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Study on Electronic Stability Program Control Strategy Based on the Fuzzy Logical and Genetic Optimization Method

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Study on Electronic Stability Program Control Strategy Based on the Fuzzy Logical and Genetic Optimization Method Special Issue Article Advances in Mechanical Engineering 2017, Vol. 9(5) 1–13 Ó The Author(s) 2017 Study on electronic stability program DOI: 10.1177/1687814017699351 control strategy based on the fuzzy logical journals.sagepub.com/home/ade and genetic optimization method Lisheng Jin1,2, Xianyi Xie2, Chuanliang Shen1, Fangrong Wang3, Faji Wang2, Shengyuan Ji2, Xin Guan2 and Jun Xu2 Abstract This article introduces the b phase plane method to determine the stability state of the vehicle and then proposes the electronic stability program fuzzy controller to improve the stability of vehicle driving on a low adhesion surface at high speed. According to fuzzy logic rules, errors between the actual and ideal values of the yaw rate and sideslip angle can help one achieve a desired yaw moment and rear wheel steer angle. Using genetic algorithm, optimize the fuzzy control- ler parameters of the membership function, scale factor, and quantization factor. The simulation results demonstrate that not only the response fluctuation range of the yaw rate and sideslip angle, but also the time taken to reach steady state are smaller than before, while reducing the vehicle oversteer trend and more closer to neutral steering. The optimized fuzzy controller performance has been improved. Keywords Sideslip angle, yaw rate, b phase plane method, fuzzy, electronic stability program, genetic algorithm Date received: 21 August 2016; accepted: 21 February 2017 Academic Editor: Xiaobei Jiang Introduction The tire friction circle principle demonstrates that the lateral force margin is less than the margin of the The main reason for traffic accidents is that the vehicle wheel longitudinal force and lateral force, and there- loses stability when driving at high speed. In recent fore, the longitudinal force does not necessarily reach decades, to enhance vehicle stability driving on low saturation. adhesion roads, vehicles were equipped with four-wheel However, as the vehicle goes into the limit-handling steering (4WS), traction control system (TCS), and elec- region and nonlinearity becomes significant at a high tronic stability program (ESP). Although the 4WS can lateral acceleration range, it becomes unstable, unfami- reduce sideslip angle to nearly zero when the vehicle liar to the drivers, and eventually difficult to turns, it becomes less effective when tire’s lateral force approaches the limit of adhesion, and vehicle dynamics 1 show nonlinear characteristics.1 The State Key Laboratory of Automotive Simulation and Control (ASCL), Jilin University, Changchun, China The TCS system was designed to maximize the 2School of Transportation, Jilin University, Changchun, China contact forces between the tires and the road during 3College of Communications Engineering, Jilin University, Changchun, braking and acceleration.2 TCS controls the output China torque of the driving wheels to control the tires’ longi- tudinal force. This is not available in the braking Corresponding author: Chuanliang Shen, The State Key Laboratory of Automotive Simulation condition. Therefore, the application scope of TCS is and Control (ASCL), Jilin University, Changchun 130025, China. limited. Email: [email protected] Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License (http://www.creativecommons.org/licenses/by/3.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/ open-access-at-sage). 2 Advances in Mechanical Engineering Figure 1. Eight-degree-of-freedom vehicle dynamic model diagram. maneuver.3 The active rear wheel steering (ARS) sys- longitudinal, lateral, and horizontal pendulum and tem employs the rear wheel steering angle as the only four-wheel rotation. The corresponding mechanical control input and selects either sideslip angle or yaw analysis of the vehicle is shown in Figure 1: rate as the control target.4 To ensure the stability of the vehicles in the non- Longitudinal movement linear area, one can apply an ESP intervention, which is the use of unsaturated tire longitudinal force on the mvx Àvy Á wr = ðÞFx1 + Fx2 cos d vehicle yaw and lateral movement, thereby improving ÀÁ ð1Þ the vehicle’s turning stability in extreme conditions. À Fy1 + Fy2 sin d + Fx3 + Fx4 ESP generates yaw moment, and direct yaw moment control is the advanced control system used to improve Lateral movement the dynamic performance of road vehicles under various ÀÁ 5–7 road conditions. ESP is introduced to control the yaw mvy + vx Á wr = Fy1 + Fy2 cos d motion and prevent oversteering and understeering.2 ð2Þ Direct yaw moment has a higher ability to stabilize the + ðÞFx1 + Fx2 sin d + Fy3 + Fy4 vehicle motion than active steering control.8 Yawing motion This article introduces the rear wheel steer angle to maintain sideslip angle in an ideal range and then ÀÁ ÀÁ Tf combines the additional yaw moment and rear wheel Iz Á wr = aFy1 + Fy2 cos d + Fy1 À Fy2 sin d steer angle to improve the lateral movement stability. 2 Tf Tr Introduce the b phase method to judge the stability + ðÞFx2 À Fx1 cos d + ðÞFx4 À Fx3 state of the vehicle. The designed ESP fuzzy control- ÀÁ2 2 + ler depends on the result of b_ Àb phase plane method À bFy3 Fy4 ð3Þ to control the vehicle’s stability or not. To overcome Roll motion the limitation of the design flaw of fuzzy controller, using genetic algorithm optimize the parameters and membership function. Simulation test of low adhesion Ixs Á P Àms Á hs Á vx + wr = ms Á g Á hs sin u ÀÁÀÁ ð4Þ road was used to verify the proposed controller À kff + kfr u À Cff + Cfr p performance. Wheel rotational balance equation Vehicle dynamic model Modeling analysis is an important means of control Iw Á w = À Rw Á Fxij + Tdij À Tbij ij ð5Þ theory research. This article required the building of ij = fl, fr, rl, rr the following models: the 8-degree-of-freedom non- linear vehicle dynamic model, the 2-degree-of-freedom vehicle model, and the Gim tire model. Gim tire model The Gim tire model9,10 has the characteristics of quick Eight-degree-of-freedom vehicle dynamic model calculating speed, adaptability, and high precision, The 8-degree-of-freedom dynamic model is utilized especially in case of the large tire slip angle. Its accu- for simulation research. This model includes a racy is far better than that for other tire models. In this Jin et al. 3 Table 1. Sideslip angle of the center of mass of the adhesion coefficient under the limit. Parameter Value m 0.2 0.4 0.5 0.6 0.8 1 bT 2.24 4.48 5.6 6.71 8.91 11.1 section, we selected the Gim tire model to calculate the Taking into account the ground conditions attached longitudinal and lateral forces of the tire. to confront limits, the sideslip angle can be expressed as follows 0 b ma bmax = mg 2 + ð10Þ Desired vehicle model u k2L The linear 2-degree-of-freedom model reflects drivers’ In considering the nominal sideslip angle, the vehicle expected vehicle steering characteristics. Yaw rate is a should reach the value of the sideslip angle taking into crucial signal for the motion control systems of ground account the physical limits at the same time. If the vehi- vehicles. cle sideslip angle reaches the feature value, the vehicle The 2 degrees of freedom in a linear model allows will become uncontrollable and enter dangerous for calculating the vehicle’s yaw rate and sideslip angle conditions. expectations as follows: The desired slip angle response cannot always be obtained when the tire force exceeds the tire’s adhesion Steady-state yaw rate limit. Thus, the desired slip angle has an upper bound, which can be expressed as follows12 u=L wr = Á d ð6Þ À1 1 + K Á u2 bT = tan ðÞ0:02mg ð11Þ 2 where K =(m=L ) Á ((a=k2) À (b=k1)) is the stability From the above formula, we can obtain the adhesion coefficient. coefficient under the center of mass of sideslip angle As the vehicle’s lateral acceleration value cannot limit value, as shown in Table 1. exceed a maximum acceleration determined by the Table 1 shows that the limit of the sideslip angle adhesion coefficient m of the tire and the road surface decreases with an increasing road adhesion friction condition, we have the following formula coefficient. Especially on a low adhesion road, the cen- troid sideslip angle itself is very small and is more diffi- m Á g cult to control precisely, so this article introduced the b w ð7Þ rmax u phase plane law. Therefore, the nominal value of the sideslip angle is The nominal value of the yaw rate can be expressed given by as follows 0 0 bd = minfgjjb , jjb max , jjbT ð12Þ wrd = minfgjj wr , jjwrmax Á sgnðÞd ð8Þ Generally, the reference sideslip angle is given as ESP control strategy zero to ensure stability,11 whereas the reference yaw rate is defined in terms of vehicle parameters, longitudi- ESP can generate the stabilizing yaw moment based on 12 the steering angle, vehicle sideslip angle, wheel speed, nal speed, and the driver’s steering input. 15 A steady-state desired slip angle (see equation (9)) is yaw rate, and lateral acceleration. To improve the deduced based on a 2-degree-of-freedom vehicle model vehicle handling stability, the yaw rate (the yaw velocity in Rajamani.12 However, a zero slip angle is selected for of the chassis) and the sideslip angle (the angle between 13 14 the directions of the velocity and chassis) of the vehicle the desired response in Nagai et al.
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