Vehicle Stability Improvement Based on Electronic Differential Using Sliding Mode Control

Transcription

1 7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 1-3, Vehicle Stability Improvement Base on Electronic Differential Using Sliing Moe Control Kaa Hartani, Yahia Milou, an Mohame Bourahla Electrotechnics Department University Center Dr Moulay Tahar of Saia BP 138 En-Nasr Saia (0000) Algeria Abstract: - This paper presents an electronic ifferential system for electric vehicle with two inepenent wheel rives using sliing moe control. When a vehicle rives along curve roa lane, the spee of the inner wheel has to be ifferent from that of the outer wheel in orer to prevent the vehicle vibrating an traveling an unsteay path. Because each wheel of this electrical vehicle has inepenent riving force, an electrical ifferential system is require to replace a gear ifferential system. However, it is ifficult to analyse the nonlinear behavior of the ifferential system in relation to the spee an steering angle, as well as vehicle structure. The propose propulsion system consists of two permanent magnet synchronous machines that ensure the rive of the two back riving wheels. The propose control structure calle inepenent machines for spee control permits the achievement of an electronic ifferential. The electronic ifferential ensures the control of the vehicle behavior on the roa. It also allows to control, inepenently, every riving wheel to turn at ifferent spees in any curve. Analysis an simulation results of this system are presente. Key-Wors: - Electric vehicle, sliing moe control, electronic ifferential, permanent magnet synchronous motor, mulimachine multiconverter system. 1 Introuction Electric vehicle with in-wheel motors has remarkable avantage in the quick generation of precise torque on each riving wheel [1,]. Some applications in the fiel of electrical rives require the use of several electric machines an as well as many static converters that have an important place among the electromechanic systems. These systems are calle multi-converter multi-machine systems (MMS). [3] A formalism has been evelope in orer to stuy systems compose of several electrical machines an/or power converters. It points out three energetic coupling insie the electromechanical conversion chains: electrical, magnetic an mechanical coupling. Aapte rules base on the inversion principle are suggeste for the control of such systems. Energetic repartition criteria have to be efine to solve the coupling problems [4]. They are recognize through the existence of the coupling system type either of an electric nature, a magnetic an/or mechanical one use in several electric machines propulsing the vehicle. In such a control we moel the coupling by using appropriate control structures incluing inepenent control, slave-master, by imposing criteria of energetic istribution in orer to obtain a single machine or a single converter system. One of these control structures can be applie to the control of electric vehicle riving wheels. Traction System Stuie The classical configuration of electric vehicle traction system is represente in Fig. 1. [5] Mechanical ifferential Wheel Fig. 1. Vehicle structure with one central motor.

2 7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 1-3, Front wheel (Steering part) Battery SC 1 SC Fig.. Vehicle structure with two inepenent rear wheel rives. Fig., shows the structure of the electric vehicle, the rear two wheels are riven by two traction motors through reuction gears an rive shafts [6]. This figure represents the implemente vehicle configuration using two permanent magnet synchronous motor for two inepenent wheels. The multi-machine systems are characterize by the coupling of ifferent electromechanical conversion systems. The system represente by the Fig. is characterise by only one coupling. It is illustrate by Fig. 3. In orer to realize the electronic ifferential, the control structure "inepenent machines" is applie to the propulsion system of two riving wheels, by a spee control, Fig. 4. rrref rlref u 1 u P 1 P y 1 1 y M 1 M Fig. 3. Stuie topology. C rrref = C 1 P 1 C rlref = C P rr C R 1 C R MS Fig. 4. Inepenent machine structure. rl Rear wheel (Driving part) MS.1 Inepenent machine control This structure is compose of two machines controlle inepenently as two single machine structures. For every machine we can impose ifferent spee reference ( ) by rrref rlref using two static converters. These machines are uncouple through the control structure an reject all isturbances like single machine control. The principle of this control is illustrate by Fig. 4. An energetic macroscopic representation (EMR) of the propulsion system was propose to obtain a global view of an electronic ifferential, Fig. 5. This investigation proposes the control of the riving wheels spees ω _ R an ω _ L by the "inepenents machines" control structure. This structure permits to impose two spee references (i.e in a curve), the ω _ R ω _ L applie torque on each wheel is ifferent T gear _ R Tgear _ L, the two wheels control system oes not receive the same torque reference. Thus, it is not possible to impose the same spee reference. Fig. 6 shows the structure of electronic ifferential. The system uses the vehicle velocity an steering angle as input parameters an calculates the require inner an outer wheels spees where the two rear wheels are controlle inepenently by two PMS motors. The inputs of the reference block are vehicle spee an steering angle, an the outputs are require rotation spees of the inner an outer wheels, referre to as commane spees. Accoring to the steering angle irection (left or right), the rotational spee of the inner wheel an outer wheel is allocate to the rotation spee of left wheel an right appropriately. Battery Inverters Machines Gears Shafts Wheels Environment i m _ R i m _ R T em _ R T gear _ R F _ R ES U c Inv 1 U c i inv _ R i inv _ L Inv u inv _ R i m _ L u inv _ L e m _ R i m _ L e m _ L M R M L m _ R ω _ R R T em _ L T gear _ R F _ L m _ L ω _ L L v v v h F res MS Fig. 5. EMR of the electronic ifferential system.

3 7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 1-3, CI Inv 1 In-wheel motor R V h α ELECTRONIC DIFFERENTIAL ω mr ω ml Battery CI Inv Fig. 6. The riving wheels control system. In-wheel motor L U c Inverter PMSM Gear U c i = 0 +,q ω m C DFO PW a,b,c ω m M Wheel,q a,b,c Fig. 8. Block-iagram of an electric rive system for PMS motors. i inv_r The power structure in this paper is compose of two permanent magnet synchronous motors which are supplie by two three-phase inverters an riving the two rear wheels of a vehicle trough gearboxes, Fig. 7. U c S 11_R S 1_R S 31_R S 1_R S _R S 3_R M R T em_r m_r T gear_r i inv_l w_r S 11_L S 1_L S 31_L T em_l V h F res M L S 1_L S _L S 3_L m_l Tgear_L w_l Fig. 7. Components of stuie system.

4 7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 1-3, Vector Control Fig. 8 gives the vector control scheme of a permanent magnets synchronous motor. It represents the spee control system with i an i current controls. q In orer to simplify the control algorithm an improve the control loop robustness, instea of using classical control, we use sliing moe control. 3.1 Sliing Moe Control The PMSM equations are as follows: i f v t = L (1.a) iq 1 = f + vq (1.b) t L q ω m = f 3 (1.c) t where R L s q f1 = i + ω miq (.a) L L f R L s f = iq ω mi ω m (.b) Lq Lq Lq Φ p f [( L Lq ) i + Φ f ] iq Tr ω m p f3 = (.c) J J J - Spee an current sliing moe controller Using the non-linear PMSM moel of equations (1), it is possible to esign both a spee an a current sliing moe controller [7,8]. Let us efine the sliing surface Sc1 = Sc1 ( ω m ) = λω ( ω m ω m ) + ( ω m ω m ) (3.a) t S = S ( i ) = ( i i ) (3.b) c c where λ f 0, ω ω m an i, are the spee reference an the reference stator current, respectively. To etermine the control law that is expecte to steer the sliing function (3) to zero in finite time, one has to consier the ynamics of [ S S ] T Sc c1 c =, escribe by:. S c = A + BV s where... ω + af = 1 bf cf A m λω ω m 3 ; i f 1 (4) B = a = p J b L 0 q a L ; 1 L p ( L L q ) i q ; b = [( L Lq ) i + Φ f ] f c = λ ω J In the Lyaponov metho of stability it is use to ensure that S c is attractive an invariant, the following conition has to be satisfie T S.. c S c p 0 (5) So, it is possible to choose the switching control law for stator voltages as follows: vq K 1 1 ω 0 sign( Sc1 ) ( ) = B F B (6) v 0 Ki sign S c where K f 0, K f 0 ω i The sliing moe causes rastic changes of the control variable introucing high frequency isturbances. To reuces the chattering phenomenon, a saturation function sat ( S c ) instea of the switching one sign ( S c ) has been introuce: Sci if ( Sci ) δ i sat( Sci ) = δ i sign( Sci ) if ( Sci ) fδ i (7) where δ i f 0 for i = 1, with δ 1 = δ ω an δ = δ i 4 Simulation Results 1 Case of curve way Case1: Curve roa at right sie with spee of 100 km / h The vehicle is riving on a curve roa on the right sie with 100 km / h spee. The assumption is that the two motors are not isturbe. In this case the riving wheels follow ifferent paths, an they turn in the same irection but with ifferent spees. The electronic ifferential acts on the two motor spees by ecreasing the spee of the riving wheel on the right sie situate insie the curve, an on the other han by increasing the wheel motor spee in the external sie of the curve. The behaviour of these spees is given by Fig. 9(a) an 9(b). J ;

5 7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 1-3, (a) Linear spees (e) Driving forces (b) Right an left wheel rotational spee (f) Total resistive torque (c) Right an left motor rotational spee (g) Phase current () Electromagnetic torques () Difference of rotation spee Fig. 9. Simulation results of case 1

6 7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 1-3, Case : Curve roa with 10% slope with right turn. This test shows the influence of the roa slope on the vehicle moving in curve roa. Figure 10 shows the effect of the slope an the curve roa on the motor parameters. The riving wheels spees are controlle an the errors create by the isturbances are quickly compensate. () Electromagnetic torques (a) ) Linear spees (e) Driving forces (b) Right an left wheel rotational spee (f) Slope torque (c) Right an left motor rotational spee (g) Phase current

7 7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 1-3, (h) Difference of rotation spee Fig. 10. Simulation results of case 5 Conclusion In the fiel of electric rives with variable spee, an application of an electric vehicle controlle by an electronic ifferential is presente. This paper proposes an "inepenent machine" control structure applie to a propulsion system by a spee control. The results obtaine by simulation show that this structure permits the realization of an electronic ifferential an ensures goo ynamic an static performances. The electronic ifferential controls the riving wheels spees with high accuracy either in flat roas or curve ones. The isturbances o not affect the performances of the riving motors. References : [1] Y. Hori, senior member IEEE, Future vehicles river by electricity an control research on four wheel motore -UOT electric march II, IEEE Transactions on Inustrial Electronics, vol. 51, no. 5, Oct. 004, pp [] F. Tahami, R. Kazami an S. Farhanghi A novel river assists stability system for all wheel river electric vehicles, IEEE Transactions on Vehicular Technology, vol. 5, no. 3, pp , May 003. [3] A. Bouscaylor, B. Davat, B. e Fornel, B. Fraçois, Multimachine Multiconverter System : application for electromechanical rives, European Physic Journal Applie Physics, vol. 10, no., May 000, pp [4] A. Bouscaylor, B. Davat, B. e Fornel, B. Fraçois, Multimachine Multiconverter System for rives: analysis of coupling by a global moeling, Proc. Of IEEE-IAS, vol.3, 000, pp [5] C. C. Chan, an K.T. Chan, An Overview of Power Electronics in Electrics Vehicles, IEEE, vol. 44, no. 1, Feb. 1997, pp [6] Y. Hori, Y. Toyoa an Y. Tsuruoka. Traction control of electric vehicule base on the estimation of roa surface conition. Basic experimental results using the test EV "UOT electric march, IEEE.Trans. on Inustry Applications vol.34, no. 5, 1998, pp [7] V. I. Utkin, Sliing moe control esign principles an applications to electric rives, IEEE. Trans. In. Electron, Vol. 40, Feb. 1993, p [8] Shin-ichiro Sakai an Yoichi Hori Avantage of electric motor for antiski control of electric vehicle, EPE Journal, vol.11, no.4, 001, pp.6-3. ABREVIATIONS DFOC : Direct Fiel Oriente Control EC : Electrical Coupling EM : Electrical Machine EMR : Energetic Macroscopic Representation ES : Electrical Source EV : Electric Vehicle MMS : Multi-machine Multi-converter System MS : Mechanical Source PMSM: Permanent Magnet Synchronous Machine PWM : Pulse With Moulation Nomenclature L, L : an q axis inuctance q i, i q : an q axis currents v, v q : an q axis voltage R s : Resistance p : Pole pairs θ : Electric position Φ : Permanent magnet flux f J : Rotor inertia J : Vehicle inertia v C : Electromgnetic torque em C r : Loa torque M : Vehicle mass R r : Wheel rauis N : Report of spee gear re η : Transmission efficiency

8 7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 1-3, l : Distance between two wheels an axes w : Distance between the back an the front w wheel ρ : Air ensity S : Front area of vehicle C x : Aeroynamic coefficient g : Acceleration of gravity f : Friction coefficient r α : Angle of the slope v : Linear spee of vehicle h U : Battery voltage c