a takagi-sugeno fuzzy model-based control strategy for

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A takagi-sugeno fuzzy model-based control strategy for variable stiffness A takagi-sugeno fuzzy model-based control strategy for variable stiffness

and variable damping suspension and variable damping suspension

Xin Tang

Donghong Ning University of Wollongong, [email protected]

Haiping Du University of Wollongong, [email protected]

Weihua Li University of Wollongong, [email protected]

Yibo Gao

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Recommended Citation Recommended Citation Tang, Xin; Ning, Donghong; Du, Haiping; Li, Weihua; Gao, Yibo; and Wen, Weijia, "A takagi-sugeno fuzzy model-based control strategy for variable stiffness and variable damping suspension" (2020). Faculty of Engineering and Information Sciences - Papers: Part B. 4013. https://ro.uow.edu.au/eispapers1/4013

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A takagi-sugeno fuzzy model-based control strategy for variable stiffness and A takagi-sugeno fuzzy model-based control strategy for variable stiffness and variable damping suspension variable damping suspension

Abstract Abstract © 2013 IEEE. As the concept of variable stiffness and variable damping (VSVD) has increasingly drawn attention, suspensions applied with magnetorheological (MR) dampers to achieve varying stiffness and damping have been an attractive method to improve vehicle performance and driver comfort further. As highly nonlinearity of MR damper dynamics and coupled interconnections in the case of multi-output control, to build a direct control system for VSVD suspension based on multiple MR dampers is difficult. Applying Takagi-Sugeno (T-S) fuzzy model on the VSVD system enables the linear control theory to be directly utilized to build the multi-output controller for multi-MR dampers. In this paper, a T-S fuzzy model is established to describe an MR VSVD suspension model, and then an H∞ controller that considers the multi-input/multi-output (MIMO) coupled interconnections characteristic and multi-object optimization is designed. To estimate state information for the T-S fuzzy model in real-time, a state observer is designed and integrated in the controller. Then, the performance of the VSVD control algorithm was evaluated by numerical simulation. The results demonstrate that the T-S fuzzy model-based H&infty; controller outperforms the independent control method for a VSVD suspension system with multi-MR dampers.

Disciplines Disciplines Engineering | Science and Technology Studies

Publication Details Publication Details Tang, X., Ning, D., Du, H., Li, W., Gao, Y. & Wen, W. (2020). A takagi-sugeno fuzzy model-based control strategy for variable stiffness and variable damping suspension. IEEE Access, 8 71628-71641.

Authors Authors Xin Tang, Donghong Ning, Haiping Du, Weihua Li, Yibo Gao, and Weijia Wen

This journal article is available at Research Online: https://ro.uow.edu.au/eispapers1/4013

https://ro.uow.edu.au/eispapers1/4013

Received March 5, 2020, accepted March 19, 2020, date of publication March 30, 2020, date of current version April 29, 2020.

Digital Object Identifier 10.1109/ACCESS.2020.2983998

A Takagi-Sugeno Fuzzy Model-Based ControlStrategy for Variable Stiffness and VariableDamping SuspensionXIN TANG 1, (Member, IEEE), DONGHONG NING 2, (Member, IEEE),HAIPING DU 2, (Senior Member, IEEE), WEIHUA LI 3, (Member, IEEE),YIBO GAO4, AND WEIJIA WEN1,41Guangzhou HKUST Fok Ying Tung Research Institute, Guangzhou 511458, China2School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, Wollongong, NSW 2522, Australia3School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong, NSW 2522, Australia4Department of Physics, Hong Kong University of Science and Technology, Hong Kong

Corresponding author: Xin Tang ([email protected])

This work was supported in part by the China Postdoctoral Science Foundation under Grant 2019M662847 and in part by the GuangzhouPostdoctoral International Training Program.

ABSTRACT As the concept of variable stiffness and variable damping (VSVD) has increasingly drawnattention, suspensions applied with magnetorheological (MR) dampers to achieve varying stiffness anddamping have been an attractive method to improve vehicle performance and driver comfort further.As highly nonlinearity of MR damper dynamics and coupled interconnections in the case of multi-outputcontrol, to build a direct control system for VSVD suspension based on multiple MR dampers is difficult.Applying Takagi-Sugeno (T-S) fuzzy model on the VSVD system enables the linear control theory to bedirectly utilized to build the multi-output controller for multi-MR dampers. In this paper, a T-S fuzzy modelis established to describe an MR VSVD suspension model, and then an H∞ controller that considers themulti-input/multi-output (MIMO) coupled interconnections characteristic and multi-object optimization isdesigned. To estimate state information for the T-S fuzzy model in real-time, a state observer is designedand integrated in the controller. Then, the performance of the VSVD control algorithm was evaluated bynumerical simulation. The results demonstrate that the T-S fuzzy model-based H∞ controller outperformsthe independent control method for a VSVD suspension system with multi-MR dampers.

INDEX TERMS MIMO, robust control, Takagi-Sugeno fuzzy model, variable stiffness and variabledamping.

I. INTRODUCTIONVehicle suspension is used to provide ride comfort, roadholding, and other dynamic functions such as supportingthe vehicle weight and maintain vehicle height. To date,active and semi-active instruments are two typical methodsused to improve vehicle suspension performance [1]. Despitethat active control performs better at reducing vibrations,the disadvantages of potential instability and large powerconsumption limit its common use. On the contrary, semi-active suspensions offer a desirable performance enhanced byactive suspensions without requiring high power consump-tion and expensive hardware [2]. Magnetorheological (MR)

The associate editor coordinating the review of this manuscript and

approving it for publication was Ning Sun .

dampers are semi-active devices that use MR fluids to pro-vide controllable damping forces while requiring only batterypower. AnMR damper is used most widely in vehicle suspen-sion [3] as a nonlinear component and its corresponding con-trol strategies has been studied by many researchers in recentyears. A variety of control algorithms, such as clipped optimalcontrol, skyhook control, sliding mode control, neural net-work control, fuzzy logic control, gain-scheduled control andH∞ control, have been proposed for MR damper to conductvehicle suspension’s damping adjustment [4], [5].

Apart from suspension damping, stiffness is another impor-tant component that affects the performance of a suspension.To date, passive spring has been widely used in vehicle sus-pension. However, it cannot satisfy the conflicting require-ment of improved both ride comfort and driving stability.

71628 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 8, 2020

https://orcid.org/0000-0001-7469-2394

https://orcid.org/0000-0001-9905-4575

https://orcid.org/0000-0002-3439-3821

https://orcid.org/0000-0002-6190-8421

https://orcid.org/0000-0002-5253-2944

X. Tang et al.: T-S Fuzzy Model-Based Control Strategy for VSVD Suspension

An idealized suspension spring is supposed to be controllableso as to provide different stiffness values depending on thespecific driving and road conditions. For this requirement, theconcept of variable stiffness has been integrated into dampingvariable suspension system to form a variable stiffness andvariable damping (VSVD) suspension system. Based on thismotivation, our group developed a full-scaledMR suspensionsystem with tunable stiffness and damping characteristicsand the dynamic effectiveness has been proved. Furthermore,a simple but proper on-off control algorithm for the advancedsuspension system has been developed in [6]. Till now, theresearch area of the VSVD control is still largely unexplored;most of them still are focusing on VSVD control mechanism[7], [8], just a few works propose the specific feasible con-troller on this topic. In [9], [10], Xu et al. proposed a hybridcontrol strategy for a VSVD suspension to improve vehiclelateral stability. The control strategy composed of a fuzzycontroller that the output is wheel slip ratio and an on-offcontroller to improve normal force at the tyre. The simulationresult verifies their usefulness in enhancing vehicle stabilityby replacing a passive front suspension system with a hybridcontrol-based variable stiffness and damping structure. In anactive VSVD system, a control algorithm [11] proposed byAnubi et al. applies the concept of nonlinear energy sink toeffectively transfer the vibrational energy in the sprung massto a control mass. This skyhook-based concept can reducethe vibration from road disturbance to the car body at a rel-atively lower cost than a traditional variable damping activesuspension. In addition, Aunbi et al. further reported a corre-sponding semi-active structure for suspension system in [12].The performance of the controller based on the nonlinearenergy sink concept has been verified by simulation work.In this case, the control algorithm is applied to a horizontalMR damper in a McPherson suspension structure to adjustthe corresponding stiffness value. Furthermore, Spelta et al.developed a VSVD controller considering the critical trade-off between the choice of the stiffness coefficient and theend-stop hitting to improve the riding comfort of vehiclesfurther [13]. The simulation result demonstrates that the vari-able stiffness and damping suspension controlled by theircontrol algorithm improves vibration isolation better thansuspensions with only variable damping.

It is noticed from all the past and present studies that differ-ent control algorithms have different advantages with respectto different aspects of performance, and the performance ofthe controlled device is highly dependent on the choice ofthe control algorithm and the nonlinear complexity of thedynamic model. To solve the nonlinear issue in modeling,Yang et al. presented a neural network-based adaptive controlmethod [14] that can provide effective control based on theoriginal nonlinear dynamics without any linearizing opera-tions. Furthermore, by adding some designed nonlinear termsand introducing the concept of lumped mass method and vir-tual spring in the dynamic model, the controllers in [15], [16]can also provide the closed-loop asymptotic stability withoutany linearization for the original model.

Till now, researchers have found that the good vibrationreduction effectiveness is often controlled by the system usingvariable stiffness to reduce the low frequency responses ofsprung mass accelerations and using variable damping toreduce the high frequency responses of wheel load fluc-tuations, respectively [17]. In the real-time VSVD control,however, the damping value and stiffness value in suspensionsystem are complementary and coupled to each other. It iscaused by the coupled interconnections between the timevarying damping and the time varying stiffness, which haveled to the fluctuation of the value of solution [18]. It is alsonoted that the above articles that most of the control methodsjust using two independent controllers based on the single on-off control method to deal with the structure’s variable stiff-ness and variable damping work. There are two problems toattenuate the effect of shock absorption in these control strate-gies. First, the simple on-off control method does not ade-quately consider the nonlinear characteristics of MR damper;second, the independent control method for stiffness moduleand damping module cannot effectively overcome the cou-pled interconnections characteristic of multiple outputs of thesystem. Indeed, as high nonlinearity of MR damper dynamicsand coupled interconnections characteristic in multi-input-multi-output (MIMO) control system, to build a direct controlsystem for a VSVD suspension with multiple MR dampers isdifficult.

At present, although direct robust control has been widelyused in vibration semi-active control, most of them aredesigned for single-input and single-output control systemand bare researches are applied toMIMO control system [19].In fact, H∞ theory regarding as a robust control algorithmis highly suitable to deal with MIMO system [20], [21]. Thegoal of single output system control is to design a closed-loopcontroller to realize the shaping of frequency response func-tion; however, applying the similar mothed that to shape everyfrequency response function to multi-input and the multi-output system is difficult and unfeasible. By defining H∞norm of transfer function matrix and then shaping H∞ normin the frequency domain, H∞ theory can be applied to dealwith the control problem in MIMO system well. Currently,a robust mixed-sensitivityH∞ output feedback controller byusing loop shaping with regional pole placement for MIMOnonlinear system was studied in [22]. More recently, an H∞output feedback controller for a class of time-delayed MIMOnonlinear systems was presented in [23]. However, the abovecontrol methods, no matter whether they were proposed forvehicle suspensions or structural vibration control, normallycompute/design the desired damping force without consid-ering the device’s highly nonlinear dynamics. As a matterof fact, it is very important to be considered to deal withhigh nonlinearity of dynamic model in a MIMO systemwith multiple MR dampers. The algorithm which is capableof solving the coupling effect and high nonlinearity of amulti-MR damper control system has rarely been developed,although papers have verified the superiority of controllers’performance for a single MR damper system.

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Based on this motivation, this paper will propose a Takagi-Sugeno fuzzymodel-basedH∞ (TSFH) VSVD control strat-egy so that the nonlinear dynamic characteristics of theVSVD suspension’s twoMR dampers can be both consideredin the controller design and the desired control performancecan be realized for a practical system. Different from theexisting control strategies, the proposed algorithm can effec-tively solve the joint control issue of a multi-MR nonlinearsystem by integrating a double Bouc-Wen T-S fuzzy modeland a multi-object-optimized H∞ controller. Furthermore,different from the study of [24], where the fuzzy model of aVSVD suspension was identified by training the input-outputdata sets and the accuracy was fully dependent on expertexperience in selecting appropriate fuzzy sets and fuzzy rules,the T-S fuzzy model of a VSVD suspension will be obtainedin this paper by considering a proposed suspension’s doubleBouc-Wen MR damper model and using the approach of‘sector nonlinearity’ [25]. Further discussion on robust multi-objective controller design, taking into consideration the cou-pled interconnections of multi-output [26], the hysteresis ofmulti-MR dampers, and the vehicle suspension performancerequirements on ride comfort, road holding, and suspensiondeflection [27], is also provided. Based on theH∞ controllerintegratingmulti-objective optimization, both the closed-loopsystem stability and the closed-loop performance can be the-oretically guaranteed. Further considering the case that notall the state variables, in particular, the evolutionary variableused to describe the MR damper dynamics by the Bouc-Wen model, are available by measurement in practice, a stateobserver is designed and integrated into the controller toobtain the estimated premise and state variables. Then, basedon the MR VSVD suspension’s dynamic characterization in[28], numerical simulations are used to validate the effective-ness of the proposed approach.

The rest of this paper is organized as follows.Section II presents the VSVD suspension’s working principleand its dynamic model. The T-S fuzzy modeling process ofthe VSVD suspension and the design of the observer andcontroller are described in section III. Section IV presentsthe numerical simulation and the results are discussed in timeand frequency domains. Finally, our findings are concludedin section V.

II. PRELIMINARIESThe proposed controller will be designed based on a quarter-car model with the MR VSVD suspension. The workingprinciple of the applied VSVD suspension is introducedin section II-A. Then, to develop a real-time controller,section II-B gives the phenomenological model of the MRVSVD suspension, and integrates it into the quarter-carmodel. In section II-C, the integrated quarter-car model isdescribed by state-space equations to conduct the preliminaryof control design.

A. THE WORKING PRINCIPLE OF THE VSVD SUSPENSIONThe working principle of the variable stiffness and dampingsuspension can be demonstrated by Fig. 1(a), where three

FIGURE 1. (a) The MR VSVD suspension working principle and(b) structure configuration.

different connection modes of this device are illustrated, andFig. 1(b) shows the structure of the system. When the currentI2 applied to the upper stiffness cylinder 2 is small enough,the cylinder’s damping force will allow the relative motionbetween the shaft and cylinder 2. In this case, the VSVD sus-pension is working in connection mode 1 where the spring k1and the spring k2 work in series because both springs deformwhen the cylinder 2 slides along the shaft.When the current I2becomes bigger, the device will work in connection mode 2.In this working mode, the larger damping force makes thesliding motion between the cylinder 2 and shaft harder andslower. It is equivalent to the growth of the stiffness value ofthe spring k2.

Furthermore, when the upper cylinder’s damping force islarge enough to prevent the relative motion between the cylin-der and the centre shaft, the VSVD suspension is working inconnection mode 3, because only spring k1 will have a defor-mation in response to the external force. The determination ofconnection mode is controlled by the magnitude of the upperdamping force, which is determined by the amount of theinput current I2. The stiffness variability, therefore, is realisedby the switch between the connection modes. The dampingvariability is realized by adjusting the current I1 applied to thelower damping cylinder 1. As shown in Fig. 1(a), no matterwhich connection mode the VSVD suspension is, the overallequivalent damping is represented by the damping c1. c1increases as the current I1 applied to the cylinder 1 increases.

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FIGURE 2. Schematic diagram of (a) the proposed MR VSVD suspension model and (b) the quarter-car model with the MR VSVD suspension.

In summary, the effective stiffness of the proposed VSVDsuspension is controlled by current I2 and the equivalentdamping is controlled independently by current I1.

B. THE QUARTER-CAR MODEL WITH THEMR VSVD SUSPENSIONThe Bouc-Wenmodel has been widely accepted in describingMR behavior for its mathematical simplicity and accuracy butwith unmeasurable state variables [29]. In real-time control,a simplified Bouc-Wen model is suggested to be applied,which has less and measurable state variables (the unmea-surable state variable y in Bouc-Wen model is replaced), butalso the accuracy to describe the hysteretic behavior of anMR structure.

To implement the real-time controller design, the pro-posed MR VSVD suspension phenomenological model inthis section is integrated with two simplified Bouc-Wen mod-els, and Fig. 2(a) shows the schematic diagram of the pro-posed model. The mathematical description for this model isas follows:

F = Fd + ks1 (z− zk)+ Fs,

Fd = α1zd1 + k01 · z+ C01 · z,

Fs = α2zd2 + k02 (z− zk)+ C02 (z− zk) ,

mk zk = Fs + ks1 (zk − z)− ks2 · zk , (1)

where

zd1 = −γ1 |z| · zd1 |zd1| − β1 · z · z2d1 + Ad1(z),

zd2 = −γ2 |z− zk | · zd2 · |zd2| − β2 (z− zk) z2d2+Ad2 (z− zk) ,

α1 = α1a + α1b · I1,

C01 = C01a + C01b · I1,

α2 = α2a + α2b · I2,

C02 = C02a + C02b · I2,

and F is the total force generated by the VSVD suspension;Fd and Fs are the force generated by the damper 1 and the

damper 2, respectively; Ad1, Ad2, β1, β2, γ1 and γ2 are used todescribe the hysteresis behavior; α1 and α2 are the evolution-ary coefficient; C01 and C01 are the viscous damping; ks1 andks2 are the spring stiffness; k01 and k02 are the accumulatorstiffness; z and zk are the displacements of the suspension andthe top damper cylinder, respectively; mk is the mass of thedamper 2; I1 and I2 are the command currents sent to the MRdamper 1 and MR damper 2, respectively.

The linear dynamicmodel of a quarter-car can be describedby the following equations [27]:

mszs + cs (zs − zu)+ (zs − xu) = 0,

muzu + kt (zu − zr )+ cs (zs − zu)− ks (zs − xu) = 0, (2)

where ms is the sprung mass; mu is the un-sprung mass; zs isthe displacement of the sprung mass; zu is the displacementof the un-sprung mass; zr represents the road profile; kt isthe tire stiffness, whereas ks is the stiffness of the springbetween the tire and the chassis; cs is the damping of a passivedamper that provides a damping force proportional to thevelocity (zs − zu).

The idea is to substitute the linear passive damper with theMR damper to provide variable damping, and to change thelinear passive spring toMR spring module to provide variablestiffness. Therefore, the linear quarter-car model is replacedby the one with the MR VSVD suspension model mentionedpreviously. The applied quarter-car model with the damperand spring replacement is shown in Fig. 2(b).

Substituting (1) into (2) gives the dynamic description ofthe quarter-car with the MR VSVD suspension as follows:

mszs = −[(α1a + α1bI1) zd1 + k01 (zs − zu)

+ (c01a + c01bI1) (zs − zu)+ ks1 (zs − zk)

+ (α2a + α2bI2) zd2 + k02 (zs − zk)

+ (c02a + c02bI2) (zs − zu)],

muzu = (α1a + α1bI1) zd1 + k01 (zs − zu)

+ (c01a + c01bI1) (zs − zu)+ ks1 (zs − zk)

− kt (zu − zr ) ,

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mk ku = ks1 (zs − zk)+ (α2a + α2bI2) zd2− ks2 (zk − zu)+ k02 (zs − zk)

+ (c02a + c02bI1) (zs − zu) . (3)

Note that the parameter F in (1) is equivalent to cs (zs − zu)+ks (zs − zu) in (2). It is also noted that the phenomenologi-cal model of the VSVD suspension is established based ontwo Bouc-Wen models, which are numerically tractable. Themodel’s parameters are determined by the experimental datawith an appropriate numerical fitting method [28], which areshown in Table 1.

TABLE 1. Parameter Values of the MR VSVD Suspension.

C. STATE-SPACE MODEL FOR REAL-TIME CONTROLFor the process of T-S Fuzzy modeling, the state variables ofthe quarter-car model are defined as follows:

x1 = zs, x2 = zu, x3 = zk , x4 = zs − zu,

x5 = zk − zu, x6 = zu − zr , x7 = zd1, x8 = zd2, (4)

and the state vector as:

x =[x1 x2 x3 x4 x5 x6 x7 x8

]T, (5)

In order to simplify the highly nonlinearity of the proposedmodel, define f1, f2 as:

f1 = −γ1 |zs − zu| · zd1 · |zd1| − β1 (zs − zu) |zd1|2 ,

f2 = −γ2 |zs − zu| · zd2 · |zd2| − β2 (zs − zu) |zd2|2 . (6)

Then define:

f1 =f1x7,

f2 =f2x8,

f3 = α1b · x7 + c01b (x1 − x2) ,

f4 = α2b · x8 + c02b (x1 − x3) . (7)

Then, equation (3) can be written as:

msx1 = − [α1ax7 + k01x4 + c01ax1 − c01ax2 + f3I1+ ks1x4 − ks1x5 + α2ax8 + k02x4− k02x5 + c02ax1 − c02ax3 + f4I2] ,

mux2 = α1ax7 + k01x4 + c01ax1 − c01ax2+ ks2x5 − ktx6 + f3I1,

mk x3 = ks1x4 − ks1x5 + α2ax8 + k02x4 − k02x5+ c02ax1 − c02ax3 − ks2x5 + f4I2,

x4 = x1 − x2,

x5 = x3 − x2,

x6 = x2 − zr ,

x7 = f1x7 + Ad1 (x1 − x2) ,

x8 = f2x8 + Ad1 (x1 − x3) . (8)

We can write a state-space for system (5) as:

x (t) = Ax + B1w+ B2u, (9)

where the output vector as u =[I1 I2

]T , the disturbancevector as w = zr , and the large matrices, A, B1, and B2 arelisted in appendix for better readability.

In addition, the input currents sent to the MR dampers ispractically limited, and therefore the asymmetry saturation ofthe control signals should be considered. In general, a controlinput with saturation limitation is defined as u = sat (u),where sat (u) is a asymmetry saturation function defined as

sat (u) =

umin, u < umin,

u, umin ≤ u ≤ umax,

umax, u ≥ umax,

(10)

where umin and umax are the control input limits, and umin <

umax. In particular, the u can be described as u =[I1 I2

]T=[

sat (I1) sat (I2)]T , where

sat (I1) =

I1min, I1 < I1min,

I1, I1min ≤ I1 ≤ I1max,

I1max, I1 ≥ I1max,

sat (I2) =

I2min, I2 < I2min,

I2, I2min ≤ I2 ≤ I2max,

I2max, I2 ≥ I2max,

(11)

and I1min < I1max and I2min < I2max are the control limits ofsignals I1 and I2, respectively. Therefore, the system (9) canbe written as

x (t) = Ax + B1w+ B2u. (12)

III. T-S FUZZY MODEL-BASED H∞ CONTROLLER DESIGNThis section investigates the design of the T-S fuzzy model-based H∞ controller for the quarter-car with MR VSVDsuspension. In section III-A, a T-S fuzzy model will be estab-lished to describe the integrated quarter-car model. To esti-mate state information for the T-S fuzzy model in real-time,in section III-B, a state observer will be designed and inte-grated in the controller. Finally, an H∞ controller for theMIMO system that considers the coupled interconnectionscharacteristic and multi-object optimization process will bedesigned in section III-C.

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A. T-S FUZZY MODELING OF QUARTER-CARWITH VSVD SUSPENSIONT-S Fuzzy modeling method is applied here to do linearapproximation considering the high nonlinearity of the sys-tem (8). It is noted that the state variables x1, x2, x3, x7,and x8 are actually limited in practice for a stable system,the nonlinear f1, f2, f3, and f4 should also be bounded inoperation. We represent f1, f2, f3, and f4 using their minimumvalues and maximum values by following ‘‘sector nonlinear-ity’’ approach [25]:

f1 = M1 · f1max +M2 · f1min,

f2 = N1 · f2max + N2 · f2min,

f3 = T1 · f3max + T2 · f3min,

f4 = H1 · f4max + H2 · f4min, (13)

where f(i)max (i = 1, 2, 3, 4) represents the maximum valuesand f(i)min (i = 1, 2, 3, 4) is the minimum values of the non-linear f(i) (i = 1, 2, 3, 4). M(i), N(i), T(i), and H(i) (i = 1, 2)are fuzzy membership functions and satisfy:

M1 +M2 = 1,N1 + N2 = 1,T1 + T2 = 1,H1 + H2 = 1, (14)

and the member functions are defined as:

M1 =f1 − f1min

f1max − f1min, M2 =

f1max − f1f1max − f1min

,

N1 =f2 − f2min

f2max − f2min, N2 =


,

T1 =f3 − f3min

f3max − f3min, T2 =


,

H1 =f4 − f4min

f4max − f4min, H2 =


. (15)

Then the nonlinear quarter-car system can be described bythe above linear subsystems. For each possibility, there is acorresponding state-space equation:

If f1 = M1, f2 = N1, f3 = T1, f4 = H1,

then x = A(1)x+ B1w+ B2(1)u.

If f1 = M1, f2 = N1, f3 = T1, f4 = H2,

then x = A(2)x+ B1w+ B2(2)u.

If f1 = M1, f2 = N1, f3 = T2, f4 = H1,

then x = A(3)x+ B1w+ B2(3)u.

If f1 = M1, f2 = N1, f3 = T2, f4 = H2,

then x = A(4)x+ B1w+ B2(4)u.

If f1 = M1, f2 = N2, f3 = T1, f4 = H1,

then x = A(5)x+ B1w+ B2(5)u.

If f1 = M1, f2 = N2, f3 = T2, f4 = H1,

then x = A(6)x+ B1w+ B2(6)u.

If f1 = M1, f2 = N2, f3 = T2, f4 = H2,

then x = A(7)x+ B1w+ B2(7)u.

If f1 = M2, f2 = N1, f3 = T1, f4 = H1,

then x = A(8)x+ B1w+ B2(8)u.If f1 = M2, f2 = N2, f3 = T1, f4 = H1,








then x = A(16)x+ B1w+ B2(16)u,

where A(i) (i = 1, 2, 3, . . . , 16). (i = 1, 2, 3, . . . , 16) areobtained by replacing f(i) (i = 1, 2) in matrix A of (12) withf(i)max and f(i)min, respectively. Then the T-S fuzzy model forthe nonlinear quarter-car under the bounded state variables isobtained as:

x =16∑i=1

hi[A(i)xB1w+ B2(i)u

]= Ahx+ B1w+ B2hu, (16)

where

Ah =16∑i=1

hiA(i),

B2h =16∑i=1

hiB2(i),

h1 = M1N1T1H1, h2 = M1N1T1H2,

h3 = M1N1T2H1, h4 = M1N1T2H2,

h5 = M1N2T1H1, h6 = M1N2T2H1,

h7 = M1N2T2H2, h8 = M2N1T1H1,

h9 = M2N2T1H1, h10 = M2N2T2H1,

h11 = M2N2T2H2, h12 = M1N2T1H2,

h13 = M2N1T1H2, h14 = M2N1T2H1,

h15 = M2N1T2H2, h16 = M2N2T1H2,

and h(i) (i = 1, 2, 3, . . . , 16) satisfy:∑16

i=1 h(i) = 1.

B. STATE OBSERVER DESIGNIn practice, not all the state variables are available to bemeasured in real-time. In particular, the evolutionary variablezd and the absolute displacement, unsprung mass displace-ment, are nearly unmeasurable while a vehicle is working;direct integration from acceleration to estimate the vertical-velocities deteriorates the accuracy of the estimation conse-quence. These variables are difficult to be obtained by the

VOLUME 8, 2020 71633


normal instrumentation of a vehicle, which typically onlyhas accelerometers and displacement sensors to be installed.To meet input requirements, a controller must be constructedusing the estimated state variables and premise variables; thatis, to estimate the state variables in real-time, a state observeris designed and integrated with the controller. In terms ofthe quarter-car suspension, both the tyre deflection, zu − zr ,and the suspension deflection (SD), zs− zu, can be measuredby laser displacement sensors; the sprung mass acceleration(SMA), zs, and the unsprung mass acceleration, zu, also canbe measured by accelerometers. Therefore, the observer mea-surement is defined as

Y =[zs zu zs − zu zu − zr

]T= C1 · x, (17)

where

C1 =

c01a + c02a−ms

−c01a−ms

−c02a−ms

k01 + ks1 + k02−ms

c01amu

−c01amu

0k01mu

0 0 0 00 0 0 0

−ks1 − k02−ms

0a1a−ms

a2a−ms

ks2mu

−ktmu

a1amu

0

1 0 0 00 1 0 0

.To effectively estimate the state by using the easily mea-

sured signals, the estimation error can be defined based onthe observer measurement as

e = x − x. (18)

So, the state observer can be designed as

˙x =16∑i=1

hi[A(i)x + L

(Y − Y

)+ B2(i)u

]= Ahx + L

(Y − Y

)+ B2hu, (19)

where L are the state observer gains to be designed.Re-arrangement of (19) gives

˙x = (Ah − LC1) x + LY + B2hu (20)

By differentiating (18), we get the dynamic equation of thestate estimation error

e = x − ˙x

= (Ah − LC1) e+ B1w. (21)

C. THE DESIGN OF H∞ ROBUST CONTROLLER WITHMULTI-OBJECTIVE OPTIMISATIONThe H∞ controller design and stability analysis of fuzzysystems based on T-S state-space model were proposed.By applying the parallel distributed compensation scheme

[30] to the MIMO nonlinear system, the observer-based con-troller can be represented as

u =16∑i=1

hiK(i)x

= Khx, (22)

where K(i) are the state feedback gains to be designed. Nowconsider the augmented state vector as

x =[x e

]T. (23)

After manipulation, the augmented system can be expressedas the following form:

x =16∑i=1

hi(G(i)x + B1w

)= Gxx + B1w, (24)

where

Gh =[Ah + B2hKh −B2hKh

0 Ah − LC1

],

B1 =[BT1 BT1

]T.

For the design of a vehicle suspension, ride comfort, sus-pension deflection and road holding ability are often regardedas themain optimizing goal in a controller design. To improvethe specific performances of the suspension, the controlledoutput s in this research can be composed of SMA, SD, tyreload (TL) as zs, zs − zu, and kt (zu − zr ), respectively, andthe values of the weighting parameters σ1, σ2, and σ3 shouldbe set with suitable trade-off and normalization. Therefore,the controlled output is defined as

s =[σ1zs σ2 (zs − zu) σ3kt (zu − zr )

]T= C2x, (25)

where

C2=

σ−1(c01a+c02a)

−ms

−σ·c01a−ms

−σ·c02a−ms

σ1(k01+ks1+k02)−ms

0 0 0 σ20 0 0 0

σ1 (ks1 + k02)ms

0σ1 · σ1a

−ms

σ1 · σ2a

−ms01×8

0 0 0 01×80 σ3kt 0 01×8

.In order to give the controller adequate response performanceunder different vibration situations, the H∞ norm is chosenas the performance measure. The L2 gain of the system (24)with (25) is defined as

‖Tsw‖∞ = sup‖w‖2 6=0

‖s‖2‖w‖2

, (26)

where ‖s‖22 = ∫∞

0 sT (t) s (t) · dt and ‖w‖22 = ∫∞

0 wT (t)w (t) · dt .

71634 VOLUME 8, 2020


The aim of the work is to design a fuzzy controller, equa-tion (22), such that the closed-loop fuzzy system, equation(24), is quadratically stable. A Lyapunov function for thesystem (24) is defined as

5(x) = xTPx, (27)

where P is a positive definite matrix and P = PT .By differentiating (27), we obtain

5 (x) = xTPx + xTPx. (28)

Adding sT s− γ 2wTw to the two sides of (28) yields

5 (x)+ sT s− γ 2wTw

= xTPx + xTPx + sT s− γ 2wTw. (29)

Substituting (24) and (25) into (29) gives


=(Ghx + B1w

)1Px + xTP

(Ghx + B1w

)+(C2x

)T (C2x

)− γ 2wTw. (30)

Re-arrangement of (30) gives


=

[xT

wT

][GTh P+ PGh + C

T2C2 PB1

∗ −γ 2

][xw

]. (31)

Considering

9 =

[GTh P+ PGh + C

T2C2 PB1

∗ −γ 2

], (32)

when the disturbance is zero, that is, w = 0, it can be inferredfrom (31) and (32) that if 9 < 0, then 5(x) < 0, and theclosed-loop fuzzy system (24) is quadratically stable. By con-sidering Schur complement equivalence, equation (32) canbe further re-arranged to linear matrix inequalities (LMIs),as given below:

9 =

GTh P+ PGh CT2 PB1

∗ −I 0∗ ∗ −γ 2

< 0, (33)

where I is a unit matrix.Considering the input saturation in (22) with the assump-

tion that ulim = umax = −umin, the input constraint can beexpressed based on the lemma in [30] as∣∣∣∣∣

16∑i=1

Kix

∣∣∣∣∣ 6 ulimε, (34)

where 0 < ε < 1 is a given scalar. If∣∣Kix∣∣ 6 (

ulim/ε), then

(34) holds. Let

�(K ) ={x||xTKT

i Kix| 6(ulimε

)2},

the equivalent condition for �(P, ρ) ={x|xTPx 6 ρ

}being

a subset of �(K ) is:

Ki

(Pρ

)−1KTi 6

(ulimε

)2. (35)

By applying Schur complement equivalence, (35) can bewritten as

(ulimε

)2Ki

(Pρ

)−1(Pρ

)−1KTi

(Pρ

)−1 ≥ 0. (36)

It should be noted that the input current sent to the MRdamper is generally 0 ∼ Imax, which means Imin = 0, andan asymmetric saturation should be considered. Therefore,the assumption of symmetric saturation in (36) should bemodified to shift the saturation centre as the average of bothsaturation limits. In this paper, the input currents are consid-ered to be I1 : 0A ∼ 0.4A and I2 : 0A ∼ 1A; hence, todesign the controller, we define ulim = (umin + umax) /2 withumin = 0, that is I1 lim = 0.2A and I2 lim = 0.5A.To ensure the T-S fuzzy system (12) with the controller

(22) is quadratically stable and for a given parameter γ > 0,the L2 gain defined by (26) is less than γ , the matricesQ > 0,Y > 0, where Q = P−1 and Y = KQ, should existsuch that (33) and (36) are satisfied. Hence, to minimize theperformancemeasure parameter γ , the controller design issuecan be modified as a minimization problem of

min γ 2

subject to LMIs (33) and (36). (37)

By solving the LMIs using MATLAB R© software, the statefeedback K(i) gains and the observer gains L(i) of TSFHcontroller are determined. By fusion of the T-S Fuzzy modelandH∞ techniques, the algorithm proposed in this paper canprovide a direct control for nonlinear MIMO system withoutthe problem ‘‘coupled interconnections’’, which leads to amuch simpler controller with less computational load, and itis easy to be implemented in real applications.

After constructing the controller, the T-S fuzzy model isleft aside in the simulation work, and the closed-loop con-trol system is shown in Fig. 3. For the convenience of thereader, the modules of TSFH controller, the quarter-car sys-tem, and processing signals are represented by blue blocks,grey block, and lines with the arrow, respectively. It canbe seen that the measured parameters, zs, zu, zs − zu andzu − zr , are transmitted to the state observer, and thus theestimated complete state variables can be determined. By run-ning the control algorithm based on the inputs consistedof the eight estimated variables, the controller calculatescommand currents with the consideration of actuator satura-tion and sends them to the two MR dampers which belongvariable damping module and variable stiffness module,respectively.

VOLUME 8, 2020 71635


FIGURE 3. The control flow of the VSVD quarter-car system.

IV. NUMERICAL APPLICATIONIn this section, the proposed method is applied to design acontroller for the quarter-car model with the MR VSVD sus-pension as described in section II and the values of the suspen-sion model parameters are listed in Table 1. In section IV-A,two kinds of road profiles will be established as the distur-bance to the tire, and a competing controller will also bedescribed in this part. Then, the designed TSFH controllerwill be applied for the quarter-car withMRVSVD suspensionand validated in section IV-B. In the simulation, it is assumedthat only the zs, zu, zs − zu, and zu − zr are available formeasurement and all the state variables defined in (4) willbe estimated.

A. ROAD EXCITATION AND COMPETING CONTROLLERIn the simulation work, two typical road profiles are consid-ered. A bump input, which is normally used to describe thetransient response characteristic, is adopted as the first roadexcitation. The corresponding road displacement is given by

zr (t) =

a2

[1− cos

(2πv0l

t)], 0 ≤ t ≤

lv0,

0, t >lv0,

(38)

where a = 0.07m and l = 0.8m are chosen as the height andlength of the bump, and the vehicle forward velocity as v0 =0.856m/s [30]. The bump road profile in the time domain isdemonstrated in Fig. 4(a).

The second type of road excitation, normally used to eval-uate frequency response, is a random road excitation. Thestandard C class road profile (ISO 8608), with Sq (�o) =

16×10−6m3, is generated with the sinusoidal approximationmethod [31]. The road irregularities can be described by thefollowing equation

zr (t) =n∑i=1

(√2Sq (i1�)1�

)sin (i2π1�vr t + ϕi) ,

(39)

FIGURE 4. Test excitation (a) the bump road profile and (b) the randomroad profile.

where ϕi is the random numbers distributed uniformly among[0, 2π ],1� is the minimum spatial frequency value we con-sidered, which equals to 0.011m−1. In this work, the vehicleis assumed to travel with a constant speed vr = 20m/s overa given road segment, and conducted under the class C roadprofile, which is shown in Fig. 4(b) in the time domain.

To validate the performance of the TSFH, a dampingand stiffness independent controller (IC) is adopted for acomparison. As the stiffness and the damping of the sus-pension are adjusted and controlled independently, for thevariable damping module, a classic skyhook controller (subcontroller 1 of IC) is applied, which is simple while effective.The description for skyhook controller is

Fsky ={Cmax zs, zs (zs − zu) ≥ 0,Cminzs, zs (zs − zu) < 0,

(40)

71636 VOLUME 8, 2020


where Cmax and Cmin are the maximum and minimum sky-hook gains, which correspond to the command currents Imaxand Imin, respectively. In this experiment, the specific sky-hook force is expressed as the MR damper force with thecontrol output current, Imax=1A and Imin = 0A. In termsof the control strategy for the stiffness component, it is toavoid the resonance of the quarter car under a pavement input.As the stiffness is controlled according to the dominant exci-tation frequency, the controller for variable stiffness module(sub controller 2 of IC) is presented as follows

ks={kmax (Is = 0.4A) , freq < fcOR |zs − zu| ≥ st ,kmin (Is = 0A) , Otherwise,

(41)

where fc is the switching frequency determined as 1.51 Hz,freq is the dominant frequency of the pavement input signalcollecting from a state observer in real time. More designdetails about this controller can be found in [28].

To validate the effectiveness of the designed controller inthe simulation, the MRVSVD suspension model will be usedto represent the real suspension in a quarter-car system. Theparameter values of the linear quarter-car model described in(2) are listed in Table 2.

TABLE 2. Parameter values of the quarter-car model [28].

B. NUMERICAL RESULTSBy applying the two kinds of road profiles to the quarter-car with MR VSVD suspension, the system response withoutcontrol (Passive), the response with IC controlled, and theresponse with TSFH controlled are evaluated.

In the first stage of the simulation, bump road is carriedout to evaluate the systems. The bump responses, input cur-rents for two MR modules, and corresponding MR damperforces are shown in Figs. 5-7, respectively. Time historiesof the test rig response in terms of the three performancecriteria, SMA, SD, TL, are recorded and plotted in Fig. 5.It can be seen from Fig. 5 that better responses are obtainedfor the controlled MR VSVD suspensions compared to thepassive one. In order to illustrate the simulation results moreclearly, the responses of the three suspensions are comparedin Table 3 in terms of the peak-to-peak (PTP) values and theimproved percentages compared to the passive suspension.It can be seen from the first row of Table 3 that the twocontrolled MR VSVD suspensions perform much better thanpassive suspension on SMA, and the response of TSFH com-paring to Passive, 37.1%, is outstanding smaller than that ofIC control, 20.3%. Regarding the time response shown in the

FIGURE 5. Response under the bump road (a) response of SMA,(b) response of SD, and (c) response of TL.

TABLE 3. PTP value of objectives under bump road profile.

third row of Table 3, the PTP value of tyre load fluctuationof TSFH is smaller than that of passive by approximately34.1%, which is much more effective comparing to 10.8%of IC control.

VOLUME 8, 2020 71637


FIGURE 6. Input current under the bump road (a-1) IC/damping,(a-2) TSFH/damping, (b-1) IC/stiffness, and (b-2) TSFH/stiffness.

FIGURE 7. MR Damper force under the bump road (a) damping moduleand (b) stiffness module.

Figs. 6 and 7 show the input currents of IC and TSFHand the corresponding damping forces generated by the MRdampers under the bump road profile excitation, respectively.In Fig. 6, the two controllers’ input currents for dampingmodule and stiffness module are separately shown in sub-figures for clarity. It is also presented from Fig. 6 that thecurrent signals obtained from TSFH is continuously variedand is almost zerowhen the system responses reach the steadystate. On the contrary, the current signals computed from ICcontrol are discrete values. Furthermore, due to the sensitivityof Heaviside step function to small errors between the desiredforce and the measured force, the control current of IC is notalways zero even when the system responses reach the steadystate.

FIGURE 8. Response under the random road (a) response of SMA,(b) response of SD, and (c) response of TL.

After the bump road evaluation, random road evaluationis further conducted. Time histories of the quarter-car sys-tem under random road excitation are recorded and plottedin Fig. 8, where the results of SMA, SD, TL, are shown inthe subfigures, respectively. In particular, the SMA under thepassive case has the biggest peak value during the whole-timehistory. TSFH case and IC case both perform better than thepassive case. However, the SMA with TSFH case is furtherreduced than with IC case.

It means that the quarter-car system performs best underthe TSFH suspension where the damping and the stiffnessof the damper are both controlled in real time. It is notedfrom the figure that the MR VSVD suspension controlledby TSFH further limits and inhibits the variation of the spe-cific objectives compared to the passive one and the systemcontrolled by IC. Whereas under excitation with wide-bandfrequency such as random road profile, the filtering perfor-mance of independent control method is worse, or even like

71638 VOLUME 8, 2020


FIGURE 9. Input current under the random road (a-1) IC/damping,(a-2) TSFH/damping, (b-1) IC/stiffness, and (b-2) TSFH/stiffness.

FIGURE 10. The MR Damper force of damping module under the randomroad.

the performance of a passive suspension. It might be dueto the coupled interconnections phenomenon of multi-outputwhich has been noted in section I. On the contrary, to controlthe MR VSVD suspension, a MIMO system with high non-linearity, the TSFH controller based on T-S fuzzy model andH∞ control has presented further better performance undera complex excitation with multi-frequency components.

To further demonstrate the performance of TSFH, the root-mean-square (RMS) values of the system responses are sum-marized in Table 4 and the controlledMR suspension with theTSFH has the lowest RMS value of the SMA. In particular,the suspension controlled by TSFH can reduce the RMSvalues for SMA, SD, and TL by about 27.6%, 22.0%, and15.8%, respectively, compared with the passive suspension.The SMAand TL reductions (−27.6% and−15.8%) of TSFH

FIGURE 11. The MR Damper force of stiffness module under the randomroad.

TABLE 4. RMS value of objectives under the random road profile.

are more effective than the ones of the typical IC control(−21.2% and −9.4%). These results demonstrate that undercomplex wide-frequency external disturbance, TSFH con-trol can further overcome the nonlinearity and multi-outputcoupling problems of the MR VSVD suspension system,comparing to the separated control method. Regarding the SDRMS values, the TSFH control is 5.42 × 10−3m, of whichone fails than the IC control, 4.66×10−3m. The indistinctiveSD effect of TSFH might be attributed to its multi-outputcontrol method, which aims at the global optimum with theconsideration of coupled interconnections between the damp-ing module and stiffness module.

Fig. 9 demonstrates the input currents of IC and TSFHfor damping module and stiffness module, respectively.The damping forces generated by the two modules under therandom road profile excitation are shown in Figs. 10 and 11.In the two figures, the damping forces of Passive, IC, andTSFH are separately shown in subfigures for clarity.

VOLUME 8, 2020 71639


V. CONCLUSIONA T-S Fuzzy model-based H∞ controller for multi-MRVSVD suspension was successfully designed in this study.The MR suspension system is a MIMO nonlinear systemcontaining input hysteresis nonlinearity, time-varying delays,model uncertainties, and external disturbances. The proposedT-S Fuzzy model can predict the stiffness and damping vari-ation characteristics of the VSVD MR suspension. Based onthe T-S fuzzy model, an H∞ controller under an optimisationonmultiple objectives can be designed to improve suspensionperformance. A fuzzy state observer design is proposed toestimate the suspension state in real-time so that the imple-mentation of the control system is feasible in practical appli-cation. Numerical simulations were conducted under bumpand random excitation. The results show that the VSVD MRsuspension system with TSFH controller performs better inimproving the multiple driving indicators including ridingcomfort and vehicle stability to the passive system and ICcontrol system. The results illustrate the TSFH with dampingand stiffness synchronic multi-output control on MR VSVDsuspension further improves the comfort and robustness ofthe vehicle system comparing with the damping and stiffnessindependent controller, with respect to different road inputconditions.

APPENDIX

A =

c01a + c02a−ms

−c01a−ms

−c02a−ms

k01 + ks1 + k02−ms

c01amu

−c01amu

0k01mu

c01amk

0−c01amk

ks1 + k02mk

1 −1 0 00 −1 1 00 1 0 0Ad1 −Ad1 0 0Ad1 0 Ad1 0

−ks1 − k02−ms

0a1a−ms

a2a−ms

ks2mu

−ktmu

a1amu

0

−k01 − ks1 − k02mk

0 0a2amk

0 0 0 00 0 0 00 0 0 00 0 f1 00 0 0 f2

,

B1 =[0 0 0 0 0 −1 0 0

]T,

B2 =

f3−ms

f3mu

0mk

0 0 0 0 0

f4−ms

0mu

f4mk

0 0 0 0 0

T

.

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XIN TANG (Member, IEEE) received the B.E.degree in automation engineering from the Uni-versity of Electronic Science and Technology ofChina, Chengdu, China, in 2012, and the Ph.D.degree from the School of Mechanical, Mate-rial and Mechatronics, University of Wollongong,Wollongong, NSW, Australia, in 2018.

He is currently a Research Fellow with theHKUST Fok Ying Tung Research Institute. Hisresearch interests include the vibration control of

semiactive vehicle suspension utilizingMR technology, robust control appli-cations, and human-like algorithms to enhance decision-making modelingfor local path planning and trajectory tracking control.

DONGHONG NING (Member, IEEE) receivedthe B.E. degree in agricultural mechanization andautomation from the College of Mechanical andElectronic Engineering, North West Agricultureand Forestry University, Yangling, China, in 2012,and the Ph.D. degree from the University of Wol-longong, Australia, in 2018.

His research interests include active and semi-active vibration control, multiple degrees of free-dom vibration control, interconnected suspension,

electromagnetic suspension, and mechanical–electrical networks.

HAIPING DU (Senior Member, IEEE) receivedthe Ph.D. degree in mechanical design and theoryfrom Shanghai Jiao Tong University, Shanghai,China, in 2002.

Hewas a Research Fellowwith theUniversity ofTechnology, Sydney, from 2005 to 2009, and wasa Postdoctoral Research Associate with ImperialCollege London, from 2004 to 2005 and the Uni-versity of Hong Kong, from 2002 to 2003. He iscurrently a Professor with the School of Electrical,

Computer and Telecommunications Engineering, University ofWollongong,Wollongong, NSW, Australia.

Dr. Du was a recipient of the Australian Endeavour Research Fellowship,in 2012. He is a Subject Editor of the Journal of Franklin Institute, an Asso-ciate Editor of IEEE Control Systems Society Conference, an EditorialBoard Member for some international journals, such as the Journal of Soundand Vibration, the IMechE Journal of Systems and Control Engineering,the Journal of Low Frequency Noise, Vibration, and Active Control, anda Guest Editor of IET Control Theory and Application, Mechatronics, andAdvances in Mechanical Engineering.

WEIHUA LI (Member, IEEE) received the B.E.and M.E. degrees from the University of Sci-ence and Technology of China, Hefei, China,in 1992 and 1995, respectively, and the Ph.D.degree from Nanyang Technological University,Nanyang, Singapore, in 2001.

He was with the School of Mechanical andProduction Engineering, Nanyang TechnologicalUniversity, as a Research Fellow, from 2001 to2003. He has been with the School of Mechanical,

Materials andMechatronic Engineering, University of Wollongong, Wollon-gong, NSW, Australia, as an Academic Staff Member, since 2003. He haspublished more than 350 technical articles in refereed international journalsand conferences.

Prof. Li received the number of awards, including the JSPS InvitationFellowship in 2014, the Endeavour Research Fellowship in 2011, and theScientific Visits to China Program Awards. He serves as an Associate Edi-tor or Editorial Board Member for nine international journals.

YIBO GAO received the B.E. degree fromZhejiang Forest University, Hangzhou, China,in 2010, theM.E. degree fromZhejiangUniversity,Hangzhou, in 2013, and the Ph.D. degree from theHongKongUniversity of Science and Technology,in 2017.

He is interested in the development of novelBio-MEMS chip technology, including silicon-based chip design, fabrication, packaging and test-ing for various biological and clinical applications.

Especially, his research areas focus on microfluidics chip design and fabri-cation technology and its application in fundamental biological research anddiagnostic technology, such as PCR molecular detection, single moleculedetection, and liquid biopsy in cancer early detection.

WEIJIA WEN received the B.E. and M.E. degreesfrom Chongqing University, Chongqing, China,in 1992 and 1995, respectively, and the Ph.D.degree from the Institute of Physics, ChineseAcademy of Sciences, China, in 1995.

From 1995 to 1999, he was a Research Fellowwith the Hong Kong University of Science andTechnology (HKUST) and UCLA. Since 1999,he has been with the Department of Physics,HongKongUniversity of Science and Technology,

Hong Kong as an Academic Staff Member. He has published more than400 articles in his major research fields, including more than 350 journalarticle and 50 conference invited report. So far, more than 300 SCI articleshave been published. His refereed journal articles have been cited morethan 10 500 times resulting in an H-index of 52. His main research interestsinclude soft condensed matter physics, electrorheological (ER) and magne-torheological (MR) fluids, field-induced pattern and structure transitions,micro- and nano-fluidic controlling, advanced functional materials includ-ing microsphere and nanoparticle fabrications, thin film physics, band gapmaterials, metamaterials, and nonlinear optical materials.

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