Stability control of vehicle electro-hydraulic composite braking system based on hierarchical control

Meng-xue LI

(1Changchun Automobile Industry Institute, Changchun 130013,China)(2Education and Training Center,China First Automobile Group Corporation, Changchun 130013,China)

Abstract: Undercomplex working conditions, the vehicle may suffer from sideslip and tail flick problems during an emergency braking. In order to improve the stability of vehicle during emergency braking,an electro-hydraulic composite braking stability control system is proposed.To this end, thehierarchical controlstructure is adopted in this paper. In detail, the upper-loop motion controller gives out the expected state of the vehicle according to the motion parameters and the driver’s intention. And the lower-loop is used to allocatethe braking pressure and the yaw moment with respect to the collaborative control decision-making module. In this way, the stability of the braking vehicle can be properly adjusted. Finally, joint simulation is carried out by Simulink and CarSim. Simulation results demonstrate that, the proposed hierarchical control strategy can guaranteethebraking efficiency, and also improve the directional stability, control accuracy and robustness of the vehicle.

Key words: Electro-hydraulic composite braking, Stability, Hierarchical control, Joint simulation

The distributed drive vehicle gainsthe advantages of short transmission chain, high transmission efficiency, and compact structure, etc.Consequently, a variety of dynamic control functions of the vehicle can be obtained via independent control of motor driving and braking. Meanwhile, the composite control of hub motor and hydraulic brake system, namely a control system with multiple actuators, can improve the stability of the vehicle [1-2]. During the process of braking, the allocation of braking torque is the bottleneckproblem to improve the stability of vehicle braking, which has become afocus in the community.

Dealing with the allocation problem mentioned above, in [3], a composite control strategy was proposed based on the multi-objective braking force allocation method of composite braking system. The modified module was used to allocate the braking force and compensate the motor torque.While, taken the EHB composite braking system into consideration, an optimal braking force allocation strategy was proposed in [4], in which the braking performance, energy recovery efficiency and braking stability were introduced as the performance indexes to formulate the multi-objective optimization problem. On the other hand, in [5], the transmission path of pedal force in normal and failure modes of the braking system was discussed. And the pedal feeling and the corresponding influencing factors in different modes were studied. In addition, the influence factors and extent of pedal force characteristics with respect to stroke distance were simulated by AMESim.

Combing the advantages of both motor braking and hydraulic braking, we propose anelectro-hydrauliccompositehierarchical brakingcontrolstrategyfor distributed drive vehicles under complex working conditions.Briefly, the proposed control system is designed to adjust the stability of vehicles during braking by collecting the motion parameters of vehicle and the driver’s intention in real-time, and then allocating the braking pressure and the yaw moment via the collaborative control decision-making module. Finally, the feasibility of the electro-hydraulic composite brake control strategy is verified through the joint simulation experiment ofSimulink and CarSim.

1 Preliminaries and formulation

1.1 Braking control system

The distributed electric vehicle braking system is driven by four independent wheel hub motors, as shown in Fig.1.

Fig.1 Structure of distributed electric vehicle braking system

In the whole scheme, the Vehicle Control Unit (VCU) collects pedal displacement, wheel slip rate, battery status and other information, meanwhile the vehicle yaw rate, lateral acceleration and steering wheel angle by the corresponding sensors. During braking process, the Regenerative Braking System (RBS) is used to transform the collected brake pedal displacement signal into the driver’s brake force demand, calculate the required brake pressure and yaw moment according to the vehicle motion model and control algorithm, and then allocate the required brake pressure to the hydraulic braking system and motor braking system.Subsequently, the obtained control demands aresent tothe Motor Control Unit (MCU)and the Hydraulic Control Unit (HCU)via the CAN bus. The functions of MCU are designed to control the motor according to the command of regenerative braking forceand then transform the electric energy generated by braking to the Battery Management System (BMS).Meanwhile, the target braking pressure is given by HCU with respect to the command of hydraulic braking force.At this moment, sensors can collect the braking pressure and wheel slip rate of each wheel cylinder, and then feedback the information of vehicle to the VCU. Following the steps mentioned above, the MCU can control the motor torques in real time according to motor braking force command, which carries out a coordinate control strategy with the help of motor braking and hydraulic braking. In this way, the braking requirements are wellmatched[6-7].

1.2 Vehicle dynamic model

In order to analyze the motion characteristics of the vehicle, a 2-DOF four-wheel vehicle model is introduced in this paper, as shown in Fig.2.

Fig.2 Vehicle dynamic model

According to Fig.2, the motion equations of the vehicle and the load of each wheel are given as follows[8-10].

(1)

(2)

(3)

whereδis the input angleoffront wheel,aandbare thedistances from vehicle centroid to the front and rear axles, respectively. Andcis the track width,Lis the wheelbase.F1is the component of tire longitudinal force in the direction of vehicle lateral axis,F2is theaxial component of tire longitudinal force,F3is the tire longitudinal force, andF4is the tire lateral force.vx,vyandhare the longitudinal velocity, the lateral velocity and the height of center of mass, respectively.mis mass of thevehicle.axandayare the longitudinal acceleration and lateral acceleration, respectively.JZis inertiamoment around axisZ,βis the sideslip angle of vehicle centroid andφis yaw rate.

1.3 Tire model

Suppose that the vehicle is braked on the road with a small coefficient of adhesion, the wheel is probably to be locked up. In such situation, the sideslip rate of the vehicle tends to be 100%, which leads to the lateral coefficient of adhesion of the wheel tends to be 0. The slip ratio is an important index affecting driving safety. The formula of the slip ratio is as follows.

(4)

wherevωis the wheel speed,ωis the wheel angular speed andris the wheel radius.

The relationship between the wheel longitudinal and lateral adhesion coefficients and the wheel sideslip rate is shown in Fig.3, where Ⅰ indicates the stable region while Ⅱ is the unstable region. It can be seen that, with the increase of the sideslip rate, the lateral adhesion coefficient of the wheel is decreasing, on the other hand, the longitudinal adhesion coefficient of the wheel increases first and then decreases. Furthermore, we known that the optimal sideslip rate of the wheel is alsoaffected by many factors such as the driving parameters of the vehicle and the adhesion coefficient of the road.

Fig.3 Relation curve between adhesion coefficient and slip rate

2 Control strategy design

2.1 Controller design

According to the vehicle dynamic model (1)～(3) and tire model (4) establishedin section 1, an electro-hydraulic composite brake control strategy based on cooperative control is proposed, as shown in Fig.4.

Fig.4 Vehicle braking stability control scheme

As can be seen in Fig.4, the proposed control strategyis carried out with a upper and lower structure, including the upper motion tracking controller with decision-making ability and the lower control allocationmodule with distribution ability. The motion controller consists of vehicle reference model, vehicle speed tracking module and motion tracking module. And also, the related state parameters are compared and discussed to realize the motion state of vehicle.The control allocator consists of cooperative control decision-making module and control allocation modulefor yaw moment and brake pressure.The collaborative control decision-making module switches the motor/hydraulic brake collaborative control mode in real time according to the vehicle braking demand. Subsequently, the yaw moment control distribution module generates the required yaw moment according to the yaw rate deviation, and then allocates the moment through the control decision. Finally, the brake pressure allocation module distributes the wheel braking pressure optimally according to the control decision.

2.2 Yaw moment control

Taking the difference between the ideal value and the actual value of yaw rate as the control variable of the dynamic stability of the vehicle, the linear proportional control rate is designed as follows[11-12].

(5)

In order to ensure the convergence and anti-interference ability of the proposed control system, the nonlinear compensation control rate is designed as follows.

(6)

Consequently, the control rate of active yaw moment is obtained as follows.

Ms=M1+M2

(7)

whereφdrepresents the actual yaw rate of vehicle,gdindicates the vehicle dynamics control gain, andgcis the stability compensation control gain.

3 Simulation verification

In order to verify the feasibility and stability of the proposed braking control strategy, a joint simulation platform is constructed based on CarSim and Simulink. The dynamic model of vehicle system is introduced from CarSim software which outputs of all kinds of vehicle state parameters and driver operation information required for vehicle braking control. On the other hand, the control strategy model of vehicle is built by Matlab/Simulink software which is used to give out the torque of front wheel motor and the hydraulic braking torque of each wheel.The braking control strategy of the whole vehicle is divided into two layers:the upper layer is the stable tracking layer of vehicle movement, and the lower layer is the specific braking force allocation layer.

Based on the joint simulation platform demonstrated above, the ‘sine stagnation steering’ simulation test is carried out according to the national standard GB/T30677—2014 in China, and the specific simulation parameters are shown in Table 1.

Table1 Simulation parameters

The input signal of steering wheel is given as a sine wave curve with a delay of 0.5sat the second peak value, as shown in Fig.5. For further discussion, the yaw rate, lateral acceleration and sideslip angle of the vehicle are taken into consideration. And the simulation results are illustrated in Fig.6～8.

Fig.5 Input signal of steering wheel

Fig.6 Simulation results of yaw rate

Fig.7 Simulation resultsof lateral acceleration

Fig.8 Simulation resultsof centroid sideslip angle

It can be seen from the simulation results that, the vehicle cannot keep tracking the reference model, and the tracking error of the output results is large when the stability control is not performed in the vehicle braking system. In addition, once the second peak value is reached, the vehicle cannot even converge, which leads to serious instability.Fortunately, the general control method and the proposed control strategyare both effective in the ‘sine stagnation’ test simulation. Moreover, compared with the general control method, the proposed hierarchical control strategy achieves a better tracking performance within a further tracking error decreasing in yaw rate, lateral acceleration and the sideslip angle of center of mass of the vehicle. In such way, the lateral stability of the vehicle has been significantly improved, which demonstrates a better braking efficiency.

4 Conclusions

In order to improve the stability of the vehicle during braking control under complex working conditions, the cooperative control strategy of the electro-hydraulic braking system is taken into consideration, and a hierarchical control scheme of the electro-hydraulic composite braking system is presented. Conclusions are drawn as follows.

Firstly, the 2-DOF four-wheel vehicle dynamic model and the corresponding tire model are established to analyze the state characteristics of the vehicle motion, so as to discuss the factors that affect the vehicle braking performance and provide the performance indexes for further discussion of vehicle braking stability.

Secondly, according to the vehicle dynamic model, a hierarchical electro-hydraulic composite braking control system is proposed, which includes the upper layer motion tracking controller with a decision-making module and the lower layer control allocation module, so as to properly address the problems of wheel motion state collection, driver intention decision and brake torque allocation.

Finally, based on CarSim and Simulink, a joint simulation platform is carried out. Simulation results demonstrate that, the proposed hierarchical cooperative braking strategy achieves high control accuracy, strong anti-interference ability, and also inherits both advantages of motor and hydraulic pressure. In such extent, the proposed braking control strategy not only ensures the braking efficiency, but also improves the directional stability and ride comfort of the vehicle during braking.