Reducing the seat vibration of vehicle by semi active force control technique

Journal of Mechanical Science and Technology 28 (2) (2014) 473~479

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-013-1204-6

Reducing the seat vibration of vehicle by semi active force control technique†

Sathishkumar. P.*, Jancirani. J. and Dennie John Department of Automobile Engineering, M.I.T, Anna University, Chennai-44, India

(Manuscript Received July 19, 2013; Revised October 1, 2013; Accepted November 13, 2013)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract This article focusses on reducing the axis acceleration and minimizing the vertical displacement by using an air spring actuator and ac-

tive force control as a main control element. In active force control loop track the developed force of an air spring actuator is fed as a feedback to the actuator. Mamdani and sugeno type fuzzy interference system are used to develop a desired force and to estimate mass of the system respectively. The performance of the system is analyzed for both time and frequency domains and contrasted with passive suspension due to the irregular road disturbances. While developing the simulation model, quarter car suspension with seat as three de-gree of freedom and an air spring actuator acting as a force generator are modeled as non-linear system. The simulation result shows the effectiveness of the proposed control scheme in suppressing the undesirable effects of the suspension system.

Keywords: Air spring actuator; Active force control; Fuzzy interference system; Quarter car suspension ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

The main objective of the automobile industry is to achieve both ride comfort and the ride stability to improve passenger comfort. A higher quality of the ride comfort can be obtained in two ways; the first is by minimizing the axis and angular acceleration of the gravity center of the vehicle body while the second is by maintaining the tire contact with the ground when the wheel strikes a bump [1]. Ride stability can be achieved by minimizing the vertical displacement of the body center. This article mainly focuses on reducing axis accelera-tion and minimizing the vertical displacement by using a pro-posed control loop. The automotive suspension system is ca-tegorized into three types, namely passive, semi-active and active suspension [2]. Passive suspension consists of spring and damper and because of its fixed characteristics it cannot control above system [3, 4]. The active suspension is charac-terized by the actuator placed in parallel with the damper and the spring [4]. Since the actuator connects the unsprung mass to the body, it can control both wheel hop as well as the body motion. Thus, the active suspension now can improve both the ride comfort and road handling. The actuator is controlled by PID [5], fuzzy [6], neural network [7], ANFIS controllers [8]. It offers significant improvements in ride comfort when com-pared with passive and semi-active suspensions. Therefore, extensive studies concerning active suspensions have been

carried out during last decade [9]. A semi-active suspension [10, 11] consists of a spring and a

damper but, unlike a passive suspension, the value of the damper coefficient “F” can be controlled and updated. In some types of suspensions, but this case is not considered here, it may also be possible to control the elastic constants of the spring [12]. Semi-active control devices that have received considerable interest, due to their mechanical simplicity, high dynamic range, low power requirements, large force capacity and robustness [13, 14]. In this work air spring actuator is used as a semi-active element and placed in parallel with conven-tional system element. Air spring actuator dynamics is quite complicated and the interaction between the actuator and the vehicle suspension cannot be ignored. It is difficult to produce the actuator force close to the target force without implement-ing force tracking controller. This is due to the fact that air spring actuator exhibits non-linear behavior, resulting in re-sidual structural damping, stiffness and unwanted effects of back-pressure. This is due to the interaction between the air spring actuator and vehicle suspension system [15, 16]. A novel Adaptive fuzzy -Active force control scheme to control an active suspension system and their study indicate that the AF-AFC scheme provides better performance for the given loading and operating conditions [3]. The novelty of this paper is the active force control scheme which is designed specifi-cally for semi-active suspensions. This paper describes an active force control (AFC) strategy with fuzzy logic and a force tracking mechanism in semi-active embedded in its con-trol loop.

*Corresponding author. Tel.: +91 9566783072, Fax.: +91 9884143073 E-mail address: [email protected]

† Recommended by Editor Yeon June Kang © KSME & Springer 2014

474 Sathishkumar. P et al. / Journal of Mechanical Science and Technology 28 (2) (2014) 473~479

2. Mathematical modeling

2.1 Quarter car modeling

The vehicle model considered in this study is quarter car model. The system consists of the passenger seat, sprung mass, unsprung mass, air spring and a passive damper as shown in Fig. 1. Assumptions of a quarter car modeling are as follows: the tire is modeled as a linear spring without damping, there is no rotational motion in wheel and body, the behavior of spring and damper are linear, the tire is always in contact with the road surface and effect of friction is neglected so that the re-sidual structural damping is not considered in the vehicle modeling [17].

Equations of motion for active quarter car model are given by the following. Equations of motion for active quarter car model are given by the following:

(1)

(2)

(3)

2.2 Air spring dynamics

The air springs for passenger cars are commercially avail-able but there is not enough research devoted to their dynamic characteristics. Some researchers [18] discussed about the vehicular air suspension from design aspects, but rarely from the control aspects [19]. The gas in the air spring can be com-pressed to the pressure required to carry the load and therefore an air spring is not required to have large static deflection. The compressibility of the gas provides the desired elasticity of the spring. The use of linear mathematical models allow us to obtain simple equations from which, more significant infor-

mation can be extracted [20]. If the load and static deflection are large, there is a large weight reduction resulting from the use of the air springs. This decreases the simple stiffness of suspension which increases comfort and decreases the transfer of shocks.

To simplify the mathematical model in Ref. [17], the fol-lowing assumptions were made. The geometry of piston is cylindrical; operating condition is at constant temperature and low-vibration frequency. The gas in the air spring is ideal gas. The spring coefficient of the air spring is nonlinear, while the air spring's spring force can be expressed as [21]:

(4)

where A: Valve active area, PA: Compressed air spring pres-sure, Pa : Indoor air spring pressure gas. We consider that the product of the gas volume and pressure in the air spring was constant. From the ideal gas equation, it yielded the following equation.

. (5) Then

(6)

where P0 : Initial air pressure in the air spring, V0 : Initial air volume in the air spring, P1 : Compressed air pressure in the air spring, V1 : Compressed air volume in the air spring, When the air spring is compressed to length h, we can summarize Eqs. (4)-(6) as:

(7)

It is supposed that when the air spring was compressed to

length h, the volume of air in the chamber of air spring and the effective piston area could be expressed as a nonlinear func-tion of h with respect to the volume co-efficient a and area co-efficient β.

. (8) From Eqs. (8) and (4),

(9) Because we assume that the operating condition for the

spring was isothermal low- frequency environment, the value

.

Fig. 1. Quarter vehicle two degree of freedom models.

.

.

Sathishkumar. P et al. / Journal of Mechanical Science and Technology 28 (2) (2014) 473~479 475

of n was equal to 1.

(10)

If the Eq. (10) is substituted into the Eq. (9), we obtain the

Eq. (11).

. (11)

Combining the Eqs. (11) and (9)

(12) Finally, we could simplify it to Eq. (13).

. (13) According to the assumption of cylindrical shape of piston,

it was clear that A0 = AA. With the piston compression height h and Eq. (5), we get

. (14)

Then the Eq. (4) is rewritten as

. (15)

According to Eq. (15) and Fig. 2, we got

. (16) Finally, based on the Eq. (14), the function of h was rewrit-

ten as:

. (17) The compressed height is controlled in order to achieve a

desired force of the air spring actuator. The Fig. 3 shows that relation between compression height and air spring stiffness of the air spring actuator.

3. Control system

3.1 Controller design

Controller design is very complex for a complicated system to obtain good control effect. In order to enable the air suspen-sion control system with a certain degree of adaptive capacity and the fuzzy controller are designed. The velocity of sprung mass and deflection of suspension were adapted as input vari-ables of fuzzy controller, while the output variable was air spring force. Their ranges are obtained through simulation; five fuzzy language subsets were used to describe two input variables and output variables. Membership functions of the subsets were triangle and trapezoidal functions. The rule is in the form of the linguistic variables using the fuzzy conditional statement. Each rule is derived from the characteristic of the passive suspension system. Fuzzy rule base is combination of all possible control rules and it is summarized in Table 1. Mamdani's minimum operation rule is used as a fuzzy impli-cation function. As the process usually requires a non-fuzzy value of control, a method of defuzzification called “centre of gravity method” (COG) is used here where μD(f) is the corre-sponding membership function in Eq. (18) [22]. The air spring force (Fa) is chosen to give ±2 KN as maximum and mini-

Table 1. Rule base.

sz& zs-zus

NL NS ZE PS PL

NL PL PS PS ZE NS

NS PL PL PS PS ZE

ZE PS PS ZE NS NL

PS PS ZE NS NL NL

PL ZE NS NS NL NL

0 10 20 30 40 50 600

2

4

6

8

10

12x 10

4

Compressed Height (m)A

ir sp

ring

stiff

ness

(N/m

m)

Fig. 3. Response of air spring actuator.

Fig. 2. Schematic diagram of the air spring.

.

.


mum values,

.

(18)

3.2 Active force control system

AFC loop is as shown Fig. 4, and designed to compensate for a system subjected to a number of disturbances and remains stable and robust due to the compensating action of the control strategy. The efficiency of the AFC strategy relies on the mass estimator, the body acceleration and the actuator force are easily obtained. Sugeno type fuzzy inference system is used for the estimation of mass. The rule base for estimating the mass is as shown in Table 2. The main aim of using the Fuzzy Logic in the study is to compute the estimated mass intelligently so that it can be utilized by the AFC mechanism to effect its control strategy. Membership functions representing the input (suspension deflection and body acceleration) and output (estimated mass) of the FLC used in the input membership functions are chosen as Gaussian functions. The output is a singleton value of the estimated mass. Once the FLC is designed, it is embedded in the overall control strategy for online estimation of the mass and thereafter estimates force [23]. A more detailed description on the mathematical treatment related to the derivation of important equations and stability criterion, can be found in Ref. [24].

Q = F - M a (19)

where ‘Q’ is the estimated disturbance force, F is the meas-ured force, ‘M’ is the estimated mass and ‘a’ is the measured acceleration.

If the parameters are appropriately measured or estimated, then a guaranteed robust AFC performance is achieved [14, 24].

4. Results and discussion

To generate the road profile of a random base excitation for the 3-DOF Active suspension simulation disturbance, a spec-trum of the geometrical road profile with road class rough-ness-D is considered as shown in the Table 3. The vehicle is travelling with a constant speed v0, the time histories data of road irregularity are described by PSD method [19, 20]. Ac-cording to International Standard Organization (ISO) 2631, the ride comfort is specified in terms of root mean square (RMS) acceleration as shown in Table 4 [25].

Matlab/Simulink is used as a computer aided-control sys-tem tool for modeling the non-physical quarter car semi active and active force control system which are included in one analysis loop. Passenger ride comfort is directly related with sprung mass acceleration and sprung mass displacement while suspension deflection is related to the road holding. Quarter car suspension system is analyzed with random road input using the Table 5 parameter values.

4.1 Robustness test for proposed control scheme

An efficient control scheme is one that it is still stable even when the disturbance signal is applied on the plant. Therefore, to establish the effectiveness of any control scheme the ro-bustness should be examined. Random road input is applied in turn to test the robustness of the proposed control scheme and semi active suspension system.

Table 2. Mass estimation Rule base.

sz&& Zs-Zus

N Z P

N N N Z

Z N Z P

P Z P P

Fig. 4. Block diagram of active force control system for air spring suspension.

Table 3. Road roughness value classified by ISO.

Classification S(Ω) Road roughness K [m2/(cycles/m)](*10-6) Range Average

A (very good) 2-8 4

B (good) 8-32 16

C (average) 32-128 64

D (poor) 128-512 256

E (very poor) 512-2048 1024

Table 4. Degree of discomfort defined by ISO 2631-1 [26].

Acceleration level Degree of comfort

Less than 0.315m/s2 Not uncomfortable

0.315-0.63 m/s2 A little uncomfortable

0.5-1 m/s2 Fairly uncomfortable

0.8-1.6 m/s2 Uncomfortable

1.25-2.5 m/s2 Very uncomfortable

Greater than 2 m/s2 Extremely uncomfortable


Figs. 5-7 shows time response of displacement of seat, sprung mass and suspension deflection respectively. Due to their lower transmissibility of air spring, the peak points of semi active and AFC system is lower at all points. The reduc-tion in seat displacement and sprung mass displacement shows improvement in passenger comfort. Fig. 7 shows that the rela-tive displacement between vehicles sprung mass and unsprung mass in terms of suspension deformation. The plot in the si-mulation show improved and a relatively stable ride comfort.

Figs. 8 and 9 shows acceleration of seat and sprung mass acceleration for time domain analysis and it gives the vertical behavior of body acceleration - ride comfort performance. The peak RMS of proposed control system is reduced by more

than a third when compared to passive suspension. Figs. 8 and 9 contain the seat and body acceleration plots

for semi active suspension with FLC and passive suspension system and the FLC has body acceleration reducing effects on the passive suspension system to some extent. This depends on the human experience according to FLC’s rule-base. Meanwhile, the lower FLC-AFC plot in Figs. 8 and 9 show the control effects of active force control technique by meas-uring force using Mamdani fuzzy controller. Also the AFC-FLC scheme RMS value of seat and sprung mass accelera-tions are 0.281& 0.254 m/s2 respectively which, according to the table of acceleration range, is not uncomfortable.

Table 6 shows RMS comparison of passive, air spring con-

Table 5. Parameters values.

Symbol Values Units

Cps 875 Ns/m

Cs 1000 Ns/m

Fa ± 2000 N

Ks 18100 N/m

Kus 196000 N/m

Kps 10507 N/m

Mps 60 Kg

Ms 290 Kg

Mus 59 Kg

P0 300 kpa

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.02

-0.01

0

0.01

0.02

0.03

0.04

Time (Sec)

Sea

t dis

plac

emen

t (m

)

PASSIVEFLCFLC-AFC

Fig. 5. Displacement of seat.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.02

-0.01

0

0.01

0.02

0.03

0.04

Time (Sec)

Spr

ung

mas

s D

ispl

acem

ent (

m)

PASSIVEFLCFLC-AFC

Fig. 6. Displacement of sprung mass.

Table 6. RMS value comparison of suspension system.

Description Passive RMS

Semi active RMS

AFC RMS % of reduc-

tion than passive

% of reduc-tion than

semi active

Seat disp (m) 0.014 0.0118 0.0112 23.80 5.08

Body disp (m) 0.015 0.0127 0.0116 25.64 8.66

Susp def (m) 0.006 0.0023 0.0016 73.33 30.43

Seat acc (m/s2) 0.438 0.3391 0.2816 35.83 16.95

Body acc (m/s2) 0.373 0.2932 0.2542 31.95 13.30

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Time (Sec)

Sus

pens

ion

defle

ctio

n (m

)

PASSIVEFLCFLC-AFC

Fig. 7. Suspension deflection.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1.5

-1

-0.5

0

0.5

1

1.5

Time (Sec)

Sea

t acc

eler

atio

n (m

/S2 )

PASSIVEFLCFLC-AFC

Fig. 8. Acceleration of seat.


trolled and air spring with active force controlled system. From this result AFC scheme is better than passive and semi active controlled system.

Figs. 10 and 11 show power spectral density of vehicle body vertical acceleration to road displacement and seat accel-eration to road displacement respectively. From these figures we can easily identify the comfort level of proposed system.

5. Conclusions

This study has been designed an active force control loop for a cylinder air spring type based on principles of thermo and fluid dynamics. Mamdani and sugeno fuzzy interference systems are used to control and estimating air spring actuator, in order to improve the ride comfort and road handling in a

quarter car model. Simulation results are obtained from Mat-lab/Simulink. Comparison between passive, semi-active fuzzy and active force control techniques are done and the results prove that the performance of air spring suspension with ac-tive force control can improve the ride comfort and road han-dling.

Acknowledgment

I would like thank university grand commission RGNF scheme for the financial support and Anna University for pro-viding research support.

Nomenclature------------------------------------------------------------------------

Mps : Passenger seat mass Ms : Sprung mass Mus : Unsprung mass Cps : Passenger seat damping Cs : Suspension damping Kps : Seat spring stiffness Ks : Suspension spring stiffness Kus : Stiffness of unsprung spring Zs : Displacement of sprung mass, Zus : Displacement of unsprung mass Zr : Road profile Fa : Air spring force A : Valve active area PA : Compressed air spring pressure Pa : Indoor air spring pressure gas P0 : Initial air pressure in the air spring V0 : Initial air volume in the air spring A0 : Initial area in the air spring A1 : Compressed area in the air spring P1 : Compressed air pressure in the air spring V1 : Compressed air volume in the air spring α : Volume coefficient β : Area coefficient h : Piston compression height Q : Estimated disturbance force F : Measured force M : Estimated mass a : Measured acceleration

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1.5

-1

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Sathishkumar. P. completed his mas-ter’s degree in Automobile Engineering from Anna University Chennai, INDIA. After which he is pursuing Ph.D. at the same Institute under the faculty of Me-chanical Engineering. His primary inter-est is control of Semi active and Active suspension system.

Reducing the seat vibration of vehicle by semi active force control technique

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