modeling+and+simulation

SPEEDAM2006International Symposium on Power Electronics,Electrical Drives, Automation and MotionModeling and Simulation of Sensorless Controlof PMBLDC MotorUsing Zero-Crossing Back E.M.F DetectionR. Somanatham, P. V. N. Prasad, A. D. RajkumarDepartment of Electrical Engineering, University College of EngineeringOsmania University, Hyderabad – 500 007, A.P. (India)Abstract--In the present scheme, modeling and simulation of sensorless control of Permanent Magnet Brushless DC (PMBLDC) motor is carried out using zero-crossing back e.m.f technique. Since the neutral point of star connected machine is floating and not accessible to detect zero-crossing points, line back e.m.f information is considered. The motor is commutated at zero-crossing point of back e.m.f at 00 delay (no delay), 18.50 delay and 280 delay instants of commutation from zero-crossing point of line back e.m.f signals. The various waveforms like line back e.m.f, phase currents, rotor position, speed, torque with respect to time at no-load, half-load and full-load are obtained. From the results it is observed that the torque developed by the motor at larger delay angles is more pulsating due to more peak to peak currents.I ndex Terms--Brushless machines, Inverters, Permanent magnet motors, Zero-crossingI.INTRODUCTIONThe latest advances in permanent magnet materials, solid-state devices and micro-electronics have contributed to new energy efficient electric drives which use Permanent Magnet Brushless DC motors. These motors have higher efficiency, better power factor, better dynamic performance and better output power per unit mass & volume than cage Induction motors without sacrificing the reliability [1]. Because of these reasons PMBLDC motors are extensively used in wide range of applications including information technology equipment such as, computers, printers & scanners, household appliances, aerospace, electric vehicles, robotics etc.There are two methods of controlling PMBLDC motors namely sensor control and sensorless control. The later can be preferred due to advantages like cost reduction, reliability improvement, elimination of difficulty in maintaining the sensors etc. The sensorless mode of control is highly advantageous if the motor is operating in dusty or oily environments, where occasional cleaning of Hall sensors is required for proper sensing of rotor position [2]. The sensorless method can also be adopted if the motor is mounted in a less accessible location. Further, in the motors rated below one-watt This work was supported by Technical Education & Quality Improvement Programme (TEQIP) of Ministry of Human Resources & Development, Govt. of India. rating, the power consumption by the position sensorscan substantially reduce the motor efficiency and in compact units such as computer hard disk drives it may not be possible to accommodate position sensors.A sensorless operation of a PMBLDC motor using zero-crossing back e.m.f technique is modeled and simulated using Simulink. The responses of line backe.m.fs, phase currents, speed, rotor position and torqueare obtained and analyzed for different delay angles at different load torques from no-load to full-load.II. SENSORLESS ROTOR POSITION DETECTIONThe rotor position information of the PMBLDC motorcan be obtained using anyone of the four techniques outlined in [1,3,4]. They are: (a) Detection of the backe.m.f (zero-crossing approach, phase locked loop technique, e.m.f integration approach) (b) Detection of stator third harmonic voltage (c) Detection of conducting interval of free-wheeling diodes connected in anti-parallelwith the solid-state switches (d) Monitoring the inductance variation in the d-q axes.The magnitude and polarity of line back e.m.fs changeat the instant of commutation. The zero-crossing of thesee.m.fs give specific instants of commutation and can be used in the same way as Hall-effect sensor signals to switch the devices in a particular sequence in power inverter. Since the neutral point of the machine is floatingand not accessible, it is better to use the line back e.m.f information to switch the devices. Each transition occursat every 60 electrical degrees and thus there are six commutation instants in one cycle.The reliability of this method depends on the measured signals. Since the back e.m.f varies with the speed, the method is suitable only when a minimum speed of about5% of the rated speed is achieved. Hence, during startingthe motor operates in open loop mode and is driven bythe inverter which operates in 1200 conduction mode. When the motor reaches the minimum speed to facilitate zero-crossing detection of back e.m.f, the control is shifted to zero-crossing detection circuit and the drive operates in the closed loop mode.The sequence of operation of the motor during startingand running periods can be seen in the block schematic diagram as shown in Fig. 1.III. MODELING AND OPERATIONA .AssumptionsThe assumptions made for the development ofPMBLDC motor model are: (a) Induced currents in therotor due to stator are neglected (b) Iron and stray lossesare neglected (c) Three phase star connected motor isconsidered.B .Simulink ModelSimulink model [3,5,6] of s ensorless controlPMBLDC motor is shown in the Fig.2. The important blocks for the sensorless operation are: (a) PMBLDC motor (b) Zero-crossing detection circuit (c) Logical Inverter (d) 1200 Inverter block (e) Changer block (f) Timer (g) Load and (h) Reset controllerThe PMBLDC motor model is developed based on the state-space form [2]Bu Ax x x(1)where,>@T C B A I I I x T Z (2) >@TL C B A T V V V u (3) and A & B are state-space matrices. V A,V B & V C are the impressed voltages on the motor windings and T L is the external load torque on the motor. The voltages are generally derived from the Simulink sources. The state-space model calculates the line currents I A,I B & I C,the speed Ȧ (radians/sec) and the rotor position ș (radians), the phase back e.m.fs E A,E B & E C , the friction faced by the motor and the neutral voltage. The Reset controller is generally used to reset the elements of the matrices A and B in the state-space model.Zero-crossing detection block is used to determine the instants of line back e.m.fs, which can be used for commutating the currents in the PMBLDC motor. It is also used for developing the delays in the instants ofcommutations. Based on these signals the Logicalinverter is operated. The Logical inverter operates onlywhen it is possible to detect the back e.m.fs. Since, backe.m.f is a function of speed of the motor, at the instant ofstarting and during starting period its value is very less. Hence the motor is fed from 1200Inverter block during starting period. The 1200Inverter block operates for a given threshold time by the end of which the developed back e.m.f can be easily sensed. This threshold time is set by the Timer block. After the threshold time, the Changer block feeds the phase voltages developed by the Logicalinverter through the driver circuits to the motor. A step load torque is applied to the motor and its value dependson load applied to the motor. C .SimulationThe PMBLDC motor is simulated for different instants of commutation. The instants of commutation are no-delay, 18.50 delay and 280delay from the instant of zero-crossing points. At no-load, half-load and full-load of themotor, simulation is carried out for the above delays andthe various plots are obtained. A step load torque is applied to the motor at 0.05 sec. The specifications of motor and inverter are given in Appendix.The waveforms of line back e.m.f’s (E) with zero-crossing detection and commutation signals, speed(N rpm), line currents (I), rotor position and torque at no-load for 00 delay and 280delay angles are shown in Fig.3 and Fig.4 respectively. The respective waveforms at full-load for the same delay angles are shown in Fig.5 andFig.6. Fig.1: Block Schematic Diagram of Sensorless Operation of PMBLDC MotorF i g .2: S i m u l i n k M o d e l o f S e n s o r l e s s C o n t r o l P M B L D C M o t o rI AI B (A) I C ș (rad.)Fig.3b: Phase currents & Rotor position plotsat No-Load & No DelayI A I B (A) (rad.)T o r q u e ( N -m )Time (sec)Fig.4c. Torque at No-Load &28 Deg. DelayE AB E BC(V)E CAN (rpm)E AB E BC (V) E CAN (rpm)Fig.4a: Line back e.m.fs & Speed plotsat No-Load & 28 Deg. DelayTime (sec)Time (sec)Fig.3c. Torque at No-Load &No DelayTime (sec)T o r q u e ( N -m )T o r q u e (N .m )Fig.5c: Torque at Full-Load & No delayo r q u e (N .m )Time (sec)Fig.6c: Torque at Full-Load & 28 Deg. delayI AI B (A) I C ș (rad.)Fig.5b: Phase currents & Rotor position atFull-Load & No delayTime (sec)I A I B (A) I Cș (rad.)Fig.6b: Phase currents & Rotor position atFull-Load & 28 Deg. delayTime (sec)E ABE BC (V) E CA N (rpm)Fig.6a: Line back e.m.fs & Speed plots atFull-Load & 28 Deg. delayTime (sec)E ABE BC (V)E CA N (rpm)Fig.5a: Line back e.m.fs & Speed plots atFull-Load& No delayTime (sec)IV. RESULTS AND ANALYSIS At no-load, a marginal increase in speed ripple (N p ) is observed as the delay angle is increased from 00 to 280.But the steady-state speed is reached in nearly half of the time taken for 00 delay operation. At larger delay angles, the decrease in frequency (f) is characterized by decrease in line back e.m.f and speed. These are evident from Fig.3a and Fig.4a. Also, the peak current (I p ) is increased by more than 1.8 times as shown in Fig.3b and Fig.4b. The torque ripple (T rp ) is found to be increased by more than four times, though the initial peak torque is same in both cases of delay angles. This can be observed in Fig.3c and Fig.4c.At full-load, there is an increase in speed ripple and no change in time of steady-state speed (t SS ) for the same change in delay angle. These responses can be seen from Fig.5a and Fig.6a. The change in frequencies of phase currents and rotor position can be observed when a step load is applied to the motor. This is in agreement with drop in speed and fall in slope of rotor position with load. The peak current is increased by more than 1.4 times. Fig.5a & Fig.5b and Fig.6a & Fig.6b match with these conclusions. The torque ripple is found to be non-uniform and increased by more than four times, when the delay angle is increased as shown in Fig.5c and Fig.6c. At any load, the high frequency pulsating torques are due to the presence of sixth harmonic torque components.The peak values of back e.mfs (E p ) are also obtained. These variations are in same proportion with the variations of frequencies. The performance of the motor at different loads is summarized as shown in Table I.TABLE IPERFORMANCE ANALYSISNo-LoadS.No. 00 Delay 18.50 Delay 280 Delay1. t SS (sec.) 0.10 0.08 0.05 2. N p (rpm) 0 17.0 34.03. f (Hz.) 80.0 60.0 53.34. N (rpm) 2400 1800 1600 5. E p (V) 25.0 18.5 17.0 6. I p (A) 14.0 20.5 25.5 7. T rp (N.m) 0.18 0.620.79 Half-Load1. t SS (sec.) 0.15 0.15 0.152. N p (rpm) 0 17.0 35.03. f (Hz.) 67.4 50.0 42.94. N (rpm) 2022 1500 1286 5. E p (V) 20.5 16.0 13.5 6. I p (A) 17.5 25.0 27.5 7. T rp (N.m) 0.19 0.660.98 Full-Load1. t SS (sec.) 0.15 0.15 0.15 2. N p (rpm) 0 39.0 77.03. f (Hz.) 53.5 41.9 36.04. N (rpm) 1603 1257 1081 5. E p (V) 17.0 13.0 11.5 6. I p (A) 20.5 27.5 29.5 7. T rp (N.m) 0.22 0.771.03V. CONCLUSIONSModeling and simulation of a sensorless controlled Permanent Magnet Brushless DC motor is carried out at different loads. Initially the stator windings of the motor are excited with an inverter which operates in 1200 mode conduction for a threshold period. When the motor reaches the minimum speed to facilitate zero-crossing detection of back e.m.f, the control is transferred to zero-crossing detection circuit. Then, a closed loop operation is carried out where a pair of stator windings of the motor is excited by the logical inverter. The main advantage of the present scheme is that the sensorless operation can be easily implemented without the neutral point. At any load, as the delay angle increases, the speed, frequency & back e.m.f decease and speed ripple, current & torqueripple increase. At any delay angle, as the load increases,the response of the motor is similar. The torque pulsations are uniform for no-delay and become non-uniform and more at higher delay angles.APPENDIXA. PMBLDC Motor Specifications:Voltage: V = 40.0 V Current: I = 17.4 A Torque: T = 0.90 N.m Self inductance of the winding: l = 2.72 mH Mutual inductance of the winding: M = 1.5 mH Back e.m.f constant: ke = 0.5128V/rad/sec Torque constant : kt = 0.049N-m/A Motor inertia: j = 0.0002 kg-m 2Winding resistance/phase: r = 0.7 :Motor damping constant: d = 0 N.m/rad/sec Number of poles: p = 4 Initial angular displacement: T = 0 rad. B. Three-Phase Inverter:Input DC Voltage: 160 V, No. of switches: 6ACKNOWLEDGEMENTThe authors express their sincere thanks to the Principal, University College of Engineering, Osmania University for continuous encouragement.REFERENCES[1] Jacek F. Gieras, Mitchell Wing: Permanent MagnetMotor Technology Design and Applications , Marcel Decker, Inc, 2002[2] 2003 Microchip Technology Inc., pp13[3] R.Krishnan: Electric Motor Drives Modeling,Analysisand Control, Prentice Hall of India Private Limited, New Delhi, 2002, pp 578-580. [4] G.K.Dubey: Power Semiconductor Control Drives ,Prentice-Hall, Eaglewood Cliffs, 1989 [5] Chee-Mun Ong: Dynamics of Electrical Machinery UsingMATLAB/ SIMULINK , Prentice Hall PTR, 1998 [6] MATLAB 6.5, The Mathworks Inc., 2002。