Nonlinear Modeling and Coordinate Optimization of a Semi-Active Energy Regenerative Suspension with an Electro-Hydraulic Actuator

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1 algorithm Article Nonlinear Modeling and Coordinate Optimization a Semi-Active Energy Regenerative Supenion with an Electro-Hydraulic Actuator Farong Kou *, Jiafeng Du, Zhe Wang, Dong Li and Jianan Xu College Mechanical Engineering, Xi an Univerity Science and Technology, Xi an 754, China; 87479@63.com (J.D.); wzwczl@63.com (Z.W.); @63.com (D.L.); alang4@63.com (J.X.) * Correpondence: koufarong@xut.edu.cn Received: 7 December 7; Accepted: 5 January 8; Publihed: 3 January 8 Abtract: In order to coordinate damping performance and energy regenerative performance energy regenerative upenion, thi paper propoe a tructure a vehicle emi-active energy regenerative upenion with an electro-hydraulic actuator (EHA). In light propoed concept, a pecific energy regenerative cheme i deigned and a mechanical propertie tet i carried out. Baed on tet reult, parameter identification for ytem model i conducted uing a recurive leat quare algorithm. On bai ytem principle, nonlinear model emi-active energy regenerative upenion with an EHA i built. Meanwhile, linear-quadratic-gauian control trategy ytem i deigned. Then, influence main parameter EHA on damping performance and energy regenerative performance upenion i analyzed. Finally, main parameter EHA are optimized via genetic algorithm. The tet reult how that when a inuoidal i input at frequency Hz and amplitude 3 mm, pring ma acceleration root meam quare value optimized EHA emi-active energy regenerative upenion i reduced by.3% and energy regenerative power RMS value i increaed by 4.5%, which mean that while meeting requirement vehicle ride comfort and driving afety, energy regenerative performance i improved ignificantly. Keyword: emi-active upenion; feed energy; parameter optimization; genetic algorithm. Introduction A upenion ytem i a key component a vehicle chai ytem, and it performance directly determine ride comfort, operational tability, and driving afety vehicle. The performance traditional paive upenion without adjutable parameter i inufficient to meet higher requirement [,]. With application enor technology and control technology, controllable upenion with uperior performance ha attracted more and more attention. Although traditional controllable upenion can realize real-time adjutment upenion performance, it i limited by it high cot and high energy conumption [3 5]. The type energy regenerative active upenion raied provide a method to olve above mentioned problem, that i, through regeneration a vehicle vertical vibration energy caued by an uneven road urface, heat energy diipated by upenion hock aborber in form friction i tranformed into a recyclable power through energy recovery device, which i ued for active upenion active control and utilization, reby reducing problem large energy conumption active upenion [6 8]. At preent, reearch on energy regenerative upenion ytem i mainly focued on how to improve efficiency energy regeneration, while ignoring original deign upenion and lacking a coordination analyi upenion ytem damping performance and energy regenerative performance [9 ]. Algorithm 8,, ; doi:.339/a

2 Algorithm 8,, x FOR PEER REVIEW 7 Algorithm 8,, 7 while ignoring original deign upenion and lacking a coordination analyi upenion ytem damping performance and energy regenerative performance [9 ]. Zuo et al. [,3] deigned a type gear rack energy regenerative upenion, carried out oretical and experimental tudie, and analyzed relationhip between vehicle ride comfort and handling tability and upenion energy regenerative performance. The bench tet reult how that upenion i effective for vibration attenuation and vibration energy regenerative efficiency i improved. Fan et etal. al. [4] integrated a aball ballcrew and anda adirect current (DC) (DC) motor motor into intoa aupenion, optimized damping characteritic upenion, and recovered vibration energy. Yu et al. [5] put forward a gear rack energy regenerative upenion, and et up a clutch mechanim in motor and gear rack mechanim. The imulation analyi reult how that it can regenerate energy at at ame time, time, baically meeting meeting requirement vehicle vehicle ride ride comfort comfort and handling handling tability. tability. On bai above above reearch, reearch, thi thi paper paper propoe propoe a tructure a tructure a vehicle a vehicle emi-active emi-active energy regenerative energy regenerative upenion upenion with anwith electro-hydraulic an electro-hydraulic actuator actuator (EHA) in (EHA) Section in Section. A quarter-car. A quarter-car model with model two with degree two degree freedom freedom i built ini Section built in 3.; Section n, a3.; mechanical n, a mechanical propertie tet propertie i carried tet out, i and carried according out, and toaccording tet reult, to we tet perform reult, we parameter perform identification parameter identification for ytemfor model ytem uing amodel recurive uing leat a recurive quare algorithm leat quare in Section algorithm 3.; and in Section nonlinear 3.; and model nonlinear emi-active model energy regenerative emi-active energy upenion regenerative with an EHA upenion i etablihed with an ineha Section i etablihed 3.3. In Section in Section 4, a LQG 3.3. control In Section trategy 4, a for LQG control emi-active trategy energy for regenerative emi-active upenion energy regenerative with an EHAupenion i deigned. with Moreover, an EHA i influence deigned. Moreover, main parameter influence EHA main on parameter damping performance EHA and on energy damping regenerative performance performance and energy upenion regenerative are analyzed performance in Section 5.; upenion n, main are analyzed parameter in Section EHA 5.; are n, optimized main via parameter genetic algorithm EHA in Section are optimized 5.; andvia bench genetic tet i algorithm carried out in in Section Section 5.; 5.4. and Finally, bench concluion tet i are carried ummarized out in Section in Section 5.4. Finally, 6. concluion are ummarized in Section 6.. Structure and Principle Semi-Active Energy Regenerative Supenion with with an an EHA EHA The baic tructure emi-active energy regenerative upenion ytem with an EHA i hown in in Figure Figure.. The The ytem ytem i mainly i mainly compoed compoed a piral a pring, piral pring, a hydraulic a hydraulic cylinder, acylinder, hydraulic a motor, hydraulic a bruhle motor, a DC bruhle motor, a DC digital motor, ignal a digital proceor ignal controller, proceor a compoite controller, energy a compoite recovery energy device, and recovery a digital device, potentiometer and a digital and potentiometer correponding and enor. correponding The hydraulic enor. cylinder The hydraulic ue a cylinder double pole ue double-acting a double pole ymmetrical double-acting hydraulic ymmetrical cylinder; hydraulic hydraulic cylinder; motor hydraulic ue a gear motor motor ue that a gear can carry motor out that poitive can carry inverion; out poitive and inverion; bruhle DC and generator bruhle ue a DC permanent generator magnet ue bruhle a permanent DC generator magnet bruhle [6]. DC generator [6]. Figure. The tructure emi-active energy regenerative upenion with an electro-hydraulic Figure. The tructure emi-active energy regenerative upenion with an electro-hydraulic actuator (EHA). DC: direct current. actuator (EHA). DC: direct current. When vehicle i running, hydraulic cylinder move with body vibration and puhe hydraulic Whenoil to vehicle drive i running, hydraulic motor hydraulic to rotate, cylinder output move with haft body hydraulic vibrationmotor and puhe drive hydraulic coaxial oil bruhle to drivedc generator hydraulicby motor coupling, to rotate, and generated output haft electrical energy hydraulic i recovered drive and tored coaxial by a bruhle compoite energy recovery by coupling, device to and realize energy regeneration electrical energy in EHA i recovered energy and regenerative tored byupenion. a compoiteat energy ame recovery time, device enor to realize end energy a ignal regeneration vehicle in EHA operation energy regenerative condition to upenion. controller. AtAccording ame time, to control enortrategy, end a ignal controller vehicle change operation external condition load

3 Algorithm 8,, 3 7 Algorithm 8,, x FOR PEER REVIEW 3 7 to controller. According to control trategy, controller change external load reitance value reitance value bruhle DC bruhle motor by DC adjuting motor by adjuting value value digital potentiometer. digital potentiometer. Therefore, Therefore, electromagnetic torque motor can be changed, and damping force electromagnetic torque motor can be changed, and damping force hydraulic hydraulic cylinder can be controlled to realize control function EHA emi-active cylinder can be controlled to realize control function EHA emi-active upenion. upenion. The compoite energy recovery device i hown in Figure. The device i mainly compoed The compoite energy recovery device i hown in Figure. The device i mainly compoed a a three-phae rectifier, a filter circuit, boot module, boot module, MOSFET A, MOSFET B, three-phae rectifier, a filter circuit, boot module, boot module, MOSFET A, MOSFET B, a a voltage equalizing circuit, uper capacitor group, a voltage enor, a DSP controller, a voltage voltage equalizing circuit, a uper capacitor group, a voltage enor, a DSP controller, a voltage tabilizing tabilizing circuit, circuit, a a diode, diode, and and a a torage torage battery. battery. Among Among m, m, uper uper capacitor capacitor group group conit conit four four capacitor capacitor from from.7.7 V V F uper F uper capacitor capacitor erie, erie, in which in which voltage voltage i.8 i V,.8 V, capacity i 5 capacity F, andi 5 optimal F, and charging optimal voltage charging ivoltage 9 V. i Boot 9 module V. Boot module boot toboot 9 V for to uper 9 V for capacitor uper charging. capacitor Referring charging. to Referring vehicle to battery, vehicle lead-acid battery, battery ued lead-acid i Vbattery 8 ampere-hour, ued i in which V 8 optimal ampere-hour, charging which voltage i 4.4 optimal ±.charging V. Booter voltage module i 4.4 boot ±. to V. 4.4 Booter V for module charging boot battery to after 4.4 V voltage for charging tabilizing battery circuit. after In order voltage to prevent tabilizing circuit. batteryin from order over-charging to prevent battery uper capacitor, from over-charging a unidirectional uper conducting capacitor, diode a unidirectional i connected conducting erie between diode i connected voltage tabilizing in erie circuit between and voltage toragetabilizing battery. circuit and torage battery. Bruhle DC motor Threephae rectifier Filter circuit Boot module MOSFET A pule width modulation Voltage equalizing circuit Super capacitor group Voltage enor DSP controller Storage battery Diode Voltage tabilizing circuit Boot module MOSFET B pule width modulation Figure Figure.. Illutrative Illutrative diagram diagram complex complex energy energy recovery recovery device. device. The pecific working proce compoite energy recovery device i a follow. The voltage enor The pecific connected working in parallel proce at both end compoite uper energy capacitor recovery group device i detected i a follow. in real-time The by voltage enor uper connected capacitor group in parallel voltage at both ignal, end which i uper collected capacitor in DSP group controller i detected by in A/D real-time ampling by uper module capacitor group DSP controller. voltagewhen ignal, which voltage collected at both end in DSP uper controller capacitor bygroup A/D i detected ampling module to reach 4 V, DSP DSP controller. controller When output voltage two pule at both width end modulation uper ignal. capacitor One group output, i detected pule to reach width 4modulation V, DSP controller, i high output and it two drive pule width MOSFET modulation witch A ignal. to open. OneThe output, or pule output, width modulation pule width, i modulation high and it, drive i low and MOSFET it drive witch MOSFET A towitch open. B The to cloe. orat output, thi moment, pule width modulation uper capacitor, i low group andi itin drive charge tatu MOSFET and witch three-phae B to cloe. alternating At thi moment, current generated uper capacitor by group bruhle i in DC charge motor tatu through and a three-phae rectifier alternating bridge and current a filter generated circuit become by bruhle a table DC DC motor voltage through that i abooted three-phae to 9 V rectifier by boot bridge module and. The a filter uper circuit capacitor become group a i table teadily DCcharged voltage by that 9 i booted V voltage to 9 Vthrough by boot module MOSFET. witch The uper A and capacitor equalizing group circuit. i teadily When charged voltage byat 9 both V voltage end through uper MOSFET capacitor witch group Ai and detected equalizing to reach circuit. 9 V, When DSP controller voltage output at both two end pule width uper capacitor modulation groupignal. i detected One output, to reachpule 9 V, width DSP modulation controller, output i high two and pule it drive width modulation MOSFET ignal. witch One B to output, open. The pule or width output, modulation pule width, i modulation high and it drive, i low and MOSFET it drive witch MOSFET B to open. The witch ora output, to cloe. pule At thi width moment, modulation uper, i low capacitor and itgroup drivei in MOSFET dicharge witch tatu Aand to cloe. output At thi moment, voltage uper uper capacitor capacitor group grope i ini dicharge booted to tatu 4.4 V and by boot output module voltage. The torage uper battery capacitor i grope teadily i booted charged to by V by V boot voltage module through. The voltage torage tabilizing battery icircuit. teadily In charged order to byprevent 4.4 V voltage over-dicharge through voltage uper tabilizing capacitor circuit. group, In order minimum to prevent dicharge over-dicharge voltage uper uper capacitor capacitor group, group i et minimum at 4 V, that dicharge i, when voltage voltage enor uper detect capacitor that group voltage i et between at 4 V, thattwo i, when end voltage uper enor capacitor detect group that reache voltage 4 V, between mode i two converted, end and uper whole capacitor ytem group perform reache cyclic 4 V, charge and dicharge. mode i converted, and whole ytem perform cyclic charge and dicharge.

4 Algorithm 8,, 4 7 Algorithm 8,, x FOR PEER REVIEW Nonlinear Modeling Semi-Active Energy Regenerative Supenion with an EHA 3.. Dynamic Model a Two Degree Freedom Supenion Sytem for a Quarter-Vehicle In thi paper, a quarter-car model with two degree freedom wa exactly etablihed [7], which i hown in Figure 3. Figure 3. The chematic diagram quarter-car model. Figure 3. The chematic diagram quarter-car model. According to Figure 3, equation motion are obtained by uing Newton law motion: According to Figure 3, equation motion are obtained by uing Newton law motion: { m x k x x c x x.. ( F m x + m k u x(x k x ) x+ c c ẋ x x ẋ ) k = t x F z F ().. ( m. u x k (x x ) c ẋ ẋ () ) + kt (x z) = F. The tate vector and output vector are elected a follow: The tate vector and output vector are elected a follow: x x z x X = [. ] T x x ẋ x z x T. ] T x x k x z x Y = [.. x x x k t (x t z) where.ẋ i prung ma acceleration, x where i prung ma acceleration, x i upenion deflection repone, k x x i upenion deflection t (x repone, x ) i tire load repone, and ż(t) i peed excitation road input. In thi way, tate equation k t x upenion x i can tire be load obtained repone, a follow: and i peed excitation road input. In thi way, tate equation upenion can be { obtained a follow: Ẋ = AX + BU X AX BU () Y = CX + DU () Y CX DU where A i tate matrix, B i input matrix, C i output matrix, and D i tranfer matrix. When where control i input tate force matrix, F i, iti become input a paive matrix, upenion. C i output matrix, and i tranfer matrix. When control input force F i, it become a paive upenion. k k c c c c A = m m m m m m B = m A m B k c k t c m u k m u c m u k m u t c m u k m c c u m u u mu mu m m m C = k c c k t D = m ( ) ż m m m U = F C m D U z z kt F The road urface input model adopt filtered white noie [8] a follow:. z(t) = π f The road urface input model adopt filtered z(t) + π G white noie uω(t) (3) [8] a follow: x A B z(t) where z i input diplacementz ( t) road, f G z( ti ) road Guirregularitie ( t) coefficient, f i lower (3) cutf frequency, u i vehicle peed, and ω(t) i unit white noie. D

5 Algorithm 8,, x FOR PEER REVIEW 5 7 Algorithm 8,, x FOR PEER REVIEW 5 7 z z G G where i input diplacement road, i road irregularitie coefficient, i Algorithm where 8, i, input diplacement road, i road irregularitie coefficient, i 5 7 lower cutf frequency, i vehicle peed, and i unit white noie. lower cutf frequency, i vehicle peed, and i unit white noie Parameter Parameter Identification Identification Nonlinear Nonlinear Model Model 3.. Parameter In order to Identification provide experimental Nonlinear ample Model In order to provide experimental ample data data for for model model parameter parameter identification, identification, a phyical phyical prototype prototype In order an to anprovide EHA, EHA, which experimental which i mainly i mainly ample compoed compoed data for a hydraulic amodel hydraulic parameter cylinder, cylinder, a identification, hydraulic a hydraulic motor, a phyical motor, and a and bruhle prototype a bruhle DC an motor, EHA, DC motor, i which developed, i i developed, mainly and compoed according and according to a hydraulic to national national cylinder, tandard tandard a hydraulic QC/T QC/T motor, and Tet a Tet method bruhle method for DC automobile motor, for automobile i telecopic developed, telecopic hock and according aborber, hock aborber, to a force national characteritic a force tandard characteritic tet QC/T an EHA tet emi-active an Tet EHA emi-active upenion method for automobile upenion ytem i carried telecopic ytem out i hock carried on an aborber, out ES-6-3 on ana numerical ES-6-3 force characteritic numerical control hydraulic control tet an hydraulic vibration EHA emi-active vibration table a table hown upenion a in hown Figure ytem in 4. Figure In i carried 4. experiment, In out experiment, on an vibration ES-6-3 vibration table numerical input table excitation control input excitation hydraulic ue inuoidal ue vibration inuoidal input table at input a at frequency hown frequency in Figure Hz 4. and In Hz and experiment, amplitude amplitude 3 vibration mm. 3 mm. An table LTR- Aninput LTR- pull excitation pull preure preure enor ue enor inuoidal i ued i ued to input collect to collect at upenion frequency upenion output Hz output and force force ignal amplitude ignal in in paive 3 mm. paive tate, An tate, LTR- and and pull change preure change enor upenion upenion i ued to output collect output force force with upenion time with time i hown output i hown in force Figure inignal Figure 5. in In 5. order In paive order to eliminate totate, eliminate and influence change influence initial initial upenion condition condition output on on force tet tet reult, with time i ampling ampling hown in time time Figure tart tart 5. from from In order 5.. to eliminate influence initial condition on tet reult, ampling time tart from 5. u u (t) (t) f f Figure 4. Force characteritic tet EHA emi-active upenion ytem. Figure Figure Force Force characteritic characteritic tet tet EHA EHA emi-active emi-active upenion upenion ytem. ytem. Tet value 5 Tet Simulation value value 5 Simulation value Time/() Time/() Figure 5. Comparion imulation and experimental reult output force. Figure 5. Comparion imulation and experimental reult output force. The parameter nonlinear model are continuouly approximated by leat quare method The baed parameter on experimental nonlinear data, model and are objective continuouly function approximated algorithm by i expreed leat quare The parameter nonlinear model are continuouly approximated by leat quare a: method baed on experimental data, and objective function algorithm i expreed a: method baed on experimental data, and objective function algorithm i expreed a: k, c arg min Fc k, c Fe (4) k argk min, c Fc k, c Fe {k (4), c } = argmin k, c F c (k, c ) F e (4) where k k i equivalent pring tiffne, c,c i inherent damping coefficient ytem, where k i equivalent pring tiffne, c i inherent damping coefficient ytem, where F c i k ioretical equivalent model pring value, tiffne, and F ec i inherent actual tet damping value. coefficient ytem, F c i oretical F c i oretical model value, model andvalue, F e i and actual F e i tet value. actual tet value. Output Output force/(n)

6 Algorithm 8,, 6 7 Through identification parameter, equivalent pring tiffne k EHA emi-active upenion ytem i 3, N/m, and inherent damping coefficient c i 5 N m/. The above parameter are introduced into two degree freedom upenion dynamic model quarter-vehicle, and imulation reult EHA actuator output force are compared with tet reult, a hown in Figure 5. Figure 5 how that output force EHA actuator obtained by parameter identification i in good agreement with actual output force, which indicate that etablihed dynamic model two degree freedom upenion ytem for a quarter-vehicle i accurate, and adopted method model parameter identification i feaible and effective Mamatical Model Semi-Active Energy Regenerative Supenion with an EHA When mamatical model EHA actuator i etablihed, friction between piton, cylinder wall, and internal leakage ytem i ignored. Thu, damping force generated by hydraulic cylinder can be expreed a: F = P A (5) where P i preure drop between upper and lower urface piton in hydraulic cylinder, and A i effective piton area. We take into account hydraulic pipeline preure lo, which include preure lo along path and local preure lo [9]. The preure lo along path hydraulic pipeline in ytem i expreed a: P λ = λ l d ( ρν ) (6) where λ i along reitance coefficient, l i length hydraulic pipe, d i diameter hydraulic pipe, ρ i hydraulic oil denity, and ν i oil flow rate in pipeline. The local preure lo hydraulic pipeline in ytem i expreed a: P ζ = ζ ρν where ζ i local reitance coefficient. It can be een that total preure lo hydraulic pipeline in ytem can be obtained a follow: P g = P λ + P ζ = (λ ld ) ρν + ζ (8) according to continuity equation liquid flow, which i given by: Q d = A ν g = πd 4 ν (9) where Q d i flow hydraulic motor, and ν g i peed piton rod. According to working principle emi-active energy regenerative upenion with an EHA, it can be een that under action body vibration oil in hydraulic cylinder enter hydraulic motor and drive hydraulic motor to work, and output torque hydraulic motor drive generator to generate electricity. At ame time, angular velocity and output torque hydraulic motor meet following relationhip: ω = πq d η ν () q T d = p dq π η m () (7)

7 Algorithm 8,, 7 7 where q i hydraulic motor diplacement, η ν i volumetric efficiency hydraulic motor, p d i preure drop between inlet and outlet hydraulic motor, and η m i mechanical efficiency hydraulic motor. The generator convert mechanical energy hydraulic motor into electrical energy, o input torque generator i equal to output torque hydraulic motor. Therefore, output voltage U and output torque T g generator meet following relationhip: U = E I(r + R) = IR () T g = J.. θ + k t I (3) where E i induced electromotive force, I i loop current, r i internal reitance generator, R i external load reitance generator, R i equivalent reitance energy regenerative circuit, J i moment inertia, θ.. i angular acceleration generator, and k t i torque contant generator. Among m, induction electromotive force i expreed a: E = k e n = 3 π k eω (4) where k e i back electromotive force contant generator, n i generator rotor peed, and ω i generator rotor angular velocity. The hydraulic motor i directly connected with generator through coupling, o ir angular velocity and torque are equal, which i expreed a ω = ω and T d = T g. If moment inertia motor i ignored, preure drop between inlet and outlet hydraulic motor can be obtained from Equation (9) (4) a follow: P d = πk ek t η v Av g q η m (r + R + R ). (5) The preure balance equation whole hydraulic circuit be expreed a: P = P d + P g = πk ( ek t η v Av g q η m (r + R + R ) + λ l ) 8ρA d + ζ νg π d 4 (6) The damping force EHA actuator can be obtained by taking Equation (6) into Equation (4) a follow: F = πk ek t η v A ( v g q η m (r + R + R ) + λ l ) 8ρA 3 d + ζ νg π d 4. (7) Therefore, equivalent damping coefficient EHA actuator can be expreed a: c eq = πk ek t η v A ( q η m (r + R + R ) + λ l ) 8ρA 3 d + ζ ν g π d 4. (8) The loop current can be obtained from Equation (), (3), and (5) a follow: I = 6k ( eη v Av g q(r + R + R ) + λ l ) 4ρqηm d + ζ A νg π 3 d 4. (9) k t In ummary, intantaneou energy regenerative power can be expreed a: [ ( P reg = I 6ke η v Av g R = q(r + R + R ) + λ l ) 4ρqηm d + ζ A νg ] π 3 d 4 R () k t In traditional paive upenion damper, diipated power in form heat energy i calculated a: P con = c ( ẋ ẋ ) ()

8 Algorithm 8,, 8 7 where c i inherent damping coefficient, and ( ẋ ẋ ) i hock aborber velocity. The energy regenerative efficiency a emi-active upenion i ratio between feedback energy and diipated energy paive upenion. Therefore, energy regenerative efficiency η i expreed a: η = T T P regdt [ c ( ẋ ẋ ) ] dt. () 4. The Control Strategy Semi-Active Energy Regenerative Supenion with an EHA The election principle witching control critical point to control force emi-active energy regenerative upenion with an EHA i expreed a follow: When ẋ (ẋ ẋ ) >, direction force applied to pring ma by actuator i oppoite to movement direction pring ma, but it ha ame direction a active control force, o it can change external load reitance actuator to make actual control output force be equal to oretical active control output force. Additionally, oretical active control output force i determined by optimal control trategy. The optimal control objective emi-active energy regenerative upenion with an EHA i to make car obtain higher comfort and handling tability, and reflecting in amount actual control i to reduce acceleration prung ma and tire dynamic load a much a poible, limit range upenion dynamic deflection, and reduce poibility upenion impact block. At ame time, it hould not conume too much energy []. Baed on above conideration, performance index function a emi-active upenion output regulator can be written a follow: [.. J = q x + q (x x ) + q 3 (x z) + rf ] dt (3) where q i weighting coefficient acceleration, q i weighting coefficient upenion dynamic deflection, q 3 i weighting coefficient tire dynamic deformation, and r i weighting coefficient energy conumption. The above optimization index i expreed in matrix a: [ ] J = Y T qy + F T rf dt (4) where q i expreed a: q = q q q 3 Generally, output regulator problem i converted to a tate regulator problem. Taking output equation Y = CX + DU into Equation (4), quadratic performance index i given by: J =. [ ] X T QX + X T NF + F T RF dt (5) where Q are poitive emidefinite ymmetric weighting matrice tate variable, N i weighted matrix two kind variable, and R i poitive definite ymmetric weighting matrix control variable. Among m, Q = C T qc, N = C T qd, R = r + D T qd. The optimal control force F, which erve for performance index J, to be minimized i exitent and unique, and it can be expreed a: F = KX = (B T P + N T )X (6) where P i a ymmetric poitive definite olution Riccati matrix equation. It meet following equation:

9 Algorithm 8,, 9 7 PA + A T P (PB + N)R (B T P + N T ) + Q =. (7) The election weighting factor in performance index optimal control depend on practical experience. After repeated trial, following option can be made: q =. 5, q =.65 8, q 3 = 9.5 9, r =. In order to obtain feedback gain matrix K, uing linear quadratic regulator function provided by Matlab tware, baic format i expreed a: (K, S, E) = LQR(A, B, Q, R, N) (8) where S i olution Riccati equation, and E i ytem eigenvalue. When ẋ (ẋ ẋ ) <, direction force applied to pring ma by actuator ha ame direction a movement direction pring ma, but it i oppoite to that active control force. In order to minimize thi difference, at thi moment damping force, which i oretically required to output from upenion, i zero, but actual output force i inherent vicou damping force ytem, and it true value i till determined by Formula (7). At ame time, motor load reitance i zero. 5. Parameter Optimization Semi-Active Energy Regenerative Supenion with an EHA 5.. Parameter Senitivity Analyi In order to coordinate damping performance and energy regenerative performance emi-active energy regenerative upenion with an EHA and improve energy regenerative performance under condition atifying requirement damping performance, influence EHA parametric variation on damping performance and energy regenerative performance upenion i analyzed. The EHA i mainly compoed a hydraulic cylinder, a hydraulic motor, and a bruhle DC generator. According to modeling proce, it can be known that main parameter EHA are: effective area hydraulic cylinder piton A, diplacement hydraulic motor q, and back electromotive force contant generator k e. Baed on initial imulation parameter value EHA and % initial imulation parameter value EHA for change interval, influence three main parameter variation EHA on damping performance and energy regenerative performance emi-active energy regenerative upenion with EHA i invetigated. Among m, damping performance take pring ma acceleration and tire dynamic load a evaluation indicator, and energy regenerative performance take energy regenerative power and energy regenerative efficiency a evaluation indicator. The influence main parameter EHA on performance evaluation indicator i hown in Figure 6 8, repectively. Figure 6 how that, firtly, with increae effective area hydraulic cylinder piton, RMS value prung ma acceleration and dynamic load tire decreae gradually. Then, y reach minimum at nearly. time value original imulation parameter hydraulic cylinder piton effective area, which make riding comfort continuouly improve and damping performance achieve an optimal effect. Finally, with increae effective area hydraulic cylinder piton, RMS value prung ma acceleration and dynamic load tire increae gradually, which lead to deterioration ride comfort and damping performance. However, with increae effective area hydraulic cylinder piton, RMS value energy regenerative power and energy regenerative efficiency increae gradually, that i to ay, energy regenerative performance improve continuouly. However, when RMS value energy regenerative power and energy regenerative efficiency reach maximum, which mean that energy regenerative efficiency i optimal, RMS value prung ma acceleration and dynamic load tire reach maximum too, which lead to damping performance deterioration without meeting deign requirement upenion.

10 Algorithm 8,, x FOR PEER REVIEW 7 indicator, and energy regenerative performance take energy regenerative power and energy regenerative Algorithm 8, efficiency, a evaluation indicator. The influence main parameter EHA 7 on performance evaluation indicator i hown in Figure 6 8, repectively. The RMS value prung ma acceleration/(m - ) The RMS value prung ma acceleration The RMS value tire dynamic load Algorithm 8,, x FOR PEER REVIEW Change from initial imulation value A/(%) The RMS value tire dynamic load/(n) The RMS value energy regenerative power/(w) 8 6 The RMS value energy regenerative power Energy regenerative efficiency Change from initial imulation value A/(%) indicator, and energy regenerative performance take energy regenerative power and energy regenerative efficiency a evaluation (a) indicator. The influence main (b) parameter EHA on performance evaluation indicator i hown in Figure 6 8, repectively. Figure Figure 6. Influence 6. Influence effective effective area area hydraulic hydrauliccylinder cylinderpiton pitonon onevaluation indicator: indicator: (a) Influence (a) Influence effective effective area area hydraulic hydraulic cylinder cylinder piton piton on on damping performance; (b) Influence 5 (b) Influence effective effective area area 6 hydraulic cylinder pitonon energy regenerative performance. 6 The RMS value prung ma acceleration/(m - ) The RMS value prung ma acceleration/(m - ) The RMS value tire dynamic load/(n) The RMS value tire dynamic load/(n) RMS value prung ma acceleration and dynamic load tire decreae gradually. Then, y reach minimum at nearly.8 time value original imulation parameter diplacement hydraulic motor, which make 4 riding comfort continuouly improve 4 and 3.5 damping.5 performance achieve an optimal effect. Finally, with increae diplacement hydraulic motor, RMS value prung ma acceleration and dynamic load 8 tire increae.5 gradually, which lead to deterioration ride comfort and damping performance..5 However, with increae diplacement hydraulic motor, RMS value energy 7 regenerative 6.5 power 8 and energy 4 regenerative 6 6 efficiency 6 decreae 8 gradually, that i to 4ay, 6 energy Change from initial imulation value A/(%) Change from initial imulation value A/(%) regenerative performance deteriorate continuouly. However, when RMS value energy 6 8 (a) (b) 4 6 regenerative power and energy regenerative efficiency reach maximum, which mean that Change from initial imulation value q/(%) Change from initial imulation value q/(%) energy Figure regenerative 6. Influence efficiency effective (a) i optimal, area hydraulic RMS value cylinder piton prung (b) on ma evaluation acceleration indicator: and(a) dynamic Influence load effective tire reach area maximum hydraulic too, which cylinder lead piton damping on damping performance performance; deterioration (b) without Figure meeting 7. Influence deign diplacement requirement hydraulic upenion. motor on evaluation indicator: (a) Influence Influence effective area hydraulic cylinder piton on energy regenerative performance. diplacement hydraulic motor on damping performance; (b) Influence diplacement hydraulic motor on energy regenerative performance. The RMS The value RMS value prung ma prung acceleration/(m ma acceleration/(m - ) - ) The RMS value prung ma acceleration The RMS value tire dynamic load Change from initial imulation value q/(%) Change from initial imulation value k e /(%) The RMS The value RMS value tire dynamic tire dynamic load/(n) load/(n) The RMS The value RMS value energy regenerative energy regenerative power/(w) power/(w) The RMS value prung ma acceleration The RMS value energy regenerative power 4.5 The RMS value tire dynamic load Energy regenerative efficiency 4 5 Figure 4 57 how that, firtly, with increae 3 6 diplacement hydraulic6 motor, The RMS value prung ma acceleration The RMS value energy regenerative power The RMS value tire dynamic load 8 Energy regenerative efficiency The RMS value prung ma acceleration The RMS value tire dynamic load 3 The RMS value energy regenerative power/(w) The RMS value energy regenerative power/(w) Energy regenerative efficiency The RMS value energy regenerative power Energy regenerative efficiency Change from initial imulation value q/(%) Change from initial imulation value k e /(%) Figure Figure 7. Influence 7. Influence (a) diplacement hydraulic hydraulic motor motor on on evaluation evaluation (b) indicator: indicator: (a) Influence (a) Influence diplacement hydraulic hydraulic motor on motor damping on performance; damping performance; (b) Influence (b) Influence diplacement Figure 8. Influence back electromotive force contant generator on evaluation indicator: diplacement hydraulic motor hydraulic on energy motor regenerative on energy performance. regenerative performance. (a) Influence back electromotive force contant generator on damping performance; (b) Influence back electromotive force contant generator on energy regenerative 4 performance. acceleration/(m - ) (a) The RMS value prung ma acceleration The RMS value tire dynamic load 9 dynamic load/(n) generative power/(w) The RMS value energy regenerative power (b) The RMS value energy regenerative power Energy regenerative efficiency Energy regenerative efficiency/(%) Energy Energy regenerative regenerative efficiency/(%) efficiency/(%) efficiency/(%) Energy regenerative efficiency/(%) Energy regenerative efficiency/(%)

11 (a) (b) Figure 6. Influence effective area hydraulic cylinder piton on evaluation indicator: (a) Influence effective area hydraulic cylinder piton on damping performance; (b) Influence effective area hydraulic cylinder piton on energy regenerative performance. Algorithm 8,, 7 The RMS value prung ma acceleration/(m - ) 5 The RMS value prung ma acceleration 3 The RMS value tire dynamic load/(n) Figure imulation The RMS value reult tire dynamic how load that, firtly, with increae Energy regenerative fficiency back electromotive force 5 5 contant 4 generator, RMS value prung ma acceleration and dynamic load tire decreae gradually. Then, y reach minimum 4 at nearly.8 time value original imulation parameter back electromotive force contant generator, which make riding comfort continuouly improve and damping performance achieve an optimal effect. Finally, with.5 increae back electromotive force contant generator, RMS value prung ma acceleration and dynamic7 load tire increae gradually, which lead to deterioration ride comfort and damping performance. However, with increae.5 back electromotive force contant generator, RMS value energy regenerative power and energy 6regenerative 8 efficiency increae 4 6 gradually, 5 that 6i to ay, 8 energy regenerative 4 performance 6 Change from initial imulation value q/(%) Change from initial imulation value q/(%) improve continuouly. However, when RMS value energy regenerative power and (a) (b) energy regenerative efficiency reach maximum, which mean that energy regenerative efficiency i Figure optimal, 7. Influence RMS value diplacement prung ma hydraulic acceleration motor and on evaluation dynamic indicator: load (a) tire Influence reach maximum diplacement too, which lead hydraulic to damping motor performance on damping deterioration performance; without(b) meeting Influence deign requirement diplacement upenion. hydraulic motor on energy regenerative performance. The RMS value energy regenerative power/(w) 6 The RMS value energy regenerative power 6 Energy regenerative efficiency/(%) The RMS value prung ma acceleration/(m - ) The RMS value prung ma acceleration The RMS value tire dynamic load Change from initial imulation value k e /(%) (a) The RMS value tire dynamic load/(n) The RMS value energy regenerative power/(w) The RMS value energy regenerative power Energy regenerative efficiency Change from initial imulation value k e /(%) (b) Energy regenerative efficiency/(%) Figure Figure 8. Influence 8. Influence back electromotive back electromotive force contant force contant generator generator on evaluation evaluation indicator: (a) Influence indicator: (a) Influence back electromotive back electromotive force contant force contant generator on generator damping on performance; damping (b) Influence performance; (b) Influence back electromotive back electromotive force contant force contant generator on generator energy onregenerative energy performance. regenerative performance. From above tudy, it can be concluded that with change parameter EHA, damping performance and energy regenerative performance cannot achieve an optimal effect at ame time, and re i mutual retriction between m. In order to balance damping performance and energy regenerative performance, three main parameter EHA, including effective area hydraulic cylinder piton A, diplacement hydraulic motor q, and back electromotive force contant generator k e, hould be coordinated and optimized. 5.. Optimization Objective and Contraint In order to improve energy regenerative performance under requirement for meeting a certain damping performance, genetic algorithm i ued to optimize parameter EHA, which can reduce rik being trapped in a locally optimal olution and make optimization reult more accurate [,]. The parameter optimization emi-active energy regenerative upenion with an EHA i a nonlinear optimization problem a ingle target and multiple variable. Taking energy regenerative power a optimization goal, taking a certain damping performance a contraint condition,

12 Algorithm 8,, 7 and taking effective area hydraulic cylinder piton A, diplacement hydraulic motor q, and back electromotive force contant generator k e a optimization variable, genetic algorithm optimization toolbox from Matlab i ued to optimize parameter. The objective function i RMS value σ Preg energy regenerative power emi-active energy regenerative upenion with an EHA, and σ Preg i given by: σ Preg = N i= P regi N. (9) In optimization toolbox, objective function i required to be minimized. In thi paper, however, RMS value energy regenerative power i required to be maximized, o method to minimize negative value objective function i feaible. The contraint condition in thi paper i to meet a certain damping performance. According to automobile ory and or related literature, damping vehicle upenion belong to mall damping, and damping ratio ξ meet condition. ξ.4. Additionally, when RMS value wheel dynamic load σ Fd doe not exceed /3 tatic load value, probability a wheel jumping f ground i le than.5%, which can enure comfort and afety upenion [3]. Meanwhile, optimization toolbox require that contraint condition are not poitive. Thu, contraint condition meet:. c + c eq (X) k m c + c eq (X) k m.4 σ Fd (X) 3 G where X = {x, x, x 3 } = {A, q, k e } i optimal parameter vector Optimization Reult Analyi The above parameter are brought into genetic algorithm optimization toolbox, and optimization reult emi-active energy regenerative upenion with an EHA are hown in Table. Table. Optimal parameter. (3) Optimal Parameter Symbol Value The effective area hydraulic cylinder piton A m The diplacement hydraulic motor q 4.5 ml/r The back electromotive force contant generator k e V min/r In order to verify effect optimized EHA parameter on performance emi-active energy regenerative upenion with EHA, performance indexe upenion before and after optimization are imulated and compared auming that vehicle i traveling at a peed m/ on a C-grade road and imulation time i [4]. Additionally, imulation reult are hown in Table and Figure 9. Table how that after optimizing parameter, RMS value prung ma acceleration i reduced by 8.6%, which indicate that ride comfort vehicle ha been improved to a certain extent, and RMS value tire dynamic load i decreaed by.6%, which how that vehicle driving afety ha been enhanced; refore, vehicle damping performance i improved. After optimizing parameter, RMS value energy regenerative power increae by 49.67%,

13 Performance Index Sprung ma acceleration Symbol a Fd Before Optimization.585 m / After Optimization.757 m / Effect Tire dynamic load Algorithm 8,, 3 7 Energy regenerative power 59.8 W W Energy regenerative efficiency 8.68 % 7.6 % and energy regenerative efficiency increae from 8.68% to 7.6%, which demontrate that vehicle energy regenerative performance wa improved ignificantly. Table how that after optimizing parameter, RMS value prung ma acceleration i reduced by 8.6%, which Tableindicate. Simulation that reult. ride comfort vehicle ha been improved to a certain extent, and RMS value tire dynamic load i decreaed by.6%, Value which how Performance that Index vehicle driving Symbol afety ha been enhanced; refore, Control vehicle Effect/% damping Before Optimization After Optimization performance i improved. After optimizing parameter, RMS value energy Sprung ma acceleration σ a.585 m/.757 m/ 8.6 regenerative power increae by 49.67%, and energy regenerative efficiency increae from Tire dynamic load σ Fd 8.7 N 7.5 N % Energy to 7.6%, regenerative which power demontrate σ Preg that 59.8vehicle W energy regenerative W performance wa improved Energy ignificantly. regenerative efficiency η 8.68% 7.6% Preg N N / % 8.6 Sprung ma acceleration/(m - ) Before optimization After optimization Time/() Figure 9. Spring ma acceleration repone curve. Figure 9. Spring ma acceleration repone curve. Algorithm 8,, x FOR PEER REVIEW Before optimization After optimization Tire dynamic load/(n) Time/() Figure Figure.. Tire dynamic load repone curve. curve. Energy regenerative power/(w) Before optimization After optimization

14 Time/() Algorithm 8,, 4 7 Figure. Tire dynamic load repone curve. Energy regenerative power/(w) Before optimization After optimization Time/() Figure Figure.. Energy regenerative power repone curve Tet 5.4. and Tet Analyi and Analyi In order In order to furr to furr verify verify optimization reult, EHA prototype i redeveloped i baed baed on on optimization reult, reult, and and bench tet i i carried carried out out a hown a hown in Figure in Figure. In addition,. In addition, EHA EHA actuator in in Figure Figure 4 i4 i original original EHA actuator EHA actuator before optimization, before optimization, and EHA and actuator EHA in Figure actuator in i optimized one. Due to limitation tet condition, tet i conducted only for pring Figure i optimized one. Due to limitation tet condition, tet i conducted only for ma acceleration and energy regenerative power emi-active upenion with an EHA. pring ma acceleration and energy regenerative power emi-active upenion with In tet, DH86 acceleration enor produced by Donghua teting company i ued to collect an EHA. In tet, DH86 acceleration enor produced by Donghua teting company i ued to pring ma acceleration ignal, and rectifier i ued to rectify three-phae alternating current collect generated pring by ma DC bruhle acceleration motor. ignal, At ame and time, rectifier Donghua i DH59 ued to data rectify acquiition three-phae ytem alternating i ued current to collectgenerated feed voltage by ignal. DC bruhle Additionally, motor. according At toame relationhip time, between Donghua power, DH59 data voltage, acquiition and ytem internal i reitance ued to collect motor, feed intantaneou voltage ignal. energy Additionally, regenerativeaccording power can be to relationhip obtained. between Under power, condition voltage, that and inuoidal internal i input reitance at frequency motor, Hz, intantaneou amplitude energy 3 regenerative mm, and power ampling can time be obtained., Under tet reult condition pring that ma inuoidal accelerationi repone input at frequency and energy regenerative Hz, amplitude power repone 3 mm, and emi-active ampling upenion time with an, EHA before tet reult and after pring Algorithm optimization ma 8, acceleration, are x FOR hown PEER repone in REVIEW Figure 3 and andenergy 4, repectively. regenerative power repone emi-active 5 7 upenion with an EHA before and after optimization are hown in Figure 3 and 4, repectively. Figure. Bench tet EHA emi-active upenion ytem. Figure. Bench tet EHA emi-active upenion ytem. 6 Before optimization After optimization cceleration/(m - ) 4

15 Algorithm 8,, 5 7 Figure. Bench tet EHA emi-active upenion ytem. Figure. Bench tet EHA emi-active upenion ytem. Spring ma ma acceleration/(m - ) - ) Before optimization Before optimization After optimization After optimization Time/() 6 8 Time/() Figure Figure3. Tet chart ma Figure 3. Tet chart pring ma acceleration repone. Energy regeneration power/(w) Before optimization Before optimization After optimization After optimization 4 Time/() 6 8 Time/() Figure 4. Tet chart energy regenerative power repone. Figure Figure Tet Tet chart chart energy energy regenerative regenerative power power repone. repone. 6. Concluion 6. Concluion 6. Concluion In thi paper, tructure emi-active energy regenerative upenion with an EHA i In thi paper, a tructure a emi-active energy regenerative upenion with an EHA i propoed. In thifollowing paper, a tructure propoed a emi-active concept, energy pecific regenerative energy regenerative upenioncheme with an EHA and icompoite propoed. propoed. Following propoed concept, a pecific energy regenerative cheme and a compoite energy Following recovery propoed device are concept, deigned. a pecific On bai energy regenerative ytem tructure, cheme and aphyical compoite prototype energy energy recovery device are deigned. On bai ytem tructure, phyical prototype are recovery trial-manufactured, device are deigned. and mechanical On bai propertie ytem tet tructure, EHA emi-active phyical upenion prototype ytem are are trial-manufactured, and a mechanical propertie tet EHA emi-active upenion ytem i trial-manufactured, carried out. Baed and on a mechanical experimental propertie data, tet parameter EHA identification emi-active for upenion ytem ytem model i i carried out. Baed on experimental data, parameter identification for ytem model i carried out. Baed on experimental data, parameter identification for ytem model i conducted via a recurive leat quare algorithm, which determine equivalent pring tiffne k and inherent damping coefficient ytem c. Moreover, nonlinear model emi-active energy regenerative upenion with an EHA i built. On bai nonlinear model, LQG control trategy emi-active energy regenerative upenion with an EHA i deigned. Then, a complete imulation model emi-active energy regenerative upenion with an EHA i etablihed in Simulink. In order to coordinate damping performance and energy regenerative performance emi-active energy regenerative upenion with an EHA, influence main parameter EHA on damping performance and energy regenerative performance upenion are analyzed. Finally, main parameter EHA are optimized uing genetic algorithm. In order to furr verify optimization reult, EHA prototype i redeveloped according to optimization reult, and bench tet i carried out. The tet reult how that when inuoidal i input at frequency Hz and amplitude 3 mm, pring ma acceleration

16 Algorithm 8,, 6 7 RMS value optimized emi-active energy regenerative upenion with an EHA i reduced by.3%, and energy regenerative power RMS value i increaed by 4.5%, which mean that under meeting requirement vehicle ride comfort and driving afety, energy regenerative performance i improved ignificantly. Acknowledgment: The author gratefully acknowledge upport National Natural Science Foundation China (577546, 57543), Service Local Special Program Support Project Shaanxi Provincial Education Department (7JF7), and Xi an Science and Technology Project Funding Project (779CG/RC4-XAKD7). The author would like to thank anonymou reviewer for ir valuable comment that ignificantly improved quality thi paper. Author Contribution: F.K. and J.D. conceived and deigned experiment; D.L. and J.X. performed experiment; J.D. and Z.W. analyzed data; J.D. wrote paper. Conflict Interet: The author declare no conflict interet. Reference. Teng, H.E.; Hrovat, D. State art urvey: Active and emi-active upenion control. Veh. Syt. Dyn. 5, 53, [CroRef]. Chen, S.A.; Li, X.; Zhao, L.J. Development a control method for an electromagnetic emi-active upenion reclaiming energy with varying charge voltage in tep. Int. J. Automot. Technol. 5, 6, [CroRef] 3. Wu, L.N.; Shi, M.M.; Wang, R.C. Parameter optimization hybrid upenion with linear motor baed on PSO. J. Chongqing Univ. Technol. (Nat. Sci.) 6, 3, Babak, E. Development Hybrid Electromagnetic Damper for Vehicle Supenion Sytem; Univerity Waterloo: Waterloo, ON, Canada, Okada, Y.; Ozawa, K. Energy Regenerative and Active Control Electro-Dynamic Vibration Damper. Tran. Jpn. Soc. Mech. Eng. C 5, 7, Zhang, H.; Guo, X.X.; Hu, S.B.; Fang, Z.G.; Xu, L. Simulation analyi on hydraulic-electrical energy regenerative emi-active upenion control characteritic and energy recovery validation tet. Tran. Chin. Soc. Agric. Eng. (Tran. CSAE) 7, 33, Efatpenah, F.; Beno, J.H.; Week, D.A. Energy requirement a paive and an electromechanical active upenion ytem. Veh. Syt. Dyn., 34, [CroRef] 8. Goldner, R.; Zerigian, P.; Hull, J. A Preliminary Study Energy Recovery in Vehicle by Uing Regenerative Magnetic Shock Aborber; SAE Paper; SAE International: Warrendale, PA, USA, ; pp.. 9. Zuo, L.; Nayfeh, S.A. Structured H optimizatioenion baed on multi-wheel model. Veh. Syt. Dyn. 3, 4, [CroRef]. Anubi, O.M.; Clemen, L. Energy-regenerative model predictive control. J. Frankl. Int. 5, 35, 5 7. [CroRef]. Clemen, L.; Margoli, D. Modeling and control a quarter car electrodynamic air-upenion. In Proceeding International Conference on Bond Graph Modeling, Monterey, CA, USA, 6 July 4; pp Zuo, L.; Scully, B.; Shetani, J.; Zhou, Y. Deign and characterization an electromagnetic energy harveter for vehicle upenion. Smart Mater. Struct., 9, [CroRef] 3. Zuo, L.; Tang, X.D. Large-cale vibration energy harveting. J. Intell. Mater. Syt. Struct. 3, 4, [CroRef] 4. Huang, K.; Zhang, Y.C.; Yu, F. Coordinate optimization for yntical performance electrical energy-regenerative active upenion. J. Shanghai Jiao Tong Univ. 9, 43, Wang, Q.N.; Liu, S.S.; Wang, W.H. Structure deign and parameter matching ball-crew regenerative damper. J. Jilin Univ. Eng. Technol., 4, Kou, F.R. Deign and energy regenerative tudy on emi-active upenion with electro-hydrotatic actuator. Tran. Chin. Soc. Agric. Mach. 6, 8, Martin, I.; Etevez, J.; Marque, G. Permanent-magnet linear actuator applicability in automobile active upenion. IEEE Tran. Veh. Technol. 6, 55, [CroRef] 8. Kou, F.R.; Fan, Y.Q.; Zhang, C.W.; Du, J.F.; Wang, Z. Time delay compenation control emi-active upenion with vehicle electro-hydrotatic actuator. China Mech. Eng. 6, 7, 7.

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