Skyhook Damper Modification Using Fuzzy Logic Control for Control Effort and NVH Reduction

Transcription

1 th International Conference on Control, Automation and Sytem Oct. 6-9, in KINTEX, Gyeonggi-do, Korea Skyhook Damper Modification Uing Fuzzy Logic Control for Control Effort and NVH Reduction Jiwon Oh and Seibum B. Choi School of Mechanical Aeropace & Sytem Engineering, Diviion of Mechanical Engineering, Korea Advanced Intitute of Science and Technology, Daejeon, Korea (Tel : ; jwo@kait.ac.kr) School of Mechanical Aeropace & Sytem Engineering, Diviion of Mechanical Engineering, Korea Advanced Intitute of Science and Technology, Daejeon, Korea (Tel : ; bchoi@kait.ac.kr) Abtract: Thi paper ugget a modified a emi-active vehicle upenion deign baed on the conventional kyhook damper mechanim. The kyhook algorithm i modified uing the fuzzy logic control and a 6D IMU which meaure the acceleration and angular rate of the vehicle about it C.G. to oberve the vertical velocitie of the prung ma of each corner. Alo, the propoed cheme utilize the pring compreion meaurement of each tire to etimate the unprung ma movement. Thee are combined to maximize the eparation performance between the road and the prung ma, while reducing the overall control effort and chattering that directly relate to vehicle NVH. A confirmatory aement of the entire ytem i arranged via imulation cenario involving an aymmetric vehicle chai excitation and a inuoidal excitation of varying frequency with the aid of well-known vehicle imulation tool, CarSim, and Matlab/Simulink. Keyword: Semi-active upenion, fuzzy logic control, vibration. INTRODUCTION A emi-active upenion ytem i known to be an efficient way to raie the upenion performance through effectively changing the damping coefficient either by controlling the variable orifice or applying electric current to the MR (magnetorheological) fluid in the damper. A emi-active upenion come with the advantage that it doe not need an energy ource like an active upenion ytem, at the cot that it can only diipate energy and the damping coefficient mut aturate to a near-zero limit when the deired damping force i in the ame direction a the damper movement. Thi indicate that the damper can only operate half of the time. Here, maximizing the operation range of the emi-active kyhook damper ued in the vehicle upenion ytem may be an effective method to reduce the vertical acceleration experienced by the paenger and to eparate the road diturbance from them. However, unretricted control effort within the phyical boundary to maximize the damper operation can bring exceive damper repone or repone rate, which directly relate to generation of an unpleaant noie from the variable orifice actuator or harhne from vehicle jerking. Aware that the comfort factor inide the vehicle cabin pace i emphaized to atify the cutomer need, the noie, vibration, and harhne generated from the emi-active upenion actuator are extremely undeirable. Such drawback have erved obtacle in the previou effort to develop a wholly atifactory emi-active upenion ytem [] [] [] [4] [5] [6] [7]. Thi paper introduce a emi-active upenion ytem control cheme baed on the kyhook control, that minimize the control effort and the actuator input rate, without deteriorating the conventional kyhook damper performance. Thi i done uing a fuzzy logic control, and it performance i verified through imulation uing CarSim, and Matlab/Simulink.. QUARTER CAR MODEL OF THE VEHICLE SUSPENSION SYSTEM A quarter car model i conidered for the modeling of the vehicle upenion for the ake of implicity, a hown in Fig.. The damping effect of the tire i aumed to be negligible, and the tire excitation i modeled through the input from the road terrain z r. In addition to the pring with the pring contant k and the paive damper with the damping coefficient b, the controllable damper i added to each corner with the damping coefficient b emi. Fig. Quarter car model From the above model, the equation of motion are derived. mz = b( z z u) k ( z zu) (a) b z z ( ) emi u 58

2 ( ) ( ) ( ( ) mz = b z z k z z k z u u u u t b z z emi u. CONVENTIONAL SKYHOOK DAMPER The fully active kyhook damping force i obtained a the following. F = b z () a a In cae of the emi-active upenion, however, b i contrained to only diipate energy fromm the upenion ytem. Within thi phyical boundary, the kyhook damper mut operate a much a poible to reduce the prung ma velocity. To reit the prung ma movement, it i required that Fa i applied to the upenion ytem. It mut be noted here that for the ideal operation of the kyhook damper ytem, it require an aumption that the unprung ma to which the controllable damper i connected only undergoe a negligible amount of movement a if the prung ma i connected to a completely tationary reference like the ky. Thi aumption i fulfilled only in the condition in which the road terrain erve no external excitation to the unprung ma. It may ound practicall in the ituation where the upenion ytem i compreed or expanded olely due to the control effort of the driver to maneuver the vehicle on a completely flat ground. However, the validity of thi aumption i the mot deteriorated when the road diturbance i the main ource of the pring damper ytem excitation, like whenn the vehicle i going over a peed bump. Conidering that the damping force actually i generated by the following equation, Fd = bemi ( z z u) () the influence of z u to the kyhook damper performance i not deirable, a mentioned. In order to take z u into account effectively, bemi i deigned o that Fd track F a. Conidering the aforementionedd point, the emi-active damping coefficient b emi can be defined a follow. bmax, γ ba > bmax bemi = γba, < γba bmax, γ ba (4) v where γ = v v u With the above b emi, Fd i indeed made to track F a within the phyical and tructural limitation of the emi-active upenion ytem, ince F = b z z = γ b z z ( ) ( ) d emi u a u = z ba z z u = bz = a F. a ( z z ) u u z r ) (b) (5) Since Eq. (4) involve abrupt dicontinuity, it increae the rik of exceive actuator input rate. A imple application of the low pa filter doe not reolve the iue, becaue the phae lag problem may lead to ytem intability (to an extent that the road diturbance eparation performance i majorly deteriorated). Thi call for the need of a modified kyhook control, which i dealt in the following ection. 4. SKYHOOK DAMPER MODIFICATION Thi ection deal with the modification of the conventional kyhook damper ytem. The following figure decribe the chematic of the fuzzy logic baed kyhook damper control. Fig.. Schematic of the fuzzy logic baed control 4.. Sprung Ma and Unprung Ma Velocity Etimation Critical information required by the kyhook control i the vertical velocity of each corner. Given the vehicle angular rate roll rate p and pitch rate q the vertical prung ma velocity of each corner can be obtained baed on the vertical velocity v z etimated at the vehicle C.G. Thi indicate the need for the oberver that etimate v z, and it i done through the vehicle velocity and attitude oberver [8]. In thi work, an oberver baed on the bicycle model and the vehicle kinematic law i deigned. With v z available, individual prung ma velocity of each corner can be obtained a follow. = l q+ (6a), fl z f = l q, fr z f = + l q+ rl, z r = + l q rr, z r Since the enor meaurement for the upenion jounce z of each corner are available, it i poible to j expre the vehicle unprung ma a the following. zj = zu z (7) z = z z j u v = z = z + z u u j z + j Thu, the etimated unprung ma velocity of each corner expreed in term of i a follow. = z + = z + lq+ (9a) u, fl j, fl, fl j, fl z = z + = z + u, fr j, fr, fr j, fr z v z f f (6b) (6c) (6d) (8) lq+ (9b) 58

3 = z + = z + l q+ (9c) url, jrl, rl, jrl, z f = z + = z + l q+ (9d) u, rr j, rr, rr j, rr z f 4. Damping Coefficient Attenuation through Fuzzy Logic Control The fuzzy logic control of the emi-active upenion damping coefficient i deigned o that it take two input value prung ma velocity, i and unprung ma velocity v ˆu, i to determine γ f. Once γ f i obtained, γ can be defined a follow. n γ = γ f () where n i a poitive contant. Here, γ hold the ame meaning a that dealt in the previou ection. Thi time, in order to eliminate dicontinuity involved in the value of γ when obtained analytically a in the cae of conventional kyhook control, it i obtained through the fuzzy logic method. Table how the linguitic variable for fuzzy control and the center value of each memberhip function. The variable on the left column and the top row are the IF element, wherea the variable elewhere are the THEN element. The logical relationhip between the two are alway AND. Figure how the hape and ditribution of the memberhip function that correpond to the two input,, i and v ˆu, i, and an output γ f graphically in order, and figure 4 how the overall urface between the variable. Once the output γ i obtained, it implementation into the emi-active upenion i analogou to that hown in Eq. (4). A difference from Eq. (4) i that, here, imply bemi = γ ba () will uffice, ince the phyical boundarie are already accounted when pecifying the variable for the fuzzy control., i Table. Linguitic variable for AN4 AN AN AN A AP AP AP AP4 [m/] u, i BN4 BN BN BN B BP BP BP BP4 [m/] γ f Y Y.5 Y.5 Y.75 Y Y. Y Y Y u, i, i Table. Rule for BN4 BN BN BN B BP BP BP BP4 AN4 Y Y4 Y Y. Y Y.75 Y.75 Y.5 Y.5 AN Y Y Y Y. Y Y.75 Y.5 Y.5 Y.5 AN Y Y Y Y Y Y.75 Y.5 Y.5 Y.5 Fig.. Fuzzy memberhip function partition AN Y Y Y Y Y Y.5 Y.5 Y.5 Y.5 A Y Y Y Y Y Y Y Y Y AP Y.5 Y.5 Y.5 Y.5 Y Y Y Y Y AP Y.5 Y.5 Y.5 Y.75 Y Y Y Y Y AP Y.5 Y.5 Y.5 Y.75 Y Y. Y Y Y AP4 Y.5 Y.5 Y.75 Y.75 Y Y. Y Y4 Y Table how the rule ued in the. Fig. 4. Fuzzy control urface between variable 58

4 Regarding Eq. (), it mut be noted that an increae in n generally bring more eparation between the road diturbance and the prung ma, but at the ame time increae the amount of control effort. 5. SIMULATION RESULTS Simulation i conducted uing the vehicle imulation program Carim and Simulink. In the firt cenario, the vehicle goe over a peed bump with the height of cm, and the longitudinal vehicle peed i maintained at 4 km/h. Thi i immediately followed by a double lane change at the ame peed in order to ee the upenion repone caued by the driver teering maneuver. The econd cenario focue more in term of the frequency variation than in term of time domain chai movement. The inuoidal road diturbance that ha an 8 phae difference between the left and the right wheel i applied to the vehicle, and it frequency i increaed from. to 5 Hz. For the imulation, the following contant are ued. m = 4.5 kg; mu = 4 kg; k = 5 N/m; kt= N/m; b = N /m; b = 5 N /m; n = a Az [m/ ] roll [deg] pitch [deg] vertical acceleration at CG roll angle at CG pitch angle at CG paive upenion kyhook upenion time [] b [N/m].5 x 4 conventional kyhook control damping coefficient.5.5 fl fr rl rr Fig a z, roll and pitch while going over a peed bump vertical jerk at CG paive upenion kyhook upenion b [N/m] x 4 damping coefficient.5 jerk [m/ ] roll rate at CG time [] roll rate [deg/] Fig. 5. Damping coefficient of each corner on a peed bump and during DLC Figure 5 how that the operation range of the damping coefficient for the conventional kyhook control i more than ten time that for the deign. Thi certainly indicate that much harhne from the paenger perpective can be reduced by the propoed cheme. Thi i proven in Figure 7 and 9, where much of the jerk involved in the conventional kyhook control i reduced. Additionally, Figure 6 and 8 how that the road diturbance eparation performance ha been well-maintained. pitch rate [deg/] pitch rate at CG time [] Fig. 7. Jerk, p and q while going over a peed bump 584

5 Az [m/ ].5 vertical acceleration at CG paive upenion kyhook upenion 5 x 4 conventional kyhook control damping coefficient fl fr rl rr b [N/m] 5 roll angle at CG roll [deg] - 5 damping coefficient pitch angle at CG b [N/m] 5. pitch [deg] time [] time [] Fig.. Damping coefficient of each corner on the cro-ine wave road Fig. 8. a z, roll and pitch during DLC 5 vertical jerk at CG paive upenion kyhook upenion.5 vertical acceleration at CG paive upenion kyhook upenion jerk [m/ ] Az [m/ ] roll rate [deg/] - - roll rate at CG roll [deg] roll angle at CG pitch rate at CG. pitch angle at CG. pitch rate [deg/] - pitch [deg] time [] time [] Fig. 9. Jerk, p and q during DLC Fig.. a z, roll and pitch on the cro-ine wave road 585

6 jerk [m/ ] roll rate [deg/] pitch rate [deg/] vertical jerk at CG roll rate at CG pitch rate at CG paive upenion kyhook upenion time [] Fig.. Jerk, p and q during DLC on the cro-ine wave road Figure diplay the damping coefficient operation range at a magnified portion of the econd imulation cenario. Not only the peak-to-peak value of the fuzzy control damping coefficient i le than that of the conventional kyhook control damping coefficient, but alo ignificant amount of chattering involved in the conventional cheme i removed in the modified cheme. At the ame time, Figure and both how that the ride qualitie are made more pleaant for the paenger. By etting a condition dependent on ˆ vu, it i actually poible to reduce the control input variation for the cae of the conventional deign a well. However, it wa verified that the performance of the conventional kyhook upenion ytem with the implementation of uch condition i far wore than that of the propoed cheme while the control input i till more vigorouly varying. conventional kyhook control cheme. A noteworthy reduction of the amount of control effort required to guarantee the imilar or better level of emi-active upenion performance leave an opportunity for the further enhancement of the vehicle noie, vibration and harhne. REFERENCES [] D. S. Joe and N. Al-Holou, Development and evaluation of fuzzy logic controller for vehicle upenion ytem, Proceeding of the Twenty-Seventh Southeatern Sympoium on Sytem Theory, pp.95-99, 995 [] T. Yohimura, Y. Iari, Q. Li and J. Hino, Active upenion of motor coache uing kyhook damper and fuzzy logic control, Control Engineering Practice, Vol. 5, No., pp , 997 [] Y. Liu, T. P. Water, M. J. Brennan, A comparion of emi-active damping control trategie for vibration iolation of harmonic diturbance, Journal of Sound and Vibration, Vol. 8, Iue -, pp. -9, 5 [4] Kefu Liu, Jie Liu, The damped dynamic vibration aborber: reviited and new reult, Journal of Sound and Vibration, Vol. 84, Iue -5, pp. 8-89, 5 [5] H. Metered, P. Bonello, S.O. Oyadiji, The experimental identification of magnetorheological damper and evaluation of their controller, Mechanical Sytem and Signal Proceing, Vol. 4, Iue 4, pp , [6] Chen-Sheng Ting, Tzuu-Heng S. Li, Fan-Chu Kung, Deign of ler for active upenion ytem, Mechatronic, Vol. 5, Iue 4, pp. 65-8, 995 [7] K. S. Hong, H. C. Sohn, J. K. Hedrick, Modified Skyhook Control of Semi-Active Supenion: A New Model, Gain Scheduling, and Hardware-in-the-Loop Tuning, Journal of Dynamic Sytem, Meaurement, and Control, Vol. 4, Iue, pp , [8] K. Yi, and B. Song, Oberver Deign for Semi-Active Supenion Control, Vehicle Sytem Dynamic, Vol., Iue, pp. 9-48, CONCLUSION Thi paper preent a newly deigned kyhook damper control cheme aided by the enor meaurement of the upenion jounce, vehicle acceleration, and angular rate at C.G. A planned, the deigned fuzzy logic kyhook damper controller effectively reduce the jerk and the exceive control effort, and at the ame time exhibit a imilar or enhanced level of performance compared to the 586