Transactions Template JOURNAL OF ENGINEERING RESEARCH AND TECHNOLOGY, VOLUME 1, ISSUE 4, DECEMBER 2014 132 PMSM Sensorless Speed Control Drive Youakim Kalaani1,Rami Haddad2, Adel El Shahat3 1Department of Electrical Engineering, Georgia Southern University, USA 2Department of Electrical Engineering, Georgia Southern University, USA 3Department of Electrical Engineering, Georgia Southern University, USA Abstract— Permanent magnet synchronous machines (PMSM) are very popular in many industrial applicationssuchasinmechatronics, automotive, energy storage flywheels, centrifugal compressors, vacuum pumps, and robotics. This paper proposes Sensorless control for a PMSM speed drive which is based on aclosedloopcontrol system using a proportional and integral (PI) controller that is designed to operate in flux weakening regions under a constant torque angle.ThisSensorlesselementwasadopted for best estimating the PMSM rotor position based on its performance characteristicseliminatingthe need for speed sensorswhich are usually required insuchcontrol applications. To achieve this goal, apulse width modulation (PWM) control scheme was developed to work in conjuction with a field oriented motor controldriveusingSimulink.Thisinnovative control system was simulated assuming realistic circuit components to maximize the accuracy of the proposed model.Finally, simulation results obtained under different operation conditions at below and above the rated speed of the motorwere presented and discussed in this paper. Index Terms——Permanent Magnet, Synchronous machine, Control, Sensorless, Simulink and Field Oriented. I INTRODUCTION The vector control of ac machines was introduced in the late 1960s by Blaschke, Hasse, and Leonhard in Germany. Fol- lowing their pioneering work, this technique, allowing for the quick torque response of ac machines similar to that of dc machines, has achieved a high degree of maturity and become popular in a broad variety of applications.For many years, PMSM have been the subject of intense studies and various speed control schemes have been proposed in the literature. For instance, C. Bowen et al. [1] have addressed the modeling and simulation of PMSMsupplied from a six step continuous inverter based on state space method. Fur- thermore, C. Mademlis et al. [2]presented an efficiency op- timization method for vector-controlled interior drive, and a modular control approach was applied by X. Jian-Xin et al [3].In motor drive applications, a shaft encoder or a hall sen- sor is typically used to measurethe rotor position [4-8]. Due to the flux-weakening technology, the operating speed range can be extended by applying negative magnetizing current component to weaken the air-gap flux [9, 10]. This has led to a new design concept of permanent magnet (PM) machine for flux-weakening operation proposed by L. Xu et al. [11]. For their part, Tapia et al. have explored a magnetic structure termed the consequent-pole(CPPM) machine which had inherent field weakening capability [12]. Soong and Miller proved that maximum torque field-weakening control can be achieved through optimal high-saliency interior PM motor design [13] and a two control techniques to enhance the per- formance of PM drives over an extended speed range were presented by Macminn and Jahns [14]. However, the tech- niques of maximum torque per ampere (MTPA) operation at a break-point speed was first investigated by Sebastian and Slemon [15]anda current-regulated flux-weakening method for reduced air-gap flux was introduced by Dhaoudi and Mohan [16]. Although current vector controlandfeed- forward decoupling compensation appeared in work done by Morimoto et al[17,18], it was not until Sudhoff et al [19] who set forth a flux-weakening control scheme that is rela- tively simple and does not require prior knowledge of the machine and inverter parameters. Along these lines, Sozer and Torrey [20] presented an adaptive control over the entire speed range ofPM motor. Several flux-weakening control methods based on voltage regulation were proposed by Y. S. Kim et al [21], J. M., Kim et al [22], and J. H. Song et al 23] in which the voltage error signalis generated between the maximum output voltage and the voltage command. In vec- tor control of PM motors, the output of the voltage regulator is used to determine the required demagnetizing curren needed to prevent saturation. However, the added controller could only operate properly under well-tuned condi- tionswhich are not easily reached [24] and the d-q axis cur- rents cannot beindependently controlled due to the cross- coupling effects which become dominant at high speeds. As a result, the dynamic performance of PM motors are de- gradedwithoutthe presence of a decoupling control scheme and effective control offast dynamic response requires accu- rate rotor position[21-27]. Adaptive control methods seem to Youakim Kalaani, Rami Haddad, Adel El Shahat/ PMSM Sensorless Speed Control Drive (2014) 133 be the most promising modern control strategy [28], [29] and a model reference adaptive control (MRAC) schemecharacterized by reducedcomputation was proposed by Cerruto et al [28]. This model was further refined by Baik et al [30] byestimating the values of slowly varying parame- ters using Lyapunov stability criteria. The use of sensors to measure motor speed can result in increased cost and re- duced control robustness and/or reliability. The first break- through in senseloss control theory was reported by A. Ros- tami, and B. Asaei [31] who developed a method for esti- mating the rotor positionas well as other proposed mothods [32-35]. However, many challengesremain in the design of sensorlesscontrolto operate over a wide speed range of PM motors. Improved position-sensorless control schemes were developed in the last decade [36-40], especially in the con- cept area of direct drive which achieved higherdynamic re- sponse, increased efficiency, and low acoustic noise.In mod- ern applications, the PMSM machine is designed to operate in constanttorqueand power modesat below and above the rated speed which can significantly reduce the cost and size of the overall drive system. The constant-torque opera- tioncaneasilybe achieved by conventional vector control but the motor will not be able to operate in constant-torque mode at above the rated speed. However, this problem was alleviated by the introduction of flux-weakening techniques which extended the operating speed range by applying nega- tive magnetizing current component to weaken the air-gap flux [41], [42]. In this paper, a Sensorlessvectorcontrol of PMSM drivesus- ing flux weakening techniquesis presented. A PI controller operating under constant-torque angle is implemented using a novel PWM controlscheme for field oriented motor con- troldrive. This controller was tested using Simulink and dif- ferent operation conditions under variable speed were pre- sented and discussed in this paper. This Sensorless drive system is also usefullin Electric Vehicle (EV) applications. II PMSM DYNAMIC MODELING The PMSM drive system with and without speed sensoris described in this section. Itincludes different components such as permanent magnet motors, position sensors, inverter, and current controller with sensor and speed estimation unit for Sensorlesscontrol. Both components are presented in Fig.1and Fig.2 respectively. Fig.1-Drive System Schematic with position sensor Control Input DC Source Load PM MotorInverter Rotor Position Controller Ia Ib Ic Ia Ib Ic Gate Signals Position Estimation Fig.2-Drive System Schematic without position sensor The PMSM equivalent circuit used to derive the dynamic equations in the d-q axisis presented in Fig.3. Fig.3- PMSM Equivalent Circuit The stator windingsareassumed to have equal turns per phase in the d-q axis. The rotor flux is also assumed to be concentrated along the d-axis while there is zero flux along the q-axis. In addition, it is assumed that the machine core losses are negligible. Variations in rotor temperature can alter the magnet fluxbut its variation with respect to time is considered to be negligible. III PMSMSTATOR FLUX – LINKAGE The equations for the stator flux-linkage along the d-q axis are given by: vq = Rq iq + ρ (q) + r d (1) vd = Rd id + ρ (d)– r q (2) Where: ρ: is the d/dtdifferential factor;Rq, Rd are the wind- ing resistancesand refered as Rs when equal. The q-d axis stator flux linkagesreflected to the rotor refer- ence frames can be written as: q = Ls iq + Laf iq (3) d = Ls id + Laf id (4) Theoritcally, the self – inductances of the stator q-d axis are equal to Ls only when the rotor magnets are at 180electrical degrees apart but this is hardly the case in practice. When the stator winding is aligned with the rotor, theinductance Ld(d-axis) is the lowest while the winding facing the interpo- lar path results in higher inductanceLq(q–axis [43]. The ex- citiation of the permanent magnetis modeled as a constant current sourceifralong the d-axis.Since there is no flux along the q-axis, the rotor currentis assumed to be zero.Therefore, the flux linkages can be written as: Control Input DC Source LoadPM MotorInverter Rotor Position Controller Ia Ib Ic Ia Ib Ic Position Sensor Gate Signals Youakim Kalaani, Rami Haddad, Adel El Shahat/ PMSM Sensorless Speed Control Drive (2014) 134 vq = Rsiq + ρ ( q ) + rd vd = Rs id + ρ ( d ) – r q q = Lqiq d = Ld id + Lmifr = Ld id + af af= Lmif Where: Lm is the mutual inductance between stator and rootorwindings;r: Electrical velocity of the rotor; af :Flux linkage due to rotor; ρ (af) = 0, af = Lmifr; ρ : Operator. IV PMSM TORQUE EQUATIONS The electromagnetic torque is given by: (5) This torque is derived fromthe input power as follow: Pin = vaia + vbib + vcic (6) Equation (6) has three parts; 1) power loss in the conductors; 2) energy rate of change in the magnetic field; and 3) con- version to mechanical energy. The electromechanical power is given by Pem = rmTe = (3/2) r( diq – q id ) (7) r = (P/2) rm (8) Where: P is the number of poles and rmthe mechanical ve- locity of the rotor. Therefore, the torque can be written as (9) Where, the first term of equation (9) presents the magnet alignmentand the second term presents the torque reluc- tance. The general mechanical equation for the motor is written as Te = Tl + Td + B rm + J ρrm (10) Where: B: Viscous frictions coefficient; J: Inertia of the shaft and load system; Td: Dry friction; Tl: Load torque V PMSM DYNAMIC SIMULATION The dynamic simulation presented in this paper was per- formed using Simulinkin MATLAB package.A PMSM block is shown in Fig. 4where the voltage and load torque are pre- sented as inputswhile the motorspeed and current are pre- sented as outputs. Fig.4- Model Block of PMSM Dynamic A more detailed model [44-46] is providedin Fig. 5. Fig.5- Detailed Model of PMSM VI PMSM CURRENT CONTROL High-performance drives utilize control strategies which develop command signals for the AC machine currents. ngCurrent controlseliminate stator dynamics (effects of sta- tor resistance, stator inductance, and induced EMF) and thus, to the extent that the current regulator functions as an ideal current supply, the order of the ystemcan significantly be reduced. However, AC current regulators which form the inner loop of the drive system are complex since both ampli- tude and phase shift of the stator currents must be controlled. They must provide minimum steady-state error and also require the widest bandwidth in the system. Both current source inverters (CSI) and voltage source inverters (VSI) can be operated in controlled current modes. PWM current controllers [47] are widely used since they can generate a control scheme based on comparing a triangular carrier wave of desired switching frequency to the error of the con- trolled signal. The error is the difference between the refer- ence signal generated in the controller and the actual motor current. If the error command is above the triangle wave- form, theVSI leg is held switched to the positive polarity (upper switch on). Contrarily, if the error command is below the triangle waveform, the inverter leg is switched to the negative polarity (lower switch on). In this study, a PWM current controller is used with generated signals as shown in Fig. 6. )( 22 3 dqqde ii P T   ))(( 22 3 dqqdqafe iiLLi P T   PMSM Dynamic Model Voltage Load Torque Speed Current Ns 1 current in q -axis u(1)/Lq current in d -axis f(u) Te Calculation f(u) Sine Wave 3 Sine Wave 2 Sine Wave 1 Poles / 2 -K - Mechanical f(u) Load Torque T_L Integrator 1 1 s Integrator 1 s Gain 4 -K - Gain B From 3-phase to d -q- In 1 V_d V_q Flux in q -axis V_q i_q Lambda_d Omega_r Lambda_q Flux in d -axis V_d i_d Lambda_q Omega_r Lambda_d Constant 1 T_d Constant J .. . Youakim Kalaani, Rami Haddad, Adel El Shahat/ PMSM Sensorless Speed Control Drive (2014) 135 Fig.6- PWM Current Controller VI I PMSM FIELD ORIENTED CONTROL A PMSM field oriented or vector control is derived from the machine dynamic model and it is based on the decoupling of the torque components. The 3-phase currents flown in the stator windings can be transformed to the rotor reference frame using Park’s transformationas follow: (11) Where α is the angle between the rotor field and stator cur- rent; ωr is the electrical rotor speed. In the rotor reference frame, the q- axis current (iq) and the d -axis current (id) are usually constant since α is fixed for a given load torque. Under this condition, iq and id are called respectively the torque and flux producingcomponents of the stator current. They can be written as: (12) And, the electromagnetic torque is given by: (13) The field oriented or vector control can be utilized under two modes of operation: A Constant Flux Operation In this mode of operation, it is possible to produce maxi- mum torque by setting angle α in equation (12) to 90º which makes id zero and iq equals to Is. Therefore, torque equation (13) can be rewritten as a function of the motor current: qte IkT . (14) (15) B Flux-weakening Operation Flux weakening is the process of reducing the flux in the d- axiswhich yieldshigher speed range. The weakening of the field flux is required for operation above the rated speed or base frequency. Under this mode, the motor drive is operat- ed at a constant voltage over frequency (V/F) ratio which results in a reduction of the torque proportional to the change in the frequency. Under this condition, the motor operates in the constant power region [48]. When permanent magnets are used, flux-weakening is achieved by increasing the negative id current and using armature reaction to reduce the air-gap flux [49]. The torque can be varied by altering the angle between the stator MMF and the rotor d-axis. In the flux weakening region where ωr>ωrated, it is possible to change the value of α by adjusting id and iqasshown below (16) Since torque is a function of iqcuyrrent, the torque will also be reduced. The generated reference signals are used by the current controller to drive the inverter and the load torque given by equation (17) can be adjusted for different refer- ence speeds ωr (17) VIII IMPLEMETINGSPEED CONTROL LOOP The precise control of speed and position is required in many applicationssuch as in robotics and factory automa- tion.A typical control system consists of a speed feedback system, a motor, an inverter, a controller, and a speed setting device. A properly designed feedback controller makes the system insensible to disturbance and changes of the parame- ters. Closed-Loop control systems have fast responsebut areexpensives due to the need of feed back components such as speed sensors. A block diagram of atypical PMSM drive system with a full speed range is shown in Fig. 7. The sys- tem consists of a motor, an inverter, a controller (constant- flux and flux-weakening operation, and reference signals) Fig.7- Block Diagram for original drive system Current Error Saw Tooth PWM Signal ) 3 2 sin( ) 3 2 sin( )sin(         tIi tIi tIi rsc rsb rsa                  cos sin s d q I i i ]sin2sin)( 2 1 [ 22 3 2  safsqde IILL P T  aft P k ) 2 )( 2 3 ( )( )( r rated ratedel TT    )(tan 1 d q i i   PMSM Voltage Source Inverter C u rr e n t C o n tr o l Flux Weakening Constant Torque Ang. PI Control Unit Iabc Id Iq  r  r  ref  r s   1/s Youakim Kalaani, Rami Haddad, Adel El Shahat/ PMSM Sensorless Speed Control Drive (2014) 136 Fig.8- Block Diagram for Sensorless drive system A PMSM speed Sensorless drive system is shown in Fig. 8 in which the speed sensor is replaced by a postion estimation and its derivative. Speed controller calculates the difference between the refer- ence speed and the actual speed producing an errorwhich is fed to the PI controller. PI controllers are widely used for motion control systems. They consist of a proportional gain that produces an output proportional to the input error and an integration to eliminate the steady state error due to a step input. A block diagram for a typical PI controller is shown in Fig. 9. Fig. 9- Block Diagram of a PI Controller Motor speed controllers consist of an inner loop for the cur- rent and an outer loop for the speed. Depending on the re- sponse of the system, the current loop is at least 10 times faster than the speed loop. The current control is performed by the comparison of the reference currents with the actual motor currents. A simplified control system may be obtained by setting the gain of the current loop to unity as displayed in Fig. 10. Fig.10- Simplified Speed Controller Block Diagram VIII INVERTER-MOTOR EQUIVALENT CIRCUIT The equivalent cuircuitof an inverterused forPMSM speed drive is provided in Fig. 11. (18) Fig. 11- Inverter-motor equivalent circuit The motor voltages provided by the inverter are equivalent to a 3-phase voltage source [50,51] that can be written with a modified expression as: (t) v- (t) v (t)v (t) v- (t) v (t)v (t) v- (t) v (t)v oncnco onbnbo onanao    (19) For a star connected system, the following relationship must be satisfied at all time: 0vvv coboao  (20) Using equations (19) and (20), the null voltage is derived as: )/3vvv(v cnbnanon  (21) The phase voltages collected at the inverter leg are a func- tion of the dc source and the switching time (da,db,dc) as follows: dc . V v db . V v da . V v dccn dcbn dcan    (22) From which the line voltages can be derived as: ) da - dc ( . V v ) dc - db ( . V v ) db - da ( . V v dcca dcbc dcab    (23) With futher derivation, the phase voltages can be written as: PMSM Voltage Source Inverter C u rr e n t C o n tr o l Flux Weakening Constant Torque Ang . PI Control Unit Iabc Id Iq r  r ref r s   1/s Position Estimation Derivative (t) v- (t) v (t)v (t) v- (t) v (t)v (t) v- (t) v (t)v ancnca cnbnbc bnanab    Youakim Kalaani, Rami Haddad, Adel El Shahat/ PMSM Sensorless Speed Control Drive (2014) 137 ) 3 / dc) db (da - dc ( . V v ) 3 / dc) db (da - db ( . V v ) 3 / dc) db (da - da ( . V v dcc dcb dca    (24) The dc-link voltage Vdc,may be obtained using Vsn (maxi- mum phase voltage) as follow [52]: ).sin(. .2 v dc sn V P P    (25) Where Vsn: peak amplitude of phase voltage IX OBSERVER FOR SPEEDESTIMATION A postion-sensorlessPMSM drive makes use of an observer instead of a sensor or encoder to estimate the speed of the motor. This concept is based on the two-axis theory to derive an equivalent quadrature-phase model to represent the three- phase machine. In fact, the d-axis and q-axis currents are related to the actual three-phase stator currents by the fol- lowing transformation: (26) Where (27) Conversion to the new stationary (α-β) frame is also known as Clark Transformation (insert referenc here). Similarly, voltage (Ѵ)and flux linkage (λ)can also be transfered from (a-b-c) frame to (α-β) frame by the following transfor- mations: (28) where T ssss iiii         00  (29) T ssss         00   Thflux linkage is transformed as ms s s iL 00. 0 0       (30) where             0 sin cos 0 0 r r m m      (31) Furthermore, the induced back EMF in the windings of the fictitious quadrature-phase machine can be written as a func- tion of the flux linkages and rotor position (angle) as:               r r mr s s s e e e       cos sin (32) Finally, the stator Iabccurrents can readily be obtained from the Idq0currents by the following reverse transformation: (33) X SIMULINK SIMULATION OF PMSM DRIVE Simulink was chosen from several simulation tools because of its flexibility in working with analog and digital devices. The PMSM drive systempresented in this paper was made of several block diagrams as shown in the following figures using Sumilinkand then connected together to build the whole system. For instance, Idq0 to Iabcreverse transformation block is shown in Fig 12, the vector control reference cur- rent block with PI speed controller depicted in Fig.13, the voltage source inverter shown in Fig. 14, and the sensorless rotor position estimation block is given in Fig 16. The block diagram for the complete PMSM drive system is presented in Fig. 17.For simulation purposes, the voltages are assumed to be the system inputs and the current are the outputs. Clark Transformation blocks with the flux linkages block were simulated to estimate the rotor position and Parks transfor- mation were used for converting Vabc to Vdqo.Also as shown, vector control requires a block for the calculation of the ref- erence current using angle α, rotor position, and the magni- tude of current Is.Inverter action is implemented using refer- ence currents to generate the gate pulses for the IGBTs. Ia =Ib Ic cos  cos ( 120) sin ( 120) sin  cos ( 120) sin ( 120) 1 1 1 Iq Id I0 abcsabc s iTi     . 0 0   ss s s pirv 00. 0 0 .       T ssss vvvv         00  Youakim Kalaani, Rami Haddad, Adel El Shahat/ PMSM Sensorless Speed Control Drive (2014) 138 Fig. 12- Idqo to Iabc Block Fig. 13- Vector Control Reference Current Block with PI Speed Controller Fig. 14- Voltage Source Inverter Fig. 15- PWM current controller block Fig. 16- Rotor Position (Speed Sensorless) Estimation block Fig. 17- Complete speed Sensorless drive system XI SIMULATION RESULTS Simulation results of the PMSM drive systemusing the pro- posed PWM current control scheme are presented in this section. The motor wasruninconstant-torque modebelow its rated speed (what is it?) and in flux-weakening modeabove rated speed.Currents, torques, and speeds were all plotted under these two operation modes. Simulation results are given at motor speeds of 2000 rpm and 2400 rpm respective- ly.As shown in Fig 18 and Fig 26, the motor speed reached the desired spe levels in less than .01s with all oscillation died out within .02s. The steady state error due to a step in- put (reference speed voltage) was shown to be zero. Fig.18- Motor Speed vs time at 2000 rpm Ic Ib Ia I _ c I _ b I _ a Integrator 1 1 s From d - q I to 3 - phase I In 1 I _ a I _ b I _ c (u (1 )* cos (u (3 )-( 2 * pi / 3 ))+ u (2 )* sin (u (3 )-( 2 * pi / 3 ))) f ( u ) (u (1 )* cos ( u ( 3 )+( 2 * pi / 3 ))+ u (2 )* sin (u (3 )+( 2 * pi / 3 ))) f ( u ) (u (1 )* cos ( u ( 3 ))+ u ( 2 )* sin (u (3 ))) f ( u ) In 1i _ q 1 i _ d 2 wr 3 Is Is 5 I*_c 4 I*_b 3 I*_a 2 I_abc _Reference 1 wr_reference -C- u(1)*sin(u(3)+u(2)-2*pi /3) f(u) u(1)*sin(u(3)+u(2)+2*pi /3) f(u) u(1)*sin(u(3)+u(2)) f(u) Reference Iabc Currents In1 I*_a I*_b I*_c PI Controller PI Ki Kp Integrator 2 1 s K Ts z-1 Alfa _Ref pi /2 Error 3 In 1 2 wr 1 Vc 6 Vb 5 Va 4 Vca 3 Vbc 2 Vab 1 u(4)*(u(3)-u(1)) f(u) u(4)*(u(3)-(u(1)+u(2)+u(3))/3) f(u) u(4)*(u(2)-u(3)) f(u) u(4)*(u(2)-(u(1)+u(2)+u(3))/3) f(u) u(4)*(u(1)-u(2)) f(u) u(4)*(u(1)-(u(1)+u(2)+u(3))/3) f(u) Vdc VDC 3 ph Inverter Voltages In 1 Vab Vbc Vca Va Vb Vc In 1 4 dc 3 db 2 da 1 dc 3 db 2 da 1 Signal Generator 2 Signal Generator 1 Signal Generator Relay _a2 Relay _a1 Relay _a i _c 6 i _b 5 i _a 4 i *_c 3 i *_b 2 i *_a 1 Lambda _af .ALFA Lambda _af .BETA gain 2/4 THeTAre f(u) Resistance1 6.8 Resistance 6.8 Integrator 1 1 s Integrator 1 s Inductance 1 -K - Inductance -K - Derivative du /dt 3-phase to ALFA & BETA Voltages In 1 V_ALFA V_BETA 3-phase to ALFA & BETA Currents In 1 I_ALFA I_BETA Iq wr Lambda _af .ALFA Lambda _af .BETA LAMBDA _BETA 3 LAMBDA _ALFA 2 Ns 1 gain 2/4 current in q -axis u(1)/(0.0115 ) current in d -axis f(u) Vdc 1 302 Te Calculation f(u) T _L 1.2 THeTAre f(u) Sign Scope 9 Scope 8 Scope 7 Scope 6 Scope 5 Scope 4 Scope 3 Scope 2Scope 15 Scope 14 Scope 13 Scope 12 Scope 11 Scope 10 Scope 1 Scope Resistance 1 6.8 Resistance 6.8 Relay _a3 Relay _a2 Relay _a Product Mechanical f(u) J -C- Integrator 4 1 s Integrator 2 1 s Integrator 1 1 s Integrator 1 s Inductance 1 -K - Inductance -K - Id 0 Gain 2 -K - Gain 1 4/2 Gain -K - From d -q I to 3-phase I 1 In 1 I_a I_b I_c From d -q I to 3-phase I In 1 I_a I_b I_c From 3-phase to d -q-0 In 1 V_d V_q V_0 Flux in q -axis V_q i_q Lambda_d Omega_r Lambda_q Flux in d -axis V_d i_d Lambda_q Omega_r Lambda_d Discrete PI Controller PI Derivative du /dt Constant 1 -C- Constant -C- ALFA & BETA to D & Q Currents In 1 I _ D I _ Q 3-phase to ALFA & BETA Voltages In 1 V_ALFA V_BETA 3-phase to ALFA & BETA Currents In 1 I_ALFA I_BETA 3 ph Inverter Voltages In1 Vab Vbc Vca Va Vb Vc Time (Sec) S p e e d ( r p m ) Youakim Kalaani, Rami Haddad, Adel El Shahat/ PMSM Sensorless Speed Control Drive (2014) 139 Fig.19 - IabcCurrents vstime at 2000 rpm Fig. 20-IdqCurrents vstime at 2000 rpm Fig.21- Torque vs time at 2000 rpm The 3-phase Iabccurrents drawn by the motor and obtained by Park's reverse transformationare shown for the two speeds in Fig 19 and 27 respectively. The corresponding Idqcurrentsare dispayedin Fig. 20 and 28 in which the value of id in Fig 20 is zero since field oriented control is used. The torqueses developed by the motor were also shown in Fig. 21 and 29 where thestarting torque is almosttwice the steady state or rated torque value. Fig 22- Iabc Reference Currents vstime at 2000 rpm Fig23- Inverter Phase (a) Pulses vs time at 2000 rpm Fig 24- Speed Error vs time at 2000 rpm Fig 25 - Phase (a) Voltage vs time at 2000 rpm Reference currentsobtained by this type of control are shown in Fig 22 and 30. Phase (a) inverter pulse, speed, error, and inverter phase (a) voltage for 2000 rpm speed are presented in Fig 23, 24 and 25respectively. And those for 2400 rpm speed are displayed in Fig 30, 31, and 32. Fig 26- Motor Speed vs time at 2400 rpm Fig 27- IabcCurrents vstime at 2400 rpm Fig 28-IdqCurrents vs time at 2400 rpm Time (Sec) T o r q u e ( N .m ) Time (Sec) Ia b c R e fe r e n c e ( A m p ) Time (Sec)I n v e rt e r P h a s e ( a ) P u ls e s Time (Sec) S p e e d E rr o r (r a d /s e c ) Time (Sec) P h a s e ( a ) In v e r te r V o lt a g e ( V ) Time (Sec) S p e e d ( rp m ) Time (Sec) Ia b c C u r r e n ts ( A m p .) Time (Sec) Id q C u r r e n t s ( A m p .) Id Iq Youakim Kalaani, Rami Haddad, Adel El Shahat/ PMSM Sensorless Speed Control Drive (2014) 140 Fig. 29- Torque vs time at 2400 rpm Fig 30- Iabc Reference Currents vs time at 2400 rpm Fig 31-Inverter Phase (a) Pulses vs time at 2400 rpm Fig 32-Speed Error with time at 2400 rpm FiFig 33- Phase (a) Voltage vs time at 2400 rpm It should be noted thatnegative speed was observed in Fig 26 due to the speed acceleration effects which make the ma- chinerunas a generator at first before rurningas a mo- tor.Without flux weakening, the torque was also observed torapidlydecrease to zero with increasing speed above the rated speed and briefelyturnednegativein response to sudden variations in the dc bus voltage. This mode of operation is unstable since the machine drive is out of control at thattime. This can be resolved by fluxweakeningwhich can en- sureproper control in the whole speed and volt- agerange.Furthermore, the negative effect ofthe pure feed- back control could be avoided by torquesetpoint rate limita- tion which is necessary to limit increase in acceleration an- yway. V CONCLUSION Although a conclusion may review the main points of the paper, do not replicate the abstract as the conclusion. A con- clusion might elaborate on the importance of the work or suggest applications and extensions. Authors are strongly encouraged not to call out multiple figures or tables in the conclusion—these should be referenced in the body of the paper. REFERENCES [1] B. Cui, J. Zhou, and Z. Ren, "Modeling and simulation of permanent magnet synchronous motor drives," 2001. [2] C. Mademlis and N. Margaris, "Loss minimization in vector-controlled interior permanent-magnet syn- chronous motor drives," Industrial Electronics, IEEE Transactions on, vol. 49, pp. 1344-1347, 2002. [3] X. Jian-Xin, S. K. Panda, P. Ya-Jun, L. Tong Heng, and B. H. Lam, "A modular control scheme for PMSM speed control with pulsating torque minimization," Industrial Electronics, IEEE Transactions on, vol. 51, pp. 526-536, 2004. [4] R. Gabriel, W. Leonhard, and C. Nordby, “Field oriented control of standard AC motor using microproces- sor,” IEEE Trans. Ind. Applicat., vol. IA-16, pp. 186–192, 1980. [5] L. Harnefors, “Design and analysis of general rotor-flux oriented vector control systems,” IEEE Trans. Ind. Electron., vol. 48, pp. 383–389, Apr. 2001. [6] M. Schroedl, “Sensorless control of AC machines at low speed and standstill based on the “INFORM” method,” in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 1, 1996, pp. 270–277. [7] P. L. Jansen and R. D. Lorentz, “Transducerless position and velocity estimation in induction and salient AC machines,” IEEE Trans. Ind. Applicat., vol. 31, pp. 240–247, Mar./Apr. 1995. [8] P. L. Jansen, R. D. Lorenz, and D. W. Novotny, “Observ- er-based direct field orientation: Analysis and com- parison of alternative methods,” IEEE Trans. Ind. Applicat., vol. 30, pp. 945–953, July/Aug. 1994. [9] T. M. Jahns and V. Blasko, “Recent advances in power electronics technology for industrial and traction machine drives,” Proc. IEEE, vol. 89, pp. 963–975, June 2001. [10] Thomas M. Jahns, “Motion control with permanent- magnet ac machines,” in Proc. IEEE, vol. 82, Aug. 1994, pp. 1241-1252. [11] L. Xu, L. Ye, L. Zhen and A. El-Antably, “A new design Time (Sec) E le c t. T o r q u e ( N .m ) Time (Sec) R e fe r e n c e C u r r e n ts (A m p .) Time (Sec) P h a s e ( a ) In v e rt e r P u ls e s Time (Sec) S p e e d E rr o r (r a d /s e c ) Time (Sec) P h a s e ( a ) In v e r te r V o lt a g e ( V ) Youakim Kalaani, Rami Haddad, Adel El Shahat/ PMSM Sensorless Speed Control Drive (2014) 141 concept of permanent magnet machine for flux weakening operation,” IEEE Trans. Ind. Applicat., vol. 31, pp. 373-378, March/April, 1995. [12] J. A. Tapia, F. Leonardi, and T. A. Lipo, “Consequent- pole permanent-magnet machine with extended field-weakening capability,” IEEE Trans. Ind. Ap- plicat.,vol. 39, pp. 1704-1709, Nov./Dec., 2003. [13] W. L. Soong and T. J. Miller, “Field-weakening perfor- mance of brushless synchronous AC motor drives,” Proc. IEE—Elect. Power Applicat., vol. 141, no. 6, pp. 331–340, Nov. 1994. [14] S. R. Macminn and T. M. Jahns, “Control techniques for improved high-speed performance of interior PM synchronous motor drives,” IEEE Trans. Ind. Applicat., vol. 2, pp. 997-1004, Sept./Oct. 1991. [15] T. Sebastian and G. R. Slemon, “Operating limits of inverter-driven permanent magnet motor drives,” IEEE CH2272-3/86, pp. 800-805, 1986. [16] R. Dhaouadi and N. Mohan, “Analysis of current- regulated voltage-source inverters for permanent magnet synchronous motor drives in normal and extended speed ranges,” IEEE Trans. Energy Conv., vol. 5, pp. 137-144, Mar. 1990. [17] S. Morimoto, M. Sanada and K. Takeda, “Wide-speed operation of interior permanent magnet synchro- nous motors with high-performance current regula- tor,” IEEE Trans. Ind. Applicat., vol. 30, pp. 920- 926, July/Aug. 1994. [18] S. Morimoto, Y. Takeda, T. Hirasa, and K. Taniguchi, “Expansion of operating limits for permanent mag- net by current vector control considering inverter capacity,” IEEE Trans. Ind. Applicat., vol. 26, pp. 866-871, Sept./Oct. 1990. [19] S. D. Sudhoff, K. A. Corzine and H. J. Hegner, “A flux- weakening strategy for current-regulated surface- mounted permanent-magnet machine drives,” IEEE Trans. Energy Conv., vol. 10, pp. 431-437, Sept. 1995. [20] Y. Sozer and D. A. Torrey, “Adaptive Flux weakening control of permanent magnet synchronous motors,” in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 1, St. Louis, MO, 1998, pp. 475–482. [21] Y. S. Kim, Y. K. Choi and J. H. Lee, “Speed-sensorless vector control for permanent-magnet synchronous motors based on instantaneous reactive power in the wide-speed region,” IEE Proc-Electr. Power Appl., vol. 152, No. 5, pp. 1343-1349, Sept. 2005. [22] J. M. Kim and S. K. Sul, “Speed control of interior permanent magnet synchronous motor drive for the flux weakening operation,” IEEE Trans. Ind. Ap- plicat., vol. 33, pp. 43-48, Jan./Feb. 1997. [23] J. H. Song, J. M. Kim, and S. K. Sul, “A new robust SPMSM control to parameter variations in flux weakening region,” IEEE IECON, vol. 2, pp. 1193- 1198, 1996. [24] J. J. Chen and K. P. Chin, “Automatic flux-weakening control of permanent magnet synchronous motors using a reduced-order controller,” IEEE Trans. Power Electron., vol. 15, pp. 881-890, Sept. 2000. [25] A. Consoli, G. Scarcella and A. Testa, “Industry appli- cation of zero-speed sensorless control techniques for PM synchronous motors,” IEEE Trans. Ind.Applicat., vol. 37, pp. 513-521, March/April, 2001. [26] M. Tursini, R. Petrella and F. Parasiliti, “Initial rotor position estimation method for PM motors,” IEEE Trans. Ind. Applicat., vol. 39, pp. 1630-1640, Nov./Dec., 2003. [27] F. J. Lin and S. L. Chiu, “Adaptive fuzzy sliding mode control for PM synchronous servo motor drives,” Proc. IEE—Contr. Theory Applicat., vol. 145, no. 1, pp. 63–72, 1998. [28] E. Cerruto, A. Consoli, A. Raciti, and A. Testa, “A ro- bust adaptive controller for PM motor drives in ro- botic applications,” IEEE Trans. Power Electron., vol. 10, pp. 62-71, Jan. 1995. [29] K. J. Åström and B. Wittenmark, “A survey of adaptive control applications,” in Proc. 34th IEEE Conf. De- cision and Control New Orleans, LA, 1995, pp. 649-654. [30] I. C. Baik, K. H. Kim, and M. J. Youn, “Robust nonlin- ear speed control of PM synchronous motor using adaptive and sliding mode control techniques,” Proc. IEE—Elect. Power Applicat., vol. 145, no. 4, pp. 369–376, 1998. [31] Alireza Rostami and Behzad Asaei, “A novel method for estimating the initial rotor position of PM mo- tors without the position sensor,” Energy Conver- sion and Management, Vol. 50, (2009), pp. 1879– 1883. [32] M.S. Merzoug and H. Benalla, “Nonlinear Backstep- ping Control of Permanent Magnet Synchronous Motor (PMSM),” International Journal of Systems Control (Vol.1-2010/Iss.1, ),pp. 30-34. [33] Jinpeng Yu, Junwei Gao, Yumei Ma, and Haisheng Yu, “Adaptive Fuzzy Tracking Control for a Permanent Magnet Synchronous Motor via Backstepping Ap- proach,” Mathematical Problems in Engineering, Hindawi Publishing Corporation, Volume 2010, Ar- ticle ID 391846. [34] H.M. Hasanien, “Torque ripple minimization of perma- nent magnet synchronous motor using digital ob- server controller,” Energy Conversion and Man- agement, Volume 51, issue 1 (January, 2010), pp. 98-104 [35] Li Dong, Wang Shi-Long, Zhang Xiao-Hong and Yang Dan, “Impulsive control for permanent magnet synchronous motors with uncertainties: LMI ap- proach,” Chinese Physics B, Vol.19,Issue1,pp.010506-7(2010). T. Markvart and L. Castaner, Practical Handbook of Photovoltaics, Fundamentals and Applications. Elsevier, 2003. [36] R. Gabriel, W. Leonhard, and C. Nordby, “Field orient- ed control of standard ACmotor using microproces- sor,” IEEE Trans. Ind. Applicat., vol. IA-16, pp. 186–192,1980. Youakim Kalaani, Rami Haddad, Adel El Shahat/ PMSM Sensorless Speed Control Drive (2014) 142 [37] L. Harnefors, “Design and analysis of general rotor-flux oriented vector controlsystems,” IEEE Trans. Ind. Electron., vol. 48, pp. 383–389, Apr. 2001. [38] M. Schroedl, “Sensorless control of AC machines at low speed and standstill basedon the “INFORM” method,” in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 1, 1996,pp. 270–277. [39] P. L. Jansen and R. D. Lorentz, “Transducerless posi- tion and velocity estimation in induction and salient AC machines,” IEEE Trans. Ind. Applicat., vol. 31, pp. 240–247, Mar./Apr. 1995. [40] P. L. Jansen, R. D. Lorenz, and D. W. Novotny, “Ob- server-based direct fieldorientation: Analysis and comparison of alternative methods,” IEEE Trans. Ind.Applicat., vol. 30, pp. 945–953, July/Aug. 1994. [41] T. M. Jahns and V. Blasko, “Recent advances in power electronics technology for industrial and traction machine drives,” Proc. IEEE, vol. 89, pp. 963–975, June2001. [42] Thomas M. Jahns, “Motion control with permanent- magnet ac machines,” in Proc. IEEE, vol. 82, Aug. 1994, pp. 1241-1252. [43] R. Krishnan, Electric Motor Drives: Modeling, Analysis & Control, Prentice Hall, 2006. [44] H. M. El Shewy, F. E. Abd Al Kader, M. El Kholy, and A. El Shahat,“ Dynamic Modeling of Permanent Magnet Synchronous Motor Using MATLAB - Simulink” EE108, 6th International Conference on Electrical Engineering ICEENG 6, 27-29 May 2008, Military Technical College, Egypt . [45] Adel El Shahat, and Hamed El Shewy, “Permanent Magnet Synchronous Motor Dynamic Modeling” Paper ID: X305, 2nd International Conference on Computer and Electrical Engineering (ICCEE 2009); Dubai, UAE, December 28 - 30, 2009. [46] Adel El Shahat, Hamed El Shewy, “PM Synchronous Motor Dynamic Modeling with Genetic Algorithm Performance Improvement”, International Journal of Engineering, ISSN 2141-2839 (Online); ISSN 2141-2820 (Print); Science and Technology Vol. 2, No. 2, 2010, pp. 93-106. [47] B. K. Bose, Power Electronics and Variable Frequency Drives, 1 ed: Wiley, John & Sons, 1996. [48] R. Krishnan, Electric Motor Drives Modeling, Analysis, and Control, Pearson Education, 2001. [49] X. Junfeng, W. Fengyan, F. Jianghua, and X. Jianping, "Flux-weakening control of permanent magnet syn- chronous motor with direct torque control consider- ation variation of parameters," Industrial Electron- ics Society, IECON 2004. 30th Annual Confer- ence of IEEE, Vol. 2, pp. 1323- 1326, 2004 [50] Kazmierkowski M.P., Tunia H.: Automatic Control Of Converter-Fed Drives, Elsevier Science & Technol- ogy (United Kingdom), 1994 [51] Ned Mohan, Tore M. Undeland and William P. Rob- bins, Power electronics, Converters, Applications and Design, Third Edition, USA ISBN 0-471- 22693-9, John Wiley & Sons, Inc. [52] A. Munoz-Garcia and D. W. Novotny, “Utilization of Third Harmonic-Induced-Voltages in PM Genera- tors,” Industry Applications Conference, 1996. Thirty-First IAS Annual Meeting, IAS apos;96., Vol. 1, 6-10 Oct 1996, Page(s):525 – 532. http://datamining.it.uts.edu.au/conferences/wi08/ http://ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=9792 http://ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=9792 http://ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=9792