Antilock braking control system for electric vehicles

: In recent years, brushless DC motors (BLDCMs) have replaced brushed DC motors in the design of electric scooters (ESs). This study proposes a new antilock braking system (ABS) based on a slip ratio estimator for ES utilising the braking force generated by the BLDCM when electrical energy is released to the virtual load, yielding an effect analogous to the ABS control in gas-powered vehicles. Compared with mechanical ABS, the proposed design possesses the advantage of rapid torque responses because no mechanical parts needed. Current control design is used to adjust the braking torque, and the sliding-mode control strategy is adopted to regulate the slip ratio to attain the optimal road adhesion during emergency braking. A variety of experiments are conducted for functional and performance veri ﬁ cation.


Introduction
Vehicle braking under critical conditions such as when wet or slippery road surfaces are encountered or when the driver commits a mistake, usually results in the wheels of the vehicle locking, making the vehicle out of control. Therefore, preventing wheel locking during emergency braking is critical to a safe driving experience, and the antilock braking system (ABS) has thus become standard equipment in modern gasoline-powered vehicles. Various design approaches can be used to improve the performance of ABS, such as sliding-mode control [1,2], fuzzy logic control [3,4], adaptive control [5], genetic neural control [6], and the Kalman filter [7]. A non-mechanical ABS controller for electric scooters (ESs) based on regenerative, kinetic, and shortcircuit braking mechanisms with a boundary-layer speed control was proposed by our research team [8], with two patents granted [9,10]. The approach involves using the ES's approximated speed to calculate the value of the slip ratio. However, the research was limited to simulations, and no real-world implementation was attempted.
Here, ABS design for ESs that has an alternate short-circuit braking function is developed; this design is based on our patented concept claimed in [11]. For the braking mechanism, a brushless DC motor (BLDCM) is directly connected to the ground to provide the largest energy dissipation in an intermittent manner with an extremely short duty cycle with the duty cycle controlled via a sliding-mode controller. The sliding-mode control, which considers the non-linear time-varying dynamics of the ES's slip ratio, is used for realising the ABS function.
We introduce a slip ratio estimator (SRE) that requires no vehicle speed measurement, unlike the conventional approach used for gasoline-powered vehicles. A sliding-mode controller is proposed for regulating the slip ratio to reach the ideal value for road adhesion. Various experiments were conducted to demonstrate the effectiveness of the proposed design.
2 System modelling

Dynamics for electric scooter
A rear-wheel electric drive equipped with a BLDCM propels the rear wheel with a fixed transmission ratio. The dynamics of the BLDCM are simply described as where T m is the driving torque of the driving motor, v m is the angular speed of the motor, J m is the inertia of the motor, B m is the damping coefficient, K m is the torque coefficient, i e is the phase current, and T L denotes the torque due to the payload. Fig. 1 shows the torque balance on the rear wheel, and the dynamic equation is expressed as where J w is the inertia of the wheel, T w is the generated driving torque, T b is the braking torque, B w is the damping coefficient of the wheel, v w is the angular speed of the wheel, r is the radius of the rear wheel, F is the friction force, M is the total mass of the ES, V is the velocity of the ES, and V w = v w r is the tangent velocity of the rear wheel. The transmission system, which has a fixed transmission ratio, can be described as where n is the gear ratio. By substituting (3) and (6) into (1), the equation of motion of the wheel speed can be obtained as where J eq = J m + n 2 J w and B eq = B m + n 2 B w . In (4), the friction force is given by where the slip ratio λ is given by Tyre model is based on Pacejka's magic formula tyre model for motorcycles in general [12,13].

Alternate short-circuit braking
In the case of a BLDCM with three pairs of stator windings, the back electromotive force (back-EMF) is regarded as the power source. It is understandable from the phase current loop generated by the back-EMF. When there is no driving current entering the motor stator and the rotor is still running by inertial rotation, it becomes a power generator with the current generated in the opposite direction to the driving current. By Fleming's left-hand rule, the opposite current would cause a retarding force against motor's forward rotation. One can refer to Fig. 2 for the fact. Consider the current conduction loop shown in Fig. 3; R and L are the inherent resistance and inductance, respectively, and E a,b,c is back-EMF. The alternate short-circuit brake uses the induced current from the motor back-EMF to control the input and output current directions of the three-phase voltage by a full-bridge inverter for generating a virtual loading effect on the BLDCM; the kinetic brake makes the BLDCM connect to a high-power low-resistance resistor for energy dissipation. When the transistors, e.g. S 1 and S 4 ,a r e'ON', the red loop is constructed as the braking current, as shown in Fig. 3. Similarly, transistors S 1 and S 4 , S 1 and S 6 , S 3 and S 2 , and S 3 and S 6 are alternately turned on to implement the alternate short-circuit braking. The electrical energy dissipates in the braking resistor R b which is variable according to the breaking current needed. Electronic components used as a dummy load R b can be a low-resistance resistor or an ultra-capacitor.

Slip ratio estimation
Precise velocity of a vehicle in motion is usually difficult to come by. Here, we formulate an SRE that does not require measuring the vehicle's velocity and acceleration [14].
From (7), the friction force is obtained as Differentiating (9) with respect to time givesl =V w /V − VV w /V 2 . Combining (5), (7), and (10) yieldṡ From the preceding equalities, the unknown variable is observed to be l. Thus, an SRE can be designed aṡ wherel denotes the estimate of the slip ratio. To analyse the convergence of the SRE, the estimation error is defined as e = l −l . The error dynamics is given bẏ Clearly, the estimation error e converges to zero iḟ   Because l is very small, the inequality is close toV w ,V (2 +l ). During vehicle braking, becauseV w ≤ 0,V ≤ 0, andV w ≤V (wheel stops before the vehicle), and because l is very small, (15) can be satisfied.

Control design
Here, a wheel-slip controller is designed to achieve a target slip ratio for a given driving condition. The ABS design utilises the braking force generated from the BLDCM of the rear wheel when electrical energy is released to the dummy load as the braking action occurs. A proportional-integral (PI) current controller is designed to determine the pulse-width modulation (PWM) duty cycle at each sampling instant according to the difference between braking and reference currents. Furthermore, a slip-ratio sliding-mode controller is proposed for calculating the reference current as the reference input to the PI current controller (Fig. 4).

Control for slip ratio
Sliding-mode control is an effective method for controlling a nonlinear plant and is a simple approach to overcoming the control problem [1,2]. Here, a sliding-mode controller is designed to regulate the slip ratio to attain optimal road adhesion. The design procedure for the sliding-mode controller comprises two steps: first, a sliding surface that models the desired tracking performance is defined. Then, a control law for forcing the state trajectories towards the sliding surface is developed. Equation (11) can be rearranged as follows:l where The sliding surface is selected as s = cl, where c is a constant, l = l − l idl with l idl being the ideal value of l. Differentiating s with respect to time givesṡ = cl.
(17) Fig. 4 Overall braking control scheme By equating (17) to zero, the equivalent control can be obtained as To satisfy the sliding condition, the total control law is set to be with β being a constant.
In real-world applications, the system parameters are frequently uncertain. Considering the major system uncertainty, the control where u 2 is to be determined, and and b 0 (l, t) = −1 where M 0 = 0.5(M max + M min ), with M, M min , and M max denoting the nominal, lower, and upper bounds, respectively. The system equation can be expressed aṡ To satisfy the sliding condition, let us consider We This can be specified based on the specifications given above.

Current control
PI current controller is designed to track the reference current computed by the slip-ratio sliding-mode controller. The input to the PI current controller is e i = i ref − i fdb , where e i is the difference between the reference and feedback currents, i ref is the reference input, and i fdb is the feedback braking current. The PI current controller with antiwindup before saturation is given by where the proportional term u p (t) = K p e i (t) and the integral term u i (t) = (K p /T i ) e i (6)d6 + K c (u(t) − u presat (t)), with u presat (t) being the output before saturation, u(t) the output of the PI-derivative controller, K p is the proportional gain, T i is the integral time, and K c is the integral correction gain. A block diagram of the PI current controller with antiwindup correction is shown in Fig. 5. Digital signal processor (DSP) is used to determine which transistors should be ON according to the Hall signals that are used to determine the rotational speed of the motor. On the basis of the feedback commands received, the DSP calculates the duty cycle to adjust the braking force and thus regulate the slip ratio to attain the ideal value for road surface adhesion.

Experimental setting
Block diagram of the designed system is presented in Fig. 6. The parameters used for simulating the control of the braking current are listed in Table 1.
The ES's initial speed was set to be 30 km/h. The PI current controller is designed to track the reference current determined by the slip-ratio sliding-mode controller as described in Section 5. The kinetic energy, however, may decrease during the braking process. The duty cycle (i.e. the percentage of time for which current flows over the sampling period) for braking current regulation was increased to maintain the optimal slip ratio. Fig. 7 shows the PI current control command with a reference current of 40 A for the braking mode.

Simulation results
Sliding-mode controller is designed to determine the appropriate braking force for maintaining the ideal slip ratio. Braking was simulated on three road surfaces: dry road, loose gravel road, and icy road. The ideal slip ratio values of the three road surfaces are 0.2, 0.18, and 0.15, respectively. Suppose that the mass of the ES Thus, its geometric mean isb = b min b max = 0.9487, and therefore, Figs. 8-10 show the simulated results for slip ratio control on dry, loose gravel, and icy road surfaces, respectively. The slip ratio is kept close to the ideal value on the icy road surface, and the braking current follows the reference current for the first 2.8 s. Because the wheel speed drops thereafter, the back-EMF is not sufficient to support the braking current. The ES speed decreases accordingly, and the ES steering cannot be controlled well. The braking current does not follow the reference current after 3.8 s, and the ABS is inactive because of the decrease in kinetic energy. This shows that the present approach performs satisfactorily on the dry and gravel surfaces but not on the icy surface.

Real-world experimental results
For the friction coefficient between the tyre and dry road surface, the appropriate slip ratio for optimal road adhesion is nearly −0.2. When the proposed design was used, the actual slip ratio converged gradually to the preset value of −0.2 during braking, as shown in Fig. 11a. The braking current followed the reference command because of the sliding-mode control, as illustrated in Fig. 11b. Fig. 11c shows the duty cycle for braking current regulation, which was adjusted by the PI current controller. Fig. 11d shows the deceleration of the wheel angular speed after braking.
Please visit the website [15] for experiments we have conducted in the lab and real-world condition. In the first video, description of the system hardware and fundamental experimental tests in a platform installing a single driving wheel are presented. In the second video, we have compared the braking performance of the traditional mechanical brake (under the situation of fully locked brake) and the proposed ABS design on the road with smooth and rough surfaces. Fig. 12 and Table 2 present performance of our proposed design. It can be seen from the video clip, how the proposed design avoiding the rear wheel from siding during emergency braking.

Conclusions
This paper proposes ABS control design for ESs based on an SRE, which utilises braking torque generated by BLDCM when regenerated energy is released to a virtual load. Mathematical models of the BLDCM and SRE were formulated for theoretical analysis of the braking behaviour. Braking performance of the ES was experimentally validated; the electrical ABS operates well because of the faster torque response of the BLDCM when the ES moves on roads with different surface adhesion. Extensive    . 12 Comparison of the slip ratio between the proposed brake (left) and the mechanical brake (right)