Advanced Control Functions Of Decoupled Electro- Hydraulic Brake System

Fig. 3. Controller layout for the decoupledelectro-hydraulic brake system. Legend: ABSact - ABS activation key, Fbrkped – Brake pedal force applied by driver, fcorr – Correction factor, mest – Estimated vehicle mass, pest,ij – Estimated brake pressure, sped – Brake pedal travel, Tbrake – Brake torque delivered from brake system, Tdistr,ij – Distributed brake torque demand, Tdem – brake torque demand, Tjud,ij – Brake judder attenuation torque, Tsup – Base pedal assistance demand, Ttotal – Total torque demand to brake force distribution, Tw,dem,ij – Torque demand in base-braking mode, Tw,ij – Torque demand to the brake system, Tw,react,ij – Reactive torque, Vx – Estimated vehicle velocity, δsw – Steering wheel angle, λact,ij – Estimated wheel slip ratio, λref,ij – Reference wheel slip ratio, θroad – Estimated road grade, dψact/dt – Actual yaw rate, ωij – wheel speed This controller part is responsible for performing the ABS functions though keeping the wheel slip ratios of the wheels close to the reference value in continuous mode. Such approach can significantly improve not only the braking performance, but positively influence on the longitudinal ride comfort of the vehicle [22]. Finally, the reactive torque is subtracted from the demand Tw,dem,ij and the torque request Tw,ij is delivered to the EHCU. In the presented paper functions of the split-µ and reference slip ratio generation are omitted due to the paper size limitations. All of the aforementioned functions are joint in one brake system controller, Fig.3, performing their contributions without negative interaction and providing simultaneous enhancements in vehicle performance and ride comfort. IV. RESULTS OF ADVANCED BRAKE CONTROL A. Continuous wheel slip control The controller is designed using the integral slidingmode (ISMC) and PID controller [23]. Such approach confirms applicability in vehicular systems (e.g. yaw rate control in [24, 25]) avoiding the chattering specific for the conventional sliding-mode control (SMC) approaches. The control torque is derived as follows: Tw,react Tw, PID Tw, sw, f , (1) where Tw,PID is the control action from PID and Tw,sw,f is the filtered control action of: Tw,sw K sign ( s ) , (2) where K is the control gain and s is the sliding variable. The reactive torque should be saturated according to the current value of the torque demand and thus requires the anti-windup function: 1 Tw, PID K P λe ( t ) λe ( t ) t D λ e ( t ) tI , (3) 1 (Tw,dem ( t ) Tw,react ( t ) ) dt ta where Kp, tI and tD are the parameters of PID and Tw,dem is the wheel torque demand. The control error is derived as follows: λact λref 0 λe , λact λref , λact λref , (4) where λact and λref is the actual and reference value of the wheel slip ratio. The results performed in real-time simulation are showing promising results in term of the performance and robustness. As represented in Fig. 4, the controller achieves smooth and precise tracking of the wheel slip ratio on low-, medium- and high-µ surfaces. As consequence, system provides maximally possible level of the deceleration according to the current friction limits.

Fig. 4. Vehicle and wheel speeds for on (a) low-, (b) medium- and (c) high-µ surfaces (from top to bottom respectively) Important to admit, that the chattering of the control signal is avoided applying this control strategy, providing applicable pressure demand to the EHCU, Fig. 5. The proposed control strategy shows not only the required robustness of the ABS operating properly in different road conditions (low-, medium- and high-µ), but also showing promising results in real-time simulation in terms of the braking performance (reduction of the braking distance up to 13.2% on low-µ surface). Fig. 5. Pressure demand generated by the controller on (a) low-, (b) medium- and (c) high-µ surfaces (from top to bottom respectively) B. Disturbance rejection The motion control at the braking is affected by disturbances of different nature. They can have short-term and long-term character of influence. The short-term disturbances as abrupt change of tyre-road friction or side wind cause unpredictable dynamics and are critical for safety. In such situations the driver has limited possibilities to correct the vehicle motion at braking. The long-term disturbances as brake pad wear have influence not only on the safety but also on the driving comfort because they can change the brake pedal feel. The rejection of external disturbances in the discussed decoupled EHB system can be realized through the correction of the brake pressure or brake torque demand. The following procedure is proposed for this purpose.

The brake pressure demand for individual wheel brake pi is defined as pi Tbr dem / ( 2 Awc η reff μL ) pout , (5) where Tbr dem is the actual brake torque demand, Awc is the effective area of wheel caliper, η is efficiency factor of the wheel caliper, reff is the effective friction radius of the brake disc, µL is the brake lining friction coefficient, pout is the base output brake pressure. The actual brake torque demand is calculated from the reference vehicle deceleration ax ref: Tbr dem m ax ref rw , (6) Fig. 6. Experimental definition of reference deceleration where m is the vehicle mass, rw is the dynamic wheel radius. The value of reference deceleration ax ref is practically calculated from the brake pedal travel, Fig. 6. However, the actual vehicle deceleration ax act is usually not equal to the reference value, in particular, due to the disturbances. When the ax act is deduced from the vehicle model m ax act Fx act Faero Froll Fgrade , (7) then the compensation can be realized through certain compensation factor m a x ref f comp Fx act Faero Froll Fgrade . (8) where Fx act is the actual total longitudinal force of the vehicle, and Faero, Froll and Fgrade are the aerodynamics, rolling and grade resistance forces correspondingly. Practically, the compensation factor can be calculated from Eq. (8) using the recursive least squares method y mˆ ax act ; φ Fx act Faero Froll Fgrade ; θ 1/ f comp (9) and then applied for the compensating brake torque to be produced by the EHB system: (f comp 1) Tbr dem Tbr comp . (10) The described method has been validated and investigated on experimental facilities connecting the brake dynamometer and hardware-in-the-loop platform with the installed EHB system, Fig. 7. The applied test procedure in accordance with standard ISO26867 “Friction behaviour assessment for automotive brake systems” allows to emulate the brake fading effect, when the lining friction coefficient µL is being changed during several consecutive braking maneuvers. Fig. 7. Brake dynamometer (top) and HIL platform (bottom) with installed EHB system Fig. 8 shows the time profile for the µL parameter during fifteen braking applications with deceleration of 0.4 g from the initial velocity of 100 km/h in each case. The resulting reduction of friction coefficient deteriorates the brake pedal feel that can lead to the wrong formulation of the brake demand by the driver. Fig. 6 confirms this fact - the integral of time-multiplied absolute value of error (ITAE) between ax ref and ax act increases for each subsequent braking in the case of non-compensated system operation. On the contrary, the EHB operation with activated compensation mechanism continuously recalculate the correction factor from Eq. (9), Fig. 8, and changes the compensating torque from Eq. (10) in

a stepwise manner. As a result, the ITAE is reduced on more than 75% to the end of the test procedure as compared with the non-compensated operation. Hence, the developed control function for the disturbance compensation prevents the loss of brake efficiency and maintain the preset brake pedal feel (interpreted as dependence between the demanded vehicle deceleration and the brake pedal displacement). Fig. 10. Amplitude spectrum of the brake torque variation profile Fig. 8. Comparison of the deceleration deviation from desired value Fig. 11. Brake torque variation compensation using the EHB systems at various frequencies without (black) and with (red) brake judder compensation TABLE I. Frequency [Hz] Fig. 9. Compensation factor calculated by disturbance compensator C. Brake judder attenuation One of the most important aspects to be considered by the brake development is the presence of critical oscillation processes in different frequency ranges. In particular, geometric unevenness of a brake disc causes the brake torque oscillations, which are perceived by the driver and affect the driving comfort. Fig. 10 shows a typical amplitude profile of brake torque variation caused by the disc thickness variation. This phenomenon is also known as the brake judder [26]. In conventional systems the judder can be reduced mainly through the passive measures connected with the design changes of the brake components. However, decoupled EHB systems give an opportunity to realize an active attenuation of the brake judder because they have high bandwidth tracking performance for the clamp forces on brake calipers. COMPARISON OF RMS OF BRAKE TORQUE VARIATION RMS of brake torque variation [Nm] Compensated No compensation 1 7.38 12.32 2 7.55 12.55 3 9.11 12.65 4 9.12 12.68 5 10.22 12.78 To introduce the judder attenuation control, the brake torque can be presented in the following form: Tbr 2 μ L reff Fwc Tbtv (θ d ) , (11) where Fwc is the clamp force from the brake caliper, Tbtv is the brake torque variation due to discrepancy θd from friction coefficient estimation error and disk rotational position. In accordance with Fig. 7 the first harmonic of the brake torque variation has the largest first amplitude, followed by several smaller amplitudes. Then a disturbance model can be constructed as follows: Tbtv (θ d ) n a k 1 k cos(kθ d φ k ), (12)

where ak and φk are the amplitude and phase-shift of the k-order harmonic. For this model the following adaptive compensator mechanism, based on the method from [27], is proposed: pi ref Γ EHB (ωd , ω d ) Φ (θ d ) γˆ 1 Tbr ref 2 μˆ rd Awc [3] [4] [5] , (13) [6] where ΓEHB is the feedforward gain matrix. The developed attenuation control has been tested on the HIL platform, Fig. 7, where the brake torque profile is taken form the experimental data obtained from the brake dynamometer tests. Fig. 11 compares the total brake torque without and with compensation. Numerical comparison is given in Table 1. It can be seen that the application of the first-order compensator reduced the recursive mean square tracking error from 20% up to 40% for 5 and 1 Hz. This fact confirms a good feasibility for the decoupled EHB system in attenuation of compensate for low-frequency periodic oscillations, which cause the brake judder. V. CONCLUSIONS The presented paper demonstrated a number of advantageous in the use of the decoupled electro-hydraulic brake system. The benefits concern in particular: Reduction of the braking distance with simultaneous improvement of ride comfort by application of the continuous wheel slip control strategy; [7] [8] [9] [10] [11] [12] [13] Improvement of the system robustness in ABS mode by utilization of ISMC; [14] Consistent brake pedal feel independently from the external disturbances with the use of brake pedal feel simulator on hardware level and brake pedal assist in the controller; [15] [16] Attenuation of the judder with adaptive control applicable for this brake system architecture; [17] Required level of the system reliability by avoiding the control effects overlap in different operational modes. 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Fig. 3. Controller layout for the decoupledelectro-hydraulic brake system. Legend: ABSact - ABS activation key, Fbrkped - Brake pedal force applied by driver, fcorr - Correction factor, mest - Estimated vehicle mass, pest,ij - Estimated brake pressure, sped - Brake pedal travel, Tbrake - Brake torque delivered from brake system, Tdistr,ij - Distributed brake torque demand, Tdem .