Simplified Modeling, Analysis and Simulation of Permanent Magnet Brushless Direct Current Motors for Sensorless Operation

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1 Amerian Journal of Applied Sienes 9 (7): , 2012 ISSN Siene Publiations Simplified Modeling, Analysis and Simulation of Permanent Magnet Brushless Diret Current Motors for Sensorless Operation Kaliappan, E. and C. Chellamuthu Department of Eletrial and Eletronis Engineering, RMK Engineering College, Kaaraipettai, Chennai , India Abstrat: Problem statement: In this study, a simplified modeling and experimental analysis of Permanent Magnet Brushless DC (PMBLDC) motors for Sensorless operation using MATLAB/SIMULINK. This model proides a mehanism for monitoring and ontrolling the oltage, urrent, speed and torque response. Approah: BLDC motor is modeled as sub-bloks. The inerter and swithing funtion are implemented as S-funtion builder blok. The Sensorless sheme employs diret bak emf based zero rossing detetion tehnique. Results: The proposed model with Sensorless ontrol tehnique with bak emf zero rossing detetion is tested in the BLDC Motor and the performane was ealuated. The simulated and experimental results show that the proposed modeling works quite well during starting and running onditions. Conlusion/Reommendation: The deeloped model onsists of seeral independent sub-bloks, that an be used in the modeling of Permanent Magnet Sinusoidal Motor and indution motor. Hene the deeloped simulation model is a design tool to study the dynami behaior of Sensorless Controlled Brushless DC Motor. Key words: PMBLDC motor, simplified modeling, sensorless sheme operation, bak emf zeroes ross Zero Cross Point (ZCP), Voltage Soure Inerters (VSI) INTRODUCTION In the literature, there are seeral simulation models aailable for PMBLDC motor dries. They are either state spae modeling or modeling based on d-q transformation, but there is no omprehensie model for the analysis of motor with Sensorless operation (Luk and Lee, 1994). The mahine models are often transformed to a rotating referene frame to simplify and to improe the omputational effiieny. But, this approah will not improe the omputational effiieny beause the d-q transformations are suitable only for mahines with sinusoidal oltage as disussed. The PMBLDC motors are normally powered by onentional three phase inerter, ontrolled by the rotor position information obtained from hall sensors, resolers or absolute position sensors. But these position sensors hae numerous drawbaks like inrease in ost, omplexity in ontrol, temperature sensitiity requiring speial arrangements. These sensors redue the system reliability and aeptability. Therefore, Sensorless tehniques hae beome a subjet of great interest in reent times. The Sensorless tehniques in the literature are based on sensing the bak emf, (Kaliappan et al., 2011) obserer based and artifiial intelligene based. An adaptie ontroller for PMBLDC Motor drie systems using Adaptie Network based fuzzy interferene system was presented (Lee and Ehsani, 2003). A PMBLDC motor operates in a two phase ON mode i.e. Two phases whih produe maximum torque is exited leaing the third phase open. The bak emf in open phase is sensed to determine the swithing sequene of the inerter (Rao et al., 2008). The Sensorless ontrol tehnique based on estimation of Zero Crossing Point (ZCP) of the bak emf is widely used for low ost appliation (Shao, 2006). A simple Sensorless tehnique using bak emf zero rossing is presented for PMBLDC motor (Kaliappan et al., 2011). In this study a MATLAB/SIMULINK model of PMBLDC motor suitable for Sensorless operation is deeloped. Using this model, the dynami behaior of the motor with the Sensorless tehnique is studied. Modeling of pmbld motor for Sensorless operation: In this modeling a three phase star onneted BLDC motor with six step ommutation is used for the analysis. Corresponding Author: Kaliappan, E., Department of Eletrial and Eletronis Engineering, RMK Engineering College, Kaaraipettai, Chennai , India 1046

2 Fig. 1: Basi PMBLDC motor Drie sheme Fig. 2: Ideal urrent and bak-emf waeform with hall the signals Figure 1 shows the simplified BLDC motor drie sheme and Fig. 2 gies Ideal urrent and bak-emf waeforms with hall signals. For 120 eletrial degree ondution, ommutation ours at eery 60 based on the position information. PMBLDC motor modeling: The equations inoled in Where: the modeling of PMBLDC motor shown in Fig. 1 are R deried as Eq. 1-3: L i ab ( a b ) d a, i b, i = R i i + L ( ia ib ) + ea e b (1) ab, b and a e a, e b and e 1047 b = R ( ib i ) + L d ( ib i ) + eb e (2) a = R ( i ia ) + L d ( i ia ) + e e a (3) = Per phase Stator resistane = Per phase Stator indutane = Instantaneous stator phase urrents = Instantaneous stator line oltages = Instantaneous phase bak-emfs

3 The relationship between the phase urrent is gien by Eq. 4: ia + ib + i = 0 (4) The equation is rewritten as Eq. 5: i = i + i (5) a b Using Eq. 5 the line oltage Eq. 1 and 2 rewritten as Eq. 6 and 7: ab = R ( ia ib ) + L d ( ia ib ) + ea e b (6) b = R ( ia + 2ib ) + L d ( ia + 2ib ) + eb e (7) The bak emf depends on the flux of the permanent magnet rotor and the speed of the rotor, it is expressed as Eq. 8: F( θe) ea k ew m 2 e b = F θ e 2 3 e 4 F θe 3 (8) The generated eletromagneti torque is gien by Eq. 9: K e Ke 2 K e 4 Te = F( θ e ) ia + F θe ib + F θe i (9) d J w T T K w = (12) m e L f m ' kf 1 w = m w m [ Te TL ] J + J (13) θ = (14) ' m w m Where: J = Moment of inertia in kg/m 2 k ƒ = Frition onstant in Nm/rad/se T L = Load torque in Nm k t = Torque onstant Inerter modeling: Inerter and the swithing sequene are modeled using S - funtions. Table 1 shows the swithing sequene, urrent diretion and the position signals. The Zero rossing of the open phase oltage is sensed to determine the rotor position. The triggering sequene generated by the ZCP of the bak emf of the open phase is similar to the one produed by the hall sensors mounted on the mahine. The operation of motor onsists of six states. The expression of the oltages and urrent are gien for the first state. State 1: (0-60 ). Commutation period: The swithes in phase A and phase B are energized and phase is freewheeling through diode D5 Eq. 15: For i 0 ab b a = s = 0 = s (15) Where: p θ e = θ m Eletrial angle, degrees 2 w m = Rotor speed, rad/se k e = Bak-emf onstant, olts/rad/se The dynamis of the motor and load is expressed as Eq : d T K w J w T = + + (10) e f m m L d T T K w J w = + (11) e L f m m 1048 On period: Phases A and B arry urrent and C phase is open Eq. 16 and 17: For i = 0 ab = s 1 = 2 + e + e 2e 1 = 2 e e + 2e b s a b a s a b For i 0 u = e e = e + e ab ab a b s a b u = e e = e + e b b b b u = e e = e + e a a a s a (16) (17)

4 where, u ab, u a and u a are the oltage drops aross the impedane onsisting of resistane and indutane of the phases. Simulation results: The speifiations of the BLDC motor used for the simulation are gien in Table 2. Equations 1-14 hae been used to deelop a simulation model using an S - funtion in MATLAB. Figure 3 shows the omplete simulation model of the PMBLDC motor drie onsisting of three bloks namely: swithing sequene blok, inerter blok and BLDC motor blok. The BLDC motor blok as labeled in the Fig. 4 represents the Eq Figure 6 represents the BLDC motor s oltage and urrent equations Eq. 5 and 6 whih take the d oltage ab, b as inputs and gies the phase urrent i s as an output. Table 1: Swithing sequene Swithing Position sensor Phase urrent interal Sequene Swith Degree number H1 H2 H3 losed A B C (0-60) T1 T4 +Ia -Ia Off (60-120) T1 T6 +Ia off -I ( ) T3 T6 off +Ib -I ( ) T3 T2 -Ia +Ib Off ( ) T5 T2 -Ia off +I ( ) T5 T4 off -Ib +I Table 2: Motor parameters Motor parameters Values Per phase resistane (R) 0.6 ohm Per phase Indutane (L) 0.42mH Moment of inertia (J) Kg-m 2 Bak Emf Constant (Kb) 0.1 V/rad/se Torque Constant (Kt) 0.1 Nm/A Number of poles 8 Fig. 3: Complete simulation model of the PMBLDC motor drie Fig. 4: Sub-bloks of BLDC motor model with bak emf zero ross detetion 1049

5 Fig. 5: The inerter S-funtion builder Fig. 6: BLDC oltage and urrent equation blok The Eletromagneti torque blok is implemented inerter and swithing logi funtional blok. The using Eq. 9, where Voltage and Current are the inputs DC oltage and sequene of the ontrol are the input along with the flux linkage and produes the to this blok. The firing signal inludes a PWM eletromagneti torque (T e ) as the output. Equation option for any 60 degree interals. The output are modeled as the mehanial blok whih oltage of the inerter depends on the DC soure takes the eletromagneti torque (T e ) and the load oltage, rotor position, phase urrent and also the torque (T L ) as input parameters and gies speed and alue of the bak emf. When a swith in a phase is position as output response. Figure 8 shows the bak turned off, the outgoing phase urrent freewheels emf zero rossing detetion blok. Phase urrent and through the diode where as the inoming phase bak emf are input to this blok. The subsystem of urrent inreases from Zero to full load alue. The the zero ross detetion iruit gies the Sensorless position of the rotor deides the inoming and position information. Figure 5 and 7 shows the outgoing phases. 1050

6 Fig. 7: Generating the swithing sequene Fig. 8: Zero rossing detetion blok (a) (b) Fig. 9: Generated Bak emf waeform and Phase urrent waeform from the rotor position 1051

7 Fig. 10: Speed waeform in rpm Fig. 11: Eletromagneti torque waeform (zoomed iew) Fig. 12: Blok diagram of the experimental setup Figure 9 shows the bak emf and the phase urrent Experimental results: The experimental setup used for waeforms obtained from the simulated model. The the alidation of the proposed modeling of BLDC deeloped model is simulated for a period of 1 seond. motor for Sensorless operation is gien in Fig. 12. It Figure 10 and 11 shows the speed and onsists of C0851F310 miroontroller, a 3 phase eletromagneti torque waeforms aptured when a MOSFET, oltage diider iruit, urrent amplifier, load of 0.5 Nm is applied at 0.4 se. speed and urrent ontroller and three dual gate driers. 1052

8 Fig. 13: Bak emf waeform with the Swithing Funtion (Experimental) Fig. 14: Swithing Funtion and oltage waeforms of the Three Phases Fig. 15: Measured phase urrent waeform 1053

9 Three simple resistie diider iruits are onneted to the three output phases with the bottom resistor onsists of a apaitor in it ating as an RC filter iruit. Motors supply oltage is sensed by onneting a resistie diider iruit aross the terminal. Figure 13 shows the bak emf waeform with swithing funtions measured from the experimental setup. Figure 14 and 15 show the expanded iew measured swithing funtions of three phases aording to onduting modes and phase urrent waeform. CONCLUSION This study presents a simplified modeling, analysis and simulation of PMBLDC motors. In the presented work, bak emf zero rossing detetion iruit is used for estimating the rotor position.the oltage and urrent waeform of the mahine is monitored and ompared with those obtained from the hall sensors. The results of the Sensorless operation mathed ery losely with those results obtained with the hall sensors. This learly demonstrates that the proposed model for based Sensorless ontrol an replae the hall sensor in the PMBLDC drie. This model an be easily extended for the other Sensorless ontrol tehniques with a minor hange in the model. Kaliappan, E., C. Chellamuthu and B. Balashankar, A Simple and improed Sensorless ontrol tehnique for PMBLDC motor. Commun. Intel. Inform. Si., 250: DOI: / _69 Lee, B.K. and M. Ehsani, Adaned simulation model for brushless DC Motor dries. Elet. Power Comp. Syst., 31: DOI: / Luk, P.C.K. and C.K Lee, Effiient Modeling of Brushless DC motor dries. Indus. Elet Control Instrumentation. Rao, K.S.R., Nagadean and S. Taib, Sensorless ontrol of a BLDC motor with bak EMF detetion method using DSPIC. Proeedings of the IEEE 2nd International Power and Energy Conferene, De. 1-3, IEEE Xplore Press, Johor Bahru, pp: DOI: /PECON Shao, J., An improed miroontroller-based Sensorless brushless DC (BLDC) motor drie for automotie appliations. IEEE Trans. Indus. Appli., 42: DOI: /TIA REFERENCES Kaliappan, E. and C. Chellamuthu, A simple Sensorless ontrol tehnique for PMBLDC motor using bak EMF zero rossing. Eur. J. Si. Res., 60: