1215畢業(yè)設(shè)計(jì)汽車制動外文翻譯(外文)

1、Nonlinear Dyn (2014) 76:125138 DOI 10.1007/s11071-013-1115-1ORIGINAL PA PER 注意：此外文來自讀秀搜索，配合“1215張杰畢業(yè)設(shè)計(jì)汽車制動外文翻譯（漢語）”使用，本人親自人工翻譯！Robust control of wheel slip in anti-lock brake system of automobilesTohid Sardarmehni · Hossein Rahmani ·Mohammad Bagher MenhajReceived: 3 November 2012 / Accepte

2、d: 9 October 2013 / Published online: 6 November 2013© Springer Science+Business Media Dordrecht 2013Abstract In this paper, performances of two model- free control systems including Fuzzy Logic Control (FLC) and Neural Predictive Control (NPC) on track- ing performance of wheel-slip in Anti-lo

3、ck Braking System (ABS) are compared. As an accurate and con- trol oriented model, a half vehicle model is devel- oped to generate extensive simulation data of the brak- ing system. Brake system identification is preformed through a Perceptron neural networks model of brake system which is trained w

4、ith offline data by Gradi- ent Descent Back Propagation (GDBP) algorithm. In order to reduce the time cost of the calculations and improving the robustness of closed loop control sys- tem, an online Perceptron neural network adaptively generates the optimum control actions. By a compara- tive simula

5、tion analysis it is shown that the NPC sys- tem has a better tracking performance, shorter stop- ping time and distance than the FLC controllers. The robustness of the proposed control systems are eval- uated under ±25 % uncertainty. It is shown that the NPC system is more robust against both e

6、xogenous disturbances and modeling uncertainties than the FLC system.T. Sardarmehni (B) · H. RahmaniFaculty of Mechanical Engineering, University of Tabriz,Tabriz, Irane-mail: t.sardarmehni88ms.tabrizu.ac.irM.B. MenhajDepartment of Electrical Engineering, Amirkabir University of Technology, Teh

7、ran, IranKeywords ABS · NPC · FLCAbbreviationsFLCFuzzy Logic Control NPCNeural Predictive Control ABSAnti-lock Braking SystemGDBP Gradient Descent Back Propagation ECUElectronic Control UnitSMCSliding Mode control MPCModel Predictive Control MLPMulti-Layer Perceptron MAE Mean Absolute Erro

8、rMATE Mean Absolute Tracking ErrorVehicle brake system parametersVVehicle velocity m/sWheel angular velocity rad/sgGravity acceleration m/s2RRadius of tire mJfMoment of inertia of front wheel kg m2JrMoment of inertia of rear wheel kg m2a Distance from center of gravity to front axle mb Distance from

9、 center of gravity to rear axle mhfHeight of front unsprung mass mhsHeight of the sprung mass mhrHeight of rear unsprung mass mmfFront unsprung mass kgmsSprung mass of the vehicle kgmrRear unsprung mass kgRobust control of wheel slip in anti-lock brake system of automobiles129Fig. 1 Friction coeffic

10、ient versus wheel slip 2mtotTotal mass of the vehicle kgPiHydraulic pressure kPaPpConstant pump pressure kPa PlowConstant reservoir pressure kPa Cd1Build valve coefficientCd2Dump valve coefficient AwcWheel cylinder area m2 hMechanical efficiencyBFBrake factorrrEffective radius of braking disk mCfCoe

11、fficient of flowKbrBrake displacement proportionality constant1 IntroductionReducing required stopping time and distance in brak- ing has always been one of the most important control goals in designing the braking systems of automobiles. Without any control on angular velocity of wheels, an ordinar

12、y braking system exerts dissident fixed brak- ing torque on wheels. This fixed torque causes abrupt decrease in wheel angular velocity with a greater rate than the vehicle speed which results in wheel lock- ups during braking. Through locking-up, friction co- efficient and road adhesion become small

13、er which re- duces the active-applied braking torque on tires. As the result, the stopping time increases and vehicle stops after a longer distance. Furthermore, directional stabil- ity of vehicle would considerably degrade. To prevent wheel lock-ups and their probable catastrophic conse- quences du

14、ring severe braking, ABS has been intro- duced to automotive industry. The main idea in ABS is controlling the active brake torque so that prevents wheel lock-ups. This procedure results in generation of maximum negative acceleration of vehicle while thedirectional stability and steering ability of

15、vehicle is guaranteed 1.In order to generate the maximum negative acceler- ation of vehicle, the longitudinal force should be kept around its peak value which requires the friction force to be at its peak amount 2. Researches show that the value of the friction coefficient greatly depends on road co

16、nditions. As shown in Fig. 1, the peak value of friction coefficient varies from 0.02 to 0.43 in different road conditions 2.In general, two different strategies are used to con- trol the braking torque in ABS for preventing wheel lock-ups. The first method is based on wheel deceler- ation. In this

17、method no information from vehicle ve- locity sensors is required. However, the operating load from the road cannot be used completely in wheel de- celeration method. The second method uses wheel slip ratio, defined by the ratio of the difference between wheel linear velocity and vehicle speed over

18、vehicle speed. The second method uses the oil pressure in an actuator to regulate the braking torque. This regulation is preformed as the wheel slip ratio tracks a predefined value regarding the friction coefficient peak value in different road conditions 3, 4.PI-controllers, which are commonly used

19、 in ABS of automobiles, require long time calibration process and would not function effectively in the presence of exogenous noises and disturbances. Furthermore, the performance of a PI controller is not satisfactory robust to the vehicle brake model severe nonlineari- ties, structured or unstruct

20、ured uncertainties, and time- varying dynamics due to variation of road and vehicle conditions. Nowadays, regarding the advancements in microcomputer industry, the intelligent and adaptive control techniques could be implemented in Electronic Control Units (ECU) of vehicles. Besides the signif-icant

21、 transient and steady-state performances, these controllers are adjusted simply and also are robust to the uncertainties 5.As the state of the art in the designing of ABSs, FLC and neural networks have been used. Regarding satisfactory transient and steady-state performance of the FLC in nonlinear t

22、ime-varying systems, signifi- cant research has been performed on these control sys- tems. Mauer designed a FLC system applied on a quar- ter vehicle model which could identify different road conditions. The proposed FLC system could generate action brake signals through considering current and past

23、 values of the brake pressure and slip ratio 6. Zhang et al. developed a FLC system by consideringdata to estimate vehicle speed. The estimated vehi- cle speed was used for predicting the amount of slip. The proposed controller calculated the modified brake torque signal based on the predicted the a

24、mount of wheel slip 11. Jacquet et al. proposed a MPC system to generate the optimal brake torque. The online recon- struction was done based upon estimation of the brake adhesion torque and estimation of the wheel speed. Furthermore, the necessity of wheel speed sensors for identifying the tire/roa

25、d characteristics was avoided by using a torque sensor located in the wheel. The simulation results showed that the proposed controller had a fast and stable response under rapid changes of the road conditions. Moreover, the designed controllerddd and ( d )/dt as inputs of the controller. The pro- p

26、osed FLC system led to better performance in pedalpushing feeling 3. Sharkawy developed a self-tuning PID controller which was accompanied by Fuzzy and Genetic algorithm to obtain the optimal modules of the designed FLC. The results showed that the proposed controller had a fast response with low ov

27、ershoot and short stopping distance 7.As a model-based nonlinear control system, the Sliding Mode control (SMC) systems are preferred due to their fast and the ease of their application on the nonlinear models. Besides the possibility of fast im- plementation, the robustness and the stability of SMC

28、 could be guaranteed in most applications 8. There has been much research work on application of SMC systems in ABS. Harifi et al. designed a SMC sys- tem for ABS which used integral switching surface for reducing the chattering effects 9. Half vehicle model was used so the designed controller provi

29、ded two separated brake torques for front and rear wheel. Furthermore, the results of this controller were com- pared with those of a Fuzzy, a self learning Fuzzy slid- ing mode and a neural network hybrid controller. It was stated that the designed controller had the shortest stopping distance. How

30、ever, the neural network hybrid controller had the least amount of wheel slip tracking error regarding to other controllers 9.Model Predictive Control (MPC) is a control tech- nique that tries to minimize the tracking error through predictions of the future outputs of a plant which de- fines the pre

31、diction horizon 10. Due to the robust and stable performance of this control system, it has al- ways attracted the attention of control engineers. An- war and Ashrafi presented a MPC system for ABS. The presented method required wheel speed sensorscould satisfactorily shorten the stopping distance 1

32、.In this paper, half vehicle model is used for gen- erating the simulation data of a braking system. Two different model-free control techniques including FLC and neural network MPC systems are developed. For a better assessment, the overall performance of the pro- posed FLC and MPC systems are comp

33、ared. A neu- ral network-based algorithm is developed in the MPC system to generate the brake torque through track- ing a modified desired slip trajectory. In the MPC system, identification of the half vehicle brake sys- tem model is performed by a Multi-Layer Perceptron (MLP) neural network for the

34、 front wheel. In order to improve the identification error and cope with the se- vere time-varying dynamics of the vehicle brake sys- tem model, a small data collection sample time is used for collecting the training patterns of the neural net- works. In order to increase the calculation speed of th

35、e MPC system, the brake system identification is per- formed by an offline MLP model. Training process of the MLP neural network model of the brake sys- tem is performed with offline data by Gradient De- scent Back-Propagation (GDBP) algorithm. In order to accelerate the computations in the MPC syst

36、em, the prediction horizon is shortened. To accelerate the op- timization and improve the robustness of the control system, adaptive strategy is used in the optimization of the MPC system. In the NPC system, an online MLP neural network is adaptively designed to generate the optimum values of brake

37、torque such that predicted amount of slip in the NPC tracks its modified desired value. Here, GDBP algorithm is used for the online training of the MLP system in the controller. At the end, robustness of the designed FLC and NPC systems against modeling uncertainties and input disturbancesFig. 2 Fre

38、e-body diagram of the half vehiclemodel 12are evaluated by imposing 25 % Gaussian noises. Be- tween the proposed model-free control systems, it was seen that the NPC system is more robust than the FLC system. The simulation results showed that the control action input is a smooth signal in the desig

39、ned NPC.The normal force can be considered as the difference between the vehicle mass distribution and mass trans- fer of the vehicle during acceleration or deceleration. The normal force due to vehicle mass distribution can be formulated as 12Besides, the stopping time and distance is shorter inbth

40、e NPC system than the FLC control system.The entire program is running in MATLAB/simu- link software.Fzf 1 = a + b (mtotg)aFzr1 = a + b (mtotg)(4)2 System dynamicsThe second part of the normal force on front wheel is obtained from using the conversion law of moment on rear wheel as 122.1 A half vehi

41、cle dynamic modelComprehensive vehicle models including all parame- ters are not control oriented models due to their com- plexity and highly nonlinearity. Therefore, a simpli- fied dynamical vehicle model that possesses all the(a + b)Fzf 2 = (mfhf + mshs + mrhr)VDividing both sides to (a + b), one

42、hasF= (m h + m h + m h )Vzf 2f fs sr r (a + b)(5)(6)main characteristics of vehicle systems is considered.A free-body diagram of the half vehicle model is shown in Fig. 2.Applying the same procedure on the front wheels, thenormal force of rear tire can be defined asVAs shown in Fig. 2, steering effe

43、cts and drag force are not considered in modeling to avoid complexity. The total traction force can be presented as 12Ftot = Fxf + Fxr(1)Fzr2 = (mfhf + mshs + mrhr) (a + b)The normal forces of tires are defined as 12Fzf = Fzf 1 Fzf 2(7)In (1), Fxf and Fxr are, respectively, the front and rear longit

44、udinal tire-road contact forces and are definedb= a + b Vmtg (mfhf + mshs + mrhr) (a + b)(8)as 12Fzr = Fzr1 Fzr2Fxf = (f)Fzf(2)a V Fxr = (r)Fzr(3)where Fzf and Fzr are the normal forces acting on the front and rear wheel. (f) and (r) are friction coef- ficients between road and front/rear tires, res

45、pectively.= a + bmtg + (mfhf + mshs + mrhr) (a + b)Through some substitutions, the total traction force is obtained as 12Ftot = (f)(m1g m3V ) + (r)(m2g + m3V ) (9)Dry asphalt1.280123.990.52Dry cobblestones1.37136.45650.6691Dry concrete1.197325.1680.5373Wet asphalt0.85733.8220.347Wet cobblestones0.40

46、0433.7080.1204Snow0.194694.1290.0646Ice0.05306.390Fig. 3 Front-wheel free-body diagram 12Table 1 Constant values for different road condition 2 Road conditionC1C2C3wherem1 =bmtotand Fzr in (14) and (15), angular acceleration for front wheel and rear wheel would be defined as1f .m2 =a + b aa + bmtot(

47、10) f = 2J1Tbf + (f)m1gR (f)m3RV + Te(16)m3 =mfhf + mshs + mrhra + b r =2Jr. Tbr + (r)m2gR + (r)m3RV .(17)In (10), is the wheel slip which can be formulated for the front and rear wheel as 12Since the main goal is controlling the wheel slip, thedefined state variables in this paper are vehicle veloc

48、- ity, the front and rear wheel slip (x1 = V and x2 = ff =r =V fRVV rRV(11)and x3 = r). Consequently, the state-space equations could be defined as 12x1 = V = f1(x2, x3)Wheel slip changes from 0 to 1 which indicates com-pletely rolling tire on the road without any slip andx2= f bfwheel lock-up, resp

49、ectively. Mostly, wheel lock-ups happen during deceleration while the angular veloc-f1(x2, x3)(1 x2) Rf2(x2, x3) + RT2Jf=V(18)ity of wheels becomes zero. Burckhardt tire friction model is used to describe the relationship between thex3 = rRTbrfriction coefficient and wheel slip 2:f1(x2, x3)(1 x3) Rf

50、3(x2, x3) +=V2Jr() = C1.1 eC2. C3(12)where C1, C2 and C3 are constants which depend onwheref1(x2, x3) = g (x2)m1 + (x3)m2road condition. Table 1 shows the different value formtot1 (x2)m3+ (x3)m3various road conditions.By assuming the front wheel to be the driver one, the engine torque only acts on t

51、he front wheel. Free- body diagram of the Front-wheel is shown in Fig. 3. Applying Newtons second law along the horizontalf2(x2, x3) =f3(x2, x3) =2Jf 12Jr.(x2)m1Rg (x2)m3Rf1. (19).(x3)m2Rg (x3)m3Rf1.direction one has 12mtotV = Ftot(13)2Jf f = Tbf + (f)Fzf R + Te(14)2Jr r = Tbr + (r)Fzr R(15)In (14),

52、 Te represents the engine torque which would become zero during deceleration. By substituting Fzf2.2 Dynamics of the hydraulic brake modelThe structure of a standard hydraulic brake actuator is shown in Fig. 4. There are two solenoid valves which can only be open or close. The amount of braking pres

53、sure is regulated through the opening condition of each valve which is simply specified by coefficients Cd1 and Cd2. For instance, when Cd1 = 1 and Cd2 = 0Robust control of wheel slip in anti-lock brake system of automobiles131Fig. 4 Structure of a standard hydraulic model 13Fig. 5a Membership funct

54、ion of velocitythe build valve is open and the dump valve is closed (see Fig. 4) which increases the braking pressure and vice versa. The hydraulic system dynamic model can be represented as 13in this section. The parallel structure of FLC systems enables the control system to activate all rules sim

55、ul- taneously. This characteristic of the FLC systems im- proves the required time for calculations 6.In general, FLC systems perform four main stagesC dpif dt, 2= A1Cd1 (Pp Pi)which are Fuzzification, rule base, inference mecha- nism and Defuzzification. Fuzzification and Defuzzi- A2Cd2, 2(PiPlow)(20)fication stages transform any numerical data to its cor- responding fuzzy value and vice