AbstractâThis paper describes a simple way to control the. Brush Less DC Motor (BLDCM) for electrical applications. To control this machine it is ge...

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Sensorless Speed Control of Brushless DC Motor with Fuzzy Based Estimation B. Mahesh Kumar, G. Ravi, and R. Chakrabarti

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trapezoidal electromotive force and quasi-rectangular current waveforms. Normally, sensors are used for the estimation of the speed and position of brushless DC motor. Due to increase in cost of the sensor and less reliability, the sensorless operation of brushless DC motor has attracted wide attention in industries. In recent years, many sensorless drive methods have been proposed for improving the performance of BLDC motors without a position sensor [2]-[6]. However, the existing sensor less drive methods of the BLDC motor which are being widely used now, have low performance in a transient state or low speed range and occasionally require additional circuits. To overcome this problem, the estimation of a back-EMF is carried out by fuzzy logic techniques to improve the performance of the system. This method proposes fuzzy back-EMF observer based on fuzzy function approximation and system state equation of the BLDC motor. Here, the fuzzy logic technique is used to estimate the speed of the BLDC motor under a variable and fixed condition of back-EMF. Therefore, the correct back-EMF estimation senses the position and speed of the BLDC motor. This method can estimate the speed of the rotor continuously at transients as well as steady state even with changes in the external condition. Recently, DC motors have been gradually replaced by BLDC motors as industrial applications require more powerful actuators in small sizes. Elimination of brushes and commutators also solves the problem associated with contacts and gives improved reliability and enhances life. The BLDC motor has low inertia, large power to volume ratio, and low noise when compared to the permanent magnet DC servo motor [7], [8] having the same output rating. Therefore, high-performance BLDC motor drives are widely used for variable speed drive systems of industrial applications. In case of the control of robot arms and tracking applications with lower stiffness, the gain of the speed controller, seen from the system stability point of view, is very large and hence difficult to be designed. The PI controller is usually employed in a BLDC motor control, which is simple in realization. In this work, input to the PI control is from the fuzzy based estimation of speed and rotor position, which is also verified with the sensor output for its correctness.

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Abstract—This paper describes a simple way to control the Brush Less DC Motor (BLDCM) for electrical applications. To control this machine it is generally required to measure the speed and position of rotor by using the sensor because the inverter phases, acting at any time, must be commutated depending on the rotor position. The position sensors make the motor system more complicated and mechanically unreliable. A method for the estimation of the speed and rotor position of a BLDCM is presented in this work. Fuzzy based Back EMF observer is employed to estimate the speed by using measurements of the stator line voltage and line current. Most existing sensorless methods of the BLDC motor have low performance at transients or low speed range and occasionally require an additional circuit. To overcome this problem, the estimation of a back-EMF is carried out by fuzzy logic techniques to improve the performance of the system. This method proposes back-EMF observer based on fuzzy function approximation and the system state equation of the BLDC motor. The fuzzy logic technique is used to estimate the speed of the BLDC motor under variable and fixed condition of the back-EMF. Finally, the speed is controlled by using Proportional-Integral (PI) Controller with the help of fuzzy based estimation of the speed and rotor position. Here, fuzzy based estimation of speed and rotor position which is also verified with the sensor, feeds input to the PI controller which does really well for good performance.

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Index Terms—Brushless DC motor, sensorless system, speed control, fuzzy logic technique.

I. INTRODUCTION

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brushless DC motor has been used in many applications such as appliances, computers, automatic office machines, robots for automation of manufacturing products, drives of many electronics and minuteness machines. The BLDC motor has several advantages of the DC motor such as simple control, high torque, high efficiency and compactness. Also, brush maintenance is no longer required, and many problems resulting from the mechanical wear of brushes and commutators are eliminated by electronic commutation. To replace the function of commutators and brushes, the BLDC motor [1] requires an inverter and a position sensor that detects rotor position for proper commutation of current. Efforts have been made to make this motor cost effective and reliable by avoiding the use of position sensors and employing estimators. The brushless DC motor has

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Manuscript received November 25, 2007; revised April 6, 2008. B. Mahesh Kumar and G. Ravi. are with the Pondicherry Engineering College, Pondicherry, India. (e-mail: [email protected], [email protected]). R. Chakrabarti is with Jadavpur University, Kolkata India. (e-mail: [email protected]). Publisher Item Identifier S 1682-0053(09)1667

II. MODELING OF THE BLDC MOTORDRIVE SYSTEM Many papers have been published on modeling of brushless dc motor [9], [10]. Fig. 1 shows the overall system configuration of the three phase BLDC motor drive. The PWM inverter topology is designed for a sixswitch voltage-source configuration with constant dc-link voltage (Vd), which is identical to the induction motor drives and the permanent magnet ac motor drives.

1682-0053/09$10 © 2009 ACECR

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v as

Rs

0

0

i as

L

v bs

0

Rs

0

i bs

v cs

0

0

Rs

i cs

0 0

M L

0

0

i as

eas

M 0 L

0 P i bs M i cs

ebs

(5)

ecs

The electromagnetic torque is given by Te

[e as i as

e bs i bs

e cs i cs ]

1

(6)

m

The equation of motion for a simple system with inertia J , friction coefficient B , load torque T l , electromagnetic torque T e and mechanical speed m is J

d

M

dt

B

m

(7)

(T e T l )

v a , v b and v c are phase voltages; R s is the stator resistances per phase; i a , i b , and i c are phase currents; La , Lb , and Lc are phase inductances and considered to be equal to L ; e a , e b , and e c are phase back EMFs and m is rotor speed.

0 Rs 0

0 0 Rs

i as Laa i bs + Lba i cs Lca

Lab Lbb Lcb

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v as Rs v bs = 0 0 v cs

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The analysis is based on the following assumption for simplification: The motor is not saturated. Stator resistances of all the windings are equal and self and mutual inductances are constant. Power semiconductor devices in the inverter are ideal. Iron losses are negligible. Among the above-mentioned assumptions, the iron loss can be approximated using empirical equations, and the dynamic characteristics of the switching devices need to be considered for the investigation of the transient state behavior. Generally, the BLDC motor drive system can be modeled as an electrical equivalent circuit that consists of a resistance, an inductance and back-EMF per phase. The drive system and electrical equivalent circuit are shown in Figs. 1(a) and 1(b). Generally the model is expressed in stator reference frame with the following assumptions. The effects of saturation in the magnetic paths of the machine is neglected, Stator inductance is assumed to be constant, Rotor speed deviation is negligible. d r / dt 0 . The coupled circuits of the stator windings in terms of the electrical constants are

Fig. 2. Conventional speed control of PMBLDC motor with sensor.

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(a) (b) Fig. 1. (a) Configuration of BLDC motor drive system, and (b) Equivalent circuit model.

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Lac i as e as Lbc p i bs + ebs (1) Lcc i cs ecs

The stator resistance per phase is assumed to be equal for all three phases. The induced back EMF is assumed to be trapezoidal and derived as E p = p m where E p is the peak value, m is the angular velocity and p is the flux linkages of a non-salient rotor. Assuming three phases are symmetric, the following equations are obtained. Laa

Lbb

Lcc

L

(2)

Lab

Lbc

Lca

M

(3)

Substituting (2) and (3) in (1), BLDC model is obtained as v as

Rs

0

0

i as

L

M

v bs

0

Rs

0

i bs

v cs

0

0

Rs

i cs

M M

L M P i bs M L i cs

M

i as

e as ebs (4) ecs

The stator phase currents are constrained to be i as i bs i cs 0 which lead to the simplification of the inductance matrix in the model as

III. CONVENTIONAL CONTROLLER WITH SENSOR In the past, very few papers only have reflected on design analysis and control strategy of brushless dc motor [11]-[13]. It is interesting to note that more than half of the industrial controllers in use today utilize PID or modified PID control schemes. Many different types of tuning rules have been proposed in the literature. Using these tuning rules, delicate and fine tuning of PID controllers can be made on-site. Automatic tuning methods have also been developed and some of the PID controllers may possess on-line automatic tuning capabilities. The usefulness of PID controls lies in their general applicability to most control systems. The measurement of speed is more important as it is really a base for the driver circuit. Currently sensors are used to feedback the speed to the PI controller which in turn decides the actual speed to be closer to the reference or set value. Based on the feedback signal, this driver will decide the switching time and frequency of the supply to BLDC motors. As the PI controller is easy to implement and cheaper, it is widely used. Sensors that are used should be reliable, of low cost and high sensitivity. The conventional method of controlling the speed with sensor is shown in Fig. 2. A. Design of PI Controller Using Ziegler-Nichols Method: Step 1: The process setup: Speed and current feedback should be from the respective drive.

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MAHESH KUMAR et al.: SENSORLESS SPEED CONTROL OF BRUSHLESS DC MOTOR WITH FUZZY BASED ESTIMATION

Fig. 3. Open loop setup.

Fig. 5. Block diagram of the fuzzy back EMF observer.

Controller Structure P PI

Proportional Gain ( K p ) T /L 0.9T / L

Integral Time Constant ( T i ) L / 0.3

Derivative Time Constant ( T d ) -

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Step 2: Apply the step input: Unit step input should be given to the reference speed as shown in Fig. 3. Step 3: Obtain the S-like curve: After applying unit step input open loop response should be observed. It should be in the shape of S like curve and it should settle at steady state. If it is not satisfying the above criteria the method is not valid for that plant. Step 4: Calculation of the PI parameters: From the response, the value of L and T are obtained by drawing tangent at inflection point of S like curve as shown in the Fig. 4. From the controller parameter given in Table I the value of proportional gain and integral gain are calculated. The values of L and T for this machine drive is: L 0.006 sec, T 0.061 sec, K p 0.9T / L 9.15 . Ti L / 0.3 0.02 , and Integral gain K i K p / T i 9.15 / 0.02 457.5 . Using a conventional PI controller, the speed of the motor is controlled to any desired value. The values of PI controller are designed by Ziegler Nichols’ method. Then controller gains which are obtained by using the relevant formulae are K p 9.15, K i 457.53 . From this gain, it has been tuned to give better performance and reached at the final value of K p 9.25, K i 463.5 .

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TABLE I CONTROLLER PARAMETER

theory, deals with uncertain or imprecise situations. In designing a Fuzzy Logic Controller (FLC), the derivation of the Rule-base and the defuzzification are important factors [14], [15]. The best applications of FLC are the time variant systems that are nonlinear and ill-defined. A variable in fuzzy logic has sets of values which are characterized by linguistic expressions such as SMALL, MEDIUM, LARGE, etc. These linguistic expressions are represented numerically by fuzzy sets (sometimes referred to as fuzzy subsets). Every fuzzy set is characterized by a membership function, which varies from 0 to 1 (unlike 0 and 1 of a Boolean set). Although fuzzy theory deals with imprecise information, it is based on sound quantitative mathematical theory. A fuzzy control algorithm for a process control system embeds the intuition and experience of an operator, designer and researcher. The control does not need an accurate mathematical model of a plant, and therefore it suits well to a process, where the model is unknown or illdefined. The fuzzy control also works well for complex nonlinear multi-dimensional system and a system with parameter variation problems. Recently it has been applied to fast response linear servo drive [16], giving superior results. The fuzzy control [17] is basically nonlinear and adaptive in nature, giving robust performance under load disturbance effect. The structure of the proposed fuzzy back-EMF observer [18] is shown in Fig. 5. The fuzzy back-EMF observer has two parts. One is the system state equation based current observer and the other one is the fuzzy function approximator which represents the back-EMF disturbance model using fuzzy logic approach. As the neural point of the BLDC motor is not known when produced, this observer is considered by the following equation

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Fig. 4. Output response of the Ziegler Nichols method.

IV. FUZZY BASED ESTIMATION OF SPEED AND ROTOR POSITION Nowadays, FLC applications are successfully used in many fields including automatic focus cameras, household materials such as dishwashers, automobile industry etc. Fuzzy Logic is recently finding wide popularity in various applications that include management, economics, medicine, and process control systems. The theory was introduced by Zadeh around twenty seven years ago, but in the recent time only its application has received large momentum. Fuzzy logic, unlike the crispy logic in Boolean

di ab dt

2R s i ab 2 Ls

1 v ab 2 Ls

1 eab 2 Ls

(8)

The equation is represented by system state equation. dx dt y

Ax Cx

Bu

Fw

(9) (10)

where

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Fig. 7. Overall structure of sensorless control of BLDC motor drive. TABLE II FUZZY RULE BASE

Fig. 6. Membership functions, (a) Error, (b) Change in error, and (c) Control output.

ce (i ab )

i ab , y

1 ,F 2 Ls

i ab , u

1 ,C 2 Ls

v ab , w

NL

1,

e ab

NL NM NS ZE PS PM PL

NL NL NL NL NM NS ZE

cerr (i ab ) err (i ab ) ( n

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err (i ab ) i ab

err (i ab )n

ZE

PS

PM

PL

(12)

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The fuzzy function approximation includes three stage; fuzzification, inference mechanism and de-fuzzification.

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A. Fuzzification Fuzzification permits to convert inputs into fuzzy variables by using membership functions. Each input and output has seven sets associated with seven linguistic labels: Negative Large (NL), Negative Medium (NM), Negative Small (NS), Zero (ZE), Positive Small (PS), Positive Medium (PM) and Positive Large (PL) as shown in Fig. 6. All fuzzy sets are defined on the same discourse universe [-1, 1]. B. Inference Mechanism In this step, the value of the fuzzy output is determined using a rule base. A typical rule is described as: IF (condition 1) AND (condition 2) THEN (conclusion) The approximation law of the fuzzy function approximator contains 49 rules. The inference method which has been chosen is the Max-Min method that was proposed by Mamdani. Table II shows the rule-base. The database contains descriptions of the input and output variables. C. Defuzzification: The output of the inference mechanism is fuzzy output

NL NL NL NM NS ZE PS

NL NL NM NS ZE PS PM

NL NM NS ZE PS PM PL

NM NS ZE PS PM PL PL

NS ZE PS PM PL PL PL

ZE PS PM PL PL PL PL

N

e ab

i 1 N

eˆab

(11)

1)

NS

variable. The fuzzy function approximator must convert its internal fuzzy output variables into crisp values so that the actual system can use these variables. One of the most common ways is the Center of Area (COA) method. The defuzzified output is given by

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The back EMF is regarded as disturbance in the equation. This disturbance is difficult to presuppose. Generally, a disturbance model can represent the most disturbed model by increasing the degree of polynomial differential equation. However this disturbance model cannot exactly represent the back EMF of trapezoidal shape, so a fuzzy function approximator that can estimate the voluntary non-linear function is applied to the back EMF disturbance model in this work. The inputs of the fuzzy function approximator are the line to line current error of the BLDC motor and the differential value of the error. These inputs are given by

iˆab

NM

e (i ab )

D

x

2R s ,B 2L s

SI

A

i 1

out

(e abi )

(13)

out (e abi )

If the defuzzified output at time k is the overall crisp output of the observer, then the equation will be ) ) ) e ab (k ) e ab (k 1) e ab (k ) (14) The relation between back EMF and speed is given below. E

Kb

e

(15)

where, E is back EMF, K b is back EMF constant, and e is electrical angular velocity. The rotor position is obtained by integrating speed. ) ) (16) e dt 0 where, 0 is initial position of rotor. The speed and rotor position are calculated by the estimated back EMF. V.CONVENTIONAL CONTROLLER WITH FUZZY BASED ESTIMATION The block diagram of the proposed sensorless drive system is given in Fig. 7. The hysteresis current controller is used for each phase current control. The line-to-line voltage is calculated using DC-link voltage and switching status of the inverter. The line currents of the BLDC motor is also calculated. Using these calculated values, back EMF is estimated with the help of Fuzzy Back EMF observer. The speed and rotor position are calculated by the estimated back EMF.

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MAHESH KUMAR et al.: SENSORLESS SPEED CONTROL OF BRUSHLESS DC MOTOR WITH FUZZY BASED ESTIMATION

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Actual Values (with sensor) Estimated Values (without sensor)

Fig. 11. Speed response (sensorless drive).

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Fig. 8. Actual and estimated back EMFs.

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Fig. 12. Speed responses (sensor & sensorless drive).

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Fig. 9. Actual and estimated speed.

Fig. 10. Actual and estimated rotor position.

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Fig. 13. Applied full load torque.

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The estimated speed is fed to the error detector which finds the difference between the actual and desired value. Output of this is fed to the PI controller which decides the current set value depending upon the gain values of controller. The output of the hysteresis controller decides exact voltage to be applied across the bldc motor from the actual current taken directly from the line and set value fixed by the controller gain. Finally, Inverter does the job of impressing the voltage across winding of the motor based on firing sequence. VI. COMPARISON OF SPEED AND ROTOR POSITION OF BOTH SENSOR AND FUZZY BASED SYSTEM

The speed measured by fuzzy logic technique is almost same as the sensor value. When compared to reliability and cost of the sensor system, this Fuzzy Logic is found to be somewhat superior. It doesn’t need any physical component for measurement. Since investment on sensor is avoided, the cost of the overall system is reduced. Maintenance problem of the sensor is also eliminated. Wave forms shown below reveal that Fuzzy Logic can replace the sensor. The back EMF of the BLDC motor has been observed using fuzzy back EMF observer which is shown in Fig. 8.The speed of the motor is determined by the estimated back EMF which is shown in Fig. 9. Similarly the rotor position of the motor is also determined by the speed of the motor which is shown in Fig. 10. Test has been conducted at various loading points and also for

Fig. 14. Phase currents (sensorless drive).

change from one point to another point like zero to full load and from half load to full load. In the same way, speed is also varied from one point to another point like zero to rated speed and half rated to full. In all these tests conducted, performance is good for the fuzzy based estimation of sensorless PI control of BLDC motor. To realize the result, some of the waveforms taken after simulation for different range of load and speed have been given here for the purpose of reference. The speed of the BLDC motor has been observed using fuzzy back EMF observer (sensorless drive) which is shown in Fig. 11. The speed of the BLDC motor that has been observed using sensor and sensorless drives are shown in Fig. 12 for comparison. The applied full load torque and the three phase currents of the motor are shown in Fig. 13, Fig. 14. The speed wave form for change in applied torque from 0.445 Nm to 0.89 Nm at rated speed of 4000 rpm and its torque waveform are shown in Figs. 15

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IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 8, NO. 2, SUMMER-FALL 2009

drive have been performed in Matlab/Simulink environment. Simulation results show that the performance of the fuzzy based drive is similar to that of the sensor based drive. Therefore, the fuzzy based drive can replace the sensor drive which has lot of demerits. APPENDIX

Fig. 15. Speed response under load change form 0.445 to 0.89 Nm at 4000.

Fig. 16. Applied torque change from 0.445 to 0.89 Nm at 4000 rpm.

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MOTOR DETAILS No. of Poles 4 Power 373 W Rated Speed 4000 RPM Supply Voltage 160 V Rated Torque 0.89 N-m Resistance per phase 0.7 Ohms Self Inductance 2.72 mH Mutual Inductance 1.5 mH Back EMF Constant 0.0489 V/(rad/sec) Moment of Inertia 0.0002 Kg-m2 Friction Co-efficient 0.002 Nm/(rad/sec)

REFERENCES

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T. J. E Miller, Brushless Permanent Magnet and Reluctance Motor Drives, Clarendon Press, Oxford, 1989. R. Krishnan and R. Ghosh, "Starting algorithm and performance of A PM DC brushless motor drive system with no position sensor," in Proc. IEEE Power Electronics Specialists Conf., PESC’89, vol. 2, pp. 815821, 26-29 Jun. 1989. T. H. Kim and M. Ehsani, "Sensorless control of the BLDC motors from near-zero to high speeds," IEEE Trans. Power Electron, vol. 19, no. 6, pp. 1635-1645, Nov. 2004. N. Ertugrul and P. Acarnley, "A New algorithm for sensorless operation of permanent magnet motors," IEEE Trans. Ind. Applicat., vol. 30, no.1, pp.126-133, Jan./Feb. 1994. S. Ogasawara and H. Akagi, "An Approach to position sensorless drive for brushless DC motors," IEEE Trans. Ind. Appl., vol. 27, no. 5, pp. 928-933, Sep./Oct. 1991. R. C. Becerra, T. M. Jahns, and M. Ehsani, "Four-quadrant sensorless brushless ECM drive," in Proc. IEEE Appl. Power. Electron. Conf., APEC’91, pp. 202-209, 1991. P. Pillay and R. Krishnan, "Application characteristics of permanent magnet synchronous and brushless dc motors for servo drives," IEEE Trans. Ind. Appl., vol. 27, no. 5, pp. 986-996, Sep./Oct. 1991. K. Ohishi, M. Nakao, K. Ohnishi, and K. Miyachi, "Microprocessorcontrolled DC motor for load-insensitive position servo system," IEEE Trans. Ind. Electron., vol. 34, no. 1, pp. 44-49, Feb. 1987. P. Pillay and R. Krishnan, "Modeling, analysis, and simulation of a permanent magnet brushless DC motor drives," in Proc. IEEE IAS Annual Meeting, Atlanta, US, pp. 7-14, 1987. N. Hemati and M. C. Leu, "A complete model characterization of brushless DC motor," IEEE Trans. Ind. Applicat., vol. 28, no. 1, pp. 172-180, Jan./Feb. 1992. J. W. Dixon and I. A. Leal, "Current control strategy for brushless DC motors based on a common DC signal," IEEE Trans. on Power Electronics, vol. 17, no. 2, pp. 232-240, Mar. 2002. A. Consoli, S. Musumeci, A. Raciti, and A. Testa, "Sensorless vector and speed control of brushless motor drives," IEEE Trans. Ind. Electron, vol. 41, no. 1, pp. 91-96, Feb. 1994. J. Gan, K. T. Chau, Y. Wang, C. C. Chan, and J. Z. Jiang, "Design and analysis of a new permanent magnet brushless DC machine," IEEE Trans. Magn., vol. 36, no. 5, pp. 3353-56, Sep. 2000. L. H. Tsoukalas and R. E. Uhrig, Fuzzy and Neural Approaches in Engineering, John Wiley & Sons, Inc., 1997. C. C. Lee, "Fuzzy logic in control systems: fuzzy logic controller-part I & Part II," IEEE Trans. Syst. Man. Cybern., vol. 20, no. 2, pp. 404435, Mar./Apr. 1990. Y. F. Li and C. C. Lau, "Development of fuzzy algorithms for servo systems," IEEE Control System Magazine, vol. 9, no. 2, pp. 65-72, Apr. 1988. M. A. Akcayol, A. Cetin, and C. Elmas, "An education tool for fuzzy logic-controlled BDCM," IEEE Trans. on Education, vol. 45, no. 1, pp. 33-42, Feb. 2002. B. G. Park, T. S. Kim, J. S. Ryu, and D. S. Hyun, "Fuzzy back-EM observer for improving performance of sensorless brushless DC motor drive," in Proc. IEEE Conf. APEC, pp. 674-678, Mar. 2006.

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Fig. 17. Speed change from 2500 to 4000 rpm at half load torque.

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and 16. The change in speed of the BLDC motor from 2500 rpm to 4000 rpm at half load of 0.445 Nm is also shown in Fig. 17. The conventional speed controls of both sensor and sensorless drive have been performed in Matlab/Simulink environment. Simulation results show that the performance of sensorless (fuzzy based estimation) is similar to the sensor based drive in the PI controller of brushless dc motor. Wave forms shown above reveal that Fuzzy Logic can replace the sensor. Therefore, sensorless drive is much better than sensor drive as it eliminates the problem associated with sensor like cost, reliability and maintenance.

[6]

[7]

[8]

[9]

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[11]

[12]

VII. CONCLUSION The estimation of the speed and rotor position is determined by Fuzzy back-EMF observer which is carried out with the help of fuzzy logic techniques to improve the performance of the system.The proposed algorithm using fuzzy back EMF observer is used to estimate the speed of the BLDC motor under variable and fixed condition of back-EMF. As a result, the proposed sensorless drive method without an additional circuit has higher performance than conventional sensorless methods. In addition, this proposed sensorless method can be easily applied to industrial applications requiring low-cost and reliable drive of the BLDC motor. With the help of a conventional speed controller, both sensor and sensorless

[13]

[14] [15]

[16]

[17]

[18]

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MAHESH KUMAR et al.: SENSORLESS SPEED CONTROL OF BRUSHLESS DC MOTOR WITH FUZZY BASED ESTIMATION B. Mahesh Kumar received the B.Tech., degree in Electrical Engineering from Madurai Kamaraj University, and M.Tech., in Process Control and Instrumentation from N.I.T.–Trichy, India. At Present, He is a faculty in Pondicherry Engineering College, Puducherry, India. He is currently pursuing the Ph.D., (Eng.) degree in Electrical Engineering at Jadavpur University, Kolkata, India. His research interests include artificial intelligent techniques in electrical machines and control.

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R. Chakrabarti was born in 1942. He received M.E.E., degree in 1968 and Ph.D. (Eng.) in 1979 from Jadavpur University, India. At present he is a Professor in Electrical Engineering department, Jadavpur University, Kolkata, India. His research area includes electrical machines, power electronics and power system optimization.

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G. Ravi received B.E., degree in Electrical & Electronics Engineering from Mysore University in 1992. M.E., from Annamalai University in 1994 and Ph.D. (Eng.) from Jadavpur University in 2005. At present he is an Assistant Professor in Electrical & Electronics Engineering department at Pondicherry Engineering College, Puducherry, India. His research area includes artificial intelligent techniques electrical machines and power system.

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