p power consumption of brushless DC motors.

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1 Send Orders for eprints to The Open lectrical & lectronic ngineering Journal, 2014, 8, Open Access Study on Speed Control Strategy of Brushless DC Motors Based on Fuzzy PID Chunfeng Li 1,*, Dandan Sun 2 and Wusheng Tang 3 1 lectronic Inforation ngineering College of Changchun University, Changchun, , China 2 Foreign Language College of Changchun University, Changchun, , China 3 Mechanical and Vehicle ngineering College of Changchun University, Changchun, , China Abstract: Firstly, this article establishes the atheatical odels and speed principles of brushless DC otors. Next, it designs fuzzy PID controllers and current adjustors based on the adjusting speed theory and characteristics of brushless DC otors, which for double closed-loops to achieve intellectualized adjustent of brushless DC otors, creating the best effects siultaneously. Keywords: Brushless DC otor, fuzzy PID controller, speed control. 1. INTODUCTION In odern society, as devices are being transfored fro electric energy to kinetic energy, otors are being widely used covering different areas of national econoy closely concerned with our daily life. Fro the invention of the first otor till now, otors have been developed for ore than 100 years. There are different types of otors now, such as asynchronous otors, synchronous otors and capacitance otors, which basically satisfy different conditions. In soe situations, which need higher property index, the odern otors could not eet the needs, so brushless DC otors have been invented which ay enlarge the space application of otors and have a wider application in fields such as national defense, cheistry, aerospace, autootive electronics, and doestic applications, etc. However, the brushless DC otors are coplicated systes having strong coupling, ore index, nonlinearity and tie varying. In the traditional adjusting speed ethod, the requireent of rotation rate control cannot be satisfied, and the control accuracy and integration are not high, and hence, an accurate atheatical odel is needed to establish for controlled objects. However, fuzzy PID rotation rate controllers are different fro the traditional rotation rate controllers, in that: they don t need to ake atheatical odels for the controlled objects; their paraeters and rules are ade according to the knowledge and experience of syste designers; and huan operations are added properly, so that otors can achieve the best effects of rotation rate control in operation. So, this article will carry out a further study on intellectualized control of brushless DC otors speed, that is the fuzzy PID control. *Address correspondence to this author at No.6543, Weixing oad, Changchun city, China, Postcard: , Tel: ; -ail: @qq.co 2. MATHNATICAL MODL OF BUSHLSS DC MOTOS Stator winding phase voltage of brushless DC otors equals to the su of voltage in equivalent resistance and induced MF in stator winding; the equivalent circuit of brushless DC otors is shown as Fig. (1), its atheatical expression is: dia A A A dib B B B dic C C C In this expression: u A, u B, u C phase voltage of otor stator winding; ia ib i C phase current otor stator winding (1) (2) (3) ea eb e C back electrootive force of otor stator winding. Transient power consuption when otors are operated is dω p = JΩ In the equation! angle velocity of otors p power consuption of brushless DC otors. (4) / Bentha Open

2 744 The Open lectrical & lectronic ngineering Journal, 2014, Volue 8 Li et al. ia ua ea ub eb ib ic uc ec Fig. (1). quivalent circuit of brushless DC otors. T e The expression of electroagnetic torque = i + i + i ω AA BB CC In the expression A, MF; ω angle velocity of rotor. B, P e is: (5) C three-phase back The equation of brushless DC otors echanical otion is: dω Te TL fω = J In the equation T e electroagnetic torque of otors T L load torque of otors; J inertial oent of otors; f daping coefficient of brushless DC otors. 3. ADJUSTING SPD THOY OF BUSHLSS DC MOTOS Fro the atheatical odel of brushless DC otors, each phase back MF of three-phase Y-shape stator winding is obtained as follows n = N B l ν = N B l 2π τ In the equation l effective length of conductor incision agnetic field N equivalent nuber of windings in three-phase Y- shape stator winding of brushless DC otors n rotating speed of brushless DC otors τ polar distance of brushless DC otors B agnetic intensity of brushless DC otors gas gap agnetic field. (6) (7) Because the ain agnetic flow in brushless DC otors is: Bl 2π τ φ = Pn Put (2-22) into (2-21), each phase back MF of brushless DC otors stator winding can be obtained as follows: N pn = φ n= Ke φ n In this equation Ke = N! pn electric potential coefficient; pn polar logarith of brushless DC otors. Because stator winding have only 2 phases broken when otor operates in noral situation at any tie in the opposite direction of flowing current, suppose the twophase average voltage on stator winding breakover is Vd, then the expression of voltage equilibriu equation is just as the following: Vd 2 I Σ 2Ke φ n I Σ (8) (9) = + = + (10) eorganizing the rotation rate n in (2-24), the following expression of rotation rate is as following Vd I Σ Vd I Σ n = = 2Ke φ 2Ke φ 2Ke φ (11) In this equation,! is the su of equivalent resistance of two-phase stator winding in brushless DC otors and equivalent resistance through power tubes, that is, the total equivalent resistance of brushless DC otors return circuit. Fro the above deduced rotation rate equation of brushless DC otors, its rotation rate equation is basically found to be the sae as the other rotation rate equation of direct current otors. Hence, the adjusting principles of brushless DC otors can be accoplished through adjusting voltage of stator winding [1].

3 Study on Speed Control Strategy of Brushless DC Motors The Open lectrical & lectronic ngineering Journal, 2014, Volue de Fig. (2). Conceptual design of fuzzy rotation rate PID control. NB NM NS Z PS PM PB Fig. (3). Mebership functions in fuzzy controller of brushless DC Motors. 4. CONCPTUAL DSIGN OF FUZZY OTATION AT PID CONTOL Scheatic diagra in Fig. (2) shows conceptual design of brushless DC otors that is controlled by fuzzy PID controller in two-diensional rotation rate. The essence of the design is to cobine fuzzy control with traditional PID control. Speed variation e and change rate of speed variation ec are taken as input value; and three paraeters kp ki and kd of PID, as linguistic output variables Table 1. According to different speed variation e and change rate of speed variation ec in the rotation of otors, three paraeters kp, ki and kd of PID are being adjusted on line to ake brushless DC otors to achieve good static-dynaic perforance and adjustent of speed [2]. 5. ACCOMPLISHMNT OF DSIGN IN FUZZY O- TATION AT PID CONTOLL Fro the functional Scheatic diagra of fuzzy rotation rate PID controller, the practical discourse doains of speed variation e, change rate of speed variation e c and three paraeters kp ki and kd of PID are separated "!Me,Me$ %, "!Mec,Mec$ %, "!Nkp,Nkp$ %, "!Nki,Nki$ %, "!Nkd,Nkd$ %, siultaneously their discourse doains of fuzzy subset are chosen as: "!l,!l +1,!,0,l!1,a$ %, "! y,! y +1,!,0, y!1,b$ %, "!z,!z +1,!,0, z!1, z$ %, "!k,!k +1,!,0,k!1,k$ %, "!e,!e +1,!,0,e!1,e$ %, and their fuzzy subset are chosen as: { NB,NM,NS,ZO,PS,PM,PB}, function of ebership degree chooses triangle function of ebership degree which are distributed syetrically and overlapped. So the triangular distribution function, which is taken as ebership functions in fuzzy controller of brushless DC otors, is shown in Fig. (3). Fro the knowledge of autoatic control theory, we found that proportionality coefficient k p, integral coefficient k i and differential coefficient k d play different roles in static-dynaic perforance of controlled objects Table 2. For exaple, proportionality coefficient k p plays iportant role in increasing response speed and iproving accuracy of syste adjustent [3]. The role of integral coefficient k i is to eliinate steady-state error, whereas the role of differential coefficient k d is to restrain the variation of deviation. So, rule lists of fuzzy control PID are based on: controlling syste, appropriate operation, self-adjustent and operation experiences of working ebers: Through the previous induction of fuzzy control rule list on output value kp ki and kd of fuzzy rotation rate PID, their fuzzy relation is established. Through the process of defuzzification, an online adjusting PID controller that has accurate control value kp ki and kd is obtained to realize the intellectualized speed adjustent of brushless

4 746 The Open lectrical & lectronic ngineering Journal, 2014, Volue 8 Li et al. Table 1. ule list of proportionality coefficient kp fuzzy control. NB PB PB PM PM PM PS ZO NM PB PB PM PS PS ZO NS NS PM PM PM PS ZO NS NS ZO PM PM PS ZO NS NM NM PS PM PS ZO NS NS NM NM PM PS ZO NS NM NM NM NB PB ZO ZO NM NM NM NB NB Table 2. ule list of integral coefficient ki fuzzy control. NB NB NB NM NM NM NS ZO NM NB NB NM NS NS ZO ZO NS NB NM NS NS ZO PS PS ZO NM NM NS ZO PS PM PM PS NM NS ZO PS PS PM PB PM NS ZO PS PS PM PB PB PB ZO ZO PS PM PM PB PB Table 3. ule List of differential coefficient k d Fuzzy Control. NB PS NS NB NB NB NM PS NM PS NS NB NM NM NS ZO NS ZO NS NM NM NS NS ZO ZO ZO NS NS NS NS NS ZO PS ZO ZO ZO ZO ZO ZO ZO PM PB PS PS PS PS PS PB PB PB PM PM PM PS PS PB DC otors [4, 5]. Fuzzy decision-aking adopt triangle functions of ebership degree as weighting coefficient, and weighted average law ethod, which are concerned with systeatic response proprieties, so decision-aking output of fuzzy value can be obtained through the following equation: u * =! i=1! i=1 kiui ki (12)

5 Study on Speed Control Strategy of Brushless DC Motors The Open lectrical & lectronic ngineering Journal, 2014, Volue In the equation ki (i = 1,2,3,!,) is the weighting coefficient (Table 3). But at the tie of choosing ebership functions as weighting coefficient, output atheatical expression is: µ A( ui) ui * u = i = 1 µ A( ui) i = 1 (13) CONCLUSION Based on the Study on Speed Control Strategy of Brushless DC Motors Based on Fuzzy PID, we can conclude that speed control of brushless DC otors adopt fuzzy PID control whose effects are superior to traditional double closed-loop control, in that fuzzy PID control achieved intellectualization and integration. So, the previous study ust supply help and reference for further study on brushless DC otors, and enlarge the application space of brushless DC otors siultaneously. CONFLICT OF INTST The author confirs that this article content has no conflict of interest. ACKNOWLDGMNTS We gratefully acknowledge the help and supervision in writing this article, of teachers in Innovation Center of Changchun University. FNCS [1] T. Jin, Study on Adjusting Speed Syste of Sensorless Brushless DC Motors, Master thesis, Northwestern Polytechnical University, [2] W. D. Qiao, Adjusting speed syste of PM brushless DC otors based on fuzzy PID control, Jiangsu lectrical Application, vol. 2008, no. 12, pp , [3] C. L. Xia, Controlling Syste of Brushless DC Motors, Science Press, [4] G. Liu, Z. Q. Wang, and J. C. Fang, Control Strategy and Application of PM Brushless DC otors, ngineering Industry Press, [5] D. S. Sun, and L. P. Bai, Application of Fuzzy Self-adaptation PID Controller in Brushless DC Motors Control Syste, lectric Drive, vol. 39, no. 10, pp , eceived: February 18, 2015 evised: March 22, 2015 Accepted: March 31, 2015 Li et al.; Licensee Bentha Open. This is an open access article licensed under the ters of the Creative Coons Attribution Non-Coercial License ( which perits unrestricted, non-coercial use, distribution and reproduction in any ediu, provided the work is properly cited.