Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 137 (16 ) 34 43 GITSS15 Vehicle Strategies Analysis Based on PID and Logic Hui-min Li a, *, Xiao-bo Wang b, Shang-bin Song a, Hao Li a a Research Institute o Highway Ministry o Transport, Beijing 188, China b China ational Construction Machinery Quality Supervision Testing Center, o.55 Dong Wai Street YanQing City Beijing 11, China Abstract Two degrees o reedom vehicle dynamic model is established. Based on theories o PID control and uzzy logic control, controller o vehicle stability is designed by using the method o direct yaw moment control and the dierent control strategies. By comparing and analyzing control eect o PID control and uzzy logic control, the result shows as ollows: slip angle and yaw rate combined control is better than slip angle and yaw rate controlled individually by comparing control eect; uzzy logic control have a better robustness and PID control is simple and practical by analyzing control theories. Dierent control methods can be used in the same control systems according to the need o practical application. The result can improve and enhance passenger car maneuverability and stability control and also can give some reerence in a way. 16 Published The Authors. by Elsevier Published Ltd. This by Elsevier is an open Ltd. access article under the CC BY-C-D license (http://creativecommons.org/licenses/by-nc-nd/4./). Peer-review under responsibility o the Department o Transportation Engineering, Beijing Institute o Technology. Peer-review under responsibility o the Department o Transportation Engineering, Beijing Institute o Technology Keywords: Vehicle dynamic; strategies;pid control; AutoTurn; logic control. 1. Introduction Vehicle Stability (VSC) is developed during the 9 s. It s a new active saety control system with a better maneuverability and stability by regulating and matching tire longitudinal orce when vehicle is steering or under the lateral orce. For tire nonlinear characteristic, main methods o vehicle maneuverability and stability control are developed rom our-wheel steering control (4WS) initial to direct yaw moment control and active ront steering control (AFS). In particular, DYC has become a more eective method in vehicle maneuverability and stability *Corresponding author. Tel.: +-1-67977. E-mail address: huimin.li@rioh.cn 1877-758 16 Published by Elsevier Ltd. This is an open access article under the CC BY-C-D license (http://creativecommons.org/licenses/by-nc-nd/4./). Peer-review under responsibility o the Department o Transportation Engineering, Beijing Institute o Technology doi:1.116/j.proeng.16.1.55
Hui-min Li et al. / Procedia Engineering 137 ( 16 ) 34 43 35 control. According to the dierence control strategies, yaw rate, slip angle, lateral acceleration tire slip ratio and combination o them are used as control variables [1]. The application o control theories is developed rom PID control, optimal control and adaptive control to variable-structure control system with sliding mode, uzzy logic control and artiicial neural network control and so on. Two degrees o reedom ( DOF) vehicle dynamic model is established. Slip angle and yaw rate are used as control variables based on control method o DYC by using control theories o PID and uzzy logic control. The characteristics and eect o dierent control theory and control strategy are compared and analyzed by simulation.. Establishment o Vehicle Model system is designed based on two degrees o reedom liner vehicle model [,3]. Vehicle movement dierential equations are given as ollows: M V( r) Y Yr I r Y l Yr lr (1) Where, M is mass o vehicle, V is vehicle velocity, Y is lateral orce o ront tire, Yr is the lateral orce o rear tire, is side slip angle, r is yaw rate, I is inertia o vehicle around the vertical axis moments, l and lr are the distance between the center o mass with ront axle and rear axle. Equations about lateral orce o tire are given as ollows: rl Y k V rlr Yr kr V () Transer unctional equations o two degrees o reedom liner vehicle model are given though Laplace transormation shown as Equ. (1). Where, s r s 1s 1 Gr s Ts Ts 1 1 1s 1 G s Ts Ts 1 1 1 V ; A 1 AV l G r m l K lr K r ; ml V 1 ; T l K K lk r r miv 4K Krl 1 AV ; mv l K lr Kr IV K Kr T1 K K l 1 AV. Raw rate o two degrees o reedom liner vehicle model can be used as vehicle nominal yaw rate, as shown in Equ. (4). r (3) lk KrV 1 V K K l mv l K l K 1 AV l r r r (4) Vehicle ideal raw rate must be restricted by road adhesion coeicient and satisied the constraints as ollowed on the condition o lateral orce in tire adhesion limitation.
36 Hui-min Li et al. / Procedia Engineering 137 ( 16 ) 34 43 a g y (5) When slip angle is very small, lateral acceleration can be expressed as ollows: ay r V (6) Vehicle ideal yaw rate must be satisied the ollowing equation. r g V (7) ominal yaw rate is shown as Equ. (8). g r min r V (8) Slip angle o two degrees o reedom liner vehicle model can be used as vehicle nominal slip angle, as shown in Equ. (9). 1 m l V K K l mv l K l K K Krllr mv K l llk r r lr 1 r AV l r r (9) Considering the restriction between tire and maximum road adhesion coeicient, slip angle is expressed in Equ. (1). lr m l lr m l V g V lkr V lkr (1) The ollowing equation can be derived rom Equ. (1). lr m l lr m l max max V g V lkr V lkr (11) ominal slip angle should be the minimum absolute value between and max. min, max (1) The design o control system is based on two degrees o reedom liner vehicle model. As it is based on dierent control algorithms applying yaw moment to vehicle, two degrees o reedom liner vehicle model is corrected as ollows. M V( r) Y Yr I r Y l Y l M z r r z (13)
Hui-min Li et al. / Procedia Engineering 137 ( 16 ) 34 43 37 Where, Mz is additional yaw moment 3. Design o System 3.1. PID control o yaw rate Feedback control o yaw rate is shown in Fig. 1. Yaw rate sensor is used to transit the dierence between vehicle yaw rate and nominal yaw rate to controller [4,5]. When input variables changed, yaw moment will be adjusted by controller. Then brake orce is distributed to every wheel. Increasing PID control algorithm is used and its equations are given as ollows: e i (14) M K e e K e K e e e (15) P i i1 I i D i i1 i Ideal model * e ler Vehicle Systems Fig. 1. Feedback control o yaw rate 3.. PID control o slip angle Feedback control o slip angle is shown in Fig.. Slip angle is used as control variable in most vehicle stability control systems. The dierence between ideal slip angle and the actual one is used as input to controller. e i M K e e K e K e e e P i i1 I i D i i1 i (16) (17) Ideal model * e ler Vehicle Systems Fig.. Feedback control o slip angle 3.3. logic control Result o double road train turns let on irst class highway intersection simulation is shown in Fig. 8. Feedback control o uzzy logic is shown in Fig. 3.The error e and its rate ec o dierence between yaw rate and nominal yaw rate are used as input variable o uzzy logic controller, output variable is yaw adjusted moment M [6]. The error e and its rate ec o dierence between ideal slip angle and the actual one are used as input variable o uzzy logic controller, output variable is yaw adjusted moment M, as shown in Fig.4 (Zhu, 5).
38 Hui-min Li et al. / Procedia Engineering 137 ( 16 ) 34 43 According to the need o uzzy logic controller design, quantiicational ield o uzzy variables EEC and U is deined as ollows [4]. e M d dt e Algorithm Judgment Vehicle Systems Fig. 3. logic control o yaw rate Algorithm Judgment Vehicle Systems Fig. 4. logic control o slip angle The uzzy sets o E and EC are deined as {B, M, S, ZE, PS, PM, PB}. The uzzy set o U is deined as {ZE, PS, PM, PB}. Universes o them are deined as: E and EC [-.1, -.8, -.6, -.4, -.,,.,.4,.6,.8, 1]; U [,.1,.,.3,.4,.5,.6,.7,.8,.9, 1]; E and EC [-.1, -.8, -.6, -.4, -.,,.,.4.6,.8, 1]; U [,.1,.,.3,.4,.5,.6,.7,.8,.9, 1]. In order to make universe o variable error e, error rate ec and control variable u to correspond the standardization, quantization actor and scale actor are deined as ollows. The quantization actor o variable error is deined as Ke=e-1. The quantization actor o the error rate is deined as Kec=ec-1. The scale actor o control variable is deined as Ku=u-1. Triangular membership unctions are adopted to input linguistic variable and output linguistic variable, which operates simply with a better eect o simulation and a higher precision, as shown rom Fig. 5 to Fig.7. Fig. 5. Membership unction o error E The rules o uzzy logic control can be expressed by conditional statement o i then, which represent decision result derived rom many change premises. In general, uzzy logic control orm is used to express those rules, as shown in table 1. Two inputs have seven uzzy linguistic variables separately, so there are 49 rules in total as ollows. Rule 1i R is R and RC is R then U is PR Rule i E is B and EC is M then U is PB Rule 49i E is PB and EC is PB then U is PB
Hui-min Li et al. / Procedia Engineering 137 ( 16 ) 34 43 39 Fig. 6. Membership unction o error rate EC Fig. 7. Membership unction o control variable Table 1 Rules o uzzy control U EC B M S ZE PS PM PB E B PB PB PB PB PB PB PB M PB PB PM PM PM PB PB S PB PM PM PM PM PM PB ZE PM PM PS ZE PS PM PM PS PB PM PM PM PM PM PB PM PB PB PM PM PM PB PB PB PB PB PB PB PB PB PB Where, B is egative Big; M is egative Medium; S is egative Small; ZE is Almost Zero; PS is Positive Small; PM is Positive Medium; PB is Positive Big. Method o Mamdani is used or uzzy logic control, and max-min is used or uzzy reasoning, bisector o area is used or deuzziication method. control toolbox in Matlab is used or uzzy logic controller. Input and out input surace o uzzy controller is showed in Fig. 8. Fig. 8. Input and output surace o uzzy controller
4 Hui-min Li et al. / Procedia Engineering 137 ( 16 ) 34 43 3.4. Combined control In general, PID control can t get the ideal control eect or interered by the method o control parameter adjustment. variable o yaw rate in PID control should be adjusted in uzzy logic controller. In practice, slip angle is estimated and yaw rate can be measured by the sensor. So the error o yaw rate can be used or PID controller input parameter, error o slip angle can be used or uzzy logic controller input parameter. The system structure o combined uzzy PID control is showed in Fig. 9. Increasing PID control algorithm is used or PI control [5]. M K P e i K e I i PID control parameters K P and K I are adjusted by uzzy controller real-time. Ideal Model PID ler Vehicle Systems (18) ler Fig. 9. Combined control 3.5. Threshold control Based on the algorithm o yaw rate PID control and slip angle uzzy control, combined PID uzzy logic controller is established about yaw rate and slip angle, as shown in Fig.1. The controller doesn t aect their independence but only increases control o the threshold rules. When vehicle need to brake, controller control slip angle to satisy constraints and control vehicle s driving by yaw rate PID controller. When slip angle doesn t satisy constraints, it is necessary to control vehicle s driving by slip angle uzzy logic controller. All above is based on steady tolerance. 4. Simulation Analysis Medium vehicle is selected as simulation test vehicle. Vehicle speed o 7 km / h and the steering wheel angle o 7 deg in the angle step input are set. The solid line o simulation curves is original with no control, the dashed line is obtained by control. 4.1. PID control PID control simulation o yaw rate and slip angle is shown in Fig. 11 and the comparison o response index is shown in table. * e * e Fig. 1. Combined control Threshold control
Hui-min Li et al. / Procedia Engineering 137 ( 16 ) 34 43 41.14.5.1.1 -.5 r.8.6.4. (rad) -.1 -.15 -. -.5 -.3 1 3 4 5 6 -.35 1 3 4 5 6 Fig. 11. PID control simulation Table Response index o PID control Yaw Rate Max Overshoot (%) Slip Angle Max Overshoot (%) o.1.134 9.91.336.34 1.7 PID.11.113.46.94.87.5 Yaw rate steady value o PID control decreases 1.7%, overshoot decreases obviously. Step time also decreases obviously, the reaction speed increases obviously. Slip angle steady value o PID control decreases 1.5%, overshoot increases slightly. Step time increases obviously, the reaction speed decreases obviously. 4.. logic control Result o double road train turns right on second class highway intersection simulation is shown in Fig. 1. logic control simulation o yaw rate and slip angle is shown in Fig. 1 and the comparison o response index is shown in table 3. Yaw rate steady value o uzzy logic control decreases 14.5%, overshoot increases obviously. Response time decreases obviously, response speed increases obviously. Yaw angle velocity o vehicle steady value o uzzy logic control decreases 14.75%, overshoot increases slightly. Response step time increases slightly, response speed increases obviously. 4.3. Combined simulation Result o double road train turn around on second class highway intersection simulation is shown in Fig. 13. shown in Fig. 13 and the comparison o response index is shown in table 4..14.5.1.1 -.5 -.1 r (rad).8.6 (rad) -.15 -..4 -.5. -.3 1 3 4 5 6 -.35 1 3 4 5 6 Fig. 1. logic control simulation
4 Hui-min Li et al. / Procedia Engineering 137 ( 16 ) 34 43 Table 3 Response index o uzzy logic control Yaw Rate Slip Angle Max Overshoot (%) Max Overshoot (%) o.1.134 9.91.336.34 1.7 Logic.14..17..87.95.7.14.5.1.1 -.5 r (rad).8.6 (rad) -.1 -.15 -..4 -.5. -.3 1 3 4 5 6 -.35 1 3 4 5 6 Fig. 13. Combined control simulation Table 4 Response index o combined control Yaw Rate Slip Angle Max Overshoot (%) Max Overshoot (%) o.1.134 9.91.336.34 1.7 Logic.11.11.79.79 Yaw rate steady value decreases 17.4% in combined control, overshoot increases obviously. Response time decreases obviously, response speed increases obviously. Slip angle steady value o uzzy logic control in combined control decreases 17.7%, overshoot decreases obviously. Response time increases slightly, response speed decreases slightly. 4.4. Threshold control Threshold control o PID control and uzzy logic control simulation o yaw rate and slip angle is shown in Fig. 14 and the comparison o response index is shown in table 5..14.5.1.1 -.5 r.8.6.4. (rad) -.1 -.15 -. -.5 -.3 1 3 4 5 6 -.35 1 3 4 5 6 Fig. 14. Threshold control simulation
Hui-min Li et al. / Procedia Engineering 137 ( 16 ) 34 43 43 Table 5 Response index o threshold control Yaw Rate Slip Angle Max Overshoot (%) Max Overshoot (%) o.1.134 9.91.336.34 1.7 Logic.988.13 4.66.87.93.7 Yaw rate steady value o PID control in logic threshold decreases 19.8%, overshoot decreases slightly. Response time decreases obviously, response speed increases obviously. Slip angle steady value o uzzy logic in logic threshold decreases 14.75%, overshoot increases slightly. Response time increases obviously, response speed decreases obviously. 5. Conclusion Conclusions can be drawn rom steering wheel angle step input simulation, there are no control theory and control strategy which can run all the conditions o the vehicle and achieve a good eect. But or general operation condition, it is necessary to study a more eective theoretical method and control strategy. For example, when the vehicle is skidding and instability, it s necessary to impose yaw moment control. It can control the size o slip angle and yaw rate eectively. In this situation, lateral acceleration will not exceed the limit o later surace attachment. I ully meet the above conditions, the control is better; basically satisied, the control eect is in general; not satisied, the control is less eective. Slip angle is relative large when the vehicle is in the middle and high velocity, vehicle shows mainly dynamic characteristics. The main purpose o control is or stability, so yaw rate control can achieve a better control preerence. With the increasing o angle, the result will become bad when control separately yaw rate. In the high adhesion coeicient road, combined control can control slip angle and yaw rate eiciently and satisy the dynamic characteristic. Reerences [1]Zhou, H.., 7. Study on Vehicle Stability Strategy, Journal o Hubei Automotive Industries Institute, 1,6-31. []Yu, Z.S.,. Automobile theory (The third edition). Beijing: Machinery Industry Press [3]Abe, M., 1998 Vehicle movement and manipulation, Machinery Industry Press [4]Yao, S.Y., 8. Study on vehicle stability control system, Xihua University, pp.16-7 [5]Yang, S.Z., Yang K.C., 5. Mechanical Engineering Basis, Huazhong science university Press [6]Zhu, J., 5. Theory and System Principle, Machinery Industry Press