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Nonlinear Modeling and Coordinate Optimization of a Semi-Active Energy Regenerative Suspension with an Electro-Hydraulic Actuator Farong Kou *, Jiafeng Du, Zhe Wang, Dong Li and Jianan Xu College of Mechanical Engineering, Xi’an University of Science and Technology, Xi’an 710054, China; [email protected] (J.D.); [email protected] (Z.W.); [email protected] (D.L.); [email protected] (J.X.) * Correspondence: [email protected] Received: 17 December 2017; Accepted: 15 January 2018; Published: 23 January 2018

Abstract: In order to coordinate the damping performance and energy regenerative performance of energy regenerative suspension, this paper proposes a structure of a vehicle semi-active energy regenerative suspension with an electro-hydraulic actuator (EHA). In light of the proposed concept, a specific energy regenerative scheme is designed and a mechanical properties test is carried out. Based on the test results, the parameter identification for the system model is conducted using a recursive least squares algorithm. On the basis of the system principle, the nonlinear model of the semi-active energy regenerative suspension with an EHA is built. Meanwhile, linear-quadratic-Gaussian control strategy of the system is designed. Then, the influence of the main parameters of the EHA on the damping performance and energy regenerative performance of the suspension is analyzed. Finally, the main parameters of the EHA are optimized via the genetic algorithm. The test results show that when a sinusoidal is input at the frequency of 2 Hz and the amplitude of 30 mm, the spring mass acceleration root meam square value of the optimized EHA semi-active energy regenerative suspension is reduced by 22.23% and the energy regenerative power RMS value is increased by 40.51%, which means that while meeting the requirements of vehicle ride comfort and driving safety, the energy regenerative performance is improved significantly. Keywords: semi-active suspension; feed energy; parameter optimization; genetic algorithm

1. Introduction A suspension system is a key component of a vehicle’s chassis system, and its performance directly determines the ride comfort, operational stability, and driving safety of the vehicle. The performance of traditional passive suspension without adjustable parameters is insufficient to meet the higher requirements [1,2]. With the application of sensor technology and control technology, controllable suspension with superior performance has attracted more and more attention. Although the traditional controllable suspension can realize real-time adjustment of the suspension’s performance, it is limited by its high cost and high energy consumption [3–5]. The type of energy regenerative active suspension raised provides a method to solve the above mentioned problems, that is, through the regeneration of a vehicle’s vertical vibration energy caused by an uneven road surface, the heat energy dissipated by the suspension’s shock absorber in the form of friction is transformed into a recyclable power through the energy recovery device, which is used for active suspension active control and utilization, thereby reducing the problem of the large energy consumption of the active suspension [6–8]. At present, the research on energy regenerative suspension systems is mainly focused on how to improve the efficiency of energy regeneration, while ignoring the original design of the suspension and lacking a coordination analysis of the suspension system’s damping performance and energy regenerative performance [9–11]. Algorithms 2018, 11, 12; doi:10.3390/a11020012

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while ignoring the original design of the suspension and lacking a coordination analysis of the suspension system’s damping performance and energy regenerative performance [9–11]. Zuo Zuo et et al. al. [12,13] [12,13] designed designed aa type type of of gear gear rack rack energy energy regenerative regenerative suspension, suspension, carried carried out out theoretical and experimental studies, and analyzed the relationship between vehicle ride comfort and handling stability and the suspension’s energy regenerative performance. The bench test results show that the suspension is effective for vibration attenuation and the vibration energy regenerative efficiency is improved. improved. Fan Fanetetal. al.[14] [14]integrated integratedaaball ballscrew screwand anda adirect directcurrent current(DC) (DC)motor motorinto into a a suspension,optimized optimizedthe thedamping dampingcharacteristics characteristicsofofthe thesuspension, suspension,and and recovered recovered the vibration suspension, energy. Yu Yu et et al. al. [15] [15] put put forward forward aa gear gear rack rack energy energy regenerative regenerative suspension, suspension, and set up a clutch mechanism in the motor and the gear rack mechanism. The simulation analysis results show that it can regenerate basically meeting thethe requirements of vehicle rideride comfort and regenerateenergy energyatatthe thesame sametime, time, basically meeting requirements of vehicle comfort handling stability. and handling stability. On the above research, thisthis paper proposes a structure of a vehicle semi-active energy the basis basisofofthe the above research, paper proposes a structure of a vehicle semi-active regenerative suspension with an electro-hydraulic actuator (EHA) in Section 2. A quarter-car model energy regenerative suspension with an electro-hydraulic actuator (EHA) in Section 2. A quarter-car with two degrees of freedom is built in Section 3.1; then, a mechanical properties test is carried model with two degrees of freedom is built in Section 3.1; then, a mechanical properties testout, is and according toaccording the test results, identification for the systemfor model using carried out, and to thewe testperform results, the we parameter perform the parameter identification the system a recursive least squares algorithm in Section 3.2; and nonlinear model the semi-active model using a recursive least squares algorithm in the Section 3.2; and theofnonlinear model energy of the regenerative suspension with an EHA is established Section 3.3. In Section 4, a LQG strategy semi-active energy regenerative suspension with aninEHA is established in Section 3.3.control In Section 4, a for thecontrol semi-active energy regenerative suspension with an EHAsuspension is designed. Moreover, LQG strategy for the semi-active energy regenerative with an EHAthe is influences designed. of the main the parameters of the on theparameters damping performance regenerative performance Moreover, influences of EHA the main of the EHAand on energy the damping performance and of the suspension are analyzed in Section then, the main parameters the EHA optimized via energy regenerative performance of the5.1; suspension are analyzed in ofSection 5.1;arethen, the main the genetic algorithm in Section 5.2; and the bench test is carried out in Section 5.4. Finally, conclusions parameters of the EHA are optimized via the genetic algorithm in Section 5.2; and the bench test is are summarized in Section 6. carried out in Section 5.4. Finally, conclusions are summarized in Section 6. 2. Structure and and Principle Principle of of the the Semi-Active Semi-Active Energy 2. Structure Energy Regenerative Regenerative Suspension Suspension with with an an EHA EHA The system with with an an EHA The basic basic structure structure of of the the semi-active semi-active energy energy regenerative regenerative suspension suspension system EHA is is shown in Figure 1. The system is mainly composed of a spiral spring, a hydraulic cylinder, a hydraulic shown in Figure 1. The system is mainly composed of a spiral spring, a hydraulic cylinder, a motor, a brushless motor, aDC digital signal processor controller, a composite energy recovery energy device, hydraulic motor, aDC brushless motor, a digital signal processor controller, a composite and a digital potentiometer and the corresponding sensor. The hydraulic cylinder uses a double recovery device, and a digital potentiometer and the corresponding sensor. The hydraulic cylinder pole cylinder; the hydraulic uses a gear motor can uses double-acting a double pole symmetrical double-actinghydraulic symmetrical hydraulic cylinder;motor the hydraulic motor usesthat a gear carry out positive inversion; and the brushless DC generator uses a permanent magnet brushless DC motor that can carry out positive inversion; and the brushless DC generator uses a permanent generator [16]. magnet brushless DC generator [16].

Figure 1. The structure of the semi-active energy regenerative suspension with an electro-hydraulic Figure 1. The structure of the semi-active energy regenerative suspension with an electro-hydraulic actuator (EHA). DC: direct current. actuator (EHA). DC: direct current.

When the vehicle is running, the hydraulic cylinder moves with the body vibration and pushes When thetovehicle is running, themotor hydraulic cylinder moves with body vibrationmotor and pushes hydraulic oil drive the hydraulic to rotate, the output shaftthe of the hydraulic drives hydraulic oil to drive the hydraulic motor to rotate, the output shaft of the hydraulic motor drives the coaxial brushless DC generator by coupling, and the generated electrical energy is recovered and the coaxial generator by coupling, the energy generated electrical energy is recovered stored by a brushless compositeDC energy recovery device toand realize regeneration in the EHA energy and stored bysuspension. a compositeAt energy recovery device to realize energy regeneration in the EHA energy regenerative the same time, the sensor sends a signal of the vehicle’s operation regenerative suspension. At the same time, the sensor sends a signal of the vehicle’s operation condition condition to the controller. According to the control strategy, the controller changes the external load


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to the controller. According to the control strategy, the controller changes the external load resistance resistance of theDC brushless DCadjusting motor by the adjusting value of the digital potentiometer. value of the value brushless motor by value the of the digital potentiometer. Therefore, Therefore, the electromagnetic torque of the motor can be changed, and the damping force of the the electromagnetic torque of the motor can be changed, and the damping force of the hydraulic hydraulic cylinder can be controlled to realize the control function of the EHA semi-active cylinder can be controlled to realize the control function of the EHA semi-active suspension. suspension. The composite energy recovery device is shown in Figure 2. The device is mainly composed The composite energy recovery device is shown in Figure 2. The device is mainly composed of a of a three-phase rectifier, a filter circuit, boost module 1, boost module 2, MOSFET A, MOSFET B, three-phase rectifier, a filter circuit, boost module 1, boost module 2, MOSFET A, MOSFET B, a a voltage equalizing circuit, a super capacitor group, a voltage sensor, a DSP controller, a voltage voltage equalizing circuit, a super capacitor group, a voltage sensor, a DSP controller, a voltage stabilizing circuit, a adiode, them,the thesuper supercapacitor capacitorgroup group consists stabilizing circuit, diode,and andaastorage storagebattery. battery. Among Among them, consists of of four capacitors from the 2.7 V 100 F super capacitor series, in which the voltage is 10.8 V, the capacity four capacitors from the 2.7 V 100 F super capacitor series, in which the voltage is 10.8 V, the is 25 F, andisthe charging 9–10 V.isBoost boosts 1toboosts 9 V for capacity 25 optimal F, and the optimalvoltage chargingisvoltage 9–10 module V. Boost 1module to super 9 V forcapacitor super charging. Referring to the vehicle battery, the lead-acid battery used is 12 V 8 ampere-hour, in capacitor charging. Referring to the vehicle battery, the lead-acid battery used is 12which V the8optimal charging voltagethe is 14.4 ± 0.2charging V. Booster module 2 boosts V formodule charging the battery ampere-hour, in which optimal voltage is 14.4 ± 0.2 to V.14.4 Booster 2 boosts to after stabilizing Inthe order to prevent thecircuit. batteryInfrom super 14.4the V voltage for charging the batcircuit. tery after voltage stabilizing orderover-charging to prevent the the battery capacitor, a unidirectional conducting diode is connected conducting in series between voltage stabilizing from over-charging the super capacitor, a unidirectional diode isthe connected in series circuit and the storage battery. between the voltage stabilizing circuit and the storage battery. Brushless DC motor

Threephase rectifier

Filter circuit

Boost module 1

MOSFET A

pulse width modulation 1

Voltage equalizing circuit Super capacitor group

Storage battery

Diode

Voltage stabilizing circuit

Boost module 2

MOSFET B

Voltage sensor

DSP controller

pulse width modulation 2

Figure2.2.Illustrative Illustrativediagram diagram of of the the complex Figure complexenergy energyrecovery recoverydevice. device.

The specific working process of the composite energy recovery device is as follows. The voltage The specific working process of the energy recovery is as follows. Theby voltage sensor connected in parallel at both endscomposite of the super capacitor groupdevice is detected in real-time the sensor connected in parallel at both ends of the super capacitor group is detected in real-time by the super capacitor group’s voltage signal, which is collected in the DSP controller by the A/D sampling super capacitor voltageWhen signal, which is collected in the DSP controller by group the A/D sampling module of the group’s DSP controller. the voltage at both ends of the super capacitor is detected module of the controller. When the voltage at both ends of the super capacitor is detected to reach 4 V,DSP the DSP controller outputs two pulse width modulation signals. Onegroup output, pulse to reach 4 V, the DSP controller outputs two pulse width modulation signals. One output, pulse width width modulation 1, is high and it drives the MOSFET switch A to open. The other output, modulation 1, is high and it2,drives the MOSFET switch A toswitch open. BThe otherAt output, pulse width pulse width modulation is low and it drives the MOSFET to close. this moment, the modulation 2, is low and it drives the MOSFET switch B to close. At this moment, the super capacitor super capacitor group is in charge status and the three-phase alternating current generated by the group is in DC charge status and athe three-phase alternating current generated by the brushless brushless motor through three-phase rectifier bridge and a filter circuit becomes a stable DCDC motor through three-phase and a filter circuit becomes a is stable DC charged voltage by that voltage that isaboosted to 9 Vrectifier by boostbridge module 1. The super capacitor group steadily 9 is boosted to 9 V by boost The super group is steadily byat9 both V’s voltage V’s voltage through themodule MOSFET1.switch A andcapacitor the equalizing circuit. When charged the voltage ends of the the super capacitor group detected to reach circuit. 9 V, theWhen DSP controller outputs two pulse width through MOSFET switch A isand the equalizing the voltage at both ends of the super modulation One output, modulation is hightwo andpulse it drives themodulation MOSFET capacitor groupsignals. is detected to reachpulse 9 V, width the DSP controller 2, outputs width switchOne B tooutput, open. The other output, pulse width 1, is low it drives the MOSFET signals. pulse width modulation 2, is modulation high and it drives theand MOSFET switch B to open. switch A to close. At this moment, the super capacitor group is in discharge status and the output The other output, pulse width modulation 1, is low and it drives the MOSFET switch A to close. At this voltagethe of the super capacitor grope boosted tostatus 14.4 Vand by the boost module 2. The battery is moment, super capacitor group is inis discharge output voltage of storage the super capacitor steadily charged V’sboost voltage through voltage stabilizing In charged order toby prevent grope is boosted to by 14.414.4 V by module 2. The storage battery iscircuit. steadily 14.4 V’s over-discharge of the super capacitor group, minimum discharge voltage ofofthe super capacitor voltage through voltage stabilizing circuit. In the order to prevent over-discharge the super capacitor group is set at 4 V, that is, when the voltage sensor detects that the voltage between the two ends ofthe group, the minimum discharge voltage of the super capacitor group is set at 4 V, that is, when the super capacitor reaches 4 V,between the mode is two converted, whole systemgroup performs cyclic4 V, voltage sensor detectsgroup that the voltage the ends ofand thethe super capacitor reaches discharge. thecharge mode and is converted, and the whole system performs cyclic charge and discharge.

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3. Nonlinear Energy Regenerative Regenerative Suspension Suspension with with an an EHA EHA 3. Nonlinear Modeling Modeling of of the the Semi-Active Semi-Active Energy 3.1. Dynamic Model of a Two Degrees Degrees of of Freedom Freedom Suspension Suspension System System for for aa Quarter-Vehicle Quarter-Vehicle In this paper, a quarter-car model with two degrees of freedom was exactly established established [17], [17], which is shown in Figure Figure 3. 3.

Figure 3. The schematic diagram of the quarter-car model. Figure 3. The schematic diagram of the quarter-car model.

According to Figure 3, the equations of motion are obtained by using Newton’s laws of motion: According to Figure 3, the equations of motion are obtained by using Newton’s laws of motion:    F ( .. ms x2  k s x2  x1   cs .x2  x.1   mk sx( x2k−xx1)x+ csc xx2 − (1) ms x2 + F  xx1.1k= u 1 s 2 1 s t x1  z    F (1) ..  .2 . mu x1 − k s ( x2 − x1 ) − cs x2 − x1 + k t ( x1 − z) = − F. The state vector and output vector are selected as follows: The state vector and output vector are selected as follows:

X  x2  x1

x1  z

x.2

T

T .x x1 1

X = x2 − x1 x 2 x1 − z .. . TT Y Y = xx2 xx2 −xx1 kkt (xx1 −zz) xx1



2

2

1

t

1

1



..

where x2 is the sprung mass acceleration, x2 − x1 is the suspension deflection response, k t ( x1 − x0 ) is where x2 is the sprung. mass acceleration, x2  x1 is the suspension deflection response, the tire load response, and z(t) is the speed excitation of the road input. In this way, the state equation tire be load response, and z (t ) is the speed excitation of the road input. In this way, kt the x1 suspension x0  is the can of obtained as follows: ( obtained the state equation of the suspension can be as follows: . X = AX + BU (2)  XY =  CX AX+DU BU (2) 

Y  CX  DU

where A is the state matrix, B is the input matrix, C is the output matrix, and D is the transfer matrix. where the is the input state force matrix, the input matrix,suspension. C is the output matrix, and D is the A control When F is B 0, itisbecomes a passive transfer matrix. When thecontrol input force F is 0, it becomes   a passive suspension.  0 1 0 −1 0 0   0   k s0 0 01   cs1 c s 1   0   −     m k s − m cs 0 c 1ms     s m s s s    A =    0 0 B =  − 1 m 1 m0       0 ms 0 ms 0 s s    A k s 1 cs 0 k t0 cs1  B  0  1 0 − −   0 − mu muk  muc  1   muk s mucs  t s  1 0  cs cs ks   − − 0 mu 0 ms  mu . !  msmu ms mu mm s u     z 0 0 U = 1 0 = C= cs 0 0 cs   ks D    1  F  0  m 0 m k t 0 0 m  00 0m  s 0 s0 1 s  D  0 0 s  U  zz  C 0

0 0 U  F  1 0 0 0  0   F   0 [18] 0 as 0 filtered kt 0 white The road surface inputmodel adopts follows:  noise 0 0  0 0 1     0 p .

z(t) = −2π f 0 z(t) + 2π G0 uω (t) The road surface input model adopts filtered white noise [18] as follows:

(3)

where z is the input displacement zof road, irregularities coefficient, f 0 is the lower (t )the  2f 0G z (0t is ) the 2road G0u  (t ) (3) cutoff frequency, u0 is the vehicle speed, and ω (t) is unit white noise.

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z is the input displacement of the road, G0 displacement of the road, G0 lower cutoff frequency, u 0 is the vehicle speed, and lower cutoff frequency, u 0 is the vehicle speed, and where

Algorithms 11, 12 where z 2018, is the input

is the road irregularities coefficient, f 0 is the 5 ofthe 17 is the road irregularities coefficient, f 0 is  (t ) is unit white noise.  (t ) is unit white noise.

3.2. Parameter Identification Identification of 3.2. Parameter of Nonlinear Nonlinear Model Model 3.2. Parameter Identification of Nonlinear Model In order to model parameter parameter identification, identification, aa physical In order to provide provide experimental experimental sample sample data data for for the the model physical prototype of an EHA, which is mainly composed of a hydraulic cylinder, a hydraulic motor, In order to provide experimental sample data for the model parameter identification, a physical prototype of an EHA, which is mainly composed of a hydraulic cylinder, a hydraulic motor, and a and a brushless DC motor, is developed, and according to the national standards of QC/T545-1999 prototype of an EHA, which is mainly composed of a hydraulic cylinder, a hydraulic motor, brushless DC motor, is developed, and according to the national standards of QC/T545-1999 and “Testa “Test method for automobile telescopic shock absorber”, a force characteristics test of an EHA brushless DC motor, is developed, and according to the national standards of QC/T545-1999 “Test method for automobile telescopic shock absorber”, a force characteristics test of an EHA semi-active semi-active suspension system is carried out on an ES-6-230 numerical control hydraulic vibration method for automobile telescopic force characteristics test of anvibration EHA semi-active suspension system is carried outshock on anabsorber”, ES-6-230 anumerical control hydraulic table as table as shown in Figure 4. In the experiment, the vibration table input excitation uses sinusoidal input suspension system is carried out on an ES-6-230 numerical control hydraulic vibration table as shown in Figure 4. In the experiment, the vibration table input excitation uses sinusoidal input at the at the frequency of 1 Hz and the amplitude of 30 mm. An LTR-1 pull pressure sensor is used to collect shown in Figure 4. In the experiment, the vibration table input excitation uses sinusoidal input at the frequency of 1 Hz and the amplitude of 30 mm. An LTR-1 pull pressure sensor is used to collect the the suspension’s force signal in the passive and the change ofsuspension’s the suspension’s output frequency of 1output Hzoutput and the amplitude ofpassive 30 mm. Anstate, LTR-1 pull pressure sensor is used to collect the suspension’s force signal in the state, and the change of the output force force with time is shown in Figure 5. In order to eliminate influence of initial conditions on the test suspension’s output force signal in the passive state, and the change of the suspension’s output force with time is shown in Figure 5. In order to eliminate the influence of initial conditions on the test results, the time starts 55 s. with time shown in Figure 5. from In order results, theissampling sampling time starts from s. to eliminate the influence of initial conditions on the test results, the sampling time starts from 5 s.

force/(N) force/(N) Output Output

Figure 4. Force characteristic test of the EHA semi-active suspension system. Figure 4. 4. Force Force characteristic characteristic test test of of the the EHA EHA semi-active semi-active suspension Figure suspension system. system. 2000 2000 1500 1500 1000 1000 500 500 0 0 -500 -500 -1000 -1000 -1500 -1500 -2000 5 -2000 5

Test value Simulation Test value value Simulation value

5.5 5.5

6 Time/(s) 6 Time/(s)

6.5 6.5

7 7

Figure 5. Comparison of simulation and experimental results of output force. Figure of output output force. force. Figure 5. 5. Comparison Comparison of of simulation simulation and and experimental experimental results results of

The parameters of the nonlinear model are continuously approximated by the least squares The parameters of the nonlinear model are continuously approximated by the least squares method on the experimental data,model and the function of the algorithm is expressed as: Thebased parameters of the nonlinear areobjective continuously approximated by the least squares method based on the experimental data, and the objective function of the algorithm is expressed as: method based on the experimental data, and the objective function of ks , cs   arg min Fc ks , cs   Fe 222 the algorithm is expressed as: (4) k s min , cs kks ,, cc s  = arg Fc k s , cs   Fe 22 (4) (4) { s s } argmin k s ,cs k Fc ( k s , c s ) − Fe k2 k ,c s s where k s is the equivalent spring stiffness, c s is the inherent damping coefficient of the system, where k s is the equivalent spring stiffness, c s is the inherent damping coefficient of the system, where k s istheoretical the equivalent spring stiffness, damping Fc is the model value, and Fecs is the inherent actual test value. coefficient of the system, Fc is the Fc is the theoretical Fe is model and thevalue. actual test value. theoretical model value, andvalue, Fe is the actual test


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Through the identification of the parameters, the equivalent spring stiffness k s of the EHA semi-active suspension system is 13,000 N/m, and the inherent damping coefficient cs is 500 N · m/s. The above parameters are introduced into the two degrees of freedom suspension dynamics model of the quarter-vehicle, and the simulation results of the EHA actuator output force are compared with the test results, as shown in Figure 5. Figure 5 shows that the output force of the EHA actuator obtained by parameter identification is in good agreement with the actual output force, which indicates that the established dynamic model of the two degrees of freedom suspension system for a quarter-vehicle is accurate, and the adopted method of model parameter identification is feasible and effective. 3.3. Mathematical Model of the Semi-Active Energy Regenerative Suspension with an EHA When the mathematical model of the EHA actuator is established, the friction between the piston, the cylinder wall, and the internal leakage of the system is ignored. Thus, the damping force generated by the hydraulic cylinder can be expressed as: F = ∆P · A

(5)

where ∆P is the pressure drop between the upper and lower surface of the piston in the hydraulic cylinder, and A is the effective piston area. We take into account the hydraulic pipeline’s pressure loss, which includes the pressure loss along the path and the local pressure loss [19]. The pressure loss along the path of the hydraulic pipeline in the system is expressed as: l ρν2 ∆Pλ = λ ( ) d 2

(6)

where λ is the along resistance coefficient, l is the length of the hydraulic pipe, d is the diameter of the hydraulic pipe, ρ is the hydraulic oil’s density, and ν is the oil flow rate in the pipeline. The local pressure loss of the hydraulic pipeline in the system is expressed as: ∆Pζ = ζ

ρν2 2

(7)

where ζ is the local resistance coefficient. It can be seen that the total pressure loss of the hydraulic pipeline in the system can be obtained as follows: 2 l ρν ∆Pg = ∆Pλ + ∆Pζ = λ + ζ (8) d 2 according to the continuity equation of liquid flow, which is given by: Qd = A · νg =

πd2 ν 4

(9)

where Qd is the flow of the hydraulic motor, and νg is the speed of the piston rod. According to the working principle of the semi-active energy regenerative suspension with an EHA, it can be seen that under the action of body vibration the oil in the hydraulic cylinder enters the hydraulic motor and drives the hydraulic motor to work, and the output torque of the hydraulic motor drives the generator to generate electricity. At the same time, the angular velocity and output torque of the hydraulic motor meet the following relationships: ω0 =

2πQd ην q

(10)

Td =

∆pd q ηm 2π

(11)


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where q is the hydraulic motor displacement, ην is the volumetric efficiency of the hydraulic motor, ∆pd is the pressure drop between the inlet and the outlet of the hydraulic motor, and ηm is the mechanical efficiency of the hydraulic motor. The generator converts the mechanical energy of the hydraulic motor into electrical energy, so the input torque of the generator is equal to the output torque of the hydraulic motor. Therefore, the output voltage U and the output torque Tg of the generator meet the following relationships: U = E − I (r + R) = IR0 ..

Tg = J θ + k t I

(12) (13)

where E is the induced electromotive force, I is the loop current, r is the internal resistance of the generator, R is the external load resistance of the generator, R0 is the equivalent resistance of the energy .. regenerative circuit, J is the moment of inertia, θ is the angular acceleration of the generator, and k t is the torque constant of the generator. Among them, the induction electromotive force is expressed as: E = ke n =

30 ke ω π

(14)

where k e is the back electromotive force constant of the generator, n is the generator rotor speed, and ω is the generator rotor angular velocity. The hydraulic motor is directly connected with the generator through the coupling, so their angular velocity and torque are equal, which is expressed as ω0 = ω and Td = Tg . If the moment of inertia of the motor is ignored, the pressure drop between the inlet and the outlet of the hydraulic motor can be obtained from Equations (9)–(14) as follows: ∆Pd =

120πk e k t ηv Av g . m (r + R + R0 )

q2 η

The pressure balance equation of the whole hydraulic circuit be expressed as: 8ρA2 νg2 120πk e k t ηv Av g l ∆P = ∆Pd + ∆Pg = 2 + λ +ζ d q ηm (r + R + R0 ) π 2 d4

(15)

(16)

The damping force of the EHA actuator can be obtained by taking Equation (16) into Equation (14) as follows: 8ρA3 νg2 120πk e k t ηv A2 v g l F= 2 + λ +ζ . (17) d q ηm (r + R + R0 ) π 2 d4 Therefore, the equivalent damping coefficient of the EHA actuator can be expressed as: 8ρA3 νg 120πk e k t ηv A2 l ceq = 2 + λ +ζ . d q ηm (r + R + R0 ) π 2 d4 The loop current can be obtained from Equations (11), (13), and (15) as follows: 4ρqηm A2 νg2 60k e ηv Av g l I= + λ +ζ . q (r + R + R0 ) d π 3 d4 k t In summary, the instantaneous energy regenerative power can be expressed as: #2 " 4ρqηm A2 νg2 60k e ηv Av g l 2 Preg = I R0 = + λ +ζ R0 q (r + R + R0 ) d π 3 d4 k t

(18)

(19)

(20)

In the traditional passive suspension damper, the dissipated power in the form of heat energy is calculated as: .

.

Pcon = cs x2 − x1

2

(21)


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. . where cs is the inherent damping coefficient, and x2 − x1 is the shock absorber velocity. The energy regenerative efficiency of a semi-active suspension is the ratio between the feedback energy and the dissipated energy of the passive suspension. Therefore, the energy regenerative efficiency η is expressed as: RT 0 Preg dt i h η= R . (22) . . 2 T dt 0 cs x2 − x1

4. The Control Strategy of the Semi-Active Energy Regenerative Suspension with an EHA The selection principle of switching the control critical point to control the force of the semi-active energy regenerative suspension with an EHA is expressed as follows: . . . When x2 · ( x2 − x1 ) > 0, the direction of the force applied to the spring mass by the actuator is opposite to the movement direction of the spring mass, but it has the same direction as the active control force, so it can change the external load resistance of the actuator to make the actual control output force be equal to the theoretical active control output force. Additionally, the theoretical active control output force is determined by the optimal control strategy. The optimal control objective of the semi-active energy regenerative suspension with an EHA is to make the car obtain higher comfort and handling stability, and reflecting in the amount of actual control is to reduce the acceleration of the sprung mass and tire dynamic load as much as possible, limit the range of the suspension’s dynamic deflection, and reduce the possibility of suspension impact block. At the same time, it should not consume too much energy [20]. Based on the above considerations, the performance index function of a semi-active suspension output regulator can be written as follows: Z ∞h i .. 2 J= q1 x2 + q2 ( x2 − x1 )2 + q3 ( x1 − z)2 + rF2 dt (23) 0

where q1 is the weighting coefficient of acceleration, q2 is the weighting coefficient of the suspension’s dynamic deflection, q3 is the weighting coefficient of tire dynamic deformation, and r is the weighting coefficient of energy consumption. The above optimization index is expressed in matrix as: Z ∞h i J= Y T qY + F T rF dt (24) 0

where q is expressed as: 

q1  q= 0 0

0 q2 0

 0  0 . q3

Generally, the output regulator problem is converted to a state regulator problem. Taking the output equation Y = CX + DU into Equation (24), the quadratic performance index is given by: J=

Z ∞h 0

i X T QX + 2X T NF + F T RF dt

(25)

where Q are the positive semidefinite symmetric weighting matrices of the state variables, N is the weighted matrix of two kinds of variables, and R is the positive definite symmetric weighting matrix of the control variables. Among them, Q = C T qC, N = C T qD, R = r + D T qD. The optimal control force F, which serves for performance index J, to be minimized is existent and unique, and it can be expressed as: F = −KX = −( B T P + N T ) X

(26)

where P is a symmetric positive definite solution of the Riccati matrix equation. It meets the following equation:


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PA + AT P − ( PB + N) R−1 (BT P + NT ) + Q = 0.

(27)

The selection of the weighting factors in the performance index of the optimal control depends on practical experience. After repeated trials, the following options can be made: q1 = 1.2 × 105 , q2 = 1.65 × 108 , q3 = 9.5 × 109 , r = 1. In order to obtain the feedback gain matrix K, using the linear quadratic regulator function provided by Matlab software, the basic format is expressed as:

(K, S, E) = LQR( A, B, Q, R, N )

(28)

where S is the solution of the Riccati equation, and E is the system eigenvalue. . . . When x2 · ( x2 − x1 ) < 0, the direction of the force applied to the spring mass by the actuator has the same direction as the movement direction of the spring mass, but it is opposite to that of the active control force. In order to minimize this difference, at this moment the damping force, which is theoretically required to output from the suspension, is zero, but the actual output force is the inherent viscous damping force of the system, and its true value is still determined by Formula (17). At the same time, the motor load resistance is zero. 5. Parameter Optimization of the Semi-Active Energy Regenerative Suspension with an EHA 5.1. Parameter Sensitivity Analysis In order to coordinate the damping performance and energy regenerative performance of the semi-active energy regenerative suspension with an EHA and improve the energy regenerative performance under the condition of satisfying the requirement of damping performance, the influence of the EHA’s parametric variation on the damping performance and energy regenerative performance of the suspension is analyzed. The EHA is mainly composed of a hydraulic cylinder, a hydraulic motor, and a brushless DC generator. According to the modeling process, it can be known that the main parameters of the EHA are: the effective area of the hydraulic cylinder piston A, the displacement of the hydraulic motor q, and the back electromotive force constant of the generator k e . Based on the initial simulation parameters’ value of the EHA and 20% of the initial simulation parameters’ value of the EHA for the change interval, the influence of the three main parameters’ variation of the EHA on the damping performance and energy regenerative performance of the semi-active energy regenerative suspension with the EHA is investigated. Among them, the damping performance takes spring mass acceleration and tire dynamic load as evaluation indicators, and energy regenerative performance takes energy regenerative power and energy regenerative efficiency as evaluation indicators. The influence of the main parameters of the EHA on the performance evaluation indicators is shown in Figures 6–8, respectively. Figure 6 shows that, firstly, with the increase of the effective area of the hydraulic cylinder piston, the RMS values of the sprung mass acceleration and the dynamic load of the tire decrease gradually. Then, they reach the minimum at nearly 1.2 times the value of the original simulation parameters of the hydraulic cylinder piston’s effective area, which makes riding comfort continuously improve and the damping performance achieve an optimal effect. Finally, with the increase of the effective area of the hydraulic cylinder piston, the RMS values of the sprung mass acceleration and the dynamic load of the tire increase gradually, which leads to deterioration of ride comfort and the damping performance. However, with the increase of the effective area of the hydraulic cylinder piston, the RMS values of the energy regenerative power and the energy regenerative efficiency increase gradually, that is to say, the energy regenerative performance improves continuously. However, when the RMS values of the energy regenerative power and the energy regenerative efficiency reach the maximum, which means that the energy regenerative efficiency is optimal, the RMS values of the sprung mass acceleration and the dynamic load of the tire reach the maximum too, which leads to damping performance deterioration without meeting the design requirements of the suspension.


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1600 The RMS value of sprung mass acceleration The RMS value of tire dynamic load

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Algorithms 2018, 11, x FOR PEER REVIEW 1 60

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The RMS value of sprung mass acceleration/(m·s-2)

indicators, and energy regenerative performance takes energy regenerative power and energy regenerative efficiency as evaluation indicators. The influence of the main parameters of the10EHA Algorithms 2018, 11, 12 of 17 on the performance evaluation indicators is shown in Figures 6–8, respectively.

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0 160

140

Change from the initial simulation value of Aperformance /(%) Change fromregenerative the initial simulation value of A/(%) and energy indicators, and energy regenerative takes energy power (a) (b)parameters of the EHA on regenerative efficiency as evaluation indicators. The influence of the main the performance evaluation indicators is shown in Figures 6–8, respectively.

1000 600 the

The RMS value of energy regenerative power Energy regenerative efficiency

50


energy regenerative RMS The power/(W)power/(W) energyofregenerative of value value The RMS

1400


The RMS value of sprung mass acceleration The RMS value of tire dynamic load

4.5 The RMS value of sprung mass acceleration/(m·s-2)


Figure 6. Influence of of thethe effective area ofof the hydraulic Figure 6. Influence effective area the hydrauliccylinder cylinderpiston pistonon onevaluation evaluation indicators: indicators: (a) Influence of the effective area of the hydraulic cylinder piston on the damping performance; (a) Influence of the effective area of the hydraulic cylinder piston on the damping performance; (b) 5 1600 cylinder1200 60 Influence of theofeffective areaarea of the hydraulic regenerativeperformance. performance. (b) Influence the effective of the hydraulic cylinderpiston pistonon onenergy energy regenerative

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of tire dynamic RMSofvalue The load/(N)load/(N) tire dynamic value The RMS

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efficiency/(%) regenerative efficiency/(%) regenerative Energy Energy

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The RMS value of energy regenerative power/(W) The RMS value of energy regenerative power/(W)


-

2) mass acceleration/(m·s sprung of mass RMS The 2) acceleration/(m·s sprung ofvalue value The RMS

5 7 shows that, firstly, with the increase 1300 4 Figure of displacement of the hydraulic 60motor, the The RMS value of energy regenerative power The RMS value of sprung mass acceleration RMS values sprung mass and the dynamic of the tire decrease gradually. 800 40 Energyload regenerative efficiency The RMS value of tire dynamicacceleration load 3.5 4.5 of the 1200 500 50 Then, they 4reach the minimum at nearly 0.81100 times the value of the original simulation parameters 3 600 30 of the displacement of the hydraulic motor, which makes and 400 riding comfort continuously improve 40 3.5 1000 2.5 the damping performance achieve an optimal effect. Finally, with the increase of the displacement 400 20 300 3 900 of the hydraulic motor, the RMS values of the sprung mass acceleration and the dynamic 30load of the 2 800 2.5 gradually, which leads to the deterioration 200 10 tire increase 200of ride comfort and damping performance. 20 1.5 However, with the increase of the displacement 2 700 of the hydraulic motor, the RMS values of the energy 1 600 0 1000decrease 60 80 100 120 140 160 80 gradually, 100 120 is to 140say,10the 160 energy regenerative that 1.5 power and the energy regenerative efficiency 60 Change from the initial simulation value of A/(%) Change from the initial simulation value of A/(%) regenerative performance deteriorates continuously. However, when the RMS values of the energy 0 0 1 500 (a) 120 regenerative 60 80 100 (b)120 140 160 80 140 160 regenerative60 power and100 the energy efficiency reach the maximum, which means that the Change from the initial simulation value of q/(%) Change from the initial simulation value of q/(%) energy efficiency RMS values of thepiston sprung acceleration and(a) the Figureregenerative 6. Influence of the effective area of the hydraulic cylinder onmass evaluation indicators: (a) is optimal, (b) dynamic load of the tire reach the maximum too, which leads to damping performance deterioration Influence of the effective area of the hydraulic cylinder piston on the damping performance; (b) Figuremeeting 7. Influence of the displacement ofof the hydraulic motor on evaluation indicators: (a) Influence without design requirements the suspension. Influence of the the effective area of the hydraulic cylinder piston on energy regenerative performance. of the displacement of the hydraulic motor on the damping performance; (b) Influence of the displacement of the hydraulic motor on energy regenerative performance.

(b)160 180 200 220 2400 80 100 120 140 Change from the initial simulation value of ke/(%)

1000 900

800

80

600

60

efficiency/(%)

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The RMS value of tire dynamic load

generative power/(W)

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dynamic load/(N)

ss acceleration/(m·s-2)

Figure 7. Influence ofofthe of the thehydraulic hydraulic motor evaluation indicators: (a) Influence (a) (b) Figure 7. Influence thedisplacement displacement of motor onon evaluation indicators: (a) Influence of of the displacement of hydraulic the hydraulic motor on the performance; damping performance; (b)theInfluence of the the displacement of the motor on the damping (b) Influence of displacement Figure 8. Influence of the back electromotive force constant of the generator on evaluation indicators: displacement of themotor hydraulic motor on energyperformance. regenerative performance. of the hydraulic on energy regenerative (a) Influence of the back electromotive force constant of the generator on the damping performance; (b) Influence of the back electromotive force constant of the generator on energy regenerative 1000 4 1100 The RMS value of energy regenerative power 100 performance. The RMS value of sprung mass acceleration Energy regenerative efficiency

(a)

(b)

Figure 6. Influence of the effective area of the hydraulic cylinder piston on evaluation indicators: (a) Influence of the effective area of the hydraulic cylinder piston on the damping performance; (b) Influence of the effective area of the hydraulic cylinder piston on energy regenerative performance. 5

1300 The RMS value of sprung mass acceleration simulation show The RMS value ofresults tire dynamic load that,


11 of 17 The RMS value of tire dynamic load/(N)


Algorithms 2018, 11, 12 600

60 The RMS value of energy regenerative power Energy regenerative increase of theefficiency back electromotive 50

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4.5 8 Figure firstly, with500the force constant of the generator, the RMS values of the sprung mass acceleration and the dynamic load 4 1100 400 40 of the tire decrease gradually. Then, they reach the minimum at nearly 1.8 times the value of the 3.5 original simulation parameters of the back electromotive force constant of the generator, which makes 300 30 3 900 riding comfort continuously improve and the damping performance achieve an optimal effect. Finally, with the 2.5 increase of the back electromotive force constant of the generator, the RMS values of the 200 20 sprung mass acceleration and the dynamic700load of the tire increase gradually, which leads to the 2 100 deterioration of ride comfort and damping performance. However, with the increase of10 the back 1.5 electromotive force constant of the generator, the RMS values of the energy regenerative power and 0 0 1 500 80 100 120 140 160 80 100efficiency 120 140 160 the energy60regenerative increase gradually, that60 isChange to say, energy regenerative performance from the initial simulation value of q/(%) Change from the initial simulation value of q/(%) improves continuously. However, when the RMS values of the energy regenerative power and the (a) (b) energy regenerative efficiency reach the maximum, which means that the energy regenerative efficiency Figure 7. Influence the displacement of the hydraulic motorand on evaluation indicators: (a) tire Influence is optimal, the RMSofvalues of the sprung mass acceleration the dynamic load of the reach the maximum too, which leads to damping performance deterioration without(b) meeting the design of the displacement of the hydraulic motor on the damping performance; Influence of the requirements of the suspension. displacement of the hydraulic motor on energy regenerative performance.

0 80 100 120 140 160 180 200 220 240 Change from the initial simulation value of ke/(%)

(b)

Figure 8. Influence of the of back force constant of the generator on evaluation indicators: Figure 8. Influence theelectromotive back electromotive force constant of the generator on evaluation (a) Influence theInfluence back electromotive force constant of the generator the damping indicators:of(a) of the back electromotive force constant of theon generator on the performance; damping (b) Influence of the back electromotive force constant of the generator energyonregenerative performance; (b) Influence of the back electromotive force constant of the on generator energy regenerative performance. performance.

From the above study, it can be concluded that with the change of parameters of the EHA, the damping performance and energy regenerative performance cannot achieve an optimal effect at the same time, and there is mutual restriction between them. In order to balance the damping performance and energy regenerative performance, the three main parameters of the EHA, including the effective area of the hydraulic cylinder piston A, the displacement of the hydraulic motor q, and the back electromotive force constant of the generator k e , should be coordinated and optimized. 5.2. Optimization Objectives and Constraints In order to improve the energy regenerative performance under the requirement for meeting a certain damping performance, the genetic algorithm is used to optimize the parameters of the EHA, which can reduce the risk of being trapped in a locally optimal solution and make the optimization results more accurate [21,22]. The parameter optimization of the semi-active energy regenerative suspension with an EHA is a nonlinear optimization problem of a single target and multiple variables. Taking energy regenerative power as the optimization goal, taking a certain damping performance as the constraint condition,


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and taking the effective area of the hydraulic cylinder piston A, the displacement of the hydraulic motor q, and the back electromotive force constant of the generator k e as optimization variables, the genetic algorithm optimization toolbox from Matlab is used to optimize the parameters. The objective function is the RMS value σPreg of the energy regenerative power of the semi-active energy regenerative suspension with an EHA, and σPreg is given by:

σPreg =

v u N u u ∑ Pregi 2 t i =1 N

.

(29)

In the optimization toolbox, the objective function is required to be minimized. In this paper, however, the RMS value of the energy regenerative power is required to be maximized, so the method to minimize the negative value of the objective function is feasible. The constraint condition in this paper is to meet a certain damping performance. According to automobile theory and other related literatures, the damping of vehicle suspension belongs to small damping, and the damping ratio ξ meets the condition 0.2 ≤ ξ ≤ 0.4. Additionally, when the RMS value of the wheel dynamic load σFd does not exceed 1/3 of the static load value, the probability of a wheel jumping off the ground is less than 0.15%, which can ensure the comfort and safety of the suspension [23]. Meanwhile, the optimization toolbox requires that the constraint conditions are not positive. Thus, the constraint conditions meet:  cs + ceq ( X )   0.2 − √ ≤0   2 k s · ms   cs + ceq ( X ) √ − 0.4 ≤ 0   2 k s · ms     σ (X) − 1 G ≤ 0 Fd 3

(30)

where X = { x1 , x2 , x3 } = { A, q, k e } is the optimal parameter vector. 5.3. Optimization Result Analysis The above parameters are brought into the genetic algorithm optimization toolbox, and the optimization results of the semi-active energy regenerative suspension with an EHA are shown in Table 1. Table 1. Optimal parameters. Optimal Parameters

Symbol

Value

The effective area of the hydraulic cylinder piston The displacement of the hydraulic motor The back electromotive force constant of the generator

A q ke

7.66 × 10−4 m2 4.25 mL/r 8.28×10−3 V · min/r

In order to verify the effect of the optimized EHA’s parameters on the performances of the semi-active energy regenerative suspension with the EHA, the performance indexes of the suspension before and after optimization are simulated and compared assuming that the vehicle is traveling at a speed of 20 m/s on a C-grade road and the simulation time is 10 s [24]. Additionally, the simulation results are shown in Table 2 and Figures 9–11. Table 2 shows that after optimizing the parameters, the RMS value of the sprung mass acceleration is reduced by 18.60%, which indicates that the ride comfort of the vehicle has been improved to a certain extent, and the RMS value of the tire dynamic load is decreased by 12.61%, which shows that the vehicle’s driving safety has been enhanced; therefore, the vehicle’s damping performance is improved. After optimizing the parameters, the RMS value of the energy regenerative power increases by 49.67%,

Performance Index

Symbol

Before Optimization

After Optimization

Effect / %

Sprung mass acceleration

a

2.1585 m / s 2

1.7571 m / s 2

−18.60

802.7 N

701.5 N

−12.61

Energy regenerative power

 Fd  Preg

59.82 W

89.53 W

49.67

Energy regenerative efficiency



18.68 %

27.26 %

45.93

Tire dynamic load Algorithms 2018, 11, 12

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and the energy regenerative efficiency increases from 18.68% to 27.26%, which demonstrates that the vehicle’s energy regenerative performance was improved significantly.

Table 2 shows that after optimizing the parameters, the RMS value of the sprung mass acceleration is reduced by 18.60%, which that the ride comfort of the vehicle has been Tableindicates 2. Simulation results. improved to a certain extent, and the RMS value of the tire dynamic load is decreased by 12.61%, Value which shows that theIndex vehicle’s driving vehicle’s damping Symbol safety has been enhanced; therefore, theControl Performance Effect/% Before Optimization After Optimization performance is improved. After optimizing the parameters, the RMS value of the energy Sprung mass acceleration 18.60 2.1585 m/s2 1.7571 m/s2 a regenerative power increases by σ49.67%, and the energy regenerative efficiency−increases from Tire dynamic load σFd 802.7 N 701.5 N −12.61 18.68% Energy to 27.26%, which demonstrates that the energy regenerative performance was σPreg regenerative power 59.82 vehicle’s W 89.53 W 49.67 Energy regenerative efficiency η 18.68% 27.26% 45.93 improved significantly. Before optimization After optimization

Sprung mass acceleration/(m·s-2)

8 6 4 2 0 -2 -4 -6 -8 0

1

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Figure response curve. Figure9.9.Spring Springmass mass acceleration acceleration response curve. Algorithms 2018, 11, x FOR PEER REVIEW 3000

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Before optimization After optimization

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Figure loadresponse response curve. Figure10. 10.Tire Tiredynamic dynamic load curve. 700

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Figure 10. Tire dynamic load response curve.

Energy regenerative power/(W)

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1

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5

Time/(s)

Figure 11.11. Energy powerresponse responsecurve. curve. Figure Energyregenerative regenerative power

5.4. Test 5.4. and Test Analysis and Analysis In order to further verify optimizationresults, results, the is redeveloped based on on In order to further verify thethe optimization theEHA EHAprototype prototype is redeveloped based the optimization results, and the bench test is carried out as shown in Figure 12. In addition, the EHA the optimization results, and the bench test is carried out as shown in Figure 12. In addition, the in in Figure 4 is 4the EHA actuator before optimization, and the EHA actuator in Figure 12 in EHAactuator actuator Figure isoriginal the original EHA actuator before optimization, and the EHA actuator is the optimized one. Due to the limitation of test conditions, the test is conducted only for the spring Figure 12 is the optimized one. Due to the limitation of test conditions, the test is conducted only for mass acceleration and the energy regenerative power of the semi-active suspension with an EHA. the spring mass acceleration and the energy regenerative power of the semi-active suspension with In the test, the DH186 acceleration sensor produced by Donghua testing company is used to collect the an EHA. In the test, the DH186 acceleration sensor produced by Donghua testing company is used to spring mass acceleration signal, and the rectifier is used to rectify the three-phase alternating current collect the spring acceleration andtime, the the rectifier is DH5902 used todata rectify the three-phase generated by themass DC brushless motor. signal, At the same Donghua acquisition system alternating current generated by the DC brushless motor. At the same time, the Donghua DH5902 is used to collect the feed voltage signal. Additionally, according to the relationship between power, data voltage, acquisition system is resistance used to collect the feed voltage signal. Additionally, to the and the internal of the motor, the instantaneous energy regenerativeaccording power can be relationship power, voltage, and the internal resistance of the motor, obtained.between Under the condition that the sinusoidal is input at the frequency of 2 Hz,the the instantaneous amplitude of 30 mm, and the sampling of 10 s, the test results of the spring acceleration energy regenerative power can time be obtained. Under the condition that mass the sinusoidal is response input at the and energy regenerative power response of the semi-active suspension with an EHA before and after frequency of 2 Hz, the amplitude of 30 mm, and the sampling time of 10 s, the test results of the optimization are shown in Figures 13 and 14, respectively. spring mass acceleration Algorithms 2018, 11, x FOR PEERresponse REVIEW and energy regenerative power response of the semi-active 15 of 17 suspension with an EHA before and after optimization are shown in Figures 13 and 14, respectively.

Figure 12. Bench test of EHA semi-active suspension system. Figure 12. Bench test of EHA semi-active suspension system.

cceleration/(m· s-2)

6 4 2 0

Before optimization

After optimization


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-2 Spring mass acceleration/(m· Spring mass acceleration/(m· s-2s) )

Figure 12. Bench test of EHA semi-active suspension system. Figure 12. Bench test of EHA semi-active suspension system.

6 6

Before optimization Before optimization

After optimization After optimization

4 4 2 2 0 0 -2 -2 -4 -4 -6 -60 0

2 2

4 6 4 Time/(s) 6 Time/(s)

8 8

10 10

power/(W) regeneration Energy power/(W) regeneration Energy

Figure acceleration response. Figure 13. 13. Test Test chart chart of of spring spring mass mass Figure 13. Test chart of spring mass acceleration acceleration response. response.

40 40

Before optimization Before optimization

After optimization After optimization

30 30 20 20 10 10 0 00 0

2 2

4 6 8 10 4 Time/(s) 6 8 10 Time/(s) Figure 14. Test chart of energy regenerative power response. Figure regenerative power power response. response. Figure 14. 14. Test Test chart chart of of energy energy regenerative

6. Conclusions 6. Conclusions 6. Conclusions In this paper, a structure of a semi-active energy regenerative suspension with an EHA is In this paper, a structure of a semi-active energy regenerative suspension with an EHA is In thisFollowing paper, a structure of a semi-active regenerative suspension scheme with an EHA proposed. proposed. the proposed concept, energy a specific energy regenerative and aiscomposite proposed. Following the proposed concept, a specific energy regenerative scheme and a composite Following the proposed concept, a specific energy scheme and composite energy energy recovery device are designed. On the basis of regenerative the system’s structure, the aphysical prototypes energy recovery device are designed. On the basis of the system’s structure, the physical prototypes recovery device are designed. On the basis of the system’s structure, the physical prototypes are are trial-manufactured, and a mechanical properties test of the EHA semi-active suspension system are trial-manufactured, and a mechanical properties test of the EHA semi-active suspension system trial-manufactured, a mechanical properties of the EHA semi-active is carried out. Based and on the experimental data, thetest parameter identification forsuspension the system system model is is carried out. Based on the experimental data, the parameter identification for the system model is carried out. Based on the experimental data, the parameter identification for the system model is conducted via a recursive least squares algorithm, which determines the equivalent spring stiffness k s and inherent damping coefficient of the system cs . Moreover, the nonlinear model of the semi-active energy regenerative suspension with an EHA is built. On the basis of the nonlinear model, the LQG control strategy of the semi-active energy regenerative suspension with an EHA is designed. Then, a complete simulation model of the semi-active energy regenerative suspension with an EHA is established in Simulink. In order to coordinate the damping performance and energy regenerative performance of the semi-active energy regenerative suspension with an EHA, the influences of the main parameters of the EHA on the damping performance and energy regenerative performance of the suspension are analyzed. Finally, the main parameters of the EHA are optimized using the genetic algorithm. In order to further verify the optimization results, the EHA prototype is redeveloped according to the optimization results, and the bench test is carried out. The test results show that when the sinusoidal is input at the frequency of 2 Hz and the amplitude of 30 mm, the spring mass acceleration


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RMS value of the optimized semi-active energy regenerative suspension with an EHA is reduced by 22.23%, and the energy regenerative power RMS value is increased by 40.51%, which means that under meeting the requirements of vehicle ride comfort and driving safety, the energy regenerative performance is improved significantly. Acknowledgments: The authors gratefully acknowledge the support of the National Natural Science Foundation of China (51775426, 51275403), the Service Local Special Program Support Project of Shaanxi Provincial Education Department (17JF017), and the Xi’an Science and Technology Project Funding Project (2017079CG/RC042-XAKD007). The authors would like to thank the anonymous reviewers for their valuable comments that significantly improved the quality of this paper. Author Contributions: F.K. and J.D. conceived and designed the experiments; D.L. and J.X. performed the experiments; J.D. and Z.W. analyzed the data; J.D. wrote the paper. Conflicts of Interest: The authors declare no conflict of interests.

References 1. 2. 3. 4. 5. 6.

7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Tseng, H.E.; Hrovat, D. State of the art survey: Active and semi-active suspension control. Veh. Syst. Dyn. 2015, 53, 1034–1062. [CrossRef] Chen, S.A.; Li, X.; Zhao, L.J. Development of a control method for an electromagnetic semi-active suspension reclaiming energy with varying charge voltage in steps. Int. J. Automot. Technol. 2015, 16, 765–773. [CrossRef] Wu, L.N.; Shi, M.M.; Wang, R.C. Parameter optimization of hybrid suspension with linear motor based on PSO. J. Chongqing Univ. Technol. (Nat. Sci.) 2016, 30, 12–17. Babak, E. Development of Hybrid Electromagnetic Dampers for Vehicle Suspension Systems; University of Waterloo: Waterloo, ON, Canada, 2009. Okada, Y.; Ozawa, K. Energy Regenerative and Active Control of Electro-Dynamic Vibration Damper. Trans. Jpn. Soc. Mech. Eng. C 2005, 70, 233–242. Zhang, H.; Guo, X.X.; Hu, S.B.; Fang, Z.G.; Xu, L. Simulation analysis on hydraulic-electrical energy regenerative semi-active suspension control characteristic and energy recovery validation test. Trans. Chin. Soc. Agric. Eng. (Trans. CSAE) 2017, 33, 64–71. Efatpenah, F.; Beno, J.H.; Weeks, D.A. Energy requirements of a passive and an electromechanical active suspension system. Veh. Syst. Dyn. 2000, 34, 437–458. [CrossRef] Goldner, R.; Zerigian, P.; Hull, J. A Preliminary Study of Energy Recovery in Vehicles by Using Regenerative Magnetic Shock Absorbers; SAE Paper; SAE International: Warrendale, PA, USA, 2001; pp. 2001–2011. Zuo, L.; Nayfeh, S.A. Structured H2 optimizatioensions based on multi-wheel models. Veh. Syst. Dyn. 2003, 40, 351–371. [CrossRef] Anubi, O.M.; Clemen, L. Energy-regenerative model predictive control. J. Frankl. Inst. 2015, 352, 2152–2170. [CrossRef] Clemen, L.; Margolis, D. Modeling and control of a quarter car electrodynamic air-suspension. In Proceedings of the International Conference on Bond Graph Modeling, Monterey, CA, USA, 6–10 July 2014; pp. 27–33. Zuo, L.; Scully, B.; Shestani, J.; Zhou, Y. Design and characterization of an electromagnetic energy harvester for vehicle suspensions. Smart Mater. Struct. 2010, 19, 145–153. [CrossRef] Zuo, L.; Tang, X.D. Large-scale vibration energy harvesting. J. Intell. Mater. Syst. Struct. 2013, 24, 1405–1430. [CrossRef] Huang, K.; Zhang, Y.C.; Yu, F. Coordinate optimization for synthetical performance of electrical energy-regenerative active suspension. J. Shanghai Jiao Tong Univ. 2009, 43, 226–230. Wang, Q.N.; Liu, S.S.; Wang, W.H. Structure design and parameter matching of ball-screw regenerative damper. J. Jilin Univ. Eng. Technol. 2012, 42, 1100–1106. Kou, F.R. Design and energy regenerative study on semi-active suspension with electro-hydrostatic actuator. Trans. Chin. Soc. Agric. Mach. 2016, 28, 352–359. Martins, I.; Estevez, J.; Marques, G. Permanent-magnets linear actuators applicability in automobile active suspensions. IEEE Trans. Veh. Technol. 2006, 55, 86–94. [CrossRef] Kou, F.R.; Fan, Y.Q.; Zhang, C.W.; Du, J.F.; Wang, Z. Time delay compensation control of semi-active suspension with vehicle electro-hydrostatic actuator. China Mech. Eng. 2016, 27, 2111–2117.


19. 20. 21. 22. 23. 24.

17 of 17

Sun, X.Q.; Chen, L.; Wang, S.H. Nonlinear modeling and parameter optimization of two-stage seriesconnected ISD suspension. Trans. Chin. Soc. Agric. Mach. 2014, 45, 7–13. Kawamoto, Y.; Suda, Y.; Inoue, H. Electro-mechanical suspension system considering energy consumption and vehicle manoeuvre. Veh. Syst. Dyn. 2008, 46, 1053–1063. [CrossRef] Kou, F.R.; Du, J.F.; Zhang, C.W.; Wang, Y.J.; Wang, Y.Z. Multi-mode switching control of self-powered active suspension with electro-hydrostatic actuator. Mech. Sci. Technol. Aerosp. Eng. 2016, 35, 1937–1943. Li, C.; Zhu, R.R.; Liang, M. Integration of shock absorption and energy harvesting using a hydraulic rectifier. J. Sound Vib. 2014, 33, 3904–3916. [CrossRef] Zhao, L.F.; Hu, J.F.; Zhang, R.Y. Integrated optimization design of cab suspension and suspension parameters for heavy tractor. China Mech. Eng. 2016, 27, 791–808. Zhan, M. Dynamic Simulation and Performance Study of Hydraulic Electromagnetic Regenerative Shock Absorber; Jilin University: Changchun, China, 2015. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).