2nd International Conference on Electronic & Mechanical Engineering and Information Technology (EMEIT-2012)

Transcription

1 nd International Conerence on Electronic & Mechanical Engineering and Inormation echnolog (EMEI-) Design o Bod Sli Angle Obserer or Vehicle Stabilit Control Liu Minghui, Zhang Yongsheng,a, Chu Liang, Wei Wenruo Cai Jianwei, Zhang Lei R&D Center, China FAW Co., Ltd., Changchun, China State Ke Laborator o Automobile Simulation and Control, Jilin Uniersit, Changchun, China a zhangongsheng@rdc.aw.com.cn Kewords: Bod Sli Angle; Lateral Velocit; Vehicle Stabilit Control; Obserer Abstract. Bod sli angle is imortant or Vehicle Stabilit Control. Due to using sensors to measure bod sli angle is er eensie, it is necessar to estimate it rom other ariables measured easil. A noel method based on non-linear robust obserer is roosed or estimation bod sli angle. Firstl, ull-dimension obserer designed based on aw rate and lateral acceleration to estimate lateral elocit. And then, the bod sli angle is estimated b using lateral elocit and longitudinal elocit. he roosed method is eriied b oline simulation. he results demonstrate that this method has a better adatabilit to dierent driing conditions and accurac. Introduction In order to achiee the ehicle stabilit control, the aw rate ψ and bod sli angle β are generall used as the control reerence ariables []. Yaw rate can be measured directl, but the bod sli angle is estimated through the other ehicle motion state arameters, such as steering wheel angle, lateral acceleration, aw-rate, etc [], because it is diicult to measure directl with low cost [3]. hereore, looking or a kind o bod sli angle estimation method with high recision and good real-time has become a ke research roblem o stabilit control. Bod sli angle estimation methods can be briel summarized into two categories: ) estimated b combinations o the dierent tes o inertial sensors; ) sli angle estimated b using the inertial sensor combined with ehicle dnamics model. According to reious research results and the second categor, based on tire cornering stiness online identiication, a robust ull-dimension obserer or estimating ehicle lateral elocit is designed. he lateral elocit and longitudinal elocit are combined to estimate the bod sli angle, and its schematic diagram is shown as Figure. It can be seen rom Figure, the bod sli angle estimation strateg is described as three arts: lateral elocit estimation, tire cornering stiness estimation and bod sli angle estimation. ψ δ C α,i a ψ δ β Fig bod sli angle estimates diagram Lateral elocit estimation. In this aer, a robust ull-order obserer [4] is used to design the car lateral elocit obserer and the robustness o the obserer gain. Lateral elocit Obserer design. Lateral elocit obserer design adots a simliied two-degree-o-reedom ehicle model: m =m ψ + F, + F. r () J ψ = l F l F + M () z a, b. r z 357

2 nd International Conerence on Electronic & Mechanical Engineering and Inormation echnolog (EMEI-) Wherein the lateral orce is eressed as: F = C α α i =, r (3) i,, i i + laψ α = δ (4) lbψ αr = (5) B ormula () to (5), the equation o state o the sstem is as shown: = A + Bu (6) Where: δ = ψ, u = M z Cα, + Cα, r lb Cα, r la Cα, m m a a A = a3 a = 4 lb Cα, r la Cα, lb Cα, r + la C α, Jz Jz Cα, b b m B = = b b la Cα, Jz Jz B the ormula (6), the sstem in the ehicle driing rocess ( ) is alwas considerable; When =, the ehicle stos and the sstem is not obserable, then the lateral elocit estimation alue is set to zero directl. In the model, tire cornering stiness is etremel an imortant arameter. he changes o the road surace riction coeicient and tire load will make it change and when the tire entering the nonlinear o μ λ cure, cornering stiness will change greatl. his change will make the model do not match the actual state o motion, which is unaorable or the robustness and conergence o the designed obserer. It must be online identiication or the tire cornering stiness, the identiication method use least-squares estimation, estimation methods are as equation (7) to (): = θ (7) Where: = θ = C α, ζ ( la + lb) δst ( la + lb) ζ = ψ m ( ζ la lb) m ( ζ la lb) ire cornering stiness can be estimated using recursie least-squares method b taking equation λ (7) into the equation (8) to (). Where: RLS is orgetting actor. ˆ ˆ Pk ( ) k ( ) θ( k) = θ( k ) e ( k) (8) λrls + ( k) P( k ) ( k) e ( k) = ( k) ˆ θ ( k ) ( k) (9) Pk ( ) k ( ) ( k) Pk ( ) Pk ( ) = Pk ( ) () λrls λrls + ( k) P( k ) ( k) When constructing lateral elocit obserer outut equation, signals o ESP sensors or lateral acceleration and aw rate are needed. hese two signals hae the ollowing relationshi: 358

3 nd International Conerence on Electronic & Mechanical Engineering and Inormation echnolog (EMEI-) a = + ψ () Using the equation (6) and (): a = a + ( a + ) ψ + b δ () he sstem outut equations can be ormulated as: = C+ Du (3) a Where, a ( a + ) = ψ, b C =, D = he ull-dimension state equation and its outut equation o the sstem obserer are as ollowing: ˆ = Aˆ+ Bu K( ˆ ) (4) ˆ = Cˆ+ Du Where, K -obserer gain matri; ˆ -the estimation o ; Estimation error o It should meet the equation: e = ( AKC) e (5) is e ˆ =. S Fig Schematic diagram o lateral seed ull-order obserer he robust o the lateral elocit obserer design. he alue o the obserer gain matri K is ke to the robustness and stabilit o the obserer. here are two asects which need to be considered about: Reduce the imact o the model error as much as ossible to the lowest leel; Ensure that the characteristic alues o the matri ( A KC) are located in the stable region. Comarison o ormula () and (3),the estimated alue o : ˆ = a ˆ + a ψ ˆ + b δ k ( ψˆ ψ ) k ( aˆ a ) (6) he actual alue o with no error: = a + a ψ + b δ (7), r, r, r a,r a,r b,r Where,,, reresent the real alues o the model arameters ecluding an error. Using the equation (6) and (7): ˆ ˆ = a ( k) ( ) + ( k) ( a a, r) + ( k) ( b b, r) δ + ( k ) ( a a, r) ψ (8) + [ a ( k) k ] ( ˆ k ψ ψ ) As or equation (8), in order to increase the robustness o the lateral elocit obserer, ( ˆ ) should be ensured. Considering ( ψ ˆ ψ ), the ollowing equation must be ulilled: k = k = (9) So,based on ole lacement and robustness, the alue o gain matri K is shown as [6] : 359

4 nd International Conerence on Electronic & Mechanical Engineering and Inormation echnolog (EMEI-) ( a+ ) a a a a K = a a + () Where, and are oles o the obserer, its alues are restricted b: ) must be negatie real number, otherwise obserer is unstable; ) when absolute alues are large, the resonse o the obserer is ast but anti-jamming is weaker; 3) when absolute alues are small, the resonse o the obserer is slow but anti-jamming is stronger. Based on the aboe conditions, it meets the requirements o resonse seed and has a good anti-jamming caabilit b adjusting the alues o in the dierent oerating conditions. Final estimation o bod sli angle. he longitudinal elocit ˆ and the lateral elocit ˆ are got through the longitudinal and lateral elocit obserer. bod sli angle is ormulated as the ollowing equation: ˆ ˆ β = arctan ma( ˆ, c) () Where, c reresents a constant greater than zero to reent zero diided in the calculation rocess. Finall bod sli angle is got ater iltering and comensation. Simulation he control algorithm is established in the MALAB/Simulink, and eriied b simulation. Figure 3, 4, and 5 show most simulation results under dierent working conditions. he actual alue reresents the measured alue o the sensor in real ehicle simulation. he measured alue is used as an accurate alue or the estimation. he estimated alue is the result o this algorithm s estimated alue. As shown in igure 3, 4, and 5, estimated alue and actual alue hae a good consistent tendenc with little error. It can be seen that the designed estimation method can eectiel estimate bod sli angle in dierent conditions. Bod sli angle (rad) Actual alue Estimated alue ime(s) Fig 3 he simulation results o double lane on high adhesion road 36

5 nd International Conerence on Electronic & Mechanical Engineering and Inormation echnolog (EMEI-) Bod sli angle (rad). -. Actual alue Estimated alue ime(s) Fig 4 he simulation results o double lane on low-high adhesion road Bod sli angle (rad) Actual alue Estimated alue ime(s) Results Fig 5 he simulation results o the snake-like conditions his aer is in the light o the roblem that ehicle bod sli angle is diicult to measure directl with low cost; A nonlinear robust obserer or bod sli angle was designed b using inertial sensors and ehicle dnamics model. hrough MALAB/Simulink modeling and simulating, the design o the algorithm was tested and eriied. he results show that the obserer has a high leel recision, and has a better adatabilit to dierent working conditions as well. Reerence [] Van Zanten A. Eolution o electronic control sstems or imroing the ehicle dnamic behaior[c].avec., : [] Hu Ai Jun, Shi Guo Biao, Lin Yi. Estimation o Automobile Steering State Parameters [J]. Journal o Highwa and ransortation Research and Deeloment, 8, 5(): [3] Fu Hao. Research on Sidesli Angle Estimation and Control Algorithm or Vehicle Electronic Stabilit Sstem [D]. Jilin Uniersit, Changchun, China., 8. [4] oshihiro Hiraoka, Hiromitsu Kumamoto, Osamu Nishihara. Side sli angle estimation and actie ront steering sstem based on lateral acceleration data at centers o ercussion with resect to ront/rear wheels[c]. JSAE, [5] Florin Moldoeanu, Mihai Cernat, Marius Georgescu, Dan Floroian. Vehicle Bod Side Sli Angle Obserer[C]. SAE: [6] Aoki, Y., Uchida,., Hori, Y. Eerimental demonstration o bod sli angle control based on a noel linear obserer or electric ehicle[c]. IECON, 5,