CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 28,aNo. 5,a2015 ·945·

DOI: 10.3901/CJME.2015.0615.081, available online at www.springerlink.com; www.cjmenet.com; www.cjme.com.cn

Hierarchical Control of 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 . 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

compressed air into/from air springs, which contains the 1 Introduction aero-thermodynamic and vehicle dynamic processes of variable mass system, and is one of the most important Electronically controlled air suspension (ECAS) can features of the ECAS system. automatically adjust ride height. Different ride heights can With the ECAS system widely used on various types of meet different driving states and thereby improve the vehicles, many studies on the model of the ride height suspension performance[1–3]. Basically, height switching or adjusting system have been performed. BURTON, et al[8], adjusting occur in straight-line driving conditions and not in performed the first research analysis, modelling and control the special conditions such as acceleration, braking and work of a prototype self-levelling system cornering due to a large time-delayed compressed air for road vehicles. Then, BEMPORAD, et al[9], proposed a process. Recently, characteristics of air suspension have novel approach to the verification of hybrid systems based been paid more attention[4–7], which is helpful to match the on linear and mixed-integer linear programming. Many air spring and chassis system. Typically, the ride height control methods for the ride height system have been adjustment is accomplished by charging/discharging the studied. CHEN, et al[10], used the PID and variable structure control algorithm to adjust the hydro-pneumatic suspension, * Corresponding author. E-mail: [email protected] which could eliminate oscillation in the system, and Supported by National Natural Science Foundation of China (Grant No. improve control accuracy. A fuzzy control was used for the 51105177), Jiangsu Provincial Natural Science Foundation of China (Grant No. BK20131255), Research Fund for the Doctoral Program of air suspension system, and the designed control system Higher Education of China (Grant No. 20113227120015), Qing Lan showed a good robustness when the structure parameter Project of Jiangsu Province of China, Scientific Research Foundation for [11] [12] Advanced Talents, Jiangsu University, China (Grant No. 11JDG047), and changed . SONG built a multi-body dynamic model of Hunan Provincial Natural Science Foundation of China (Grant No. an air suspension vehicle based on Lagrange’s method and 12JJ6036) performed a ride height simulation under step input using © Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2015

XU Xing, et al: Hierarchical Control of Ride Height System for Electronically Controlled ·946· Air Suspension Based on Variable Structure and Fuzzy Control Theory

PID and PD control strategy. Jiangsu University Air When the ride height lifts, gas is pumped from the Suspension Research Team did further studies in the reservoir into the air springs through the pipelines. When charging/discharging gas system of ECAS[13]. The team the ride height lowers, gas is pumped into the atmosphere analyzed the nonlinear stability of the ride height system[14], from the air springs through the pipelines. Whether the ride presented a variable integral PID/PWM approach to height lifts or lowers is decided by the driving conditions improve the stability of ride height adjustment system[15], (automatically or manually). and adopted the inductance integral to design the ride height measuring system for tracking the real-time 3 Mathematical Model of Ride Height information of ride height[16]. Recently, FENG, et al[17], Control System used the Fuzzy/PWM algorithm on an electrically controlled air suspension for a semi-trailer based on the It is shown by the ride height adjustment system that the quarter-vehicle model, and the overshoot and oscillation of sprung mass is supported by four groups of air springs. the control system were improved effectively. KIM, et According to the principle that three points determine a al[18–20], designed a sliding mode control algorithm to plane, three height sensors are installed in the middle of improve the tracking accuracy of the control and to front suspension, the rear left suspension and the rear right overcome nonlinearities and uncertainties in the air suspension, which takes the vehicle floor as the horizontal suspension system of full vehicle, but the using model is a plane. In this case, it is able to eliminate over positioning. complex and high order system. The ride height is adjusted by using the height decentralized Although several aspects of ride height control design control and the body attitude centralized control. Therefore, have been investigated in the literature, the research about according to Ref. [15], the three independent systems is ECAS vehicle, especially the stability of body attitude is described as a quarter ride height tracking model (only a still minimal. In this paper, the variable structure control model with different parameters), the equation that (VSC) algorithm will be used to design the ride height describes the behaviour of this system is given by control system for four quarter-vehicle models. All VSC height control inputs will be reassigned by calculating the ïìmZ =-() p P A - mg - ï ss 3 a e s real-time body attitude of full vehicle based on the ï (1) (2) 2 (3)  3 ï ()CZ33ss++ CZ CZ 3 s, hierarchical control theory, which will ensure the stability í (1) ïVp =- p VZ + RTq , of the full-vehicle ride height. ï 33 3sm 3 ï This paper is organized as follows. Firstly, the ride height îïVV330=+ VZs , system and working principle are given. Secondly, the nonlinear model of the ride height system is built. And then, where the meaning of each symbol is given in Table 1. It a control structure of full vehicle based on VSC and Fuzzy should be noted that the stability of body attitude needs to control algorithm is presented, and the results of the be considered during the ride height adjusting process. The proposed algorithm are presented. Finally, the work is pitch and roll deviation is calculated by the ride heights in summarized in the last section. different positions, which can obtain the current body attitude. 2 Structure of Ride Height Control System Table 1. Notation of Eq. (1) The structure of the ECAS system is shown in Fig. 1, Symbol Notation Unit which is principally composed of an air compressor, air  Adiabatic index – dryer, four-loop protective , filter inflation valve, air Mass flow of inflow gas (or the outflow q kg/s reservoir, one-way valve, combined solenoid valve, air m gas, which is negative) springs and other suspension components. The T3 Internal temperature of air spring C characteristics of air springs and compressed gas lead to the Volume of air spring (0 is the initial value V m3 nonlinearity of the ride height adjustment system. 3 of system)

p3 Internal absolute pressure of air spring Pa

Z s Absolute displacement of sprung mass m

Pa Atmospheric pressure Pa 2 Ae Effective area of air spring m

ms Sprung mass kg g Gravity acceleration m/s2 One degree term, quadratic term and three C ()i N • s/m 3 degree term of damping (i=1, 2, 3) V Volume change rate of air spring m3/m

The nonlinear ride height adjusting system is regularized Fig. 1. Structure of ride height system for ECAS by using differential geometry theory. The state variables of

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·947· the ride height tracking system can be represented as  T X = [],ZZpss3 then Eq. (1) can be rewritten as

ïìXX = , ï 12 ï 1 ïXXPAmg =---[( ) ï 23ae s ï ms íï (2) ï (1) (2) 2 (3) 3 ï ()],CX32++ CX 3 2 CX 32 ï ï VX  RT ïX =-2 Xq + 3 , ï 33m îï VVXVVX30++ 1 30 1

yhXX==() . (3) 1

Because the Lie derivatives are Fig. 2. Hierarchical architecture of ride height control system

Ride height control is a tracking movement problem and 0 1 LLhXgf()== LhX g () 0, LLhXgf()= 0, the differential equations are obtained by the deviation Ae kRT between the detected height and given height. LLhX2 ()=¹3 0, g f Define eXX=- =- ZX, eZX=-, mVs ()30+  VX 1 11dd 1 21d eZX=-  , and X as the given height. Substituting 31d d the relative degree of the system is 3. This degree can meet into Eq. (4) yields the input-state linearization and input-output linearization ïìee === ZZ , demands, and hold the equality yv(3) = . A set of linear ï 12 1 2 ï   differential equations are obtained by the non-singular íeeZZZ23== 1 = 2 = 3, (5) ï coordinate transformation in the new coordinate system, ï == îïeZv33. and can be represented as Here we choose the switching function ïìZ = Z ï 12 éùe ï  êú1 íZ23= Z (4) êú ï sCe()tccec==[][]121 2 = 1e , ï  êú ïZ3 = v êú îï ëûe3

In this paper, the suitable control algorithm can be and the coefficient matrix C is determined by optimal introduced into the design of ride height control system quadratic form index control theory. A reasonable matrix C based on Eq. (4). can guarantee the sliding mode with good quality: when t tends to infinity, et() will converge to zero. Then, the 4 Design of Ride Height Control System control input is determined to ensure that any movement can reach the switching surface. The exponential approach 4.1 Ride height tracking system via VSC algorithm law is adopted to ensure the stable motion of sliding mode. Ride height adjustment system has the complexities of Let s =- sgn(sks ) - (  > 0, k > 0 ). Combining the load uncertainties, and nonlinearity of air spring and shock above equations, the derivative of the switching function absorber. Variable structure control algorithm shows strong can be represented as [21–22] robustness to perturbation and interference . ì Consequently, the ride height control system is designed, ï ïs=+ce11 ce 2  2 +=+ e 3 ce 12 ce 2 3 += v and includes the three height-controllers based on VSC ï ï ce12++ c 23 e B() X + A () X u = algorithm in the three measurement points and the body ï íï --ks sgn( s ), (6) attitude controller for the pitch and roll stability according ï ï 2 to the hierarchical control theory. All control inputs of three ïAX()= LLhXgf (), ï measurement points are calculated by the height error and ï = 3 îïBX() LhXf (), then fed into the control reassigning system (the decentralized control), so three control inputs will be where modified to meet the requirements of ride height adjustment 3(1)(2)2(3)3 and body attitude stability (the centralized control). Fig. 2 BX()== LhXf () -( C32 X+´ C 3 X 2+ C 32 X ) shows the model structure of ride height control system, æö ()XPaAemg3 --s Ae kX V X ç ÷ 2 32 where uF , uRL , uRR are the modified control inputs of ç ÷ ms - . ç (1) (2) 2 (3) 3 ÷ mV( +  VX) front, rear left and rear right. èø--CX32CX 3 2- CX 32 s 30 1

XU Xing, et al: Hierarchical Control of Ride Height System for Electronically Controlled ·948· Air Suspension Based on Variable Structure and Fuzzy Control Theory

By Eq. (6), the VSC input is correction proportion value of pitch and roll is calculated by

using the fuzzy control law. Define the pitch deviation xp , -1 uAX=-----()[ BXceceks () 12 23  sgn(). s] (7) the pitch deviation rate d(xp ) dt , the roll deviation yr and the roll deviation rate d(ytr ) d as the feedback According to the reaching condition ss  < 0, the variables of fuzzy controller. The outputs of the fuzzy reasonable parameters k and  can be chosen to ensure controller are the attitude correction proportion values the globally stability of the system. Although the control uxp and uyr . law for a quarter-vehicle is obtained, we need to consider For the body attitude stability controller, the current body the body attitude, which can ensure the stability when the attitude is calculated according to the deviation of ride height is changing. height measuring points. The proportion of modified control variable is calculated by the fuzzy algorithm. It is 4.2 Attitude control system via fuzzy control algorithm obtained by unitary processing and the maximum Uneven distribution of the vehicle sprung mass, proportion is 1. For example, during the body lifting difference between front and rear air spring system process (charging), if the front height is higher than the parameters (including pipe length and diameter), will rear’s (the average of rear left’s and the rear right’s), and inevitably cause the asynchrony of the height adjusting meanwhile the rear left’s is higher than the rear right’s, the process, which may lead to the instability of body attitude. control input of the front needs to be multiplied by 1-pitch According to the system characteristics, the fuzzy algorithm correction proportion value. But the rear-right control is introduced to solve the instability of body attitude, to variable is invariant, and its correction proportion value ensure that when the body height is adjusted, the body depends on the size of deviation and the speed of deviation attitude can still be stable. change. Tables 2 and 3 show the control strategies of lifting Two-dimensional fuzzy controller is adopted and the and lowering, respectively.

Table 2. Control strategy when ride height lifting

Control input Pitch attitude Roll attitude Front ride height Rear-left ride height Rear-right ride height

yr > 0 (1--uxprF uy) u (1- uyrRL ) u uRR xp > 0 yr ≤ 0 (1--uxprF uy) u u RL (1- uyrRR ) u

yr > 0 uF (1--uxprR uy) u L (1- uyrRR ) u xp ≤ 0 yr ≤ 0 uF (1- uyrRL ) u (1--uxprR uy) u R

Table 3. Control strategy when ride height lowering

Control input Pitch attitude Roll attitude Front ride height Rear-left ride height Rear-right ride height

yr > 0 uF (1--uxprR uy) u L (1- uyrRR ) u xp > 0 yr ≤ 0 uF (1- uyrRL ) u (1--uxprR uy) u R

yr > 0 (1--uxprF uy) u (1- uyrRL ) u uRR xp ≤ 0 yr ≤ 0 (1--uxprF uy) u u RL (1- uyrRR ) u

configuration of the semi-physical rig test platform. The 5 Vehicle Test and Validation pressure of the air springs is measured by installed pressure sensors, and the changing ride height is measured by The actual height adjusting test is conducted with a installed height sensors. 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 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 ·950· Air Suspension Based on Variable Structure and Fuzzy Control Theory

Fig. 5. Test results of ride height lifting without disturbances

Fig. 6. Test results of ride height lowering without disturbances

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·951·

Fig. 5(e) and Fig. 6(e) are body accelerations of different In practical driving conditions, the road disturbance positions when ride height is changing. It is similar to cannot be avoided. Since the natural frequency of an air adding an extra force by charging or discharging, so the spring is about 1 Hz, we may create a 1 Hz sine wave signal riding performance turns poor, but it can be controlled acting on the teasing vehicle by using the Road Simulator by calibrating ECU parameters. Since controller Machine. As shown in Fig. 7 and Fig. 8, the height calibration signals are not synchronous with the data adjusting time is nearly the same as that without acquisition system according to Fig. 5(f) and Fig. 6(f), it disturbances, and pitch angles and roll angles of body can be found that the data trigger is different. However, the attitude are well adjusted even if there is uneven whole adjusting process matches to other signals. Moreover, distribution of payload. The whole height adjusting process the control input PWM of solenoids is automatically has no significant overshoot and weakens the effect of adjusted by ECU which is calculated by the ride height disturbances. So, testing results show the robustness of the errors and attitude deviation. 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 ·952· Air Suspension Based on Variable Structure and Fuzzy Control Theory

Fig. 8. Test results of ride height lowering with 1 Hz sine disturbances

the characteristics of system. 6 Conclusions (3) Considering the stability of body attitude, the control input calculated by the VSC algorithm should be modified, (1) The mathematical model for ride height adjustment and the current body attitude is calculated according to the coupled with aero-thermodynamic and is ride height of three measuring points. The fuzzy controller proposed. With the differential geometry theory used, the for body attitude is designed to modify the control input by nonlinear ride height system can be exactly linearized. use of the fuzzy algorithm. (2) Considered the over-positioning of system design, a (4) For the purpose of investigating the application of the ride height adjustment system based on three-point proposed control method, a test bench is developed measurement is proposed. Decentralized control of the including sensors and controller. Test results of height vehicle ride height and centralized control of body attitude switch indicate the effectiveness of control algorithm and are adopted to design a ride height controller that matches the potential for application in a real vehicle system.

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