湖南工程职业技术学院学报

Sensorless torque control scheme ofinduction motor for hybrid electric vehicleYan LIU 1,2, Cheng SHAO1(1.Research Institute of Advanced Control Technology, Dalian University of Technology, Dalian Liaoning 116024, China;2.School of Information Engineering of Dalian University, Dalian Liaoning 116622, China)Abstract: In this paper, the sensorless torque robust tracking problem of the induction motor for hybrid electric vehicle(HEV) applications is addressed. Because motor parameter variations in HEV applications are larger than in industrialdrive system, the conventional field-oriented control (FOC) provides poor performance. Therefore, a new robust PI-basedextension of the FOC controller and a speed-flux observer based on sliding mode and Lyapunov theory are developed inorder to improve the overall performance. Simulation results show that the proposed sensorless torque control scheme isrobust with respect to motor parameter variations and loading disturbances. In addition, the operating flux of the motor ischosen optimally to minimize the consumption of electric energy, which results in a significant reduction in energy lossesshown by simulations.Keywords: Hybrid electric vehicle; Induction motor; Torque tracking; Sliding mode1 IntroductionBeing confronted by the lack of energy and the increasinglyserious pollution, the automobile industry is seekingcleaner and more energy-efficient vehicles.A Hybrid ElectricVehicle (HEV) is one of the solutions. A HEV comprisesboth a Combustion Engine (CE) and an Electric Motor(EM). The coupling of these two components can be inparallel or in series. The most common type of HEV is theparallel type, in which both CE and EM contribute to thetraction force that moves the vehicle. Fig1 presents a diagramof the propulsion system of a parallel HEV [1].Fig. 1 Parallel HEV automobile propulsion system.In order to have lower energy consumption and lower pollutantemissions, in a parallel HEV the CE is commonlyemployed at the state (n > 40 km/h or an emergency speedup), while the electric motor is operated at various operatingconditions and transient to supply the difference in torquebetween the torque command and the torque supplied bythe CE. Therefore fast and precise torque tracking of an EMover a wide range of speed is crucial for the overall performanceof a HEV.The induction motor is well suited for the HEV applicationbecause of its robustness, low maintenance and lowprice. However, the development of a drive system basedon the induction motor is not straightforward because of thecomplexity of the control problem involved in the IM. Furthermore,motor parameter variations in HEV applicationsare larger than in industrial drive system during operation[2]. The conventional control technique ranging from theinexpensive constant voltage/frequency ratio strategy to thesophisticated sensorless control schemes are mostly ineffectivewhere accurate torque tracking is required due to theirdrawbacks, which are sensitive to change of the parametersof the motors.In general, a HEV operation can be continuing smoothlyfor the case of sensor failure, it is of significant to developsensorless control algorithms. In this paper, the developmentof a sensorless robust torque control system for HEVapplications is proposed. The field oriented control of the inductionmotor is commonly employed in HEV applicationsdue to its relative good dynamic response. However the classical(PI-based) field oriented control (CFOC) is sensitive toparameter variations and needs tuning of at least six controlparameters (a minimum of 3 PI controller gains). An improvedrobust PI-based controller is designed in this paper,Received 5 January 2005; revised 20 September 2006.This work was supported in part by State Science and Technology Pursuing Project of China (No. 2001BA204B01).Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46 43which has less controller parameters to be tuned, and is robustto parameter variation.The variable parameters modelof the motor is considered and its parameters are continuouslyupdated while the motor is operating. Speed andflux observers are needed for the schemes. In this paper,the speed-flux observer is based on the sliding mode techniquedue to its superior robustness properties. The slidingmode observer structure allows for the simultaneous observationof rotor fluxes and rotor speed. Minimization of theconsumed energy is also considered by optimizing operatingflux of the IM.2 The control problem in a HEV caseThe performance of electric drive system is one of thekey problems in a HEV application. Although the requirementsof various HEV drive system are different, all thesedrive systems are kinds of torque control systems. For anideal HEV, the torque requested by the supervisor controllermust be accurate and efficient. Another requirement is tomake the rotor flux track a certain reference λref . The referenceis commonly set to a value that generates maximumtorque and avoids magnetic saturation, and is weakened tolimit stator currents and voltages as rotor speed increases.In HEV applications, however, the flux reference is selectedto minimize the consumption of electrical energy as it is oneof the primary objectives in HEV applications. The controlproblem can therefore be stated as the following torque andflux tracking problems:minids,iqs,we Te(t) − Teref (t), (1)minids,iqs,we λdr(t) − λref (t), (2)minids,iqs,we λqr(t), (3)where λref is selected to minimize the consumption of electricalenergy. Teref is the torque command issued by thesupervisory controller while Te is the actual motor torque.Equation (3) reflects the constraint of field orientation commonlyencountered in the literature. In addition, for a HEVapplication the operating conditions will vary continuously.The changes of parameters of the IM model need to be accountedfor in control due to they will considerably changeas the motor changes operating conditions.3 A variable parameters model of inductionmotor for HEV applicationsTo reduce the elements of storage (inductances), the inductionmotor model used in this research in stationary referenceframe is the Γ-model. Fig. 2 shows its q-axis (d-axisare similar). As noted in [3], the model is identical (withoutany loss of information) to the more common T-model inwhich the leakage inductance is separated in stator and rotorleakage [3]. With respect to the classical model, the newparameters are:Lm = L2mLr= γLm, Ll = Lls + γLlr,Rr = γ2Rr.Fig. 2 Induction motor model in stationary reference frame (q-axis).The following basic w−λr−is equations in synchronouslyrotating reference frame (d - q) can be derived from theabove model.⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩dλdrdt= −ηλdr + (we − wr)λqr + ηLmids,dλqrdt= −(we − wr)λdr − ηλqr + ηLmiqs,didsdt= ηβλdr+βwrλqr−γids+weiqs+1σLsVds,diqsdt=−βwrλdr+ηβλqr−weids−γiqs+1σLsVqs,dwrdt= μ(λdriqs − λqrids) −TLJ,dθdt= wr + ηLmiqsλdr= we,Te = μ(λdriqs − λqrids)(4)with constants defined as follows:μ = npJ, η = RrLm, σ = 1−LmLs, β =1Ll,γ = Rs + RrLl, Ls = Ll + Lm,where np is the number of poles pairs, J is the inertia of therotor. The motor parameters Lm, Ll, Rs, Rr were estimatedoffline [4]. Equation (5) shows the mappings between theparameters of the motor and the operating conditions (ids,iqs).Lm = a1i2ds + a2ids + a3, Ll = b1Is + b2,Rr = c1iqs + c2.(5)4 Sensorless torque control system designA simplified block diagram of the control diagram isshown in Fig. 3.44 Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46Fig. 3 Control structure.4.1 PI controller based FOC designThe PI controller is based on the Field Oriented Controller(FOC) scheme. When Te = Teref, λdr = λref , andλqr = 0 in synchronously rotating reference frame (d − q),the following FOC equations can be derived from the equations(4).⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩ids = λrefLm+ λrefRr,iqs = Terefnpλref,we = wr + ηLmiqsλref.(6)From the Equation (6), the FOC controller has lower performancein the presence of parameter uncertainties, especiallyin a HEV application due to its inherent open loopdesign. Since the rotor flux dynamics in synchronous referenceframe (λq = 0) are linear and only dependent on thed-current input, the controller can be improved by addingtwo PI regulators on error signals λref − λdr and λqr − 0 asfollowids = λrefLm+ λrefRr+ KPd(λref − λdr)+KId (λref − λdr)dt, (7)iqs = Terefnpλref, (8)we = wr + ηLmiqsλref+ KPqλqr + KIq λqrdt. (9)The Equation (7) and (9) show that current (ids) can controlthe rotor flux magnitude and the speed of the d − q rotatingreference frame (we) can control its orientation correctlywith less sensitivity to motor parameter variations becauseof the two PI regulators.4.2 Stator voltage decoupling designBased on scalar decoupling theory [5], the stator voltagescommands are given in the form:⎧⎪⎪⎪⎨⎪⎪⎪⎩Uds = Rsids − weσLsiqs = Rsids − weLliqs,Uqs = Rsiqs + weσLsids + LmLrweλref= Rsiqs + weσLsids + weλref .(10)Because of fast and good flux tracking, poor dynamics decouplingperformance exerts less effect on the control system.4.3 Speed-flux observer designBased on the theory of negative feedback, the design ofspeed-flux observer must be robust to motor parameter variations.The speed-flux observer here is based on the slidingmode technique described in [6∼8]. The observer equationsare based on the induction motor current and flux equationsin stationary reference frame.⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩d˜idsdt= ηβ˜λdr + β ˜ wr˜λqr − γ˜ids +1LlVds,d˜iqsdt= −β ˜ wr˜λdr + ηβ˜λqr − γ˜iqs +1LlVqs,d˜λdrdt= −η˜λdr − ˜ wr˜λqr + ηLm˜ids,d˜λqrdt= ˜wr˜λ dr − η˜λqr + ηLm˜iqs.(11)Define a sliding surface as:s = (˜iqs − iqs)˜λdr − (˜ids − ids)˜λqr. (12)Let a Lyapunov function beV = 0.5s2. (13)After some algebraic derivation, it can be found that when˜ wr = w0sgn(s) with w0 chosen large enough at all time,then ˙V = ˙s · s 0. This shows that s will converge tozero in a finite time, implying the stator current estimatesand rotor flux estimates will converge to their real valuesin a finite time [8]. To find the equivalent value of estimatewr (the smoothed estimate of speed, since estimate wr is aswitching function), the equation must be solved [8]. Thisyields:˜ weq = wr˜λqrλqr + λdr˜λdr˜λ2qr +˜λ2dr −ηnp˜λqrλdr − λqr˜λdr˜λ2qr +˜λ2dr. (14)The equation implies that if the flux estimates converge totheir real values, the equivalent speed will be equal to thereal speed. But the Equation (14) for equivalent speed cannotbe used as given in the observer since it contains unknownterms. A low pass filter is used instead,˜ weq =11 + s · τ˜ wr. (15)Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46 45The same low pass filter is also introduced to the systeminput,which guarantees that the input matches the feedbackin time.The selection of the speed gain w0 has two major constraints:1) The gain has to be large enough to insure that slidingmode can be enforced.2) A very large gain can yield to instability of the observer.Through simulations, an adaptive gain of the slidingmode observer to the equivalent speed is proposed.w0 = k1 ˜ weq + k2. (16)From Equation (11), the sliding mode observer structureallows for the simultaneous observation of rotor fluxes.4.4 Flux reference optimal designThe flux reference can either be left constant or modifiedto accomplish certain requirements (minimum current,maximum efficiency, field weakening) [9,10]. In this paper,the flux reference is chosen to maximum efficiency at steadystate and is weaken for speeds above rated. The optimal efficiencyflux can be calculated as a function of the torquereference [9].λdr−opt = |Teref| · 4Rs · L2r/L2m + Rr. (17)Equation (17) states that if the torque request Teref iszero, Equation (8) presents a singularity. Moreover, theanalysis of Equation (17) does not consider the flux saturation.In fact, for speeds above rated, it is necessary toweaken the flux so that the supply voltage limits are not exceeded.The improved optimum flux reference is then calculatedas:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩λref = λdr-opt,if λmin λdr-opt λdr-rated ·wratedwr-actual,λref = λmin, if λdr-opt λmin,λref = λdr-rated ·wratedwr-actual,if λdr-opt λdr-rated ·wratedwr-actual.(18)where λmin is a minimum value to avoid the division byzero.4.5 SimulationsThe rated parameters of the motor used in the simulationsare given byRs = 0.014 Ω, Rr = 0.009 Ω, Lls = 75 H,Llr = 105 H, Lm = 2.2 mH, Ls = Lls + Lm,Lr = Llr + Lm, P = 4, Jmot = 0.045 kgm2,J = Jmot +MR2tire/Rf, ρair = 1.29, Cd = 0.446,Af = 3.169 m2, Rf = 8.32, Cr = 0.015,Rtire = 0.3683 m, M = 3000 kg, wbase = 5400 rpm,λdr−rated = 0.47 Wb.Fig.4 shows the torque reference curve that representstypical operating behaviors in a hybrid electric vehicle.Fig. 4 The torque reference curve.Load torque is modeled by considering the aerodynamic,rolling resistance and road grade forces. Its expression isgiven byTL = RtireRf(12ρairCdAfv2 +MCr cos αg +M sin αg).Figures in [5∼8] show the simulation results of thesystem of Fig.3 (considering variable motor parameters).Though a small estimation error can be noticed on the observedfluxes and speed, the torque tracking is still achievedat an acceptable level as shown in Figs. [5, 6, 8]. The torquecontrol over a wide range of speed presents less sensitivityto motor parameters uncertainty.Fig.5 presents the d and q components of the rotor flux.Rotor flux λr is precisely orientated to d-axis because of theimproved PI controllers.Fig.8 shows clearly the real and observed speed in thedifferent phases of acceleration, constant and decelerationspeed with the motor control torque of Fig.4. The variablemodel parameters exert less influence on speed estimation.Fig.7 shows the power loss when the rotor flux keeps constantor optimal state. A significant improvement in powerlosses is noticed due to reducing the flux reference duringthe periods of low torque requests.Fig. 5 Motor rotor flux λr.46 Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46Fig. 6 Motor torque.Fig. 7 Power Losses.Fig. 8 Motor speed.5 ConclusionsThis paper has described a sensorless torque control systemfor a high-performance induction motor drive for aHEV case. The system allows for fast and good torquetracking over a wide range of speed even in the presence ofmotor parameters uncertainty. In this paper, the improvedPI-based FOC controllers show a good performance in therotor flux λdr magnitude and its orientation tracking. Thespeed-flux observer described here is based on the slidingmode technique, making it independent of the motor parameters.Gain adaptation of the speed -flux observer is used tostabilize the observer when integration errors are present.

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