LI Rui , CHEN Weimin LIAO Changrong and DONG Xiaomin

1 Key Laboratory of Optoelectronic Technology and Systems of Ministry of Education, Chongqing University,Chongqing 400030, China

2 Key Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

1 Introduction

The vibration suppression of an automotive vehicle for better performance has been cared[1–2]. A magnetorheological(MR) semi-active suspension system has received more attention because it offers both the reliability of a passive system and the versatility or high performance of an active control system[1–3].

It is very important to control the vibration of an automotive suspension system for reducing roll, pitch,heave motion of the vehicle body (the sprung mass) and the vertical vibration of the wheels (the unsprung mass)[4]. The vibrations of the full vehicle are so complicated under actual operating condition that it is not easy to develop an effective full-car control strategy. Since there are conflicting requirements of improved the passenger comfort and the vehicle manipulability[5], conventional single control strategies such as skyhook control[6], ground hook control[7]can not give attention to whole vehicle vibration at different conditions. Modern control and linear feedback control[8]that depends on complete model, have limited result. CHOI, et al[9], developed a skyhook controller for a passenger vehicle via MR dampers. It only improved ride comfort through hardware-in-the-loop simulation. DAVID, et al[10], adopted an on-off-skyhook policy to reduce heave acceleration of a heavy truck body via MR dampers. NOVAK, et al[7], studied experimental evaluation of MR suspensions for passenger vehicles with ground hook control. MAKOTO, et al[11], designed a model following sliding mode controller for MR suspension system according to skyhook control based on a quarter-car.WANG, et al[12], studied modeling and control of MR dampers using neural networks. YU, et al[13], studied a quarter car MR suspension system accounting for nonlinearity and time delay. CHEN, et al[14], designed a fuzzy controller for MR suspension to improve ride quality.

Above-mentioned semi-active control strategies only discussed one or two vibration states of the vehicle based on a quarter-car model or a half vehicle model. They cannot provide satisfying ride comfort and handling stability on a road test[13]. Skyhook or ground-hook control is suitable for reducing the vertical vibration of the vehicle[5].However,the relations between heave, roll and pitch motion of the vehicle body are so complicated that it is very difficult to build an accurate model. And it is not easy to achieve the vibration relation between the vehicle body and the wheels.A fuzzy reasoning methodology is very suitable for a system that has non-linearity and no precise mathematical model[15–16]. It can be adopted to design control strategies for vibration attitude of full car.

Hence, the vibration attitude of a full car with four MR suspensions is considered with the objective of improving ride comfort and road holding concurrently. A fuzzy hybrid control(FHC) system is proposed, which takes advantage of fuzzy reasoning and hybrid damping parameters adjustment.Finally, actual road tests are developed to evaluate the vibration attitude of full car via different suspension systems.

2 Seven DOF Dynamic Model of Full Car via Magneto-rheological Suspensions

As it is very difficult to design a controller based on a complete whole vehicle model, it is necessary to simplify the vehicle vibration system. The main vibration attitudes of a car with four wheels can be indicated by seven degrees-of-freedom(DOF) vehicle model[4], which includes the vertical motion (heave) of the vehicle body and the wheels, the angular motion (pitch and roll) of the vehicle body. It is shown in Fig. 1.

Fig. 1. Vibration model of full car

The vehicle body is considered as a rigid body. The tires are modeled as simple linear springs without damping. The angular motion is assumed to be small. The equations for this model can be given as follows:

Where msis the mass of the vehicle body; z is the vertical displacement of the center; Ffl, Ffr, Frl, Frrare the support force of front left(FL), front right(FR), rear left(RL) and rear right(RR), respectively; Ixxis the roll inertia; θ is the roll angular radian; 2w is the distance between left wheel and right wheel; Iyyis the pitch inertia; φ is the pitch angular radian; a, b are the distance between front wheel and center, rear wheel and center, respectively; mufl, mufr,murl, murrare the unsprung mass of each part; zufl, zufr, zurl,zurrare the displacement of each wheel; ktfl, ktfr, ktrl, ktrrare the tire stiffness coefficient of each suspension; zrfl, zrfr, zrrl,zrrrare the road input displacement of each part; kfl, kfr, krl,krrare the suspension stiffness coefficient of each part; cfl,cfr, crl, crrare the damping coefficient of each part; zfl, zfr, zrl,zrrare the displacement of each sprung mass; Fdfl, Fdfr, Fdrl,Fdrrare the MR damping force of suspension.

Eqs. (1)–(2) describe an MR suspension vibration system if cfl, cfr, crland crrare zero and describe a passive suspension system if Fdfl, Fdfr, Fdrland Fdrrare zero.

There are some motion relations among the displacements of heave, pitch and roll motion. It can be concluded as follows:

In the control system for an MR suspension vibration, an MR damper is the key executer that can produce a controllable damping force by supplied proper electric current to change the MR fluids rheological behavior. An MR damper with both large scalability and low base damping force at different current is critical for suppressing suspension vibration. A new type of MR damper with an inner bypass and a magnetic bias has been designed and fabricated to fulfill the requirements of a damping force[17].The polynomial model[18]is more effective to express the input and output characteristics of this new MR damper.When the piston movement velocity is achieved, the input current can be adjusted to change magnetic field intensity in the MR damper so that the MR damping force is controllable.

3 Design of a Fuzzy Hybrid Controller for Automotive Vibration Attitude

Based on the seven DOF dynamic models, the aim of control system is to reduce the heave, roll, pitch motion of the vehicle body and the vertical vibration of each wheel at different operating conditions.

On the one hand, reducing the heave, roll, pitch motion of the vehicle body is benefit to enhance the ride comfort. A skyhook strategy[6]can suppress the vertical vibration of the sprung mass, which is the main vibration state of the vehicle body. However, there are couplings among heave,roll, and pitch motion. It is very difficult to build a model for these coupling relations. And an MR damper has nonlinearity, some time compensation, etc[13]so that the polynomial model approximately describes its characteristics. Therefore, to reduce roll and pitch, the fuzzy reasoning methodology is adopted to tune the sky-hook control force. On the other hand, a ground hook control[7]is adopted to decrease the vertical vibration of the wheels, which is useful for the wheel contact force or handling stability. However, we know that accomplishing ride comfort and better road handling concurrently is challenging[4]. Finally, a hybrid damping force control scheme[5]is adopted. It is not easy to build an accurate model for the complex variety of vibrations between the vehicle body and the wheels. A fuzzy reasoning method is also used to modify hybrid damping factor so that appropriate damping force will be calculated for reducing the attitude of full car.

The FHC system for the vibration attitude of full car via MR suspensions is proposed and shown in Fig. 2.

Fig. 2. Structure of the FHC system

The characteristics of the polynomial model of an MR damper, which is expressed in Eq. (13) later, should be considered in the FHC system design. Additionally, the parameter ranges of the MR damper are as follows. The output damping forcer is [0 N, 3 200 N]. The input drive current is [0 A, 2 A]. The test vibration velocity of the piston movement velocity is supposed as [–10 m/s, 10 m/s].

3.1 Skyhook-fuzzy control of the vehicle body vibration

3.1.1 Skyhook control of the vertical vibration of the vehicle body

It is known that a skyhook strategy can enhance vehicle ride comfort by suppress the vertical vibration of the sprung mass[6]. Although skyhook control is a traditional typical control strategy, it is necessary to revise it before practical implementation.

Hence, an equivalent control strategy is adopted to realize the skyhook damping control strategy in an MR suspension system under some conditions, which are shown as follows:

Where Fsis the skyhook damping force, Csis the skyhook coefficient, vsis the vertical vibration velocity of the sprung mass, vuis the vertical vibration velocity of the unsprung mass, FdMis the maximal tuneable damping force.

3.1.2 Fuzzy control of roll and pitch of the vehicle body

Skyhook control is suitable for reducing the vertical vibration of the vehicle body. However, there are couplings among heave, roll and pitch motion of the real vehicle body so that it is necessary to develop a fuzzy control scheme to tune the skyhook damping force (Fs) for decreasing vibration attitude of the vehicle body.

Heave, pitch and roll motion of the vehicle body are active at the same time when fuzzy coordination rules are designed. Therefore, the vertical vibration acceleration (z˙˙),pitch angular acceleration( )φ˙˙, and roll angular accelerationcan be calculated based on Eq. (3) as follows:

The fuzzy coordination control rules for vibration attitude of the vehicle body are proposed. In order to decrease the whole vehicle vertical vibration, pitch and roll motion, the skyhook damping force of each MR damper could be tuned by adjusting coordination coefficient:where Fbiis the ith attitude control force of the vehicle body, μirepresents the damping force coordination coefficient of each MR damper, Fsiis the skyhook damping force of each MR damper. When i=1, 2, 3, 4, it represents the FL, FR, RL and RR MR suspension system,respectively.

Fig. 3. Membership functions of?˙˙,θ˙˙and μi

Table 1. Rules for the skyhook damping force coordination coefficient

3.2 Ground hook control of the vertical vibration of the wheel

Since ground hook control can suppress unsprung mass vibration[7], it improves road holding. However, ground hook control is a traditional typical control strategy. It is necessary to be revised before practical implementation. An equivalent control strategy can be adopted in an MR suspension system under some conditions, which are

where Fgis a ground hook damping force, Cgis a ground hook coefficient.

3.3 Hybrid damping control based on a fuzzy reasoning method

A traditional hybrid damping control strategy[5]gives attention to decrease the vertical vibration of the sprung mass and unsprung mass concurrently. In this paper, an equivalent control strategy can be adopted to reduce the vibration attitude of the vehicle body and the wheels, which is presented as

where Fhis the hybrid control force, ρ is the tuneable hybrid weighting parameter and is [–1, 1]. This control strategy could improve ride comfort and road holding.

In Eq. (10), the parameter ρ plays an important role for control performance. Hence, appropriate determination of ρ based on the different dynamic behaviors of the car is required.

Since accomplishing the ride comfort and better road handling concurrently is challenging, it is not easy to propose an accurate model for the complex variety of the parameter ρ. Fuzzy reasoning is adopted to modify ρ.

From Eqs. (4), (8)–(10), it can be seen that vsand vuare important variables for adjusting performance. Hence, their absolute valuesare two inputs variables.Parameter ρ is the output. The fuzzy language of inputs and output is defined as ZE for zero, PS for positive small, PB for positive big. The fuzzy sets of inputs and output are A,B and H. Membership functions of the inputs and output are trapezoid and triangle, respectively. The basic value fields of vs, vuand ρ are [–3 m/s, 3 m/s], [–15 m/s, 15 m/s]and [0, 1], respectively.

The fuzzy rules are described in Table 2. The MR suspension will be soft enough to minimize the effect on the vehicle of violent wheel motion. It will be stiffened selectively to minimize violence vibration of wheels on acceleration, dive on braking and roll in cornering[19]. An example of the fuzzy linguistic rules is: ifis ZE andis PB, it indicates the vibration of the vehicle body is little but the wheel has large vibration energy. Therefore,the ground hook damping force could be increase to reduce the wheel contact force. Hence, ρ is PB.

If the vibration inputs areand, ρ can be calculated by the Mamdani method. Where the fuzzy reasoning value Hρis

where vs0, vu0are inputs; RAn, RBnare corresponding rules of A and B, respectively; kρis output scale factor;andrepresents the weight of the corresponding activated rules.

Table 2. Fuzzy reasoning rules for calculating the hybrid damping parameter

Finally, the ideal control force Fhiis the output of the FHC system. If the piston movement velocity viis approximately equal to the relative velocity vsuithat is produced by vssubtracting vu, the drive current Iiof each MR damper can be calculated by using the polynomial model. When the MR damper is inspirited by the drive current, the magnetic field intensity in it is changed so that the actual MR damping force is controllable:

where ξi, ξjand m are constants. When i=1, 2, 3, 4, it represents the FL, FR, RL and RR MR damper,respectively.

4 Road Test for Vibration Attitude of Full Car

4.1 Test device and system

An MR semi-active suspension test and control system is set up and is implemented on a car equipped with four MR controllable dampers, which adopt an operation method of an inner bypass and a magnetic bias[17]. The acceleration sensors installed on the vehicle are shown in Fig. 4.

The test and control system includes eight acceleration sensors, a dSPACE Auto-Box control system with the hybrid control software or the FHC software, four MR dampers, A/D and D/A modules, a signal processing module and four electronic current drivers which are controlled by controller outputs and provide driver current for the MR dampers. Eight acceleration sensors are adopted to measure the accelerations at various points on the car.The four measurement points are on the axles below the MR dampers. Another four measurement points are on the four corners on the vehicle body over the MR dampers. The test and analyses system include a B&K cushion placed on driver seat for testing easement, eight accelerometers, an amplifier, one data collection box and the analysis software.The main parts of control and test system are shown in Fig. 5. Parameters of the vehicle suspension system are shown in Table 3.

Fig. 4. Acceleration sensors installed on the vehicle

Fig. 5. The main parts of the test and control system

Table 3. Parameters of an automotive suspension system

Since the vertical vibration velocities of the sprung mass and the unsprung mass, the pitch angular acceleration?˙˙,and the roll angular acceleration θ˙˙ are inputs of the FHC system, these parameters should be achieved. To enhance calculation speed, a hardware integrator is designed to calculate the vibration velocities based on the vertical vibration acceleration of the sprung mass and the unsprung mass, respectively. Additionally, when the parameters a,b and w are tested, the pitch angular acceleration and the roll angular acceleration will be indirectly achieved by four vibration accelerations of the sprung mass, based on Eqs. (6)and (7), respectively.

4.2 Road test and analysis

Tests on a random highway road, a rough road and a bump input road are carried out. The data sampling frequency is 200 Hz. ISO2631 is adopted to evaluate the results. This car equipped with the original passive suspension system, the MR suspension system with the hybrid control and the FHC are tested under the same condition, respectively.

4.2.1 Highway road test

The test car with a half load and a full load is driven along a straight stretch highway at a constant vehicle velocity of 10 m/s and 20 m/s, respectively. Since the pitch and roll motion of the vehicle are very small, only the vertical vibration is considered.

The accelerations of different points on the driver’s seat,the vehicle body and the axles are sampled. The vertical acceleration of the vehicle body is calculated by Eq. (5).Comparisons of the acceleration power spectrum density(PSD) and the root mean square(RMS) are based on the experimental data of the original suspension system and the MR suspension system.

Here, the test result of the car with a half load at 10m/s is shown in Fig. 6. It includes the PSD of the acceleration of the vehicle body and the driver seat, and the average acceleration of four wheels.

4.2.2 Rough road test

When a car is operating on the roads with undulations in terrain from rough ground, the roll and pitch motions are strongly related to vehicle handling. To evaluate the FHC strategy, more tests on a complex road profile are studied.

A rough road with a curve sinusoidal shape, amplitude of 0.6 m and wavelength of 30 m, is adopted. The velocity of the half-loaded vehicle is 10 m/s and 20 m/s. It will lead to cornering, acceleration, and braking operations, which helps to introduce pitch and roll motion simultaneously.

The accelerations of the driver’s seat, the vehicle body and the wheels are also sampled. Hence, the heave acceleration, pitch angular acceleration and roll angular acceleration of the vehicle body are calculated by Eqs.(5)–(7), respectively. The acceleration PSD of the car with 10 m/s is shown in Fig. 7.

The accelerations RMS of the vehicle body, the seat and the axle on a random road are shown in Table 4.

4.2.3 Bump road test

The car passes a 0.1 m bump with the speed of 6 m/s and 10 m/s more than 10 times. Since the roll motion is very small, it is ignored. The maximal peak-to-peak value of vibration acceleration is adopted to evaluate different suspension systems, which are expressed in Table 5.

4.3 Discussion

Figs. 6(a), 6(b) and Figs. 7(a)–7(d) show that the FHC scheme applied on the MR suspension system effectively reduces the first resonance of the heave, roll and pitch accelerations of the vehicle body and driver seat. It has better results than a passive suspension system and hybrid control for an MR suspension system especially on a rough,bumpy road. It also visibly decreases vibration energy between 4 Hz and 12.5 Hz. Fig. 6(c) and Fig. 7(e) show that the FHC system applied on the MR suspensions has suppressed the vibration of the wheels more significantly than the hybrid control and a passive suspension system.

Fig. 6. Acceleration PSD of the vehicle on a highway road

Fig. 7. Acceleration PSD of the vehicle on a rough road

Table 4 shows that the RMS of the vibration accelerations of the full car is reduced by the FHC scheme for an MR suspension system. The FHC system has better performance on rough road and higher velocity. It is benefit to enhance the ride comfort and road holding concurrently.

Table 5 indicates that the hybrid control or the FHC strategy reduced the vertical motion of the vehicle on a bump input road. The FHC has better result.

Table 4. RMS of the heave acceleration and angle acceleration (0–30 Hz )

Table 5. The maximal peak-to-peak value of the vertical acceleration and pitch acceleration

5 Conclusions

(1) Road test data show that the FHC for the MR suspension system can decrease the vibration accelerations of the vehicle body and the wheels to 65%–80% and 80%–90%, respectively. It achieves better ride comfort and road holding concurrently than the hybrid control for an MR suspension system or a passive suspension system,especially on rough road at higher velocity.

(2) The test results confirm that the FHC scheme can effectively suppress the heave, pitch and roll motion of the vehicle body and the vertical vibration of the axle. It indicates that it is reasonable to adopt the fuzzy reasoning methods to realize hybrid damping parameter correction for reducing the vibration attitude. It is suitable for solving the vibration attitude difficulties of full car. It also indicates that an MR suspension system has great value in improving the performance of full car.

[1] MUHAMMAD A, YAO Xiongliang, DENG Zhongchao. Review of magnetorheological (MR) fluids and its applications in vibration control[J]. Journal of Marine Science and Application, 2006, 5(3):17–29.

[2] WANG Enrong, YING Liang, WANG Wanjun, et al. Semi-active control of vehicle suspension with magnetorheological dampers:part I—controller synthesis and evaluation[J]. Chinese Journal of Mechanical Engineering, 2008, 21(1): 13–19.

[3] RAKHEJA S, SANKER S. Vibration and shock isolation performance of a semi-active on-off damper[J]. Transactions of the ASME,Journal of Vibration, Acoustics, Reliability in Design, 1985, 107:398–403.

[4] CROLLA D. Vehicle dynamics and control[M]. Beijing: Communications Press, 2004. (in Chinese)

[5] AHMADIAN M, VAHDATI N. Transient dynamics of semi active suspensions with hybrid control[J]. Journal of Intelligent Material Systems and Structures, 2006, 17: 145–153.

[6] KARNOPP D C. Active and semi-active vibration isolation[J].Transactions of ASME, Journal of Special 50th Anniversary Design Issue, 1995, 117: 177–185.

[7] NOVAK M, VALASEK M. A new concept of semi-active control of trucks suspension[C]//Proceedings of the 8th International Symposium on Advanced Vehicle Control, Taipei, China, August 20–24, 2006: 141–151.

[8] LAUWERYS C, SWEVERS J, SAS P. Robust linear control of an active suspension on a quarter car test-rig[J]. Control Engineering Practice, 2005, 13(5): 577–586.

[9] CHOI S B, LEE B K, HONG S R. Control and response characteristics of a magnetorheological fluid damper for passenger vehicle[J]. SPIE, 2000, 3 985: 438–443.

[10] DAVID S, MEHDI A. Vehicle evaluation of the performance of magneto-rheological dampers for heavy truck suspensions[J].Vibration and Acoustics, 2001, 123: 365–375.

[11] MAKOTO Y, HEDRICK J K, SHIGEHIRO T. A model following sliding mode controller for semi-active suspension systems with MR dampers[C]//Proceedings of the American Control Conference,Arlington, USA, June 25–27, 2001: 2 652–2 657.

[12] WANG Daihua, LIAO Weihsin. Modeling and control of magnetorheological fluid dampers using neural networks[J]. Smart Materials and Structures, 2005, 14: 111–126.

[13] YU Miao, DONG Xiaomin, LIAO Changrong, et al. Adaptive fuzzy neural network control for magneto-rheological suspension[J].International Journal of Computer Science and Network Security,2006, 6(10): 66–71.

[14] CHEN Weimin, DONG Xiaomin, YU Miao, et al. Design of fuzzy controller for magneto-rheological suspension using a hybrid taguchi genetic algorithm to improve ride quality[J]. Journal of Advanced Science, 2006, 18: 107–113.

[15] LI Shiyong. Fuzzy control, neuro-control and intelligent cybernetics[M]. Harbin: Harbin Industry University Publisher, 1996. (in Chinese)

[16] NIZAR A L, HOLOU. The development of fuzzy logic based controller for semi-active suspension system[C]//Proceedings of the 1995 American Control Conference, Seattle, USA, June 21–23,1995: 105–112.

[17] ZHANG Honghui, LIAO Changrong, YU Miao, et al. A study of an inner bypass magneto-rheological damper with magnetic bias[J].Smart Materials and Structures, 2007, 16: 40–46.

[18] CHOI S B, LEE S K, PARK Y P. A hysteresis model for the fielddependent damping force of a magnetorheological damper[J]. Sound and Vibration, 2001, 245: 375–383.

[19] TAEHYUN S, DONALD M. Dynamic normal force control for vehicle stability enhancement[J]. International Journal of Vehicle Autonomous Systems, 2005, 3(1): 1–14.