Sliding mode observer and controller for Performance improvement of Brushless DC Motor

Transcription

1 ISSN (Print) : ISSN (Online) : Sliding mode oberver and controller for Performance improvement of Bruhle DC Motor Devendra Potnuru #, Y.Santoh Kumar *2 # Aociate Profeor, EEE department, GMRIT, Srikakulam, A.P., India devendra.p@gmail.com * M.Tech tudent, EEE department, GMRIT, Srikakulam, A.P., India 2 yadlapalli.antohkumar@gmail.com Abtract The preent paper propoe a control cheme compriing of a new liding mode controller (SMC) with liding mode oberver (SMO) for improved performance of a Bruhle DC (BLDC) motor. The SMO i ued to etimate rotor peed and rotor poition uing terminal voltage and current of the BLDC motor. The error between actual and etimated current taken a the liding urface from which the back emf i etimated which i further ued to etimate rotor poition and peed. The SMC conit of both peed control and current control loop where the reference to the current i derived from peed error uing PI controller. The peed error and current error together comprie the liding urface. The propoed SMC i an alternative to econd order SMC and it eliminate the derivative of the liding variable for peed control thu eliminating complexity while preerving the benefit. The imulation reult of the propoed cheme are compared with thoe of the conventional cheme to prove it effectivene. Keyword-BLDC Motor, Sliding mode controller, Sliding mode oberver I. INTRODUCTION There ha been a tremendou interet in permanent magnet drive in recent year due to their excellent characteritic like low power requirement, high energy aving and eae of control. Majority of the BLDC motor advantage attributed to it contruction in which it armature winding placed in tator and field i provided withthe permanent magnet placed in rotor. Thi make the cooling arrangement i eaier for BLDC motor a compared to the conventional dc motor. Due to the permanent magnet rotor, the commutation proce i not poible from the rotor ide like a DC motor []. So an electronic commutation i ued in which the upply to the motor will be controlled through inverter. In order to make a phae to conduct, we need to find the exact location of the rotor pole and the commutation equence mut be enured uch that a phae difference of 9o mut be maintained between tator flux and rotor flux to get imum torque [2]. To attain information regarding the poition of rotor, tranducer like hall enor are ued. The hall enor tranmit logic high or logic low ignal baed on the proximity of a pole a the magnetic field of a pole induce emf in it. For a three phae BLDC motor, three enor are aligned with 2 phae hift to get complete information regarding back emf voltage in all phae and thi hall enor circuit i placed on the non-rotating part of motor [3]. The poition enor circuit require a pecial arrangement to be mounted on the motor and need dedicated electronic circuitry. If the motor i far away from the control center, then we need a eparate cabling ytem for ignal tranmiion. All thee requirement increae the cot and reduce the reliability of the drive [4]. Hence enor control cheme cannot be utilized in ituation where high reliability i needed and the motor ha to operate in harh environment. One of the olution i to etimate the poition of the rotor uing voltage and current meaurement. Since we are eliminating the need of poition enor, it can be treated a enorle control. Senorle control can alo be utilized a a backup cheme where hall enor are already in ue. For rotor poition etimation, enorle algorithm depend on meaured value of motor current and motor terminal voltage. In many of the enorle method, poition and peed information i etimated uing back emf voltage. Thi back emf etimated either by direct or indirect method. Further, in direct back emf ening zero croing detection of the back emf uing voltage divider i utilized. The principle of thi method i that whenever two of the three phae are conducting, the remaining phae will carry only the back emf which can be ued for poition ening. But it contain high frequency noie o low pa filter are eential in reducing harmonic. But the filter introduce delay and reduce enitivity. The zero croing of the back emf doe not repreent the commutation period and it hould be enured that there will be a phae hift in ignal ued for commutation. Thee limitation can be eliminated with the indirect back emf ening method uch a voltage integration method or terminal current ening method [4]. DOI:.287/ijet/27/v9i2/79287 Vol 9 No 2 Apr-May 27 82

2 ISSN (Print) : ISSN (Online) : Senorle method are further diverified into the open loop and cloed loop method. In open loop enorle method, the rotor poition obtained directly from ening of terminal voltage without any correction mechanim o thee method are enitive to parameter variation. In cloe loop method, oberver cheme that ue internal correction mechanim are implemented. Oberver are again claified into full order and reduced order model. Full order oberver can etimate the tate baed meaurement of all the tate but the reduced order oberver i baed meaurement of ome of the tate. Reduced order oberver may be a flux oberver or a current oberver. In the flux oberver the reference model i a magnetic model and inthe reduced order current oberver it i the electrical model from which rotor poition i attained by etimating the back emf voltage [5]. SMO i a reduced order current oberver which uethe terminal voltage and current of BLDC motor to etimate the rotor peed and rotor poition [6]. Several method are implemented in the SMO technique for better reult. A hybrid SMO propoed in [7] i ued for the peed and rotor poition etimation in the multiple reference frame (MRF). Another SMO cheme preented in [8] etimate the back emf from which the Zero Croing Detector etimate commutation point. The propoed cheme made an effort to reduce the number of gain to be elected properly to enure the convergence of both tate. A new method to ene the rotor poition and peed for PMSM baed on SMO i preented [9] in which the ignum function i replaced with a aturation function and calculation of differential peed i ubtituted with a phae locked loop (PLL) and a low-pa filter with variable cut-off frequency i ued for improved filtering. The paper [] implemented an Iterative SMO which improve the motor peed and angle etimation by reducing the etimation error in the back emf by iteratively uing the oberver and thi cheme ued a igmoid function a the witching functionto reduce chattering. The paper [6] repreented a modified SMO in which the peed component i added in the back emf etimation which minimied the phae hift at higher peed and multiple zero at lower peed. In the propoed cheme phae current are etimated within the SMO and then compared with actual current. The error between actual and the etimated current contitute the liding urface. A aturation function i ued a witching function to reduce chattering. Integration of the witching function provide the back emf etimation. Rotor peed i calculated uing etimated back emf and integration of peed provide rotor poition. A BLDC motor a a variable peed drive ha feature like eae of control and low maintenance. For fater and accurate control, current controlled voltage ource inverter are preferred. The conventional PI controller and hyterei controller are imple technique for the peed control of the BLDC motor. But for higher order circuit like thi motor thee technique reult in poor performance []. The SMC approach i a mot uitable cheme to deal with thee type of ytem under uncertain condition a it deliver better performance in term of imple and robut control. On the otherhand SMC uffer with the undeirable phenomenon of ocillation called chattering effect a alo it control action i dicontinuou in nature and it ideally operate at infinite witching frequency. It i mainly due to the ue of ignum function in the liding urface. It i reponible for le accurate control and high tre in the power circuit. Chattering can be minimied by uing a continuou function to moothen the witching term before the liding variable reache the liding phae. It can alo be reduced by uing SMC with carrier-baed fixed witching frequency method with proper deign of the parameter [2]. There are many approache in the field of SMC. The paper [3] propoed a econd order SMC algorithm which require only the actual motor parameter information and doe not need any current feedback. An adaptive fuzzy SMC trategy wa developed in the paper [4], in which the control law of the controller i governed by the control algorithm depending on the output of the SMC to minimie uncertain delay in the network control ytem. A hybrid method of SMC cheme conit of a non-ingular terminal liding mode method and the high-order liding-mode method in [5]. A cacade SMC with PID controller i developed in [6] baed on an integral control which ue the concept of weight function and error window concept.the paper [7] give a new two-degree-of-freedom PID controller tructure baed on Takagi-Sugeno fuzzy controller for peed and poition control of BLDC drive. A econd order SMC with anti-windup for BLDC motor i propoed in [8] in which the peed control i baed on the uper twiting algorithm baed on the dq field oriented frame model. A dual loop control trategy implemented in [9] in which a SMC for peed control and a SMO for torque etimation are deigned. The paper [2] propoe a SMC with unidirectional auxiliary urface to deal with indefinite friction force and inertia. A cacade SMC method i implemented in [2] for the cloed loop control of torque and peed baed on the firt order SMC and Super-Twiting algorithm repectively. A control methodology of SMC i propoed in [22] in which the SMC i ued in the inner control loop and PI controller i ued in the outer control loop to minimie the teady-tate error. The drive controller comprie of an outer peed control loop and an inner current control loop. The reference of the inverter phae current in the current control loop i derived from the peed error uing a PI controller. The tability of the ytem will be improved a the teady tate error can be minimied by the PI controller and liding mode i ued in the inner current control loop. The peed error and the current error together comprie the liding urface. The aturation function i ued a a witching function baed on which the proper witching equence of the inverter can be attained. DOI:.287/ijet/27/v9i2/79287 Vol 9 No 2 Apr-May 27 83

3 ISSN (Print) : ISSN (Online) : In thi paper, firtly baed on the modeling equation of BLDC motor, SMO i deigned to etimate the rotor poition and peed. Then SMC i implemented to control the inverter for the optimum performance of the motor. The model i imulated uing MATLAB/SIMULINK and the imulation reult have been preented. To prove it effectivene, thee reult are compared with thoe of the conventional control cheme of hyterei current controller with SMO. II. SLIDING MODE OBSERVER AND CONTROLLER In thi preented approach, the oberver and the controller are deigned baed on the dynamic model of BLDC motor and their detail are given in the following ection A. Sliding Mode Oberver In SMO, the reference current taken from the motor model and the adaptive model produce the etimated motor current. The error between etimated and actual current i fed back to adaptive model to etimate the back emf [5]. The liding mode oberver equation for the current and back emf etimation for the phae-a i propoed a, diˆ a R ˆ Va ia eˆ a aat( σ ) () dt L L L deˆ a a2at( σ ) (2) dt Where î a, êa are the etimated value of phae current and back emf repectively and i the liding urface which i the error between actual and etimated current. The chattering effect eliminated with the ue of the aturation function which i defined a, at( σ σ ; ) ε ign( σ ); σ σ ε ε Where ε i the liding urface band. The liding urface reache to zero when both actual and etimated current converge. To enure convergence, oberver gain a and a2 mut be elected properly. An etimation algorithm baed on liding mode with a combination of a tability theorem enure tability and convergence of etimation. The oberver gain value can be choen uch that, a e and a2 (4) L Where e i the imum value of phae back emf. For implicity, conider the abolute value of current oberver gain a a, (3) a e L The value of back emf oberver gain i proportional to the ratio of actual peed N to imum peed N i multiplied with the back emf oberver gain a, N a2 γ e (6) L N Where γ i a contant. The imum value of phae back emf can be reented a e k b 2 N m kb (7) 6 Where kb i the back emf contant and m i rotor peed. (5) DOI:.287/ijet/27/v9i2/79287 Vol 9 No 2 Apr-May 27 84

4 ISSN (Print) : ISSN (Online) : After inerting (2) and contant in both () and () thee equation tranformed a, a 2 N (8) a 2 2 N N The rotor peed i etimated with the help of back emf voltage a, ˆ m eˆ a eˆ b eˆ c () k b Whereˆ m i the etimated value of rotor electrical peed. (9) The rotor poition ˆ r i calculated with the etimated rotor peed a, dθˆ dt r p ˆ m () 2 Where p i the number of pole. B. Sliding Mode controller The propoed controller i a modified verion of the econd order liding mode controller. For peed control of BLDC motor, the liding urface α of a econd order liding mode control i given a, dω dt e α e (2) Where e i the error in the rotor peed which can be repreented a, e ref (3) Where ref reference i peed and i actual peed. From the electromagnetic torque equation, the tate equation of rotor peed i obtained a, dm ( Te Tl ) B m (4) dt J J From (4) the derivative of peed error i given a, de B ( Teref Te ) ( ref ) (5) dt J J Where Te ref i the reference electromagnetic torque which can be derived from peed error uing PI controller a, ki T eref k p ref (6) A electromagnetic torque and current are related a, T e k i t (7) Where i the phae i current, kt i the torque contant. Equation (6) can be modified a, i ref k k t p ki ref (8) Where i ref i the reference current. DOI:.287/ijet/27/v9i2/79287 Vol 9 No 2 Apr-May 27 85

5 ISSN (Print) : ISSN (Online) : After ubtituting (2) and (22) in (9), de kt dt J B ( iref i) ( ref ) J The liding urface can be modified by inerting (23) in (7) a, kt B α ( iref i) ( )( ref ) (2) J J Where e ref the error in the rotor i peed and ie iref i i the error in the current. The propoed liding urface can be redefined a, α b i i) b ( ) (2) ( ref 2 ref Once the liding urface i calculated, the control input to the inverter i elected with reference to witching function a, (9) u ; V u ; V V V dc dc for for α α (22) III. RESULT ANALYSIS AND DISCUSSIONS The propoed cheme of enorle control of the BLDC motor uing SMO and SMC are imulated uing MATLAB/SIMULINK uing the motor parameter lited in the Table.. A. Rotor poition and peed etimation The poition and peed etimated with SMO i compared with that of actual value to check the accuracy of the SMO. Figure repreent actual and etimated rotor poition and rotor peed uing SMO and SMC at 3 r/min R [degree] Actual rotor poition Etimated rotor poition Actual peed Etimated peed Figure. Actual and etimated parameter uing a liding mode oberver and controller at 3 r/min: rotor poition R veru time t, rotor peed N veru time. From Figure, it i oberved that the etimated rotor poition ha an error of 2 with repect to the actual rotor poition and etimated peed ha an error of.5 r/min from actual peed. B. Speed and torque performance To ae the effectivene of the propoed controller, a hyterei current controller cheme i ued for comparion. The imulation model run at different peed uch a 5 r/min, 5 r/min and 3 r/min with a load.5 N.m applied at 3.When the propoed cheme i imulated at 5 r/min, the peed charactertic are hown in Figure.2. But their torque curve a hown in Figure 3 expoe that torque ripple i well minimized to.5 N.m in the propoed controller while in cae of a hyterei controller, it i. N.m. DOI:.287/ijet/27/v9i2/79287 Vol 9 No 2 Apr-May 27 86

6 ISSN (Print) : ISSN (Online) : Figure 2. Speed N veru time (Sec) curve at 5 r/min: with liding mode oberver and hyterei controller, with liding mode oberver and controller Figure 3. Electromagnetic torque T veru time (t) curve at 5 r/min: with liding mode oberver and hyterei controller, With liding mode and controller Figure 4. Speed N veru time (ec) curve at 5 r/min: with liding mode oberver and hyterei controller, with liding mode oberver and controller. DOI:.287/ijet/27/v9i2/79287 Vol 9 No 2 Apr-May 27 87

7 ISSN (Print) : ISSN (Online) : Figure 5. Electromagnetic torque T veru time t curve at 5 r/min: with liding mode oberver and hyterei controller, with liding mode oberver and controller. When the propoed cheme i run at 5 r/min, peed characteritic are much imilar with an accuracy of.5 r/min in both controller a hown in Figure 4 but their torque curve a hown in Figure 5 depict that the torque ripple i. N.m uing the propoed controller and it i.3 N.m uing hyterei controller.when both model are imulated at 3 r/min, the correponding peed curve are hown in Figure 6 and their torque curve a hown in Figure 7 and it i evident that the ripple in the torque i.3 N.m in cae of SMC and it i.6 N.m with hyterei controller Figure.6. Speed N veru time (ec) curve at 3 r/min: with a liding mode oberver and hyterei controller, with liding mode oberver and controller. DOI:.287/ijet/27/v9i2/79287 Vol 9 No 2 Apr-May 27 88

8 ISSN (Print) : ISSN (Online) : Figure.7. Electromagnetic torque T veru time curve at 3 r/min: with liding mode oberver and hyterei controller, with liding mode oberver and controller. TABLE I. BLDC MOTOR PARAMETERS Parameter name Symbol Value Unit Pole P Stator reitance R.75 Ω Stator elf-inductance L.75 mh Mutual inductance M.6 mh Back emf contant kb.56 V/rad/ec Torque contant kt.55 Nm/A Moment of inertia J.27 Kg.m/2 Friction coefficient B.98 N.m/rad/ec DC voltage Vdc 6 V Maximum peed N 4 r/min IV. CONCLUSION Thi paper a cloed loop control cheme of BLDC motor uing SMC in conjunction with SMO i propoed. The SMO i deigned to etimate the rotor poition and rotor peed to eliminate the neceity of enor. To check the accuracy of the oberver, etimated peed and rotor poition are compared with the actual parameter of BLDC motor and both are identical. The new SMC i implementedwhich i an alternative to the econd order SMC and it eliminate the derivative of the liding variable for peed control. The propoed controller i compared with the conventional hyterei current controller and it i proven that the propoed cheme exhibit more accurate and fater repone in performance improvement of BLDC motor without the need of any poition enor. REFERENCES [] Sawathi Swapna Da,Byamakeh Nayak, Subrath Kumar,Feedback control and Dynamic behavior of Z-ource converter fed eparately excited DC motor and centrifugal pump et, International Journal of Engineering and Technology (IJET), pp.6-64, 24. [2] Paul Acarnley, Waton J., Review of poition-enorle operation of bruhle permanent magnet machine, in IEEE Tranaction on Indutrial Electronic, vol. 53, no. 2, pp: , 26. [3] Gamazo Real, Joé Carlo, Erneto Vázquez Sánchez, Jaime Gómez Gil, Poition and Speed Control of Bruhle DC Motor Uing Senorle Technique and Application Trend, Senor (Bael, Switzerland).7,2. [4] Suneetha, R.Srinivaan, Ramagar, Co-imulation of BLDC motor commutation by uing MATLAB/Simulink and Xilinx Sytem Generator, International Journal of Engineering and Technology (IJET), pp ,26. [5] Bojoi R., Patorelli M., Bottomley J., Giangrande P., Gerada C., Senorle control of PM motor drive A technology tatu review, Electrical Machine Deign Control and Diagnoi (WEMDCD), 23 IEEE Workhop on, Pari,, pp: (23). DOI:.287/ijet/27/v9i2/79287 Vol 9 No 2 Apr-May 27 89

9 ISSN (Print) : ISSN (Online) : [6] Deenadayalan, A., Saravana Ilango G., Modified liding mode oberver for poition and peed etimation in bruhle DC motor, In 2 Annual IEEE India Conference, pp: -4,2. [7] Hao, Lei, Toliyat., BLDC motor full-peed operation uing hybrid liding mode oberver, In Applied Power Electronic Conference and Expoition, Eighteenth Annual IEEE, vol., pp: ,23. [8] Fakham, Hicham, Mohamed Djemai, Krihna Buawon, Deign and practical implementation of a back-emf liding-mode oberver for a bruhle DC motor, IET Electric Power Application 2, no. 6, pp: ,28. [9] Jianbo, Chu, Hu Yuwen, Huang Wenxin, Wang Mingjin, Yang Jianfei, Shi Yuxia, An improved liding mode oberver for poition enorle vector control drive of PMSM, In Power Electronic and Motion Control Conference, IEEE 6th International, pp: ,29. [] Lee, Hyun, Jangmyung Lee, Deign of iterative liding mode oberver for enorle PMSM control, IEEE Tranaction on control ytem technology 2, no. 4, pp: , 23. [] Satih Kumar Gudey, Rajeh Gupta, Reduced tate feedback liding-mode current control for voltage ource inverter-baed higherorder circuit, IET Power Electronic, Vol. 8, I. 8, pp: , 25. [2] Satih Kumar Gudey, Rajeh Gupta, Second order liding mode control for a ingle phae voltage ource inverter, In TENCON IEEE Region Conference, pp: -6.,24. [3] Damiano, Alfono, Gianluca L. Gatto, Ignazio Marongiu, Aleandro Piano, Second-order liding-mode control of DC drive, IEEE Tranaction on Indutrial Electronic 5, no. 2, pp: ,24. [4] Xiaojuan, Yan, Liu Jinglin, A novel liding mode control for BLDC motor network control ytem, In 2 3rd International Conference on Advanced Computer Theory and Engineering (ICACTE), vol. 2, pp: V2-289,2. [5] Wang, Yaonan, Xizheng Zhang, Xiaofang Yuan, Guorong Liu, Poition-enorle hybrid liding-mode control of electric vehicle with bruhle DC motor, IEEE tranaction on vehicular technology 6, no. 2, pp: ,2. [6] Jeon, Jonghyun, Sanggun Na, Hoon Heo, Cacade Sliding Mode New Robut PID control for BLDC motor of In-wheel ytem, In Environment and Electrical Engineering (EEEIC), th International Conference on, pp: -4,2. [7] Stînean, Alexandra Iulia, Stefan Preitl, Radu Emil Precup, Emil Petriu, Claudia Adina Dragoş, Mircea Bogdan Rădac, 2-DOF PI (D) Takagi-Sugeno and liding mode controller for BLDC drive, In Power Electronic and Motion Control Conference (EPE/PEMC), 22 5th International, pp: DS2a-7,22. [8] Quintero Manríquez, Eduardo, Ramón Félix, Second-order liding mode peed controller with anti-windup for BLDC motor, In 24 World Automation Congre (WAC), pp: 6-65,24. [9] Shao, Yunbin, Rongrong Yang, Jianwen Guo, Yongling Fu, Sliding mode peed control for bruhle DC motor baed on liding mode torque oberver, In Information and Automation, IEEE International Conference on, pp: ,25. [2] Fang, Shipeng, Changhua Hu, Xiaoxiang Hu, Hongzeng Li, Adaptive robut control of bruhle DC (BLDC) motor baed on liding mode control (SMC) with unidirectional auxiliary urface, In Chinee Automation Congre (CAC), 25, pp: ,25. [2] Qingchao, Zhang, Ma Ruiqing, Deng Junjun, Zhao Ben, A cacade firt and econd order liding mode control approach for peed control of bruhle DC motor, In Control Conference (CCC), 25 34th Chinee, pp: ,25. [22] Satih Kumar Gudey, Rajeh Gupta, Sliding-mode control in voltage ource inverter-baed higher-order circuit, International Journal of Electronic 2, no. 4, pp: , 25. AUTHOR PROFILE Devendra Potnuru i currently working a Aociate Profeor in department of EEE, GMR Intitute of Technology (GMRIT), Rajam. Chennai.He ha around 5 year of teaching experience. Hi area of current interet are enorle peed control, Energy conervation, Energy efficient drive and control ytem. Y Santoh Kumar i Pot Graduate (M.Tech) tudent of EEE department, GMRIT, Srikakulam, A.P., India and Hi area of current interet are enorle peed control of BLDC motor and Adaptive control ytem. DOI:.287/ijet/27/v9i2/79287 Vol 9 No 2 Apr-May 27 82