Implementation of Adaptive Neuro Fuzzy Inference System in Speed Control of Induction Motor Drives

Transcription

1 J. Intellgent Learnng Systems & Applcatons, 00, : 0-8 do:0.436/jlsa Publshed Onlne May 00 ( Implementaton of Adaptve Neuro Fuzzy Inference System n Speed Control of Inducton Motor Drves K. Naga Sujatha, K. Vasakh Department of Electrcal Engneerng, AU College of Engneerng, Andhra Unversty, Vsakhapatnam, Inda. Emal: vasakh_k@yahoo.co.n Receved December 8 th, 009; revsed January 6 th, 00; accepted January 5 th, 00. ABSTRACT A new speed control approach based on the Adaptve Neuro-Fuzzy Inference System (ANFIS) to a closed-loop, varable speed nducton motor (IM) drve s proposed n ths paper. ANFIS provdes a nonlnear modelng of motor drve system and the motor speed can accurately track the reference sgnal. ANFIS has the advantages of employng expert knowledge from the fuzzy nference system and the learnng capablty of neural networks. The varous functonal blocks of the system whch govern the system behavor for small varatons about the operatng pont are derved, and the transent responses are presented. The proposed (ANFIS) controller s compared wth PI controller by computer smulaton through the MATLAB/SIMULINK software. The obtaned results demonstrate the effectveness of the proposed control scheme. Keywords: ANFIS Controller, PI Controller, Fuzzy Logc Controller, Artfcal Neural Network Controller, Inducton Motor Drve. Introducton Over the last three decades, varable speed drves are the most complex of all power electronc systems. Drve technology has been a confluence of many professonals from other felds, such as electrcal machnes, control systems and tradtonal power engneerng. To a tradtonal power electroncs engneer wth expertse n the desgn of, such as thyrstor phase-controlled converters, swtchng mode power supples, or unnterruptble power supply systems, the technology s ncomprehensble because of ts complexty and multdscplnary characterstcs. Modern varable speed drve applcatons requre steeples control and sutable dynamc response and accuracy. These consderatons have been met to a large extent n the past decade by thyrstor-controlled dc machnes. However, the dc machne remans expensve n relaton to the types of rotatng machnes. For the hgher power drves n ndustres, the lghter, less expensve, relable smple, more robust and commutator less nducton motors are desrable and these motors are beng appled today to a wder range of applcatons requrng varable speed. Unfortunately, accurate speed control of such machnes by a smple and economcal means remans a dffcult task. Wth the development of the slconcontrolled rectfer, trac and related members of the thyrstor famly, t has become most feasble to desgn varable-speed nducton motor drves for a wde varety of applcatons. Dfferent technques have been used, usng SCR controllers. A back-to back connected SCR are used n seres wth the rotor phases to control ther effectve mpedance [-4]. A chopper-controlled external resstance s used to control the speed by varyng the duty cycle of the chopper. A controlled rectfer s used n the rotor crcut to feed the external resstance, and by varyng the frng angle, the effectve rotor mpedance s controlled. enerally, varable speed drves for Inducton Motor (IM) requre both wde operatng range of speed and fast torque response, regardless of load varatons. Ths leads to more advanced control methods to meet the real demand. Very recently, the artfcal ntellgence tools, such as expert system, fuzzy logc and neural network are showng mpact on varable frequency drves. Copyrght 00 ScRes.

2 Implementaton of Adaptve Neuro Fuzzy Inference System n Speed Control of Inducton Motor Drves They are appled to mportant felds such as varable speed drves, control systems, sgnal processng, and system modelng. Artfcal Intellgent systems, means those systems that are capable of mtatng the human reasonng process as well as handlng quanttatve and qualtatve knowledge. It s well known that the ntellgent systems, whch can provde human lke expertse such as doman knowledge, uncertan reasonng, and adaptaton to a nosy and tme-varyng envronment, are mportant n tacklng practcal computng problems. ANFIS has gan a lot of nterest over the last few years as a powerful technque to solve many real world problems. Compared to conventonal technques, they own the capablty of solvng problems that do not have algorthmc soluton. Neural networks and fuzzy logc technque are qute dfferent, and yet wth unque capabltes useful n nformaton processng by specfyng mathematcal relatonshps among numerous varables n a complex system, performng mappngs wth degree of mprecson, control of nonlnear system to a degree not possble wth conventonal lnear systems [5-]. To overcome the drawbacks of Neural networks and fuzzy logc, Adaptve Neuro-Fuzzy Inference System (ANFIS) was proposed n ths paper. The ANFIS s, from the topology pont of vew, an mplementaton of a representatve fuzzy nference system usng a Back Propagaton neural network structure. The purpose of ths paper s to present a general method for estmatng both the nature of the dynamc response and the values of the sgnfcant parameters and operatng constrants of typcal nducton machnes controlled by SCR controllers [,3]. The dynamc behavor of a closed-loop speed-control system wth deltaconnected SCR s n the rotor s dscussed. The varous functonal blocks of the feedback system whch governs the system behavor for small varatons about the operatng pont are derved, and responses for speed perturbatons are obtaned analytcally and smulated.. State Space Approach A Set of nonlnear dfferental equatons can descrbe the behavor of the nducton motor [4-6]. If a complete soluton of the dynamc behavor of the nducton ma- chne s desred, these equatons must be solved n detal. By lnerarzng these questons about a steady state operatng condton, the resultng equatons n state form can descrbe the dynamcs, and provde the future state and output of the system. Perturbatons n reference voltage or frng angle and load torque leads to changes n rotor speed. The analytcal results used to nvestgate these speed changes are obtaned consderng the varous prevous functonal blocks, where the dfferent nput and output varables are denoted by X, X, X 3 and X 4. These varables are defned as follows: X =, X = V, X 3 = V c and X 4 = () The dfferental equatons, whch govern the small varatons about the operatng pont, are wrtten n terms of the above varables and representng n matrx form n Equaton (), where T, u T V T = u u X x x x x System Descrpton T L R The system conssts of a slp-rng nducton motor wth three equal external resstances, each connected to the rotor phase and three delta-connected phase-controlled SCR's placed at the open star pont of the rotor as shown n Fgure. In varable speed ac nducton motor drves, a contnuous montorng or control of slp speed or slp frequency s requred. A permanent magnet tachogenerator s mounted on the rotor shaft to provde a dc sgnal proportonal to the rotor speed to the feedback control crcut. The block dagram of the feedback control scheme of the nducton motor s shown n Fgure. The nducton motor stator s suppled wth constant voltage, constant frequency supply. The rotor speed s controlled and adjusted by advancng or retardng the frng angle of the SCRs. The tachogenerator output voltage proportonal to the rotor speed and s compared KK5 KK T T T K 0 x K x T 0 0 x T T x 0 0 TL x 3 KK x K K 3 K V R x 4 T x T T 4 T K T3 T 3 () Copyrght 00 ScRes.

3 Implementaton of Adaptve Neuro Fuzzy Inference System n Speed Control of Inducton Motor Drves 3 Phase Supply a R ex R ex T To Trgger Crcut b T 3 c R ex T Fgure. Schematc dagram of phase controlled SCR s n delta (Δ) confguraton 3-PHASE SUPPLY TACHO ENERATOR SLIP RIN I.M ROTOR SLIP RIN DELTA CONNECTED SCR s V R _ ERROR SINAL REF.VOLTAE P/PI/PID CONTROLLER Fgure. Block dagram of feedback system V c CONTROL VOLTAE FIRIN CIRCUIT FIRIN ANLE wth a fxed dc level VR whch represents the set speed. The error voltage s forwarded to the controller. The set peed s changed by varyng V R automatcally or manually. The controller may be a proportonal, or proportonal ntegral or proportonal ntegral dervaton type. The functon of the controller s to gve the requred control voltage whch wll adjust the frng angle to the sutable value and can be used also as a stablzng sgnal f more than one controller s used. The smulnk block dagram of feedback control scheme of the nducton motor s shown n Fgure 3. Transfer functons for the functonal blocks: The transfer functons for the varous functons blocks of the feedback system are shown n Fgure 4, and gven n detals as follows: ) Tachogenerator and flter: The transfer functon of ths block s represented by: K (3) ST s where K s the combned gan of the tachogenerator and the assocated flter, and T s the effectve tme constant of the flter. ) Controller: The change n the output voltage of the tachogenerator s compared wth the reference voltage VR and the resultant error voltage s fed to the controller. The controller output voltage s corrected n accordance wth the nput change n voltage. The change n the controller output voltage s denoted as V c. The transfer functon of the proportonal ntegral controller s: K( ST ) s (4) ST 3) Frng Crcut: The frng crcut decdes the change n frng angle n accordance wth the change n control voltage V c. It conssts of a ramp generator and a comparator. The ramp s synchronzed wth the sgnal avalable across the slp-rngs of the machne. For a gven change n the control voltage V c, the change n frng angle s gven by: V c (5) m where m s the slope of the ramp. For the present study, the frng crcut transfer functon can be wrtten as K3 3 s (6) ST where K3 s equal to l/m, and the tme constant s equal to one half of the maxmum expected delay. If the slp of the rotor at the operatng pont s s, then the tme constant T 3 s gven by: T 3 s f 3 (7) 3 Copyrght 00 ScRes.

4 Implementaton of Adaptve Neuro Fuzzy Inference System n Speed Control of Inducton Motor Drves 3 ANFIS Controller PI Controller Transfer Functon Step - Wthout any controller Swtch S an -K -K Transfer Functon Scope an Transfer Functon Step - Fgure 3. The smulnk block dagram of feedback control scheme of the nducton motor drve V R _ ERROR SINAL c K( ST) K3 ST ST3 V FIRIN ANLE Td c K4 () K ST SPEED (6) () (3) I.M.TECH K ST CHARACT. T _ (5) Td c T L K5 ELECTRICAL TORQUE (4) T d Fgure 4. Functonal blocks of closed-loop system 4) Inducton Motor: The torque developed by the machne at a gven operatng pont s a functon of speed of the machne and the frng angle of the thyrstors. The dfference between the developed torque and the load torque s appled to the rotatng elements. The torque developed by the machne s presented by Td F(, ) (8) where s the rotor speed n rad/sec, and s the frng angle. For the dynamc behavor of the nducton machne about any operatng pont for a gven perturbaton, the small change n the developed torque can be represented n terms of the small changes n rotor speed and frng angle as: Td Td Td (9) cons tan t cons tan t or T K K (0) d 4 5 The constants K4 and K 5 depend upon the operatng pont and are to be obtaned from the steady-state characterstcs of the system. The resultant change n the developed torque s represented as the summaton of the outputs of the two blocks (4) and (5). The change n the developed torque s compared wth the change n load torque and the resultant value s forwarded to the mechancal system, whose transfer functon can be expressed as: where K = m s F and T = K () ST J F Copyrght 00 ScRes.

5 4 Implementaton of Adaptve Neuro Fuzzy Inference System n Speed Control of Inducton Motor Drves F s the frctonal constant n N.m/rad/s, and J s the moment of nerta of the rotatng system n K m. 4. ANFIS Based Speed Controller Artfcal Intellgent tools such as Fuzzy Logc and Artfcal Neural Networks have shown great potental on varable frequency drves. Artfcal Neural Networks are concerned wth adaptve learnng, nonlnear functon approxmaton, and unversal generalzaton; fuzzy logc wth mprecson and approxmate reasonng [7,8]. But they share some common shortcomngs that hnder them from beng used more wdely. For example, neural networks, often suffer from a slow learnng rate. Ths drawback renders neural networks less than sutable for tme crtcal applcatons. Therefore, new and enhanced methods can be put forward. The fuzzy neural network s constructed to merge fuzzy nference mechansm and neural networks nto an ntegrated system so that ther ndvdual weaknesses are overcome. The ANFIS system determnes a control acton by usng a neural network whch mplements a fuzzy nference. In ths way, the pror expert s knowledge can be ncorporated easly. The controller has two states, a learnng state and a controllng state. In the learnng state, the performance evaluaton s carred out accordng to the feedback whch represents the process state. If nput-output tranng data s avalable, the performance can be assessed easly, and supervsed learnng can be employed. 5. Adaptve Neuro-Fuzzy Prncple The fuzzy nference commonly used n ANFIS s frst order Sugeno fuzzy model because of ts smplcty, hgh nterpretablty, and computatonal effcency, bultn optmal and adaptve technques. A typcal archtecture of an ANFIS s as shown n Fgure 5. Among many FIS models, the Sugeno fuzzy model s the most wdely appled one for ts hgh nterpretablty and computatonal effcency, and bult-n optmal and adaptve technques. For a frst order Sugeno fuzzy model, a common rule set wth two fuzzy f-then rules can be expressed as: Rule : f x s A and y s B, then z = p x q y r Rule : f x s A and y s B, then z = p x q y r where A and B are the fuzzy sets n the antecedent, and p, q and r are the desgn parameters that are determned durng the tranng process. Layer : Every node n ths layer contans membershp functons. o x,, () A B o y, 3,4 (3) where A and B can adopt any fuzzy membershp functon (MF). Fuzzfcaton Inference entgne Defuzzfcaton w w x A nput z Controlled output y B Input Layer Input layer Layer Fuzzfer layer Input layer Layer 3 Inference layer Input layer Layer 4 Defuzzfler layer Interence layer Input layer Fgure 5. Adaptve neuro fuzzy structure Copyrght 00 ScRes.

6 Implementaton of Adaptve Neuro Fuzzy Inference System n Speed Control of Inducton Motor Drves 5 Layer : Ths layer chooses the mnmum value of two nput weghts. A B o w x y,, (4) Layer 3: Every node of these layers calculates the weght, whch s normalzed. 3 w o w,, w w (5) where w s referred to as the normalzed frng strengths. Layer 4: Ths layer ncludes lnear functons, whch are functons of the nput sgnals. o wz w ( p xq yr),, (6) 4 where w s the output of layer 3, and {p, q, r } s the parameter set. The parameters n ths layer are referred to as the consequent parameters. Layer 5: Ths layer sums all the ncomng sgnals. 5 wz wz o wz (7) w w The output z n Fgure 5 can be rewrtten as: z w x p w y q w r wx p wy q w r (8) In ths paper the normalzed membershp functons of nput varables and output varable are shown n Fgures 6 and 7. The Three-dmensonal plot of Fuzzy Control surface s shown n Fgure Smulaton Results In ths paper, performance of the proposed ANFIS speed controller s evaluated and s compared wth PI controller and wthout any controller. The controller parameters are chosen to optmze the performance crteron of the dynamc operaton, and then the tunng was emprcally mproved. The smulaton s carred out to observe the performance of the system at dfferent load perturbatons. Fgure 6. Trangular membershp functons for nput varables e and e Fgure 7. Trangular membershp functons for output varable Fgure 8. Three-dmensonal plot of control surface The software envronment used for ths smulaton s Matlab ver. 7., wth smulnk package. The change n rotor speed s due to the perturbatons n reference voltage or frng angle and load torque. The analytcal results used to nvestgate these speed changes are obtaned consderng the varous prevous functonal blocks, where the dfferent nput and output varables are denoted by X, X, X 3 & X 4. The dfferental equatons whch govern the small varatons about the operatng pont n terms of above varables are gven n Equaton (). The perturbaton studes were carred out at dfferent operatng ponts wth dfferent system parameters (gans and tme constants) whch are gven n Appendx. Studes are carred out at operatng ponts wth varous system parameters (gans and tme constants). The smulaton results gve the present perturbaton study for step change n the load torque and reference voltage. From the Fgures 9 to the startng transents are realzed for ANFIS controller at dfferent operatng condtons. It can be observed from the fgures that the performance of the ANFIS gves better response compared wth PI controller and wthout any controller. 7. Conclusons A framework for tunng and self organzng ANFIS controller has been presented. Ths approach has been con- Copyrght 00 ScRes.

7 6 Implementaton of Adaptve Neuro Fuzzy Inference System n Speed Control of Inducton Motor Drves trasted wthout any controller and wth PI controller. The dynamc behavor of a closed-loop, varable speed nducton motor drve whch uses three slcon controlled rectfers has been studed n ths paper. Transfer functon blocks of the system for small varatons about an operatng pont are derved, and the transent responses wth the analytcal studes have been carred out. Comparson of ANFIS controller, wthout any controller and wth PI controller under normal operaton for a gven load torque and reference speed perturbatons has been presented. It Fgure 9. Varaton of speed devaton at 5% load change Fgure 0. Varaton of speed devaton at 0% load change Copyrght 00 ScRes.

8 Implementaton of Adaptve Neuro Fuzzy Inference System n Speed Control of Inducton Motor Drves 7 Fgure. Varaton of speed devaton at 5% load change has been demonstrated that the proposed method gves a good response, regardless of parameter varatons or external force. Smulaton results have shown the capabltes of the proposed controller n trackng predetermned desred speed trajectory. REFERENCES [] R. P. Basu, A Varable Speed Inducton Motor Usng Thyrstors n the Secondary Crcut, IEEE Transactons on Parer Apparatus and Systems, Vol. 90, 97, pp [] M. Ramamoorthy and M. Arunachalam, A Sold-State Controller for Slp Rng Inducton Motors, The IEEE Industry Applcatons Socety Annual Meetng, Los Angeles, Calforna, October -6, 977. [3] M. Ramamoorthy and M. Arunachalam, Dynamc Performance of a Closed Loop Inducton Motor Speed Control System wth Phase-Controlled SCR's n the Rotor, IEEE Transactons on Industry Applcatons, Vol. 5, No. 5, 979, pp [4] Y. Hsu and W. Chan, Optmal Varable-Structure Controller for DC Motor Speed Control, IEEE Proceedngs D on Control Theory and Applcatons, Vol. 3, No. 6, 984, pp [5] B. S. Zhang and J. M. Edmunds, On Fuzzy Logc Controllers, IEEE Internatonal Conference on Control, Ednburg, UK, 99, pp [6] H. Yng, W. Sler and J. J. Buckley, Fuzzy Control Theory: A nonlnear Case, Automatca, Vol. 6, No. 3, 990, pp [7] D. Drankov, H. Hellendorn and M. Renfrank, An Introducton to Fuzzy Control, Sprnger-Verlag, New York, 993. [8] M. Maeda and S. Murakam, A Self-Tunng Fuzzy Controller, Fuzzy sets and Systems, Vol.5, No., 99, pp [9] T. J. Procyk and E. H. Mamdan, A Lngustc Self- Organzng Process Controller, Automatca, Vol. 5, No., 979, pp [0] R. Storn and K. Prce, Dfferental Evoluton-A Smple and Effcent Adaptve Scheme for lobal Optmzaton over Contnuous Spaces, ICSI Techncal Report, March 995. [] D. Karaboga and S. Okdem, A Smple and lobal Optmzaton Algorthm for Engneerng Problems: Dfferental Evoluton Algorthm, Turk Journal of Electrcal Engneerng, Vol., No., 004, pp [] D. Borojevc, L. arces and F. Lee, Performance Comparson of Varable Structure Controls wth PI Control for DC Motor Speed Regulator, IEEE Industry Applcatons Conference, 984, pp [3] J. Zhao and B. K. Bose, Evaluaton of Membershp Functons for Fuzzy Logc Controlled Inducton Motor Drve, IEEE 00 8th annual Conference of the Industral Electroncs Socety, Vol., 00, pp [4] A. S. A. Farag, State-Space Approach to the Analyss of DC Machnes Controlled by SCRs, IEEE Proceedng Publcaton-on the Control of Power Systems Conference, Oklahoma, March 0-, 976, pp [5] N. Mohan, Electrc Drves: An Integratve Approach, Mnnesota Power Electroncs Research & Educaton, Mnnesota, 003. [6] N. Mohan, Advanced Electrc Drves: Analyss, Control and Modelng usng Smulnk, Mnnesota Power Electroncs Research & Educaton, Mnnesota, 00. [7] B. K. Bose, Fuzzy Logc and Neural Network Applcatons n Power Electroncs, Proceedngs of the IEEE, Vol. 8, No. 8, 994, pp [8] M.. Smoes and B. K. Bose, Neural Network Based Estmaton of Feedback Sgnals for Vector Controlled Inducton Motor Drve, IEEE Transactons on Industry Applcatons, Vol. 3, No. 3, 995, pp Copyrght 00 ScRes.

9 8 Implementaton of Adaptve Neuro Fuzzy Inference System n Speed Control of Inducton Motor Drves Appendx Varous ans and Tme Constants used for Perturbaton Study (Motor Speed 'N = 050 rpm) K = 0.03 T = K = 0.5 T = 0. K 3 = 60 T 3 = 0.0 K 4 = K 5 = K 5 = 40.0 T = 5.6 Copyrght 00 ScRes.