CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 28,aNo. 5,a2015
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DOI: 10.3901/CJME.2015.0615.081, available online at www.springerlink.com; www.cjmenet.com; www.cjme.com.cn
Hierarchical Control of Ride Height System for Electronically Controlled Air Suspension Based on Variable Structure and Fuzzy Control Theory
XU Xing1, *, ZHOU Kongkang1, ZOU Nannan1, JIANG Hong2, and CUI Xiaoli3
1 School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang 212013, China 2 School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China
3 School of Mechanical Engineering, Hunan Institute of Technology, Hengyang 412002, China
Received November 7, 2014; revised March 16, 2015; accepted June 15, 2015
Abstract: The current research of air suspension mainly focuses on the characteristics and design of the air spring. In fact, electronically
controlled air suspension (ECAS) has excellent performance in flexible height adjustment during different driving conditions. However,
the nonlinearity of the ride height adjusting system and the uneven distribution of payload affect the control accuracy of ride height and
the body attitude. Firstly, the three-point measurement system of three height sensors is used to establish the mathematical model of the
ride height adjusting system. The decentralized control of ride height and the centralized control of body attitude are presented to design
the ride height control system for ECAS. The exact feedback linearization method is adopted for the nonlinear mathematical model of
the ride height system. Secondly, according to the hierarchical control theory, the variable structure control (VSC) technique is used to
design a controller that is able to adjust the ride height for the quarter-vehicle anywhere, and each quarter-vehicle height control system
is independent. Meanwhile, the three-point height signals obtained by three height sensors are tracked to calculate the body pitch and
roll attitude over time, and then by calculating the deviation of pitch and roll and its rates, the height control correction is reassigned
based on the fuzzy algorithm. Finally, to verify the effectiveness and performance of the proposed combined control strategy, a
validating test of ride height control system with and without road disturbance is carried out. Testing results show that the height
adjusting time of both lifting and lowering is over 5 s, and the pitch angle and the roll angle of body attitude are less than 0.15. This
research proposes a hierarchical control method that can guarantee the attitude stability, as well as satisfy the ride height tracking
system.
Keywords: electronically controlled air suspension (ECAS), ride height, body attitude, hierarchical control
1 Introduction
Electronically controlled air suspension (ECAS) can automatically adjust ride height. Different ride heights can meet different driving states and thereby improve the suspension performance[1–3]. Basically, height switching or adjusting occur in straight-line driving conditions and not in the special conditions such as acceleration, braking and cornering due to a large time-delayed compressed air process. Recently, characteristics of air suspension have been paid more attention[4–7], which is helpful to match the air spring and chassis system. Typically, the ride height adjustment is accomplished by charging/discharging the
* Corresponding author. E-mail: [email protected] Supported by National Natural Science Foundation of China (Grant No.
compressed air into/from air springs, which contains the aero-thermodynamic and vehicle dynamic processes of variable mass system, and is one of the most important features of the ECAS system.
With the ECAS system widely used on various types of vehicles, many studies on the model of the ride height adjusting system have been performed. BURTON, et al[8], performed the first research analysis, modelling and control work of a prototype self-levelling active suspension system for road vehicles. Then, BEMPORAD, et al[9], proposed a novel approach to the verification of hybrid systems based on linear and mixed-integer linear programming. Many control methods for the ride height system have been studied. CHEN, et al[10], used the PID and variable structure control algorithm to adjust the hydro-pneumatic suspension, which could eliminate oscillation in the system, and improve control accuracy. A fuzzy control was used for the air suspension system, and the designed control system showed a good robustness when the structure parameter changed[11]. SONG[12] built a multi-body dynamic model of an air suspension vehicle based on Lagrange’s method and performed a ride height simulation under step input using
XU Xing, et al: Hierarchical Control of Ride Height System for Electronically Controlled Air Suspension Based on Variable Structure and Fuzzy Control Theory
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PID and PD control strategy. Jiangsu University Air Suspension Research Team did further studies in the charging/discharging gas system of ECAS[13]. The team analyzed the nonlinear stability of the ride height system[14], presented a variable integral PID/PWM approach to improve the stability of ride height adjustment system[15], and adopted the inductance integral to design the ride height measuring system for tracking the real-time information of ride height[16]. Recently, FENG, et al[17], used the Fuzzy/PWM algorithm on an electrically controlled air suspension for a semi-trailer based on the quarter-vehicle model, and the overshoot and oscillation of the control system were improved effectively. KIM, et al[18–20], designed a sliding mode control algorithm to improve the tracking accuracy of the control and to overcome nonlinearities and uncertainties in the air suspension system of full vehicle, but the using model is a complex and high order system.
Although several aspects of ride height control design have been investigated in the literature, the research about ECAS vehicle, especially the stability of body attitude is still minimal. In this paper, the variable structure control (VSC) algorithm will be used to design the ride height control system for four quarter-vehicle models. All VSC height control inputs will be reassigned by calculating the real-time body attitude of full vehicle based on the hierarchical control theory, which will ensure the stability of the full-vehicle ride height.
This paper is organized as follows. Firstly, the ride height system and working principle are given. Secondly, the nonlinear model of the ride height system is built. And then, a control structure of full vehicle based on VSC and Fuzzy control algorithm is presented, and the results of the proposed algorithm are presented. Finally, the work is summarized in the last section.
2 Structure of Ride Height Control System
The structure of the ECAS system is shown in Fig. 1,
which is principally composed of an air compressor, air dryer, four-loop protective valve, filter inflation valve, air reservoir, one-way valve, combined solenoid valve, air springs and other suspension components. The characteristics of air springs and compressed gas lead to the nonlinearity of the ride height adjustment system.
Fig. 1. Structure of ride height system for ECAS
When the ride height lifts, gas is pumped from the reservoir into the air springs through the pipelines. When the ride height lowers, gas is pumped into the atmosphere from the air springs through the pipelines. Whether the ride height lifts or lowers is decided by the driving conditions (automatically or manually).
3 Mathematical Model of Ride Height
Control System
It is shown by the ride height adjustment system that the sprung mass is supported by four groups of air springs. According to the principle that three points determine a plane, three height sensors are installed in the middle of front suspension, the rear left suspension and the rear right suspension, which takes the vehicle floor as the horizontal plane. In this case, it is able to eliminate over positioning. The ride height is adjusted by using the height decentralized control and the body attitude centralized control. Therefore, according to Ref. [15], the three independent systems is described as a quarter ride height tracking model (only a model with different parameters), the equation that describes the behaviour of this system is given by
3
(1) (2) 2 (3) 33 3 3
3 3 3 3
3 30
( )
( ),
,
,
s s a e s
s s s
s m
s
m Z p P A m g
C Z C Z C Z
V p p VZ RT q
V V VZ
ìï = - - -ïïïï + +ïíï =- +ïïïï = +ïî
(1)
where the meaning of each symbol is given in Table 1. It should be noted that the stability of body attitude needs to be considered during the ride height adjusting process. The pitch and roll deviation is calculated by the ride heights in different positions, which can obtain the current body attitude.
Table 1. Notation of Eq. (1)
Symbol Notation Unit
Adiabatic index –
mq Mass flow of inflow gas (or the outflow gas, which is negative)
kg/s
3T Internal temperature of air spring C
3V Volume of air spring (0 is the initial value of system)
m3
3p Internal absolute pressure of air spring Pa
sZ Absolute displacement of sprung mass m
aP Atmospheric pressure Pa
eA Effective area of air spring m2
sm Sprung mass kg
g Gravity acceleration m/s2
( )3
iC One degree term, quadratic term and three degree term of damping (i=1, 2, 3)
N • s/m
V Volume change rate of air spring m3/m
The nonlinear ride height adjusting system is regularized
by using differential geometry theory. The state variables of
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the ride height tracking system can be represented asT
3[ ] ,s sZ Z p=X then Eq. (1) can be rewritten as
1 2
2 3
(1) (2) 2 (3) 33 2 3 2 3 2
323 3
30 1 30 1
,
1[( )
( )],
,
a e ss
m
X X
X X P A m gm
C X C X C X
RTVXX X q
V VX V VX
ìï =ïïïïï = - - -ïïïïíï + +ïïïïï =- +ïï + +ïïî
(2)
1( ) .y h X X= = (3)
Because the Lie derivatives are
0 ( ) ( ) 0g f gL L h X L h X= = , 1 ( ) 0,g fL L h X =
3
30 1
2
( )( ) 0,f
sg
Ae kRT
m V V XL L h X
+= ¹
the relative degree of the system is 3. This degree can meet the input-state linearization and input-output linearization demands, and hold the equality (3) .y v= A set of linear differential equations are obtained by the non-singular coordinate transformation in the new coordinate system, and can be represented as
1 2
2 3
3
Z Z
Z Z
Z v
ìï =ïïïï =íïïï =ïïî
(4)
In this paper, the suitable control algorithm can be
introduced into the design of ride height control system based on Eq. (4).
4 Design of Ride Height Control System
4.1 Ride height tracking system via VSC algorithm
Ride height adjustment system has the complexities of load uncertainties, and nonlinearity of air spring and shock absorber. Variable structure control algorithm shows strong robustness to perturbation and interference[21–22]. Consequently, the ride height control system is designed, and includes the three height-controllers based on VSC algorithm in the three measurement points and the body attitude controller for the pitch and roll stability according to the hierarchical control theory. All control inputs of three measurement points are calculated by the height error and then fed into the control reassigning system (the decentralized control), so three control inputs will be modified to meet the requirements of ride height adjustment and body attitude stability (the centralized control). Fig. 2 shows the model structure of ride height control system, where Fu , RLu , RRu are the modified control inputs of front, rear left and rear right.
Fig. 2. Hierarchical architecture of ride height control system Ride height control is a tracking movement problem and
the differential equations are obtained by the deviation between the detected height and given height.
Define 1 1 1 ,d de X X Z X= - = - 2 1 ,de Z X= -
3 1 ,de Z X= - and dX as the given height. Substituting into Eq. (4) yields
1 2 1 2
2 3 1 2 3
3 3
,
,
.
e e Z Z
e e Z Z Z
e Z v
ìï = = =ïïïï = = = =íïïï = =ïïî
(5)
Here we choose the switching function
[ ] [ ]1
1 2 2
3
( ) 1 1 ,
e
t c c e c
e
é ùê úê ú= = =ê úê úë û
s Ce e
and the coefficient matrix C is determined by optimal quadratic form index control theory. A reasonable matrix C can guarantee the sliding mode with good quality: when t tends to infinity, ( )e t will converge to zero. Then, the control input is determined to ensure that any movement can reach the switching surface. The exponential approach law is adopted to ensure the stable motion of sliding mode.
Let sgn( )s s ks=- - ( 0, > 0k > ). Combining the above equations, the derivative of the switching function can be represented as
XU Xing, et al: Hierarchical Control of Ride Height System for Electronically Controlled Air Suspension Based on Variable Structure and Fuzzy Control Theory
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By Eq. (6), the VSC input is
[ ]11 2 2 3( ) ( ) sgn( ) .u A X B X c e c e ks s-= - - - - - (7)
According to the reaching condition 0,s s < the
reasonable parameters k and can be chosen to ensure the globally stability of the system. Although the control law for a quarter-vehicle is obtained, we need to consider the body attitude, which can ensure the stability when the height is changing.
4.2 Attitude control system via fuzzy control algorithm
Uneven distribution of the vehicle sprung mass, difference between front and rear air spring system parameters (including pipe length and diameter), will inevitably cause the asynchrony of the height adjusting process, which may lead to the instability of body attitude. According to the system characteristics, the fuzzy algorithm is introduced to solve the instability of body attitude, to ensure that when the body height is adjusted, the body attitude can still be stable.
Two-dimensional fuzzy controller is adopted and the
correction proportion value of pitch and roll is calculated by using the fuzzy control law. Define the pitch deviation ,pxthe pitch deviation rate d( ) d ,px t the roll deviation ryand the roll deviation rate d( ) dry t as the feedback variables of fuzzy controller. The outputs of the fuzzy controller are the attitude correction proportion values
pux and .ruy For the body attitude stability controller, the current body
attitude is calculated according to the deviation of ride height measuring points. The proportion of modified control variable is calculated by the fuzzy algorithm. It is obtained by unitary processing and the maximum proportion is 1. For example, during the body lifting process (charging), if the front height is higher than the rear’s (the average of rear left’s and the rear right’s), and meanwhile the rear left’s is higher than the rear right’s, the control input of the front needs to be multiplied by 1-pitch correction proportion value. But the rear-right control variable is invariant, and its correction proportion value depends on the size of deviation and the speed of deviation change. Tables 2 and 3 show the control strategies of lifting and lowering, respectively.
Table 2. Control strategy when ride height lifting
Pitch attitude Roll attitude Control input
Front ride height Rear-left ride height Rear-right ride height
0px > 0ry > (1 )p r Fux uy u - - (1 )r RLuy u- RRu
0ry ≤ (1 )p r Fux uy u - - RLu (1 )r RRuy u-
0px ≤ 0ry > Fu (1 )p r RLux uy u - - (1 )r RRuy u-
0ry ≤ Fu (1 )r RLuy u- (1 )p r RRux uy u - -
Table 3. Control strategy when ride height lowering
Pitch attitude Roll attitude Control input
Front ride height Rear-left ride height Rear-right ride height
0px > 0ry > Fu (1 )p r RLux uy u - - (1 )r RRuy u-
0ry ≤ Fu (1 )r RLuy u- (1 )p r RRux uy u - -
0px ≤ 0ry > (1 )p r Fux uy u - - (1 )r RLuy u- RRu
0ry ≤ (1 )p r Fux uy u - - RLu (1 )r RRuy u-
5 Vehicle Test and Validation The actual height adjusting test is conducted with a
semi-physical rig equipped with a ride height control system. To validate the effectiveness of body attitude control, the sprung mass parameters are purposely changed to make it unevenly distributed. Payload of the ride height system can be changed by increasing or decreasing the amount of the iron-sand bags. Random road input is simulated by the Road Simulator Machine of MTS 320. Meanwhile, the proposed VSC and Fuzzy combined approach is programmed by means of Matlab/Simulink and directly downloaded into the D2P/RapidPro platform. In addition, a compressor is used to supply the high pressure air for the ride height system. Fig. 3 shows the
configuration of the semi-physical rig test platform. The pressure of the air springs is measured by installed pressure sensors, and the changing ride height is measured by installed height sensors.
Fig. 3. Testing rig of ride height adjusting system
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The control input calculated by SVC and Fuzzy combined approach is the mass flow rate u, but the ON-OFF solenoid valve has just two states which cannot continuously adjust the mass flow rate. So the average mass flow rate during 0.062 s of the pulse period is controlled by the PWM duty cycle. Since the response of the solenoid valve is limited, a working dead-zone of the solenoid valve should be no less than 0.025 s. In addition, the solenoid valve for charging and discharging the compressed gas does not allow for simultaneous opening which can save the energy of system. The control scheme of the ride height adjusting system is shown in Fig. 4. The ride height adjustment of ECAS has three switch-modes of “HIGH MODE”, “NORMAL MODE”, and “LOW MODE” in this study. “NORMAL MODE” is normal driving height, and other modes are applied in special conditions. According to parameters that match the current testing vehicle, the height changing distance between “NORMAL MODE” and “HIGH MODE” is 20 mm, and the height changing distance between “NORMAL MODE” and “LOW MODE” is 30 mm. In practical implementations, the ride height of the vehicle can be changed by the driver or ECU. Because the changed height is a new target, the control system needs to track a new one by charging or discharging.
Fig. 4. Control scheme
When the vehicle is stopped and the payload (e.g., passengers on or off) will be changed, the ride height needs to be a constant value by charging or discharging. Testing results of ride height lifting and lowering are shown in Fig. 5 and Fig. 6. The adjusting time of both height lifting and height lowering is over 5 s. The route losses of the pipeline, the pressure decreasing of the air reservoir and the saturation of control input all contribute to an increased adjusting time. The payload of vehicle shown in Fig. 5(b) and Fig. 6(b) is not well-distributed because of the different original pressure values. Then, as shown in Figs. 5(c), 5(d) and Figs. 6(c), 6(d), pitch angle and roll angle of body attitude are less than 0.15°, which can ensure the body stability. The pitch angle and roll angle cannot return to the original balance point, because the ride height control is working in the dead zone and the ride height can be controlled in a reasonable region.
XU Xing, et al: Hierarchical Control of Ride Height System for Electronically Controlled Air Suspension Based on Variable Structure and Fuzzy Control Theory
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Fig. 5. Test results of ride height lifting without disturbances
Fig. 6. Test results of ride height lowering without disturbances
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Fig. 5(e) and Fig. 6(e) are body accelerations of different positions when ride height is changing. It is similar to adding an extra force by charging or discharging, so the riding performance turns poor, but it can be controlled by calibrating ECU parameters. Since controller calibration signals are not synchronous with the data acquisition system according to Fig. 5(f) and Fig. 6(f), it can be found that the data trigger is different. However, the whole adjusting process matches to other signals. Moreover, the control input PWM of solenoids is automatically adjusted by ECU which is calculated by the ride height errors and attitude deviation.
In practical driving conditions, the road disturbance cannot be avoided. Since the natural frequency of an air spring is about 1 Hz, we may create a 1 Hz sine wave signal acting on the teasing vehicle by using the Road Simulator Machine. As shown in Fig. 7 and Fig. 8, the height adjusting time is nearly the same as that without disturbances, and pitch angles and roll angles of body attitude are well adjusted even if there is uneven distribution of payload. The whole height adjusting process has no significant overshoot and weakens the effect of disturbances. So, testing results show the robustness of the proposed controller.
Fig. 7. Test results of ride height lifting with 1 Hz sine disturbances
XU Xing, et al: Hierarchical Control of Ride Height System for Electronically Controlled Air Suspension Based on Variable Structure and Fuzzy Control Theory
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Fig. 8. Test results of ride height lowering with 1 Hz sine disturbances
6 Conclusions
(1) The mathematical model for ride height adjustment
coupled with aero-thermodynamic and vehicle dynamics is proposed. With the differential geometry theory used, the nonlinear ride height system can be exactly linearized.
(2) Considered the over-positioning of system design, a ride height adjustment system based on three-point measurement is proposed. Decentralized control of the vehicle ride height and centralized control of body attitude are adopted to design a ride height controller that matches
the characteristics of system. (3) Considering the stability of body attitude, the control
input calculated by the VSC algorithm should be modified, and the current body attitude is calculated according to the ride height of three measuring points. The fuzzy controller for body attitude is designed to modify the control input by use of the fuzzy algorithm.
(4) For the purpose of investigating the application of the proposed control method, a test bench is developed including sensors and controller. Test results of height switch indicate the effectiveness of control algorithm and the potential for application in a real vehicle system.
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Biographical notes XU Xing, born in 1979, is currently a lecturer and a master candidate supervisor at School of Automotive and Traffic Engineering, Jiangsu University, China. He received his PhD degree from Jiangsu University, China, in 2010. His research interests include vehicle system dynamics and control. Tel: +86-511-88782845; E-mail: [email protected]
ZHOU Kongkang, born in 1938, is currently a professor and a PhD candidate supervisor at School of Automotive and Traffic Engineering, Jiangsu University China. He received his master degree from Jiangsu University, China, in 1980. His research interests include vehicle dynamic performance simulation and control. Tel: +86-511-88780178; E-mail: [email protected]
ZOU Nannan, born in 1990, is currently a master candidate at School of Automotive and Traffic Engineering, Jiangsu University China. His research interests include vehicle system modeling and fault-tolerant control. E-mail: [email protected]
JIANG Hong, born in 1963, is currently a professor and a master candidate supervisor at School of Mechanical Engineering, Jiangsu University, China. She received her master degree from Jiangsu University, China, in 1992. Her research interests include vehicle dynamics simulation and system design. E-mail: [email protected]
CUI Xiaoli, born in 1962, is currently a professor at School of Mechanical Engineering, Hunan Institute of Technology, China. She received her PhD degree from Zhongnan University, China, in 2011. Her research interests include vehicle CAE and integration. E-mail: [email protected]
