An Improved Flux Observer for Sensorless Permanent Magnet Synchronous Motor Drives with Parameter Identification

Transcription

1 J Electr Eng Technol Vol. 8, No. 3: , 13 ISSN(Print) ISSN(Online) An Improved Flux Oberver for Senorle Permanent Magnet Synchronou Motor Drive with Parameter Identification Hai Lin*, Kyu-Yun Hwang** and Byung-Il Kwon Abtract Thi paper invetigate an improved tator flux linkage oberver for enorle permanent magnet ynchronou motor (PMSM) drive uing a voltage-baed flux linkage model and an adaptive liding mode variable tructure. We propoe a new oberver deign that employ an improved liding mode reaching law to achieve better etimation accuracy. The deign include two model and two adaptive etimating law, and we illutrate that the deign i table uing the Popov hyper-tability theory. Simulation and experimental reult demontrate that the propoed etimator accurately calculate the peed, the tator flux linkage, and the reitance while overcoming the hortcoming of traditional etimator. Keyword: Permanent magnet ynchronou motor, Oberver, Stator flux linkage 1. Introduction AC motor drive had been widely ued in mot indutry application of aircraft, robot, automobile and houehold electric appliance becaue of it high performance and low cot [1]. Recently, the PMSM i very popular in AC motor application for it mall ize, light weight and high efficiency, epecially in the application without poition or peed enor []. Generally, the rotor poition of the PMSM i detected by a Hall enor, reolver or an abolute encoder. However, thee enor bring not only more cot but alo ome defection to tructure deign of the motor. Moreover, the performance of the enor get degradation for exterior environment contraint uch a air humidity, vibration and temperature. Recently, ome enorle method of PMSM drive had been developed for the motor drive by the etimated rotor poition and velocity. A full order Luenberger oberver [3] for tator flux etimation and a implified Kalman filter for peed etimation have been developed for a direct-torque-controlled IPM motor drive. To implify the tructure of traditional full order oberver, a reduced-order poition oberver [4] with tator reitance adaptation for alient PMSM drive i developed. A econd-order oberver [5] with the phae-locked loop (PLL) tructure and a predictive direct current controller are deigned to realize the enorle control of the PMSM. To improve the robutne of the traditional oberver, the technique of liding mode variable tructure had been introduced to the enorle control of the PMSM drive. The liding mode oberver [6-8] are propoed to etimate Correponding Author: Department of Electronic Sytem Engineering, Hanyang Univerity, Korea (bikwon@hanyang.ac.kr) * Department of Automation, School of Electronic and Control Engineering, Chang an Univerity, PRC (linhai@chd.edu.cn) ** Department of Electronic, Electrical, Control and Intrumentation Engineering, Hanyang Univerity, Korea (kyuyun7@hanmail.net) Received: March 1, 1; Accepted: December 11, 1 the poition and peed of a permanent magnet ynchronou motor (PMSM) by the etimated back-emf. The propoed oberver are derived from traditional current model and mot employed the dicontinuou witching function in liding mode control. More importantly, much harmonic component among the etimation of back-emf degrade the etimation accuracy of the rotor poition. To etimate accuracy rotor poition, a implified Kalman filter [6-7] or a low pa filter [8] wa ued to eliminate the high frequency component to etimate the rotor poition in the traditional liding mode oberver. To reduce the undeirable chattering in the traditional liding mode technique, a igmoid witching function [8] with a variable boundary layer wa ued to replace the traditional ign function. In [9], an adaptive liding oberver for tator flux etimation and a implified Kalman filter for peed etimation have been developed for a direct-torque-controlled IPM motor drive. The propoed oberver baed on the motor current model need the etimation of the back-emf of the motor and a Kalman filter to eliminate it high frequency component. The tator flux linkage are calculated by the etimated back-emf and the meaured tator current. Therefore, current oberver have the complex tructure and the problem of the chattering from the witching function in the traditional liding mode technique. In the paper, an improved adaptive tator flux linkage oberver i invetigated by a flux model and the liding mode variable tructure with a variable exponent reaching law. The traditional witching function in the reaching law i replaced by a hyperbolic witching function, which can reduce the chatting problem of the traditional liding mode control. Two etimation law of the peed and reitance deduced by the given oberver model and Popov-tability theory have an accuracy peed and reitance etimation. The imulation and experiment reult how the effecttivene of the propoed oberver for enorle PMSM drive. 516

2 Hai Lin, Kyu-Yun Hwang and Byung-Il Kwon. Motor Mathematical Model For a urface mount permanent magnet ynchronou motor, the phae voltage in the rotating frame are expreed a did ud = Rid + Ld ωlqiq diq uq = Riq + Lq + ωld id + ωφ where u d, u q, i d, and i q are the tator phae voltage and current in the rotating frame, repectively, Ld and L q are the inductance in the rotating frame, R i the reitance of the tator winding, ω i the motor peed, and φ i the rotor magnet flux linkage. The tator flux linkage in the rotating frame can be expreed by λ λ d = Ld id + q = Lqiq where λ d and λ q are the tator flux linkage in the rotating frame. The amplitude of the tator flux linkage i φ λd λq (1) () λ = + (3) Subtituting () into (1), the phae voltage in term of the tator flux linkage and the peed in the rotating frame are given by R dλd R ud = d + q Ld Ld R dλ q uq = λq + + ωλ d Lq λ ωλ φ The compact matrix form of (4) can be written a follow: dx (4) = AX + Bu (5) where R R ω λd ud φ L + X, u L =, A, B I λ = = =, q R u q ω L and I i an identity matrix. 3. Improved Flux Linkage Etimation Scheme In mot method for etimating the tator flux linkage, the current-baed flux model in () can be eaily ued to calculate the flux. It i known from () that the flux linkage can be calculated uing the current in the rotating frame and the two motor parameter of rotor flux and tator inductance. However, the current-baed flux model uffer from a DC current hift caued by the meaured error and ignal noie. Subequently, a voltage-baed tator flux linkage model [1] in the tationary frame i more imple and practical, given a follow: λα = ( uα Riα ) λβ = ( uβ Riβ ) where λ α, λ β, u α, u β, iα, and i β are the tator flux linkage, voltage, and current in the tationary frame, repectively. In (6), the tator flux linkage are etimated by tator phae voltage, phae current, the reitance, and an integrator. The voltage-baed flux model i ued in the tationary frame, and it depend on one motor parameter. However, the problem of the DC hift in two meaured current will caue error in the integrator, which can make it ineffective. To overcome the hortcoming of traditional flux linkage etimation method (6), in thi paper, we propoe a new method to accurately etimate the tator flux linkage of the motor uing the voltage-baed flux linkage mode of (5) and the technology of a liding mode variable tructure. To etimate the tator flux linkage a well a the reitance and rotor peed, we chooe the tator flux linkage of λ d and λ q in the rotating frame a the etimated variable, and reitance R and peed ω a the regulated object. Therefore, a traditional flux oberver can be given a dx where the tate error coefficient matrix, and (6) = AX + Bu + Ge (7) e= X X, G i a contant R R ω λ d ud + φ,, L X = u= L A= λ. q R u q ω L To improve the etimation performance relative to thoe of traditional flux etimation cheme, a new flux oberver with variable exponent reaching law i deigned uch that: 517

3 An Improved Flux Oberver for Senorle Permanent Magnet Synchronou Motor Drive with Parameter Identification dx b = AX + Bu G e hyp( S) G e S (8) a 1 t where S = e( t) + K e( τ ) dτ ( K i a contant coefficient matrix), G 1 and G are contant coefficient matrixe, and a and b are contant. In (8), G1 e a hyp( S) + G e b S i the deigned variable exponent reaching law. In thi paper, a=b=1. To reduce the chatting problem of the traditional liding mode control, a hyperbolic function hyp() i introduced in (8) and defined a follow: hyp( x) = 1 (9) 1+ mx e where m i a poitive contant that regulate the lope of the function output. The variable peed and variable exponent in the deigned oberver produce the tate variable approach to the liding mode urface under two different peed. The tate variable quickly approache the urface under the variable exponent part, and the variable peed part i the main regulator to approach the urface in a mall ditance. After that, the liding mode control law allow the tate variable to reach the urface and be table at the origin. The variable exponent reaching law employed in (8) can effectively repre the chatting problem of the traditional liding mode technology. Subequently, baed on (5) and (8), the time derivative of the tate error e i de = Ae+ AX + B u+ Z( e) (1) where Z( e) = G1 e hyp( S) + G e S, the error coefficient matrix A and the error input matrix u are defined a follow: R ω L R A= A A= = I ωj, R L ω L R φ R 1 L u= u u= = φi, I =, L (11) the error reitance i R = R R, and the error peed i ω = ω ω. Defining an output vector a υ = AX + B u+ Z( e) (1) and ubtituting (1) into (1) yield de = Ae Iυ ν = De (13) where ν i an input vector, and D i a contant coefficient matrix. Defining D= I, thenν = Ie= e. According to the Popov hyper-tability theory, the ytem i table under the following condition: (I). 1 H ( ) = D( I A) i a trictly poitive matrix. (II). t t, T η(, t) = ( ν υ) γ, where γ i a finite poitive contant, which i independent of t. Therefore, lim e( t) =, and the ytem (1) i table. t In a deigned error ytem (1), the table condition (I) decribed above can be eaily atified. According to the table condition (II), ubtituting (1) into a variable T ν υ, yield T T T T ν υ = e AX + e B u+ e Z( e) (14) Subtituting (11) into (14) give T T R ( ) T R ν υ e = I+ ωj X + e B φi L L T + e ( G e hyp( S) + G e S) 1 Thi lead to the following equation: µ φ µ ω d( R ) R T T 1 = ( e IX + e BI) L d( ω) T = e JX where µ 1 and µ are two poitive contant. Simplifying (16) to d R 1 T T µ 1 = ( e IX + φe BI) L d ω T µ = e JX (15) (16) (17) From the above definition, it i known that R = R R and ω = ω ω. Auming that the derivation of actual peed and reitance in the teady operation i zero, the implified form of (17) can be implified a following: 518

4 Hai Lin, Kyu-Yun Hwang and Byung-Il Kwon dr 1 T ( T = e IX φe I) µ 1L d ω 1 T = e JX ω µ L (18) Subtituting (18) into (1), the table condition (II) decribed above can alo be atified when parameter γ, µ 1, µ, G 1, and G are choen appropriately according to the following inequality condition: T e ( G1 e hyp( S) + G e S) (19) Thu, (18) can now be olved for the deigned adaptive law of R and ω. To peed their repone, a proportional term i added. The final peed and reitance adaptive law are 1 T T R = k p1 ( e IX φe I) + L 1 T T ki1 ( e IX φe I) L () T T ω = k pe JX + ki ( e JX ) (1) where k p1, k p, k i1, and k i are poitive contant. The configuration of the deigned enorle cheme for a PMSM drive with the propoed oberver deign i hown in Fig. 1. In thi cheme, the reference and etimated flux linkage are calculated uing a reference flux model and an adaptive flux oberver in the rotating frame. The peed and reitance are etimated uing two PI regulator with the input of two deigned adaptive law. According to (8) to (19), Popov hyper-tability theory can enure the tability of the deigned etimating ytem if we chooe the appropriate contant coefficient in (8), (), and (1). In the oberver, while the regulating object of peed and reitance are changed ynchronouly, the regulating model continuouly track the reference model. That i, when the deigned ytem i table, the regulating model i cloe to the actual motor ytem baed on a PLL tructure oberver. In Fig. 1, the coordinate converion from tationary frame to rotating frame i X d coθ X = q inθ inθ Xα coθ X β () To verify the etimated flux linkage of (8) in the rotating frame with a voltage-baed tator flux linkage model of (6) in the tationary frame, the revere coordinate converion of () i given by Xα coθ inθ X d X = β inθ coθ X q where X i the phae current, voltage, or flux linkage. (3) 5. Verification by Simulation and Experimental Reult The control cheme for the propoed oberver i hown in Fig.. In thi cheme, we ue the technique of pace vector pule-wih modulation (SVPWM) to obtain the contant inverter witching frequency. The tate frame tranformation of Clark, Park, and invere-park are ued to tranform the current and reference voltage. Two proportion integral (PI) controller are ued to regulate the d-axi and q-axi current, and a PI controller i ued to regulate peed. Uing the reference voltage from the revere-park tranformation and two meaured tator current from the Clark tranformation, the tator flux linkage, rotor poition, and peed are etimated accurately, and the motor peed and reitance are imultaneouly obtained by the propoed adaptive flux oberver. Fig. 1. The configuration of the deigned enorle cheme with the deigned adaptive oberver Fig.. The configuration of a PMSM drive with the propoed oberver 519

5 An Improved Flux Oberver for Senorle Permanent Magnet Synchronou Motor Drive with Parameter Identification Fig. 3 The experiment of a enorle PMSM drive with a propoed adaptive oberver To verify the propoed cheme hown in Fig., a imulation model i built uing Matlab oftware, and an experiment i performed a hown in Fig. 3. The experiment i implemented in a DSP of TMS3F835, and a three-phae voltage ource inverter i implemented with a chip of DRV84 from Texa Intrument. In both the imulation and the experiment, we ue a PMSM motor with phyical parameter of armature reitance.79 ohm, inductance 1. mh, and number of pole 8. In the digital realization, the PWM witching frequency of the inverter i et a 1 KHz. The DC link voltage for the inverter i et to 4 V. The reference peed of the motor i et to 3 rpm. To reduce the tartup current of the motor, a tep ignal of input peed command i tranformed to a ramp ignal with a lope value of.1. According to the inequality (19), the coefficient matrixe of G1 and G in the propoed oberver are given by.65.8 G1 =, G.65 =.8 In the parameter and tate etimation law of () and (1), it coefficient of time after time tet are 4 4 Speed (rpm) 3 1 Speed Error (rpm) t () t () (a) Etimated peed (Simulation) (d) Speed error (Simulation) R (ohm) Poition Error (rad) 4 x t () -1 t () (b) Etimated reitance (Simulation) (e) Rotor poition error (Simulation) (c) Etimated peed and reitance (Experiment) (f) Speed error and rotor poition error (Experiment) Fig. 4. The imulation and experiment reult for the propoed oberver in a PMSM drive (Etimated peed and reitance and the error of peed and rotor poition) 5

6 Hai Lin, Kyu-Yun Hwang and Byung-Il Kwon k p1 =.6, ki1 =.5, k p., ki1 1.1, = = m=.45. Fig. 4 how the repone of etimated peed and reitance R and the peed error e ω and rotor poition error e θ in the imulation and experiment, repectively. In the experimental reult, the etimated peed near it et value of 3 rpm in.5 econd, and the reitance reache it rated value of.79 ohm in 4.5 econd, a hown in Fig. 4. To further reduce the chatting from the (a) Etimated flux linkage (Simulation) (a) Etimated flux linkage (Simulation) (b) Etimated flux linkage (Experiment) (b) Etimated flux linkage (Experiment) (c) Spatial ditribution of etimated flux linkage (Simulation) (c) Spatial ditribution of etimated flux linkage (Simulation) (d) Spatial ditribution of etimated flux linkage (Experiment) Fig. 5. The etimated flux linkage for a traditional flux oberver (6) in a PMSM drive (d) Spatial ditribution of etimated flux linkage (Experiment) Fig. 6. The etimated flux linkage for the propoed oberver in a PMSM drive 51

7 An Improved Flux Oberver for Senorle Permanent Magnet Synchronou Motor Drive with Parameter Identification traditional witching function, we deigned a variable exponent reaching law with a hyperbolic witching function in the propoed oberver. The peed error between the reference and etimated peed i reduced to zero in.5 econd, and the poition error between the actual and etimated poition i reduced to zero in 4. econd. During the proce of motor tarting, the motor ha a fat dynamic performance. The error between the reference tate and actual tate i changed from the maximum cloe to zero quickly. A hyperbolic witching function will regulate the poitive or negative feedback of the error dynamic automatically according to the error. In the imulation reult, imilar dynamic performance i achieved by the propoed oberver. Fig. 5 and 6 how the repone of etimated flux linkage ( λ α and λ β ) and it pace ditribution in the imulation and experiment for the traditional and propoed oberver, repectively. Fig. 5(a) and (c) how the imulation reult for the traditional oberver (6), and Fig. 5(b) and (d) how the experimental reult. Thee reult how that the integration of the traditional etimator (6) will increae the input error from meaurement and calculation, and, unle reet, they will become large and lead to intability. When there are DC hift of the meaured current and voltage or an unknown initial value of the tator flux linkage, the etimated tator flux linkage from a traditional etimating cheme i divergent, and the origin (O) of it planar circle path leave that of the coordinate. Subequently, the traditional method ued to etimate the flux linkage with integration i invalid. Fig. 6 (a) and (c) how the imulation reult for the propoed oberver, and Fig. 6(b) and (d) how the experimental reult. The propoed etimator provide the advantage of overcoming the limitation of the traditional integration. The origin of the planar circle path of the flux linkage i fixed to the frame origin (O), a hown in Fig. 6(c) and 6(d). A better teady performance of flux etimation i thu achieved by the propoed oberver. 5. Concluion An adaptive tator flux linkage oberver for enorle vector control of PMSM drive i preented in thi paper. The deigned oberver ha a phae-locked loop tructure, which contain two model of an adaptive liding mode flux oberver and a reference flux model. Two adaptive law are derived by the Popover hyper-tability theory to imultaneouly etimate the peed and the reitance. The propoed cheme achieve more accurate peed and tator flux linkage etimation compared to the traditional method, a demontrated by the imulation and experimental reult. Acknowledgement Thi project wa upported by the World Cla Univerity (WCU) program through the National Reearch Foundation of Korea funded by the Minitry of Education, Science and Technology (R ). Reference [1] Idri, N.R.N.; Yatim, A.H.M., An improved tator flux etimation in teady-tate operation for direct torque control of induction machine, IEEE Tranaction on Indutry Application, Vol. 38, No. 1, Page(): ,. [] Hyunbae Kim; Harke, M.C.; Lorenz, R.D.; Senorle control of interior permanent-magnet machine drive with zero-phae lag poition etimation, IEEE Tranaction on Indutrial Electronic, Vol. 39, No. 6, Page(): , 3. [3] Po-ngam, S.; Sangwongwanich, S.; Stability and Dynamic Performance Improvement of Adaptive Full-Order Oberver for Senorle PMSM Drive, IEEE Tranaction on Power Electronic, Vol. 7, No., Page(): 588-6, 1. [4] Hinkkanen, M.; Tuovinen, T.; Harnefor, L.; Luomi, J.; A Combined Poition and Stator-Reitance Oberver for Salient PMSM Drive: Deign and Stability Analyi, Vol. 7, No., Page(): 61-69, 1. [5] Preindl, M.; Schaltz, E.; Senorle Model Predictive Direct Current Control Uing Novel Second- Order PLL Oberver for PMSM Drive Sytem, IEEE Tranaction on Power Electronic, Vol. 58, No. 9, Page(): , 11. [6] Changheng Li, Elbuluk M, A Sliding Mode Oberver for Senorle Control Of Permanent Magnet Synchronou Motor, in Proc. Indutry Application Conf. 1, Vol., pp [7] K. Paponpen and M. Konghirun, An improved liding mode oberver for peed enorle vector control drive of PMSM, in Proc. CES/IEEE 5th Int. Power Electron. Motion Control Conf., Aug. 6, Vol., pp [8] Hongryel Kim; Jubum Son; Jangmyung Lee, A High-Speed Sliding-Mode Oberver for the Senorle Speed Control of a PMSM, IEEE Tranaction on Indutrial Electronic, Vol. 58, No. 9, Page(): , 11. [9] Zhuang Xu; Rahman, M.F.; An Adaptive Sliding Stator Flux Oberver for a Direct-Torque-Controlled IPM Synchronou Motor Drive, IEEE Tranaction on Power Electronic, Vol. 54, No. 5, Page(): , 7. 5

8 Hai Lin, Kyu-Yun Hwang and Byung-Il Kwon [1] Rahman, M.F.; Zhong, L., Problem of tator flux oriented torque controller for the interior permanent magnet motor, IPEMC, Vol. 1, Page(): ,. Hai Lin He received hi B.S. degree in Indutry Automation from Xi an Petroleum Univerity, China, and hi M. S. and Ph.D. degree in Control Theory and Control Engineering and in Weapon Science and Technology from Northwetern Poly-technical Univerity, China. He i currently with Chang an Univerity, China. Hi reearch interet are multilevel inverter and motor drive. Kyu-Yun Hwang He received hi B.S. degree in Electronic and Electrical Engineering from Hanyang Univerity, Korea. He i currently Ph.D tudent in the Hanyang Univerity and a Reearch Engineer in a Komotek. Hi reearch interet include the deign and analyi of PMSM and BLDC motor. Byung-Il Kwon He received hi B. S. and M. S. degree in Electrical Engineering from Hanyang Univerity, Korea, and hi Ph.D. degree in Electrical Engineering from Tokyo Univerity, Japan. He i currently a Profeor at Hanyang Univerity. Hi reearch interet are linear drive ytem, numerical analyi of machine, and motor control. 53