be utilized for slight braking requests. (2) The electro-hydraulic braking distribution of distributed electric vehicles is converted to a global optimal problem under the constraints of ECE-R13 regulations (Economic Commission for Europe, 1994) and, motor and battery characteristics. GA algorithm is adopted to obtain the optimal solution of three distribution coefficients. (3) The distribution coefficients are implemented as look-up tables which replace online optimization under different braking situations, allowing for a real-time implementation such as Rapid Control Prototyping (RCP) test. The rest of this paper is organized as follows. We first analyze the influencing factors of maximum regenerative braking torque, and the evaluation indexes of energy regeneration and braking stability. Based on it, the objective function and constraint conditions in the distribution optimization of electro-hydraulic braking are determined. Specifically, we adjust the weighting coefficients to take into account the real-time braking intention. Then, the optimal solution of three distribution coefficients under different braking conditions is obtained by GA. Finally, the proposed GA distribution is verified and compared with the I curve distribution under a typical braking condition and driving cycle condition.

where, 𝑇max_𝑏𝑎𝑡 is the maximum regenerative braking torque limited by battery, n is the motor speed, 𝜂b and 𝜂m are electric efficiency of the battery and motor respectively. In addition, the battery capacity is represented by state of charge (SOC). When the SOC is higher than 0.9, the battery is not allowed to be charged, hence the regenerative braking torque is 0 at this time. (3) Limitation of ECE braking regulations To ensure braking safety, the maximum regenerative braking torque generated by each in-wheel motor should be limited due to braking regulations. In this paper, the braking distribution between the front and rear axle is based on the ECE-R13 regulations, which can be expressed as follows: ⎧𝜑𝑓 ≤ 𝜑𝑟 ⎪𝜑 > 𝜑 𝑟 ⎨ 𝑓 ⎪𝜑 , 𝜑 ≤ (𝑧 + 0.07) ⎩ 𝑓 𝑟 0.85

⎧ 𝛽𝑧𝐿 ⎪𝜑𝑓 = 𝑏 + 𝑧ℎ𝑔 ⎪ ⎨ ⎪𝜑𝑟 = (1 − 𝛽) 𝑧𝐿 𝑎 − 𝑧ℎ𝑔 ⎪ ⎩

(5)

where, 𝛽 is the braking distribution coefficient between the front axle and rear axle, a and b are the distance of center to the front axle and rear axle respectively, L is the wheelbase, ℎg is the height of the center of mass, z is the severity of braking, which is the ratio of braking deceleration a and gravitational acceleration g. From Eq. (4) we can see that if 𝑧 ∈ [0.3, 0.45], and 𝜑𝑟 ≤ 𝑧 + 0.05, 𝜑𝑓 ≤ 𝜑𝑟 is required. Else, 𝜑𝑓 > 𝜑𝑟 should be satisfied for the most of braking conditions. Based on Eqs. (4) and (5), the limitation of the ECE-R13 regulations on the distribution coefficient 𝛽 can be expressed as Eq. (6), and the braking stability region can be plotted in Fig. 1. The shadow scope is the braking stability region which is formed by the limit curves corresponding to Eq. (6).

The following limiting factors of the maximum regenerative braking torque should be taken into account in the coordinated control strategy: (1) Limitation of the characteristic of in-wheel motor The maximum regenerative braking torque depends on the external characteristics of the in-wheel motor in generating state, that is: 𝑇𝑚𝑖 ≤ 𝑇max _𝑖 ∑

(4)

𝑧 ∈ [0.1, 0.61]

where, 𝜑𝑓 , 𝜑𝑟 are the utilization adhesion coefficient of front axle and rear axle respectively, which are defined as,

2. Limiting factors of maximum regenerative braking torque

𝑇max _𝑚𝑜𝑡 =

𝑖𝑓 𝑧 ∈ [0.3, 0.45] 𝑎𝑛𝑑 𝜑𝑟 ≤ 𝑧 + 0.05 𝑒𝑙𝑠𝑒 𝑖𝑓 𝑧 ∈ [0, 1]

(1)

⎧ 𝑏 + 𝑧ℎ𝑔 ⎪⃝ 1 𝛽 > ⎪ 𝐿 ( ) ⎪ (𝑧 + 0.07) 𝑏 + 𝑧ℎ𝑔 2 𝛽 ≤ ⎨⃝ 0.85𝑧𝐿 ( ) ⎪ (𝑧 + 0.05) 𝑎 − 𝑧ℎ𝑔 ⎪ 𝑏 + 𝑧ℎ𝑔 3 ⃝ > 𝛽 ≥ 1 − ⎪ 𝐿 𝑧𝐿 ⎩

𝑇max _𝑖

where, 𝑇max_𝑚𝑜𝑡 is the maximum regenerative braking torque limited by motor, 𝑇𝑚𝑖 is the regenerative braking torque of each in-wheel motor, and i = fl, fr, rl, rr represents four wheels respectively. 𝑇max_𝑖 is the maximum motor torque at the current speed, which could be seen as a function of the motor speed within the range of constant power. Since the speed of the in-wheel motor is equal to the wheel speed, 𝑇max_𝑖 can be obtained by a look-up table of the wheel speed. (2) Limitation of the characteristic of battery charging The regenerative braking energy is stored in the power battery, and it is limited by the battery’s receiving capacity, including the maximum charging power and battery capacity. According to the charging characteristics of the battery, the maximum charging power of constant-voltage charge and constant-current charge can be expressed as: ( ) ⎧𝑃 = 𝑈 ⋅ 𝐼m𝑎𝑥 = 𝐸 + 𝐼m𝑎𝑥 𝑅 𝐼m𝑎𝑥 ⎪ 𝑐ℎ𝑔_𝐼m𝑎𝑥 ( ) (2) ⎨ 𝑈m𝑎𝑥 𝑈m𝑎𝑥 − 𝐸 ⎪𝑃𝑐ℎ𝑔_𝑈 m𝑎𝑥 = 𝑈m𝑎𝑥 ⋅ 𝐼 = 𝑅 ⎩

𝑧 ∈ [0, 0.3] ∪ [0.45, 1] 𝑧 ∈ [0.1, 0.61]

(6)

𝑧 ∈ [0.3, 0.45]

3. Performance evaluation of electro-hydraulic braking 3.1. Evaluation indexes of energy regeneration Fig. 2 presents the energy flow in the process of braking energy regeneration. The braking energy is input into the wheel and converted into the electric energy by in-wheel motor which works as a generator at this moment. Finally, it is input into the battery through electric circuitry. Due to the energy loss mainly including the loss of the mechanism, motor, circuitry and battery, the recovered energy is only part of the initial dynamic energy. In order to evaluate energy conversion efficiency better, we define two indexes as follows. (1) Braking energy regeneration efficiency: the ratio between the regenerative braking energy and total braking energy.

where, E is the open circuit voltage of the battery, R is the equivalent internal resistance. I and U are the current and voltage of battery charging respectively. Hence, the charging of power battery is restricted by the maximum current 𝐼𝑚𝑎𝑥 and the maximum voltage 𝑈𝑚𝑎𝑥 .

𝜓= 2

𝐸_𝑔𝑒𝑛 𝐸_𝑏𝑟𝑘

=∫

𝑇 ⋅𝑛 𝜂 𝑑𝑡 9550 𝑚

(

∕

) 1 ( 2 𝑚 𝑣𝑡 −𝑣0 2 −∫ 2

(

) ) 𝑚𝑔𝑓 + 12 𝐶𝐷 𝐴𝜌𝑣2 𝑣𝑑𝑡

(7)

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Control Engineering Practice 96 (2020) 104324

Fig. 1. The braking stability region.

Fig. 2. Energy flow during braking energy regeneration.

where, m is vehicle mass, f is the rolling resistance coefficient, 𝐶d and A are the airflow coefficient and vehicle frontal area respectively, v, v 0, 𝑣𝑡 are current vehicle velocity, initial velocity and terminal velocity respectively. (2) Braking energy recovery efficiency: the ratio between the total charging energy and discharging energy of the battery. It is used during the driving cycle including the driving condition and braking condition.

𝜓=

𝐸𝑏𝑎𝑡_𝑐ℎ𝑔 𝐸𝑏𝑎𝑡_𝑑𝑖𝑠

=∫

𝑈𝑐ℎ𝑔 ⋅𝐼𝑐ℎ𝑔 𝑑𝑡∕∫ 𝑈𝑑𝑖𝑠 ⋅𝐼𝑑𝑖𝑠 𝑑𝑡

it is used to evaluate control performance under cycle condition in Section 5.2. 3.2. Evaluation indexes of braking stability To achieve the maximum utilization of adhesion coefficient and the optimum braking stability, the ideal braking force distribution condition is 𝜑𝑓 = 𝜑𝑟 . Therefore, I curve which simultaneously guarantees wheel lock on both the front wheel and rear wheel can be expressed as follows: √ ( )⎤ ⎡ 4ℎ𝑔 𝐿𝑅 𝑚𝑔𝑏𝑅 1 ⎢ 𝑚𝑔 𝑇𝐼𝑓 − 𝑇𝐼𝑟 = 𝑏2 𝑅 2 + + 2𝑇𝐼𝑓 ⎥ (9) ⎥ 2 ⎢ ℎ𝑔 𝑚𝑔 ℎ𝑔 ⎣ ⎦ ( ) 𝑚𝑔 𝑏 + ℎ𝑔 ∗ 𝑧 𝑧 ⎧ 𝑅 ⎪𝑇𝐼𝑓 = 𝐿 ( ) (10) ⎨ 𝑚𝑔 𝑎 − ℎ ∗ 𝑧 𝑧 𝑔 ⎪𝑇 = 𝑅 ⎩ 𝐼𝑟 𝐿

(8)

where, 𝑈𝑑𝑖𝑠 and 𝐼𝑑𝑖𝑠 are the discharging voltage and current respectively, 𝑈𝑐ℎ𝑔 and 𝐼𝑐ℎ𝑔 are the charging voltage and current respectively. Comparing these two indexes, we find that the former is more intuitive for a single braking process and the parameters in Eq. (7) are easy to access. Therefore, it is adopted in the control design. While the latter is more effective for a long driving cycle since the characteristic of inverter and battery charging are taken into account. In this paper, 3

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Control Engineering Practice 96 (2020) 104324

coefficients should be determined under different driving conditions. ⎧ 𝑇𝑓 ⎪𝛽 = ( ) ⎪ 𝑇𝑓 + 𝑇𝑟 ⎪ 𝑇𝑓 _𝑟𝑒𝑔 𝑇𝑓 _𝑟𝑒𝑔 ⎪ = ( ) ⎨𝛼𝑓 = 𝑇 𝑇𝑓 _𝑟𝑒𝑔 + 𝑇𝑓 _ℎ𝑦𝑑 𝑓 ⎪ ⎪ 𝑇 𝑇𝑟_𝑟𝑒𝑔 ⎪𝛼𝑟 = 𝑟_𝑟𝑒𝑔 = ( ) 𝑇𝑟 ⎪ 𝑇𝑟_𝑟𝑒𝑔 + 𝑇𝑟_ℎ𝑦𝑑 ⎩

(12)

where, 𝛼𝑓 and 𝛼𝑟 are the electro-hydraulic braking distribution coefficient of front axle and rear axle respectively, 𝑇𝑓 _𝑟𝑒𝑔 and 𝑇𝑓 _ℎ𝑦𝑑 are the regenerative braking torque and hydraulic braking torque of front axle respectively, 𝑇𝑟_𝑟𝑒𝑔 and 𝑇𝑟_ℎ𝑦𝑑 are the regenerative braking torque and hydraulic braking torque of rear axle respectively. Fig. 4 shows the overall framework of coordinated control strategy for electro-hydraulic braking. Firstly, the desired braking torques 𝑇_total with driver’s intention Int_brk is achieved according to the pedal signal including pedal force 𝐹ped and pedal displacement 𝑆ped . Secondly,

Fig. 3. Stable difference between the actual and ideal brake torque.

where, 𝑇𝐼𝑓 and 𝑇𝐼𝑟 are the ideal braking torque of the front and rear axle, respectively, R is the tire radius. In Fig. 3, the area upper I curve means the rear wheel locks before the front wheel. In general, it is unstable and should be as limited as possible. If the braking distribution is not strictly according to I curve, the braking stability should be indicated quantitatively. In this paper, we define the stable coefficient 𝜅 as follows: √( )2 ( )2 𝑇𝑓 − 𝑇𝐼𝑓 + 𝑇𝑟 − 𝑇𝐼𝑓 𝛥𝑇 = (11) 𝜅= 𝑇𝑡𝑜𝑡 𝑧𝑚𝑔𝑅

three distribution coefficients are determined using an offline generated look-up table under current braking condition. Then, the regenerative braking torques 𝑇𝑚_𝑜𝑝𝑡_𝑖𝑗 and the hydraulic braking torques of each wheel 𝑇ℎ_𝑜𝑝𝑡_𝑖𝑗 are obtained based on the total braking demand and the distribution coefficients. In addition, regenerative braking torques need to be further modified according to the practical limitations of in-wheel motor, and battery charging which can be achieved from battery management system (BMS) by SOC, permitted charging power 𝑃𝑏𝑎𝑡_𝑝𝑒𝑟 and torque 𝑇𝑏𝑎𝑡 . Finally, after the torque correction module, the regenerative braking torques 𝑇𝑚_𝑡𝑎𝑔_𝑖𝑗 and the hydraulic braking torques 𝑇ℎ_𝑡𝑎𝑔_𝑖𝑗 are implemented by motor controller and electric controlled braking (ECB) controller respectively.

where, 𝑇𝑓 and 𝑇𝑟 are the actual braking torque of the front and rear axle, respectively. The stable difference 𝛥𝑇 between the actual braking point and ideal braking point is shown in Fig. 3. If the actual braking distribution between the front and rear axle is closer to I curve, it represents the vehicle has more relatively stable. Hence, we evaluate the braking stability for proposed control strategy based on this stable coefficient in Section 5.1. It is notable that the I curve has a higher safety standard than the ECE-R13 regulations, which has a well-distributed requirement on both axles.

4.2. Objective function and constraint conditions In this paper, three distribution coefficients are obtained by optimization. The objective function is given in Eq. (13), the first item represents energy regeneration index and the latter two items represent the braking stability performance. ( ) ( ) | | 𝑓 (𝑥, 𝑡) = 𝑤1 ⋅ 𝜓 + 𝑤2 ⋅ 1 − |𝜑𝑓 − 𝑧| + 𝑤3 ⋅ 1 − ||𝜑𝑟 − 𝑧|| (13) | | where, 𝜓 is the energy regeneration efficiency, 𝑤1 , 𝑤2 , 𝑤3 are three weight coefficients and their sum is 1. Then, we take the definition of energy regeneration efficiency into Eq. (13). Here, constant values are assumed within the control cycle 𝑇𝑠 which allows removal of the integrals in Eq. (7). ( ) 𝑇𝑠 𝑇𝑓 _𝑟𝑒𝑔 ⋅ 𝑛 ⋅ 𝜂𝑓 + 𝑇𝑟_𝑟𝑒𝑔 ⋅ 𝑛 ⋅ 𝜂𝑟 𝑓 (𝑥, 𝑡) = 𝑤1 ⋅ ( ( )) 9550 𝐸𝑑𝑦𝑛 − 𝑣𝑇𝑠 𝑚𝑔𝑓 + 12 𝐶𝐷 𝐴𝜌𝑣2 (14) ( ) ( ) | | | | + 𝑤2 ⋅ 1 − |𝜑𝑓 − 𝑧| + 𝑤3 ⋅ 1 − |𝜑𝑟 − 𝑧| | |

4. Optimization strategy of electro-hydraulic braking torque distribution 4.1. Overall control strategy To achieve coordination during braking distribution, three distribution coefficients are defined in Eq. (12). In order to improve the performance of energy regeneration and braking stability, these optimized

Fig. 4. Overall control strategy of electro-hydraulic braking.

4

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Control Engineering Practice 96 (2020) 104324

Fig. 5. Optimal solution of the distribution coefficients.

where, 𝐸𝑑𝑦𝑛 is the consumed dynamic energy which can be expressed as, ) 1 [ ( )2 ] 1 ( (15) 𝐸𝑑𝑦𝑛 = 𝑚 𝑣2 − 𝑣𝑡 2 = 𝑚 𝑣2 − 𝑣 − 𝑧𝑔𝑇𝑠 2 2 Finally, rearranging gives the objective function in the form by combine Eqs. (12), (14) and (15), ( ) 𝑛 ⋅ 𝑇_𝑡𝑜𝑡𝑎𝑙 ⋅ 𝑇𝑠 𝛽 ⋅ 𝛼𝑓 ⋅ 𝜂𝑓 + (1 − 𝛽) ⋅ 𝛼𝑟 ⋅ 𝜂𝑟 𝑓 (𝑥, 𝑡) = 𝑤1 ⋅ [ ( )) ( ( )2 ] − 𝑣𝑇𝑠 𝑚𝑔𝑓 + 12 𝐶𝐷 𝐴𝜌𝑣2 9550 12 𝑚 𝑣2 − 𝑣 − 𝑧𝑔𝑇𝑠 ( ) ( ) | 𝛽𝑧𝐿 | | | (1 − 𝛽) 𝑧𝐿 | | | | + 𝑤2 ⋅ 1 − | − 𝑧| + 𝑤3 ⋅ 1 − | − 𝑧| | 𝑏 + 𝑧ℎ𝑔 | | | 𝑎 − 𝑧ℎ𝑔 | | | | (16) where, x is control variable, 𝑥 ∈ {𝑧, 𝑛}, 𝜂𝑓 and 𝜂𝑟 is the motor efficiency of front axle and rear axle respectively. In addition, the limiting factors of the maximum regenerative braking torque in Section 2 need to be converted into constrained conditions of the optimization problem, as shown in Eq. (17), 0 ≤ 𝛽 ≤ 1, 0 ≤ 𝛼𝑓 ≤ 1, 0 ≤ 𝛼𝑟 ≤ 1 𝑇_𝑡𝑜𝑡𝑎𝑙 ⋅ 𝛽 ⋅ 𝛼𝑓 ≤ 𝑇max _𝑓 , 𝑇_𝑡𝑜𝑡𝑎𝑙 ⋅ (1 − 𝛽) ⋅ 𝛼𝑟 ≤ 𝑇max _𝑟 ( ) min 𝑃𝑐ℎ𝑔_𝐼 max , 𝑃𝑐ℎ𝑔_𝑈 max 𝜂𝑏 ( ) 𝛽 ⋅ 𝛼𝑓 + (1 − 𝛽) ⋅ 𝛼𝑟 𝑇_𝑡𝑜𝑡𝑎𝑙 ≤ 9550 𝑛 ⋅ 𝜂𝑚 𝑏 + 𝑧ℎ𝑔 (17) 𝑠.𝑡. 𝛽> 𝑧 ∈ [0, 0.3] ∪ [0.45, 1] 𝐿 ( ) (𝑧 + 0.07) 𝑏 + 𝑧ℎ𝑔 𝛽≤ 𝑧 ∈ [0.1, 0.61] 0.85𝑧𝐿 ( ) 𝑏 + 𝑧ℎ𝑔 (𝑧 + 0.05) 𝑎 − 𝑧ℎ𝑔 >𝛽 ≥1− 𝑧 ∈ [0.3, 0.45] 𝐿 𝑧𝐿

Fig. 6. The look-up tables of the distribution coefficients.

axle and rear axle respectively. Through the real-time recognition of braking intention, these weight coefficients can be adjusted dynamically. Four braking intentions including slight braking, mild braking, moderate braking and severe braking could be recognized based on an HMM method. HMM is suitable for braking intention by regarding as a continuous time sequential problem. The recognition procedure of braking intention contains signal acquisition, feature extraction, cluster, off-line self-learning and on-line identification. More details can

4.3. The effect of braking intention The driver has different prioritizing requirements for energy regeneration and braking stability under various braking intentions. Therefore, driver’s braking intention which represents braking demand in future should be incorporated into the objective function of optimization. As shown in Eq. (13), three weight coefficients reflect the coordination between energy regeneration, braking stability of front 5

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Table 1 The setting of weight coefficient. Intent

Speed <10 m/s

10 m/s ∼ 20 m/s

20 m/s ∼ 30 m/s

30 m/s <

Slight brake

𝑤1 =1 𝑤2 = 0, 𝑤3 = 0

𝑤1 =1 𝑤2 = 0, 𝑤3 = 0

𝑤1 = 0.8 𝑤2 = 0.1, 𝑤3 = 0.1

𝑤1 = 0.7 𝑤2 = 0.2, 𝑤3 = 0.1

Mild brake

𝑤1 =1 𝑤2 = 0, 𝑤3 = 0

𝑤1 = 0.8 𝑤2 = 0.1, 𝑤3 = 0.1

𝑤1 = 0.7 𝑤2 = 0.2, 𝑤3 = 0.1

𝑤1 = 0.6 𝑤2 = 0.2, 𝑤3 = 0.2

Moderate brake

𝑤1 = 0.7 𝑤2 = 0.2, 𝑤3 = 0.1

𝑤1 = 0.6 𝑤2 = 0.2, 𝑤3 = 0.2

𝑤1 = 0.5 𝑤2 = 0.3, 𝑤3 = 0.2

𝑤1 = 0.4 𝑤2 = 0.3, 𝑤3 = 0.3

Severe brake

𝑤1 = 0.5 𝑤2 = 0.3, 𝑤3 = 0.2

𝑤1 = 0.4 𝑤2 = 0.3, 𝑤3 = 0.3

𝑤1 = 0.2 𝑤2 = 0.4, 𝑤3 = 0.4

𝑤1 = 0.2 𝑤2 = 0.4, 𝑤3 = 0.4

Fig. 7. The electro-hydraulic braking system of distributed electric vehicle.

be found in Hao, Xuexun, and Xiaofei (2018) and Pan, Guo, Pei, and Sun (2019). The value of the weight coefficients depends on vehicle velocity as well as braking intention. Table 1 gives the rules used to set the weight coefficients versus different velocity and braking intention. When braking intention becomes urgent, the value of 𝑤1 decreases, while 𝑤2 and 𝑤3 increase, since greater weight has to be assigned to braking stability. In addition, 𝑤2 > 𝑤3 is used since the braking stability of the front axle is more important than the rear axle. As the vehicle velocity increases, the weighting of braking stability is increased. Hence, the performance of energy regeneration is sacrificed to ensure sufficient braking safety at high speed.

look-up tables of distribution coefficients under various braking conditions. Taking the severe braking as an example, the optimized results of the distribution coefficients with and without braking intention are given as shown in Fig. 6. As shown in Fig. 6(a), the coefficient 𝛽 increases gradually with the increasing severity of braking, and the maximum value is near 0.8. At the same time, 𝛽 is less affected by the vehicle velocity. In addition, it can be seen from Fig. 6(b) and (c) the coefficients 𝛼𝑓 and 𝛼𝑟 decrease with the increase of the vehicle velocity and the severity of braking. In comparison, for the result without braking intention, the three coefficients are smaller and the coefficient 𝛽 is closer to the value of the I curve. That is because the weight of the braking stability is increased when the braking intention is severe. In addition, with the increasing severity of braking, the total braking demand is greater and the maximum regenerative braking torque is limited.

4.4. Search for optimal solution The torque distribution optimization problem is big spaced, multimodel and strongly nonlinear. To solve the optimization, GA was chosen as it is suitable for solving these types of problems. The concept of genetic evolution is introduced in GA to evaluate the quality of the solution using a fitness function, and searching for the optimal solution in the solution space. As an example, Fig. 5 presents the optimized curve of the fitness function and three distribution coefficients. The population size is 50, the number of iterations is 1000, the crossover probability is 0.7, and the mutation probability is 0.01. In addition, the vehicle driving conditions are set including the severity of braking is 0.1, the wheel speed is 700 rpm, and the braking intention is moderate. After 100–200 iterations, three distribution coefficients all reach the optimal value. It shows the fast convergence for GA optimization. The optimal solution is searched by GA with different speed, braking intension and severity of braking, resulting in the construction of four

5. Simulation and analysis 5.1. Simulation of typical braking conditions Fig. 7 shows the overall structure of the electro-hydraulic braking system for a two-axle distributed electric vehicle. A CarSim vehicle model is modified so that the wheels are controlled by hub motors independently (Lu, Chen, & Yuan, 2014), and its parameters are set according to Table 2. In addition, the RC model of the battery and the torque-speed MAP of the motor using the experiment data are built in the Matlab/Simulink. The simulation results of the I curve in a typical braking process is shown in Fig. 8. The initial velocity of braking is 108 km/h, and the severity of braking is below 0.2 for the most of time which lasts about 5 s. From Fig. 8 we can see the maximum torque of the regenerative 6

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Control Engineering Practice 96 (2020) 104324

Table 2 Vehicle parameters. Name

Symbol

Value

Dimension

Wheelbase Height of mass center

𝐿𝑎 ℎ𝑔 𝑅𝑟_𝑓 𝑅𝑟_𝑟 M 𝑀_𝑓 𝑀_𝑟

1890 540 325 325 800 440 360

mm mm

Wheel rolling radius Vehicle mass Axle load

mm kg kg

Fig. 9. The braking torque of GA distribution.

Fig. 8. The braking torque of I curve.

braking at rear axle is only 12.1 N m. The regenerative braking of rear axle is activated only if the severity of braking is less than 0.1. Hence, regenerative braking is employed on the front axle and hydraulic braking is employed on the rear axle during most of braking time. Compared to the I curve distribution, the braking torque of GA distribution has significant difference as shown in Fig. 9. In the whole braking process, both the front-axle and rear-axle take part in the regenerative braking. When the severity of braking is more than 0.2, the regenerative braking torques of two axles reach its peak value. The maximum regenerative torque of front axle and rear axle is 31.4 N m and 33.8 N m respectively, which is much more than the value of the I curve. The proposed GA distribution can adjust the weight coefficient dynamically according to the wheel speed and the severity of braking, which is different than the distribution accordance with the I curve. The curve of utilization adhesion coefficients of front axle and rear axle are shown in Fig. 10 for three different initial vehicle velocities. We can see the GA distribution makes use of the ground adhesion effectively and meets the ECE regulations. In addition, when the severity of braking is 0.1–0.61, 𝜑𝑓 > 𝜑𝑟 which means that the braking distribution between front axle and rear axle is reasonable. At the same time, the curve of 𝜑𝑓 and 𝜑𝑟 are closer to the I curve with the increasing velocity. That is because the weight coefficients 𝑤2 and 𝑤3 increase with the vehicle velocity, the control objective of GA distribution tends to improve the vehicle braking stability under high speed condition. The Fig. 11 gives the stable coefficient and wheel slip rate of GA distribution with the initial velocity of 108 km/h. From Fig. 11, the stable coefficient is kept below 0.05 and the slip rate of four wheels is less than 0.04. That means a good performance of braking stability (wheel slip rate is less than 0.2 for stability usually). In addition, when the severity of braking is 0.8, the stable coefficient decreases to almost 0. At this time, the braking distribution is nearly according to the I curve, hence the braking stability is ensured when severely braking.

Fig. 10. Utilization adhesion coefficient of front axle and rear axle.

Table 3 details a statistical comparison between GA and I curve distribution for a single braking process. Since the value of braking stable coefficient and wheel slip rate are both very small, the braking stability of two control strategies are thought to be almost the same. In the respect of energy recovery, the regeneration efficiency of GA is obviously higher than I curve distribution under initial velocity of 72 km/h. With the increasing velocity, the regenerated braking energy of GA decreases gradually. When initial velocity of braking is 90 km/h, the difference of regeneration efficiency is only 0.9%. The regeneration efficiency of I curve is even higher than GA until 108 km/h, because the weight of energy regeneration is sacrificed to improve the braking safety under high speed condition. The regenerative energy distribution between front axle and rear axle under two control strategies are shown in Fig. 12. For the I curve distribution, the regenerative energy of front axle is more than rear axle, which accounts for 80%–85% of the total regenerative energy. However, the GA distribution has less difference of energy regeneration between two axles. Especially when initial velocity is 72 km/h, the regenerative energy of front axle and rear axle are almost the same, indicating that the energy recovery is more balanced. 5.2. RCP test of driving cycle The next example uses the NEDC to compare the performance between the proposed GA and traditional I curve distribution. The MicroAutoBox is used as a real-time controller which communicates with 7

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Control Engineering Practice 96 (2020) 104324

Table 3 Comparison of two control strategies. Strategy

Initial speed (km/h)

Total braking energy (kJ)

Regenerated energy (kJ)

Regeneration efficiency (%)

Braking stable coefficient

Slip rate of front axle

Slip rate of rear axle

Peak/10−3

Mean/10−3

Peak/10−3

Mean/10−3

Peak/10−3

Mean/10−3

I curve distribution

72 90 108

75.89 103.76 136.14

15.16 16.47 17.06

19.9 15.9 12.5

/ / /

/ / /

40 40 41

16 5 5

25 24 24

7 4 4

GA distribution

72 90 108

76.40 103.88 136.16

17.63 17.39 15.46

23.1 16.8 11.4

45 42 45

35 31 29

41 40 39

16 5 5

25 24 23

7 3 3

Note: According to the definition of the stable coefficient, the theoretical value under I curve distribution is 0, and it is a minimum in simulation.

Fig. 11. The curve of stable coefficient and wheel slip rate.

Fig. 12. The distribution curve of the regenerated energy.

other key components including battery management system (BMS), inwheel motor controller and ECB controller by CAN bus. In addition, the BLDC motor and lithium-ion battery are used in the RCP test platform as shown in Fig. 13 and Table 4. The electro-hydraulic braking torques of two control strategies under NEDC are shown in Figs. 14 and 15 respectively. In the urban condition, the vehicle velocity is less than 50 km/h and the severity of braking is less than 0.1. Hence for the GA distribution, the hydraulic braking is only employed at the end of each brake and the rest of the braking torque is provided by the regenerative braking, as shown in Fig. 14(a). The regenerative braking is sufficient to meet the demand

of total torque except it quits under low velocity. In the suburban condition, the braking torques of front axle and rear axle are provided by the regenerative braking and the hydraulic braking for most of the time. In addition, the hydraulic braking torque of I curve is obviously higher than GA distribution by comparing Figs. 14(b) and 15(b). From Fig. 15(c) we can see the coefficient 𝛽 remains the range of 0.6–0.7. Meanwhile, the coefficients 𝛼𝑓 and 𝛼𝑟 are very close to 1 indicating that the regenerative braking is very high in the proportion of the total torque under the urban condition. However, the coefficients 𝛼𝑓 and 𝛼𝑟 decrease in the suburb condition. The weights are adjusted to ensure braking stability due to the high speed. 8

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Control Engineering Practice 96 (2020) 104324 Table 4 Parameters of hub motor and power battery. Motor Nominal voltage Nominal power Peak power Nominal speed Peak speed Nominal torque Peak torque

Battery 72 8 12 800 1300 140 200

V kW rpm N m

Configuration Capacity Nominal voltage Maximum charging current Maximum charging voltage Maximum discharging current Maximum discharging voltage

20S/73P 201 72 100 83 600 57

/ Ah V A V A V

As shown in Fig. 16, the stable coefficient is less than 0.05 and the wheel slip rate is below 0.03 under NEDC condition. It shows the vehicle has good braking stability by GA distribution for a long driving cycle. Besides, Table 5 gives a quantitative comparison of two control strategies under NEDC and UDDC (Urban Dynamometer Driving Condition) in the respect of braking energy regeneration. We can see GA distribution have better performance of energy regeneration under both two cycle conditions. The energy recovery efficiency which considers total loss of energy are improved by 4.29% and 12.71% compared to I curve under NEDC and UDDC, respectively. From Fig. 17, the results also show GA distribution has more regenerated energy and SOC of battery under NEDC condition. The regenerative energy of front axle

Fig. 13. RCP test platform.

Fig. 14. The braking torque of I curve distribution.

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Fig. 15. The braking torque of GA distribution.

10

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Fig. 16. The stable coefficient and slip rate under NEDC.

Fig. 17. Comparison of regenerated energy under NEDC.

Table 5 Comparison of regenerated energy under driving cycle conditions. Strategy

Cycle condition

Dissipated energy of battery (kJ)

Consumed dynamic energy (kJ)

Regenerated energy (kJ)

Charging energy of battery (kJ)

Energy recovery efficiency (%)

GA distribution

NEDC UDDC

2625.8 919.97

891.36 648.17

534.92 430.36

478.25 390.33

18.21 42.43

I curve distribution

NEDC UDDC

2625.8 919.97

891.36 648.17

418.80 300.01

365.54 273.46

13.92 29.72

Declaration of competing interest

and rear axle are 307.10 kJ and 227.82 kJ respectively, which is both more than I curve correspondingly.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

6. Conclusion This paper focuses on the coordinated control strategy of electrohydraulic braking for distributed electric vehicles. The problem of the composite braking distribution is converted to the optimization of three distribution coefficients. Finally, the look-up tables of the distribution coefficients are obtained by GA under different vehicle velocity, the severity of braking and braking intention. The simulation and RCP results of a short braking situation and a long driving cycle show that, the proposed strategy has better comprehensive performance of the energy regeneration and braking stability compared to the I curve distribution. Besides, the distribution of energy regeneration between the axles is more balanced. Moreover, the braking distribution is more consistent with the driver’s braking demand under corresponding condition, since the real-time braking intention is incorporated into the weight coefficients of optimization objective. In the future, ABS algorithm will be integrated with regenerative braking in emergency condition, and road test is needed considering the uncertainty of signals.

Acknowledgments The authors would like to thank the reviewers and the Associate Editor for their helpful and detailed comments, which have helped to improve the presentation of this paper. References Chiara, F., & Canova, M. (2013). A review of energy consumption, management, and recovery in automotive systems, with considerations of future trends. Proceedings of the Institution of Mechanical Engineers, Part D (Journal of Automobile Engineering), 227(6), 914–936. Economic Commission for Europe (1994). ECE-R13. Geneva, Switzerland: ECE. Gao, Y., & Ehsani, M. (2001). Electronic braking system of EV and HEV - Integration of regenerative braking, automatic braking force control and ABS: SAE Paper, 2001-01-2478. 11

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Control Engineering Practice 96 (2020) 104324 Pennycott, A., De Novellis, L., Gruber, P., et al. (2014). Optimal braking force allocation for a four-wheel drive fully electric vehicle. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 228(8), 621–628. Rauh, Jochen, & Ammon, Dieter (2011). System dynamics of electrified vehicles: some facts, thoughts, and challenges. Vehicle System Dynamics, 49(7), 1005–1020. Sangtarash, F., Esfahanian, V., Nehzati, H., et al. (2008). Effect of different regenerative braking strategies on braking performance and fuel economy in a hybrid electric bus employing CRUISE vehicle simulation: SAE Paper, 2008-01-1561. Sun, F., Liu, W., He, H., et al. (2016). An integrated control strategy for the composite braking system of an electric vehicle with independently driven axles. Vehicle System Dynamics, 54(8), 1031–1052. Wang, Chunyan, Zhao, Wanzhong, Li, Wenkui, et al. (2019). Multi-objective optimisation of electro– hydraulic braking system based on MOEA/D algorithm. IET Intelligent Transport Systems, 13(S1), 183–193. Wu, Jian, Wang, Xiangyu, Li, Liang, et al. (2018). Hierarchical control strategy with battery aging consideration for hybrid electric vehicle regenerative braking control. Energy, (145), 301–312. Xiao, Boyi, Lu, Huazhong, Wang, Hailin, et al. (2017). Enhanced regenerative braking strategies for electric vehicles: Dynamic performance and potential analysis. Energies, 1875(10), 1–19. Xu, W., Zhao, H., Ren, B., et al. (2016). A regenerative braking control strategy for electric vehicle with four in-wheel motors. In Proceedings of the 35th chinese control conference (pp. 8671–8676). Yu, J., Chen, J., & Peng, Y. (2016). Observer-based regenerative braking control for four-wheel-independent-actuated electric vehicles. In Proceedings of the 35th chinese control conference (pp. 8951–8955). Zhang, J., Li, Y., Lv, C., et al. (2014). New regenerative braking control strategy for rear-driven electrified minivans. Energy Conversion and Management, (82), 135–145. Zhang, Lei, Yu, Liangyao, Pan, Ning, et al. (2015). Cooperative control of regenerative braking and friction braking in the transient process of anti-lock braking activation in electric vehicles. Proceedings of the Institution of Mechanical Engineers, Part D (Journal of Automobile Engineering), (229), 1–18. zhou, Zhou, & Miaohua, Huang (2018). Regenerative braking algorithm for the electric vehicle with a seamless two-speed transmission. Proceedings of the Institution of Mechanical Engineers, Part D (Journal of Automobile Engineering), (232), 1–12.

Gong, Xiaoxiang, Chang, Siqin, Jiang, Lichen, et al. (2016). Research on regenerative brake technology of electric vehicle based on direct-drive electric-hydraulic brake system. International Journal of Vehicle Design, 70(1), 1–28. Guo, Hongqiang, He, Hongwen, & Sun, Fengchun (2013). A combined cooperative braking model with a predictive control strategy in an electric vehicle. Energies, (6), 6455–6475. Hao, Pan, Xuexun, Guo, & Xiaofei, Pei (2018). Research on regenerative braking control strategy of distributed EV based on braking intention: SAE Papers, 2018-01-1342. Lee, Wah Ching, Tsang, Kim Fung, Chi, Hao Ran, et al. (2015). A high fuel consumption efficiency management scheme for PHEVs using an adaptive genetic algorithm. Sensors, (15), 1245–1251. Lu, XIONG, Chen, CHEN, & Yuan, FENG (2014). Modeling of distributed drive electric vehicle based on co-simulation of Carsim/Simulink. Journal of System Simulation, 26(5), 1143–1155. Lv, C., Zhang, J., Li, Y., et al. (2015a). Mechanism analysis and evaluation methodology of regenerative braking contribution to energy efficiency improvement of electrified vehicles. Energy Conversion and Management, 92, 469–482. Lv, C., Zhang, J., Li, Y., et al. (2015b). Mode-switching-based active control of a powertrain system with non-linear backlash and flexibility for an electric vehicle during regenerative deceleration. Proceedings of the Institution of Mechanical Engineers, Part D (Journal of Automobile Engineering), (229), 1429–1442. Maia, R., Silva, M., Araújo, R., et al. (2015). Electrical vehicle modeling: a fuzzy logic model for regenerative braking. Expert Systems with Applications, 42(22), 8504–8519. McGehee, Jeffery, & Yoon, Hwan-Sik (2015). Optimal torque control of an integrated starter–generator using genetic algorithms. Proceedings of the Institution of Mechanical Engineers, Part D (Journal of Automobile Engineering), 229(7), 875–884. Meng, Wang, Zechang, Sun, Guirong, Zhuo, et al. (2012). Maximum braking energy recovery of electric vehicles and its influencing factors. Journal of Tongji University, (04), 583–588. Pan, H., Guo, X., Pei, X., & Sun, D. (2019). Pressure controlling of integrated electrohydraulic braking system with considering driver brake behavior. International Journal of Vehicle Design, 79(4), 248–272. Paul, D., Velenis, E., Cao, D., et al. (2017). Optimal mu-estimation-based regenerative braking strategy for an AWD HEV. IEEE Transactions on Transportation Electrification, 3(1), 249–258.

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