This paper presents VHDL-AMS model of an automotive vibration isolation seating system with an active electromechanical actuator. Five control algorithms for the actuator are implemented and their efficiencies are investigated by subjecting the system to a number of stimuli, such as a single jolt or noisy harmonic excitations. Simulations were carried out using the SystemVision simulator and results are shown to compare the relative performance merits of the control methods

Kazmierski, Tom

Wang, Leran

English

Southampton (e-Prints Soton)

VHDL-AMS MODELING OF AN AUTOMOTIVE VIBRATION ISOLATIONSEATING SYSTEMLeran Wang and Tom J. KazmierskiSchool of Electronics and Computer ScienceUniversity of SouthamptonSouthampton SO17 1BJ, UK{lw04r,tjk}@ecs.soton.ac.ukABSTRACTThis paper presents VHDL-AMS model of an automotivevibration isolation seating system with an active electro-mechanical actuator. Five control algorithms for the actu-ator are implemented and their efﬁciencies are investigatedby subjecting the system to a number of stimuli, such as asingle jolt or noisy harmonic excitations. Simulations werecarried out using the SystemVision simulator and resultsare shown to compare the relative performance merits ofthe control methods.KEYWORDSVHDL-AMS, Automotive systems, Mixed-domain model-ing, Control algorithms.1 IntroductionIn automotivesystems, the electronics with embeddedsoft-ware typically controls some mechanical components likeairbags, anti-blocking systems for the brakes or activewheelsuspensions[1]. Thesesystems usuallycoverat leasttwo physical domains, electrical and mechanical. Some-times hydraulic, magnetic or thermal components are alsoincluded. This makes the design and test of the whole in-tegrated system difﬁcult to perform since typically each ofthese domains uses a different design languageand simula-tion environment. The appearance of VHDL-AMS [2] hasmade it possible to incorporatecomponentsof differenten-ergy domains in a single model, because VHDL-AMS sup-ports modeling of electrical and non-electrical systems atvarious abstraction levels [3]. Several sources have alreadyrecommendedVHDL-AMS to be the uniﬁed modelinglan-guage for the automotive industry [4, 5]. However, its usein actual automobile design has so far been limited, partlybecause mature simulators supporting VHDL-AMS haveonly recently begun to appear.The VHDL-AMS model presented here is an auto-motive vibration isolation seating system with an activeelectro-mechanical actuator [6, 7] (see Fig.1). It reducesvibrations between the vehicle ﬂoor and the passenger seatso that the driver’s ride quality could be improved. The ac-tuator is a force generator that is acting between the seatand chassis. It is the main component of the system and itsperformance is much dependent on the control algorithm.Five control algorithms for the actuator are investigatedhere: RelativeControl(RC) [8], Proportional-IntegralCon-trol (PIC) [9] , Fuzzy Logic Control (FLC) [10], VariableStructure Control (VSC) [11] and Optimization Control(OC) [12]. The model consists of three parts: the plant(i.e. the passenger seat and the vehicle chassis), actuatorand control algorithm. The newly-developed IEEE VHDL1076.1.1 standard packages [13] for multiple energy do-main support are incorporated in the model.Figure 1. Vibration isolation seating system.2 Chassis and Seating SystemFig.1 shows the model of the chassis and seating system.The passenger seat motion equation is written as:d2xsdt2 = −CsMs dxsdt−dxcdt −KsMs(xs − xc)−ApMs(P1 − P2) (1)Similarly, the chassis motion equation can be presented as:d2xcdt2 = −CsMc dxcdt−dxsdt −KsMc(xc − xs)−KcMc(xc − xd) −CcMc dxcdt−dxddt +ApMc(P1 − P2) (2)The actuator force, Fa, is expressed as Ap(P1 − P2). Thedynamic state and output vectors are selected as x =[xs,x c, dxsdt , dxcdt ]T and y =[ xrel,V rel]T, where xrel =xs−xc and Vrel = dxsdt − dxcdt . Two sensors monitoringtheseat and chassis generate input signals to the controller.3 Actuator DesignThe actuator is an electro-mechanical hydraulic design,which operates in parallel with the passive springs anddampers. It consists of a DC motor, some mechanical parts(such as the gear train and rack) and a hydraulic vibrationabsorber (see Fig.2). The actuator input from the controlleris a DC voltage (ea), which drives the motor to output a ro-tational torque (Tm). The gear train converts the rotationaltorqueinto the translationalvelocityof the rack, whosedis-placement impacts the pressures of the upper and lowerchambers of the hydraulicpiston (P1 and P2, respectively).The vehicle ﬂoor is attachedto the hydrauliccylinder’spis-ton rod and the seat sits on the cylinder cap. The actuatorforce is dependent on the pressure difference between theupper and lower chambers. The generated force attenuatesthe vibrations by acting on the vehicle ﬂoor and passengerseat.VcVrelVehicle chassisAr2Ar1Gear trainApP2,U 2Passenger seat VsP1,U 1RackVrωg1eaiaeb TmDC motorRa LaFigure 2. Actuator model for the vibrationisolation seatingsystem.The motor develops a torque proportional to the ar-mature current (ia):Tm = Ktia (3)Whenthearmaturerotates,the backEMFinducesavoltageproportional to the angular velocity:eb = Kbdθg1dt(4)The circuit can be analyzed using Kirchoff’s voltage law:Ladiadt+ Raia + eb = ea (5)Newton’s second law is applied to the input dynamics (Jl1)as follows:Jl1d2θg1dt2 + bl1dθg1dt+ Tg1 = Tm (6)The gear train is considered ideal so that the relationshipbetween the input and output angular velocity (ωg1 andωg2) and torque (Tg1 and Tg2) can be written as:ωg2ωg1=rg1rg2=ng1ng2and Tg1ωg1 = Tg2ωg2 (7)Application of Newton’s second law to the load shaft (Jl2)yields:Jl2d2θg2dt2 + bl2dθg2dt+ TL = Tg2 (8)The rack linear velocity (Vr2) can be determined from:Vr2 = ωg2rg2 and Vr2 = Vr1 (9)The load torque (TL) acting on the load shaft is:TL = Frrg2 where Fr = Ar2P2 −Ar1P1 +Mrar −Mrg(10)The hydraulic pressure in the upper and lower actuatorchambers are described as:dP1dt=( + ApVrel − Ar1Vr1) β1U1 (11)dP2dt=( −ApVrel + Ar2Vr2) β2U2 (12)Theabovedifferentialalgebraicequations(DAEs)describethe behavior of the actuator components. In VHDL-AMS,DAEs can be deﬁned by simultaneous statements. Theabove equations cover electrical, mechanical and hydraulicdomains.4 Control AlgorithmsFive control algorithms were implemented in VHDL-AMSto investigate the efﬁciency of the actuator drive. They arebrieﬂy described as follows. The inputs to the controllerare the dynamic seat and chassis motions, i.e. the displace-ment, velocity and acceleration of the passenger seat (xs,vs and as), the displacement and velocity of the vehiclechassis (xc and vc). Different methods may use differentnumbers of inputs. The output is the voltage sent to the DCmotor, ea.4.1 Relative ControlThe relative control strategy offers an elegant approachwith minimal algorithm and hardware demands [8]. Theequations for this algorithm are:ea=⎧⎨⎩0 if|as|<asmin;−sgn(as)(k[|as|−asmin]+eamin) if asmin<|as|<asmax;−sgn(as)eamax if|as|>asmax;(13)where k = 20(eamax − eamin)/(asmax − asmin).4.2 Proportional-Integral ControlThe PI controller offers good stability and a low steady-state error [9]. The equation for this controller is:ea = Kpe + KI ed t (14)where e = −as is the error signal, Kp and KI are propor-tional and integral gains, respectively.4.3 Fuzzy Logic ControlFuzzy logic controllers, due to their ability of handling un-certain and complex systems, are also used in the vibrationisolation systems [10]. The inputs to the FLC are the ve-locity (vs) and acceleration (as) of the seat. The fuzzy re-lationship of the input and output variables are representedbythreelinguistic variables: positive (P),zero (Z) andneg-ative (N).Withtheselinguisticvariables,a setofninefuzzyrules is developed, as shown in Table 1.AccelerationPZNP NNZVelocity Z NZPN ZPPTable 1. Fuzzy rules base.The fuzzy inference procedure used is the max-product composition and the defuzziﬁcation method em-ployed is the center of gravity approach.4.4 Variable Structure ControlVariable structure control uses a high-speed switchingfeedback strategy to realize robust control authority for un-certain plant descriptions and modeling errors [11]. A lin-ear sliding surface σ(x) may be deﬁned asσ(x)=Sx =0 (15)whereS is the slidingsurfacecoefﬁcientvectorandx is thestate vector deﬁned in Section 2.The switching control algorithm drives the plant’sstate trajectory to a user selected sliding surface and thenmaintains the trajectory at that surface. The sliding surfaceis selected such that system motion, when restricted to thissurface, exhibits the desired stability and tracking charac-teristics.4.5 Optimization ControlThe optimization-basedcontrollerfeatures a full state feed-back control algorithm that minimizes a speciﬁed linearquadratic performance index [12]:J =  ∞0(xTFx+ uTRu)dt (16)where x and u = Kx are the state vector and feedbackrespectively. The feedback gain vector K is selected tominimize the performance index.5 VHDL-AMS Implementation of theSystemFig.3 shows the system diagram of integrated chassis, seat,actuator and controller. The VHDL-AMS model containsthree entities: the plant, actuator and controller. The quan-tities between the blocks show how different componentsfromelectrical, mechanicaland hydraulicdomainsarecon-nected.Figure 3. System diagram.In the actuator part, the quantities in the upper roware ”through” quantities and the ones in the lower row are”across” quantities. The VHDL-AMS code of the actua-tor is given below. It models the behavior of the actuatordescribed above in Section 3.library ieee 1076 1 1;use ieee 1076 1 1.mechanical systems.all;use ieee 1076 1 1.electrical systems.all;use ieee 1076 1 1.fluidic systems.all;use work.VibIso System.all;entity Actuator isport(quantity ea: in VOLTAGE;--applied armature voltage(V)quantity Vrel: in VELOCITY;--relative velocity of piston(m/s)quantity deltaP: out PRESSURE--pressure difference(N/mˆ2));end entity Actuator;architecture Behaviour of Actuator isquantity Tm: TORQUE;--motor torque(N*m)quantity ia: CURRENT;--armature current(amp)quantity eb: VOLTAGE;--back emf(V)quantity omegag1,omegag2: ANGULAR VELOCITY;--angular velocity of gear(rad/s)quantity Tg1,Tg2: TORQUE;--torque applied on gear(N*m)quantity TL: TORQUE;--load torque back to shaft(N*m)quantity Vr: VELOCITY;--linear velocity of rack(m/s)quantity P1,P2: PRESSURE;--chamber pressure(N/mˆ2)quantity U1,U2: VOLUME;--volume of chamber(mˆ3)beginTm == Kt*ia;eb == Kb*omegag1;ea == eb + Ra*i a+L a *ia’DOT;Jl1*omegag1’DOT + bl1*omegag1 + Tg1 == Tm;omegag2 == N*omegag1;Tg1 == Tg2*N;Jl2*omegag2’DOT + bl2*omegag2 + TL == Tg2;TL == (Ar2*P2 - Ar1*P1)*rg2;Vr == omegag2*rg2;P1’DOT == (Ap*Vrel - Ar1*Vr)*(beta1/U1);P2’DOT == (-Ap*Vrel + Ar2*Vr)*(beta2/U2);deltaP == P1 - P2;U1’DOT == Ap*Vrel - Ar1*Vr;U2’DOT == -Ap*Vrel + Ar2*Vr;end architecture Behaviour;The actuator covers three different physical domains:electrical, mechanical and hydraulic. The VHDL-AMScode presented here incorporates components from thesedomains into one single model. Using the IEEE 1076.1.1multipleenergydomainstandardpackages[13], eachquan-tity is deﬁnedby its physical name, such as torque,voltage,pressure, etc. These names are connected with their corre-sponding physical natures as shown in the code above.6 Simulation ResultsSimulations were carried out using the SystemVision [14]VHDL-AMS simulatorfromMentorGraphics. Thesysteminput deﬁned in the testbench is the road displacement xdand the main response of the system is the seat displace-ment xs which displays the vibration isolation effect of thesystem. Two types of stimuli were applied to the model, asingle sine wave jolt and multiple sine waves with a WGN(white Gaussian noise). In both cases, the sine wave hasthe amplitude of 5cm, and its wavelength is 240cm. If thevehicle maintains a constant forward velocity of 12.3m/s,the disturbance frequency is 5.1Hz.A single jolt Fig.4 shows the road displacement, the re-sponse from the passive system (i.e. without the actuator)and the responses of ﬁve active control algorithms. Table 2gives the peak-to-peak value and RMS (root mean square)of each response. The passivespring anddampercan atten-uate the peak-to-peak value of the displacement Xpp from10cm to 3.2cm, while all the active methods can achieve atleast 50% improvement(i.e. Xpp less than 1.6cm). Amongthese ﬁve algorithms, the OC method gives the best result.Figure 4. Responses to a single jolt stimulus.Control algorithm P-to-P value(mm) RMS(mm)Passive 30.720 4.9304RC 12.926 3.3913PIC 15.163 2.8669FLC 12.642 2.0718VSC 6.8608 1.1236OC 5.7807 0.96846Table 2. Responses to a single jolt stimulus.Multiple sine waves with WGN The standard deviationof the added WGN is 1cm. The simulation results of pas-siveandactivesystems are shownin Fig.5andTable3. TheRC, PIC and FLC algorithms show relatively poor perfor-mance while the VSC and OC results are satisfactory.In both of the test cases, VSC and OC give superiorperformancetothe otherthree, whileFLC has betterresultsthan those of RC and PIC. The cause of the difference maybe the number of inputs into the controller: RC and PIConly use as as input, FLC uses as and vs, VSC and OC usexs, vs, xc andvc. Basically speaking,the moreinformationgiven to the controller, the better performance it generates.However, using more inputs to a controller means a morecomplex implementation.Figure 5. Responses to a noisy sine wave stimulus.Control algorithm P-to-P value(mm) RMS(mm)Passive 26.500 6.5085RC 14.987 5.1171PIC 13.702 4.2012FLC 15.688 3.9063VSC 7.3798 1.8710OC 6.0416 1.5655Table 3. Responses to a noisy sine wave stimulus.Relative complexity of the control algorithms can becompared by their simulation CPU times. To simulate a1 second run of the system, the corresponding CPU timeson a Pentium 4 PC for these methods were: RC–2.016s,PIC–1.609s, FLC–2.547s, VSC–3.531s, OC–1.891s.7 ConclusionAn efﬁcient VHDL-AMS model of a vibration isolationseating system with an active electro-mechanical actuatorhas been developed and investigated. Several control al-gorithms were implemented and tested with two types ofstimuli, a single jolt and a harmonic wave with WGN.Simulation results show the superior performance of theVariableStructureandOptimizationbasedalgorithmscom-pared with the Relative, Proportional-Integral and FuzzyLogic ones. Among the ﬁve methods, VSC is the mostcomplex and PIC is the simplest, judged by the CPU time.References[1] G. Pelz, J. Bielefeld, and G. Zimmer. Modeling ofembedded software for automotive applications. InIEEE/VIUF Workshop on Behavioral Modeling andSimulation 1997, pages 123 – 128, 1997.[2] E. Christen and K. Bakalar. 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VHDL-AMS modeling of an automotive vibration isolation seating system

VHDL-AMS modeling of an automotive vibration isolation seating system

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