Design and Power-Assisted Braking Control of a Novel Electromechanical Brake Booster.
With the development of active safety technology in vehicle, the function of the brake system will no longer be limited to slowing the vehicle. Firstly, acceleration slip regulation (ASR), electronic stability control (ESC), adaptive cruise control (ACC), automatic emergency braking (AEB), and other chassis electronic control systems require the brake system to achieve the function of active braking [1, 2, 3]. Secondly, alternative energy vehicles, such as battery electric vehicles, have created higher requirements for the braking system. The energy recovery system and the release of the vacuum source are great challenges to the traditional braking system [4, 5]. Finally, the intelligent vehicles and the automatic driving vehicles also put forward to the requirement of active braking.
Therefore, brake-by-wire system (refers to the brake systems that human force provides only the braking signal, and the braking energy is usually supplied by other energy supply devices such as high-pressure accumulator or motor torque) represented by electric hydraulic brake (EHB) and electromechanical brake (EMB) has been widely developed [6, 7]. However, for EHB system, there are potential safety problems. For example, the accumulator may cause high-pressure liquid leakage in case of collision, threatening passenger's or driver's safety. At the same time, the arrangement of hydraulic pipeline is complicated. The high cost and the lack of fail-safe make EMB system difficult to obtain the favor of automobile manufacturers.
Then, a novel electric brake booster, comprising a motor, a control unit, and a transmission, is the good solution to satisfy the aforementioned new requirements of braking system. As a novel and available assist actuator, it has also attracted the attention of some researchers. In ref. , an integrated electronic hydraulic brake system with reduction mechanism of worm gear is designed. Though this is a low-cost scheme, it has a poor performance in shock resistance. In ref. , a smart booster system suit for cooperative braking application is proposed, which contains two schemes designed for different applications. In ref. , Hitachi of Japan developed an electrically driven intelligent braking booster system installed on Nissan Fuga Hybrid and Nissan LEAF, aiming to achieve ideal brake force distribution. For E-ACT, a scheme of hollow motor and ball screw was designed with a decoupling function; however, this scheme has complex manufacturing process and occupies a larger clearance. Intended to be applied to automatic drive and regenerative braking, as early as 2013, Bosch proposed a servo hydraulic system-iBooster; there have already been two generations of iBooster so far . The scheme of iBooster is worm gear and gear bar, which has a compact structure and good dynamic characteristic. However, it has slightly worse performance in eliminating the radial forces between the rack and the shell. In summary, many research institutes and producers of foundation brakes have developed prototype of electric brake boosters; however there needs further study and improvement in reduction mechanism and transfer mode of force for the aforementioned scheme.
This article describes a novel electromechanical assist actuator braking system. It is designed to achieve the function of improving pedal feeling, realizing automatic emergency braking (AEB) or active braking, and being independent of vacuum source. EMB booster presented in this article mainly consisted of the permanent magnet synchronous motor (PMSM), a two-stage reduction transmission composed of gear and a ball screw, a servo body, a reaction disk, an input rod, and an output rod. Together with the hydraulic control unit, it has two working modes: active braking for automatic drive and passive braking for driver intervention. In addition, a power-assisted braking control method is presented, which could be divided into three parts: (i) signal processing, (ii) driver's braking behavior recognition, and (iii) precise position controlling of the PMSM. The same characteristic of power assist as vacuum brake booster is achieved by controlling the position and torque of PMSM exactly. However, compared to vacuum brake booster systems, EMB booster has the ability of active braking, regenerative braking, and being independent of vacuum source. Compared to brake-by-wire system, it can also be easily integrated with ABS/ESC, ESP, HEV, and other chassis systems. At the same time, it has advantages of achieving fail-safe with simple components. Therefore, the EMB booster is a kind of ideal device to solve the above problems, and it is widely used in battery electric vehicle and intelligent vehicle.
The rest of this article is organized as follows. In part 2, the structure and work principle of the electric brake booster system is introduced. In part 3, the design process of the control system is described in detail, including the signal processing, the braking behavior recognition, the obtaining of target position, and the position tracking control of the PMSM. In the last, a series of experiments based on RCP environment were implemented to verify the validity of nonlinear controller.
The Electromechanical Brake Booster Structure and Principle
The schematic graph of the integrated EMB booster is shown in Figures 1 and 2. Such a mechanical-electronic-hydraulic system mentioned in this article mainly consisted of PMSM, gears, ball screw, motor angle sensor and current sensor, booster body, and reaction disk. The first-state reduction includes a pinion and a gear. The pinion is connected to the shaft of the DC motor, and the gear is connected to screw nut rigidly. The second-state reduction is achieved by the ball screw. The PMSM, as the power source of the assist actuator, is embedded in the interior of the integrated EMB booster. The ball screw transfers the rotational motion of motor-to-linear motion together with gears. The motor angle sensor and the current sensor are used for the position control of PMSM. With the input rod, it has a direct connection to the driver via the brake pedal. By using the angle sensor, the EMB booster determines the driver's brake request. The necessary boost force is calculated based on the determined driver's brake request and a specific project defined by boost characteristic. Thus the servo body cooperates with the input rod, pushing the reaction disk under the action of the motor. The output rod is connected to the first piston of master cylinder, as the result of generating pressure.
There are two working modes for the electronic brake booster: When the passive brake is applied, the motor torque is used as abooster device to provide auxiliary braking for manpower. Under this working mode, it served as the brake booster function, and the manpower and motor force act on output putter in parallel by reaction disk. The second mode of the electric brake booster is active braking mode; the manpower does not participate in the braking process in this mode. As a pure power supply device, the motor provides braking force for the whole braking system. The transmission route of motor torque is acting on the output rod by the reaction disk directly, forming the braking pressure in the main cylinder.
In active brake mode, such as for the automated driving, we get the lane information and environment information through radar and camera. ADAS upper-level controller makes planning decisions to produce demand braking deceleration. So, the Ebooster realizes the brake deceleration as a lower-level control actuator. An inverse model of the brake system can be realized. Then, the PV map and variable gain PI feedback controller give the referent motor position 9*. Lastly, the position tracking is completed by the electric brake booster controller. Therefore, the active braking control strategy of the electronic brake system can be described in Figure 3. The control variable is transferred from an expected acceleration a* to the wheel cylinder pressure p*, to the motor position [theta]*, to the current of d-axle/q-axle i*, and to the control object.
In passive brake mode, the primary task of the EMB booster is to boost the pedal force of the driver during pedal actuation. With the input rod, it has a direct connection to the driver via the brake pedal. By using a pedal travel sensor, the EMB booster determines the driver brake request for the pedal force boost. The necessary boost force is calculated based on the determined driver brake request and a project-specific defined boost characteristic. In contrast to the vacuum-based system, the EMB booster can adapt the boost characteristic via software, taking system limits into account.
Inspired by the design method of reaction disk in brake vacuum booster, the integrated electromechanical booster chooses reaction disk as the transfer medium of force, where the pedal force and servo force are coupled in parallel. The characteristic of the reaction disk is liquid-like, since it is made of rubber materials. Therefore, the inner pressure of reaction disk is the same everywhere . So the booster ratio (refer to the ratio of pedal force to servo force) of the actuator is related to area ratio between main surface (refer to the action zone of the input rod) and edge surface (refer to the action zone of the servo body) directly, as shown in Figure 4.
The reaction disk would present three states in the process of braking: (i) the deformation of the main surface is the same as that of the edge surface, namely, the two surfaces are flat. (ii) The deformation of the main surface is greater than that of the edge surface, namely, the main surface heaves. (iii) The deformation of the main surface is smaller than that of the edge surface, namely, the edge surface heaves. If it is the flat state, the booster ratio of the actuator is equal to the area ratio of them; if it is the second state, the booster ratio of the actuator is greater than the area ratio of them; and if it is the third state, the booster ratio of the actuator is smaller than the area ratio of them. Consequently, by controlling travel difference of the main surface and edge surface, then the boost ratio can be well controlled.
The vacuum booster has been widely applied in the braking system. So, people are used to its pedal feel. To maintain the driver's accustomed to the pedal feel, the electromechanical booster is designed to the same characteristic curve as the brake vacuum booster, as shown in Figure 5. The black curve represents the applied process and the red curve represents the release process of braking. The power-assisted process is divided into several stages with 0-8 digits . The working state of the feedback disk at each stage corresponds to pictures in Figure 4.
When the driver depresses the brake pedal, a force is generated on the main surface of the reaction disk, and then there will be a deformation of the reaction disk under the human force. The motor will be controlled to generate a force on the edge surface of the reaction disk to eliminate the deformation, so that the human force and motor force work together to push the reaction disk and then push the master cylinder to generate the brake pressure.
In Figure 6, [F.sub.peo] represents the human force, [F.sub.sup]represents the servo force from motor, [F.sub.mas] represents the hydraulic load from master cylinder, and [F.sub.spr] is the force generated from return spring. When the brake system is not in working state, the electromechanical booster is under the stage of the "free state." There exists a clearance between the push rod and the reaction disk, corresponding to the (1) state in Figure 5. Figure 6(b) describes the stage of "before-jump-in," where human force gradually increases to "jump-in-value" so as to overcome the preload of the small spring. Figure 6(c) describes the "jump-in" stage, where human force will hold the value and the output force is increasing. Figure 6(d) describes the "linear power-assisted braking" stage. In this state, the main surface and edge surface remain flat and the booster ratio is the constant. Figure 6(e) describes the "run-out" stage, where [F.sub.sup] reached the maximum and remain unchanged.
So, in the whole power-assisted braking process, the power-assisted characteristic of the electromechanical booster is determined by the relative position between main surface and edge surface.
In order to further study the force characteristic of the reaction disk, a special stiffness test of reaction disk is designed, which describes the relationship between the deformation of the feedback disk and the force (Figure 7). We can get the stiffness curve of the reaction disk by the fitting of the experimental data, which provides a theoretical support for adjusting the booster characteristic. The test is implemented with the device of the reaction disk, the motor cylinder, the position sensor, and other brackets. And the test scheme and result are as follows.
The stiffness curve of the reaction disk is fitted in (1):
[mathematical expression not reproducible] Eq. (1)
The stiffness of reaction disk can be divided into two stages: the nonlinear area for the front and the linear area for the rear. Actually, the nonlinear area is soft and corresponds to the irregular transition section (shown in Figure 5, [R]). The linear area is the reason of achieving linear power assist brake stage.
Control System Design
The schematic diagram of control system mainly consists of three modules: the braking behavior recognition, target position obtaining, and the position tracking control of PMSM, as shown in Figure 8. The braking behavior recognition module is used for judging the braking intention (apply, hold, and release) of the driver via a pedal rod travel sensor. The target position module is used for obtaining the expected travel of servo body. The position controller module is used for controlling the travel of servo body exactly, namely, the angle of PMSM. Next we will explain these three parts in detail.
The signal processing is necessary before other operations are performed. So in this part, a Kalman filter is applied for de-noising and filtering of the signal from the encoder and the pedal travel sensor . Let the original measurement from the travel sensor pass through it, and the output of the filter is the initial target position. For linear system, the Kalman filter could be described as follows:
[mathematical expression not reproducible] Eq. (2)
where [x.sub.k] = [[y.sub.k] [v.sub.k].sup.T ] is the system state vector, [v.sub.k] is the velocity of the pedal stroke, [u.sub.k] is a known input of system, [y.sub.k] is the measured output, and [w.sub.k] ~ N(0, [s.sub.w]) and [z.sub.k] ~ N(0, [s.sub.z]) are the process and measurement noise, which are independent of each other. Here, we define [u.sub.k] as pedal stroke acceleration and [y.sub.k] as measured pedal stroke from sensor. Thus, the stroke and velocity of the pedal can be expressed as
[mathematical expression not reproducible] Eq. (3)
[mathematical expression not reproducible] Eq. (4)
where [T.sub.s] is the sample time and assigned to 0.001 s. Therefore, the state transition matrix in (2) is
[mathematical expression not reproducible] Eq. (5)
The optimal value of state observation in the system could be described as
[mathematical expression not reproducible] Eq. (6)
where [??] and [??] are system predicted and corrected state value. [P.sup.-sup.k+1] and [P.sub.k+1] are the predicted and corrected system state error covariance. [P.sub.k+1] is the Kalman gain. As a result of sufficient iteration under the condition of [u.sub.k] = 0, there are
[mathematical expression not reproducible] Eq. (7)
Braking Behavior Recognition
Different braking behaviors (apply, hold, release) correspond to different target positions and control strategies in this control system. For example, the calibration [DELTA]S (refer to the travel difference between edge surface and main surface) is different in positive travel and negative travel of the brake pedal. So, in order to judge the movement state of the brake pedal accurately, the method of logical threshold is adopted to recognize the brake pedal behavior. The working process is shown in Figure 9. In order to reduce the misjudgment caused by signal fluctuation, the part of consistency detection was added in the algorithm.
Set the flag to indicate the status of pedal as follows:
[mathematical expression not reproducible] Eq. (8)
The value of the flag is decided by setting the threshold [DELTA][S.sub.1] and [DELTA][S.sub.2] and the cumulative number [N.sub.p], [N.sub.p] and [N.sub.n], The misjudgment rate will be smaller with the larger value of [DELTA][S.sub.1], [DELTA][S.sub.2], [N.sub.p], [N.sub.p] and [N.sub.n], but the delay time will also be longer. So, in order to ensure the accuracy of the flag value and a shorter delay time, lots of experiments are implemented to determine the values of threshold and cumulative number. The threshold parameters used in the aforementioned flowchart are shown in Table 1.
Using the above algorithm, the result of the pedal movement state recognition is shown in Figure 10. The maximum value of delay time [t.sub.d] = 0.08 s, which is less than response time. The black line represents the pedal travel and the red line is the direction flag. When the driver applies the brake pedal and the direction is positive, the flag is "1." When the driver holds on, the flag is "0." And when the driver releases the brake pedal and the direction is negative, the flag is "-1." So, results show that the braking behavior is judged accurately by using the logical threshold recognition method.
Target Position Obtaining
In order to obtain the same characteristic curve as the brake vacuum booster, we calibrate a set of AS according to the travel of the push rod to obtain the suitable target positions. Actually, the position of edge surface is equal to the servo body, and the position of main surface is equal to the push rod. Taking the clearance between the input rod and the reaction disk into account, the position of push rod is described in (9), where [x.sub.input] is the travel of input rod. [x.sub.0] is the clearance between the input rod and the reaction disk into account:
[mathematical expression not reproducible] Eq. (9)
Therefore, the target travel [x.sub.target] could be described in (10):
[x.sub.target] = [x.sub.input] + [DELTA]s Eq. (10)
The calibration result based on appropriate power-assisted brake characteristic (according to Figure 5) is shown in Figure 11.
Position Tracking Control of Permanent Magnet Synchronous Motor
As mentioned earlier, we translate the control problem of the power assist brake control to position tracking control. Position tracking control of PMSM is mainly a three closed-loop control. As shown in Figure 12, the control strategy can be divided into three parts: the basic PMSM controller, current distribution, and current compensation decoupling.
For position control of the PMSM, some prior work has followed the approach of a cascaded proportional-integral-derivative (PID) control architecture, which is consisting of an outer-loop position control and inner-loop motor current control . However, the strong nonlinearity and the load-dependent friction make a single PI controller cannot carry the entire operational envelope. So, in order to solve the above problems, we add a feedforward compensation module to the original basic controller.
Then, the modified PI controller of the PMSM is shown in Figure 13, where [w.sub.e] is the error between the desired angular velocity and the actual angular velocity. [K.sub.t] is the torque coefficient. [I.sub.qc] is the compensational current of the q-axle.
Apparently, the total reference current is described in (11):
where [I.sub.qref] is the final control q-axle current, [I.sub.PI] is the decision currents from PI controller, [I.sub.qc1] is the velocity compensation current, and [I.sub.qc2] is the inertia compensation current.
Current Distribution There are two kinds of current distribution control used in this controller: maximum torque current ratio control and flux-weakening control , We adopt the maximum ratio of torque and current control in the constant torque area, and the flux-weakening control strategy was carried out in the constant power area.
When motor mechanical angular velocity is less than the base velocity, it is in the constant torque area, and the maximum torque current ratio control strategy works. In order to make the electromagnetic torque as bigger as possible under the condition of certain stator current, there will be
[mathematical expression not reproducible] Eq. (12)
In Equation 12. [i.sub.s] is stator current vector.
When the motor mechanical angular velocity is greater than the base velocity, it is in the constant power area, and the weak magnetic control works. Due to the constant power, there are
[mathematical expression not reproducible] Eq. (13)
[mathematical expression not reproducible] Eq. (14)
In Equations 13 and 14, [w.sub.r] is mechanical angular velocity and [w.sub.rt] is basic mechanical angular velocity.
Current Compensation Decoupling In the d/q coordinate system, the voltage equation of PMSM is
[mathematical expression not reproducible] Eq. (15)
In Equation 15, [u.sub.d], [u.sub.q] is the q, d axis voltage of the motor. [i.sub.d], [i.sub.q is the q, d axis stator current. [L.sub.d], [L.sub.q] is the q, d axis inductance. W is the rotor electrical angular velocity. [r.sub.s] is the stator resistance.[[psi].sub.f] is the rotor flux linkage.
From the voltage Equation 15. it can be seen that d axis and q axis exist coupling voltage, which will increase with the rise of rotor electrical angular velocity. It will seriously affect the current loop regulation performance during the high speed range. In this article, the current feedback is adopted to compensate current loop, which weakens the effect of the rotating electromotive force:
[mathematical expression not reproducible] Eq. (16)
In Equation 16, [u.sub.q] and [u.sub.d] are the q, d axis voltage of the motor after current compensation decoupling.
Consequently, an accurate position controller is obtained by the above nonlinear method, which is the basic for the power-assisted braking control. Some experiments are designed to verify the position control performance of the PMSM. The test result is shown in Figure 14.
The sinusoidal signals and the step signals are taken as the target positions to verify the performance of the position tracking controller with the technique of current distribution and current compensation decoupling. In Figure 13, the maximum of position tracking error is about 0.4 mm, showing that the position control of the motor performs well. At the same time, we also show the control results of the current distribution algorithm in Figure 13 (c), (d) and (C), (D). The magnetic flux control makes the motor speed enough to achieve satisfactory position tracking. So, test results show that the position controller performs well, providing a guarantee for precise force control.
Experiment Platform and Results Analysis
In order to identify system parameters and verify the controller algorithm, the test bench based on dSPACE was set up. The test platform mainly includes the following parts, and the structural diagram and the full view of test environment are shown in Figures 15 and 16-
1. Signal acquisition part: Pedal travel sensor could gauge the push rod signal which is used as an input part of the control system. Current sensor and motor angle sensor provide a current feedback and travel feedback for the closed-loop control of the motor. Pedal force sensor and the master cylinder pressure sensors are used for detecting control results.
2. Rapid prototype controller platform: The platform mainly includes MicroAutoBox 1401/1512/1513, BOB interface board, and PC. MicroAutoBox is the rapid prototype controller, which can run the Simulink model directly by importing SDF files into the control desk software. The SDF file is the index of the corresponding simulink model. In ControDesk, we can monitor and change model parameters in real time so that an optimal control algorithm is obtained.
3. Driving system: The part includes electric cylinder and its driver. The electric cylinder replaces the brake pedal and works as an input unit that can be controlled conveniently. Tests including various kinds of pedal input rod speeds and travels could be achieved by the electric cylinder.
4. Electromechanical booster system: The system includes an electromechanical booster and motor driver RapidPro from dSPACE. And the electric booster consists of an electric motor and a rotational-to-linear motion mechanism. The motor driver receives PWM signals from the MicroAutoBox to drive the motor.
5. The hydraulic load system: To demonstrate the hydraulic load of a real vehicle as much as possible, we choose the real device and the pipeline instead of the model. The hydraulic load system includes the original brake master cylinder, an ABS valve, brake wheel cylinders, oil tubes, etc.
In order to ensure the same brake feeling as the vacuum brake booster, the contrast tests covering various kinds of pedal rod speeds (3 mm/s, 6 mm/s, 10 mm/s, 20 mm/s, 50 mm/s) and travels (10 mm, 15 mm, 20 mm, 25 mm, 30 mm) are designed and implemented based on RCP environment.
The first picture in Figure 17 shows the power-assisted characteristic of EMB booster at different pedal rod travels. As mentioned above, by combining the pedal travel with calibration AS, the motor is controlled to follow the target position. Two important points are shown in Figure 17 to describe their characteristic quantitatively. The value of "jump-in" point is about 73 N (the B point), and the "run-out" 0point is the point A (624, 3556), where pedal force is about 600 N and output force is about 3500 N. The booster ratio in "linear assistance" stage is 5.9 by the calculation of expression i = [DF.sub.out]/[DF.sub.in]. After the point of "run-out," the servo force of the motor is no longer increasing.
Compared with the conventional vacuum brake booster shown in the second picture in Figure 17. the values of "jump-in" point and "run-out" point are almost the same. The booster ratio of vacuum brake booster in "linear assistance" stage is about 6. The similar characteristic points guarantee the consistency of the pedal feel in the electronic booster and vacuum brake booster. However, the booster ratio of EMB booster can be adjusted via software. What's more, after the point of "run-out," it is very difficult to further increase the brake pressure for the vacuum brake booster. In order to improve the situation, the electronic booster program is designed to achieve greater braking pressure with smaller brake pedal force after the point of "run-out."
At the same time, we have done multiple sets of test made in different pedal travels. Tests show that the consistency is performed well in assistance characteristic, contributing to maintain the driver's sense of braking.
For different applied pedal rod speeds, the assistance characteristic of two kinds of brake boosters is plotted in Figure 18. We also give the characteristic points made in different speeds. The "jump-in" point is the "a" or "a" point, and the "run-out" point is the "b" or "b" point. By comparing the two pictures, it is found that the electromechanical brake booster keep pace with vacuum brake booster at the "jump-in" point and "run-out" point. However, the electromechanical booster shows better stability and consistency in different pedal rod speeds, ensuring a better brake pedal feeling. Therefore, test results show that the performance of the EMB booster system behaves well in consistency of brake assist characteristic.
As mentioned above, the electronic brake booster has two working modes: active braking for automatic drive and passive braking for driver intervention. The previous tests verify the good assist performance in the driver braking mode. The Ebooster can realize the ACC or AEB function for automated driving in active brake mode. In order to verify the pressure control performance of active braking, sine and step pressure following experiments (for simulating the condition of ACC and AEB) are designed and implemented.
As shown in Figure 3, an accurate wheel pressure tracking is the key for active brake of automated driving. Figure 19 is the following result of the sinusoidal target pressure, which can basically reflect the braking requirements of ACC. The maximum pressure tracking error is 0.8 bar, which meets the brake pressure accuracy of ACC function. The second and third pictures are the motor position tracking result and the current tracking result of axis q decided by the mentioned nonlinear controller. The Ebooster controller performs well in position tracking and current tracking.
Figure 20 is the following result of the step target pressure. The purpose is to verify the response speed in the case of automatic emergency braking (AEB). It requires 163 ms for the electronic brake booster to produce 80 bar braking pressure, which is about 200 ms less than the traditional ESC. For example, when the vehicle makes an emergency braking of 60 km/h, the moving distance is reduced about 2 m compared with ESC system. So, the response speed of automatic emergency brake is improved.
In this article, we proposed a novel-assisted actuator of the brake system, which is mainly composed of a PMSM, a two-stage reduction mechanism, a servo body, and a reaction disk. The primary task of EMB booster is to boost the pedal force of the driver during pedal action. The working principle of the electronic booster and the working state of the reaction disk are subsequently stated, which is the key to adjusting the assisted characteristic of the electromechanical booster. Then, for such a mechanical-electronic-hydraulic system, we design a control method to obtain satisfactory power-assisted characteristic, including braking behavior recognition, obtaining the target travel, and position controlling of PMSM, where a Kalman filter and the logic threshold method are designed and applied to the braking behavior recognition. At the same time, a lot of calibration workhas been done to obtain the target position for PMSM. Next, the position tracking control of PMSM is achieved by a cascaded modified PI controller, including the weak magnetic control and current compensation decoupling technology. Finally, a set of experiments covering different pedal rod speeds and travels are carried to verify the performance of EMB booster. Test result shows the similar characteristic with vacuum brake booster but better consistency. And the active pressure tracking performance for ACC/AEB function is also behaving well for automated driving. A further research will be done for the braking energy recovery in the future.
Rui He is an instructor of College of Automotive Engineering at Jilin University. His research interests are mainly in intelligent vehicles and brake-by-wire systems. The email is firstname.lastname@example.org.
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Pengcheng Chen, Jian Wu, Jian Zhao, and Rui He, Jilin University, China
Received: 08 Mar 2018
Revised: 03 May 2018
Accepted: 21 May 2018
e-Available: 28 Dec 2018
TABLE 1 The threshold parameters used in the aforementioned flowchart. Sign Details Valve [DELTA][S.sub.1] First threshold 0.23 [DELTA][S.sub.2] Second threshold 0.3 [N.sub.a] Applying cumulative number 80 [N.sub.h] Holding cumulative number 40 [N.sub.r] Releasing cumulative number 50
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|Author:||Chen, Pengcheng; Wu, Jian; Zhao, Jian; He, Rui|
|Publication:||SAE International Journal of Passenger Cars - Electronic and Electrical Systems|
|Date:||Aug 1, 2018|
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