Hybrid Position Controller for an Indirect Field- Oriented Induction Motor Drive

Transcription

1 Hybid Position Contolle fo an Indiect Field- Oiented Induction Moto Dive Antonio B. de Souza Junio; Tobias R. Fenandes Neto; Dalton de A. Honóio; Luiz Henique S. C. Baeto; Lauinda L. N. dos Reis Robotic and Automation Reseach Goup GPAR / Depatment of Electical Engineeing / Fedeal Univesity of Ceaá Cento de Tecnologia Campus do Pici, Bl. 705 Fotaleza-CE, Bazil, / Phone: babosa@dee.ufc.b,tobias@dee.ufc.b Abstact This pape pesents a conception and implementation of a hybid contolle technique applied in an indiect fieldoiented (FOC) induction moto dive. The main goal is to impove the position tacking pefomance with a hybid contolle based on the classical popotional (P) contolle and the genealized pedictive contol (GPC) appoach. It has shown though expeimental esults, the effectiveness of the poposed hybid contolle. Indeed, the contolle has the fast tacking capability as a P contolle and the obustness as a GPC contolle. I. INTRODUCTION Afte the 1950s, the industial automation field has been deeply eseached. The advanced of micoelectonics, semiconducto techniques and electical machines ae the main easons of this. In fact, the induction machines (IM) ae widely used in this aea, because its low manufactuing cost, obustness and low maintenance need. Howeve, IM has a non-linea mathematical model, which is closely dependent on the cetainty of its paametes, e.g. oto s esistance and inductance. When the application goal is the use of this kind of machine as a high-pecision sevo moto dive, this issue becomes an obstacle. Theefoe, some modeling techniques wee designed in ode to ovecome this baie. The FOC is one of them [1]. This technique allows modeling the IM similaly as a diect cuent (DC) machine. The machine vaiables effects can be decoupled due to a pope oientation of its magnetic fields, esulting in a simple model as an independent excited DC moto []. Thus, classical fixed gain contolles, like P and popotionalintegal (PI), can be applied in the contol loops of the IM, including the position loop. In geneal, thee ae two main pefomance equiements fo moto dive applications: high distubance ejection chaacteistics and the fast tacking of the set-point without oveshoot [3]. Due to the need of highpecision applications, new appoaches to obtain bette esults with the typical contolles ae emeging. Recently, stuctues mixing vaious types of contolles known as hybid contolles have been poposed by seveal eseaches in ode to achieve the best pefomance fo each stategy. In [4], a hybid PID contolle is pesented. The latte contolle has the advantage of being easily tuned by a fuzzy contolle, impoving the system obustness. A new obust MRAC using a hybid stategy is poposed in [5]. The implementation of a hybid contol fo moto dive applications is poposed in [6]. This technique takes in count the powe invete state as a contol vaiable in a switchingbased hybid system (HS), which is nomally neglected by the classical contol appoaches. In [7] a hybid contolle fo obot manipulato is obtained by using the impedance contol within the position contolle and a vaiable stuctue model eaching contol (VSMRC) in the foce loop. The study made in [8] shows a hybid speed contol of a compound DC moto mixing a fuzzy contolle with a popotional-integal-deivative (PID) contolle. In the same line, [9]poposes a fuzzy hybid contolle fo the position and foce contol loops, in ode to educe the numbe of sensos in an eye-to-hand obotic manipulato. The pape deals with theoetical development and pactical implementation of a hybid position contolle suitable fo obotic applications, i.e., the use of IMs in the joint of a obot am as a sevomoto. The poposed contolle mixes the advantages of two well known contol techniques: the fast tacking esponse of the P contolle and the obustness of the GPC contolle. Theefoe, expeimental esults will be depicted in ode to demonstate the main featues of the developed system, to validate the employed methodology. The pape is oganized as follows. Section II descibes the mathematical model of the decoupled IM, as well as the poposed hybid contolle desciption in subsection contolles design. Section III pesents the expeimental setup and esults. Finally, the conclusions ae given in section IV. II. MOTOR MODEL AND PROPOSED HYBRID STRATEGY A. Moto Model The FOC block diagam is shown in Fig. 1. The voltage souce invete (VSI), the space vecto modulato and the contol block with the position efeence compose the system configuation. The SVPWM modulato convets the cuent /15/$ IEEE 1541

2 contol signals in the specifics switching functions fo the VSI. The moto cuents and the shaft position ae used in its espective feedback loop. Lm σ = 1 (3) L L s λ = L i + L i (4) q m qs d λ = L i + L i (5) d m ds q In the field-oiented technique, the oto flux linkage λ is assumed to be always aligned with the d-axis. Thus, the oto flux linkage and its deivative in the q-axis is zeo. Then, fom (1) the d- and q- stato voltage equations ae given in equations (6) and (7): Figue 1. The field-oiented induction moto dive with the position contol loop. The state-space model of the induction moto in the otating dq- efeence fame is given as follows []: Whee: x = Αx+ Β u (1) ids vds i qs 1 v qs x = ; Β = ; λ d σ L s 0 λ q 0 Rs R(1 σ) LR m PωLm ωe σls σl σll s σll s Rs R(1 σ) PωLm LR m ωe σls σl σll s σll s Α= ; LR m R P 0 ωe ω L L LR m P R 0 ( ωe ω) L L The electomagnetic toque T e is given by: 3P Lm Te = ( iqsλd idsλq) () 4 L While expessions (3), (4), (5) give the following paametes: L v R L s i L i m qs = s + s qs + ωe s ds L v i ω L L i m ds = s ds e s qs L The oto flux linkage can be found fom (1) and assuming that the magnetizing stato cuent i ds will be kept constant, it is possible to obtain: d m ds (6) (7) λ = L i (8) Then, ewiting () the electomagnetic toque is given by: 3P Lm Te = iqsids (9) 4 L The vaiable i qs epesents the toque cuent command geneated fom the speed contolle and the vaiable i ds emains constant because of the fixed value of the oto flux linkage in (8). The slip angula speed ω sl is necessay to calculate the oto flux linkage angula positionθ e in the indiect FOC theoy. Thus, with the equations (4) and (1), the slip angula speed is obtained: sl L Ri Ri ω = = (10) m qs qs Lλd Li ds With the value of the slip angula speed and shaft positionθ given by the encode, it is possible to obtain the oto flux linkage angula position: 154

3 R i θe = θ dt (11) + L i qs ds θ sl The equation (11) poves the indiect field-oiented contol. In othe wods, it is possible to obtain the position of the oto flux linkage indiectly though the position of the machine shaft and the slip angle between the stato and oto magnetic fields. All this steps could be bette visualized in Fig., whee the poposed hybid contol stategy is detailed. Figue 3. Step esponse using Yawana and Sebog smethod. The Table I shows the acquied paametes. TABLE I. Method vaiables PARAMETERS EXTRACTED FROM THE STEP RESPONSE OF THE YUWANA AND SEBORG IDENTIFICATION METHOD [11] Desciption Value c Steady state value ads c m c p1 c p Minimum of the output esponse Fist peak of the output esponse Second peak of the output esponse 0.96 ads 1.14 ads 1.01 ads Δt Half-peiod of oscillation 0.16 Figue. Contol block diagam epesenting the indiect field-oiented induction moto dive with the position contolle. It could be noted that this kind of contol appoach is stongly dependent on the machine paametes, which may change duing the moto unning. Theefoe, the contol stategy must be obust enough against paametic uncetainties. B. Poposed Hybid Stategy 1) System modeling In ode to achieve a good pefomance fom the contolles, it is necessay fo the identification of the moto model. Then, it was appoximated by a fist-ode plus time delay (FOPTD) model [10] and the chosen identification method was the Yuwana and Sebog[11]. Fom the step esponse shown Fig. 3, it is possible to extact the paametes needed to feed the model. Using the Yuwana and Sebog[11] identification method with the acquied paametes, the position open loop tansfe function in continuous-time was obtained and discetized by assuming a sampling ate of 0.1ms, esulting in: z H( z) = 1 1 z 1 (1) ) Popotional and GPC-Based I+P contolles design The step esponse of the obtained tansfe function model (1) is used in the Ziegle-Nichols tuning method [1]. As esult, it was detemined the paamete Kp = fo the position contolle. The othes paametes fo the cuent and speed contolles wee calculated in [13]. The time-seies model chosen fo the pedictive contol is the Contolled Auto Regessive and Integated Moving Aveage Model (CARIMA) [14]. The stuctue RST fo the I+Pcontolle [1] was used, in ode to obtain the GPC- Based I+P contolles, which is pesented in Fig. 4.Moe details fo the design and tuning method ae pesented in [15]. Figue 4. Poposed hybid position contolle block. 3) Stuctueof hybid contolusingfuzzy logic Fig. 5 shows with detail the poposed hybid contolle with fuzzy logic pesented in Fig. 1. The action of two contolles can be weighted by the fuzzy algoithm. As it can be seen, thee ae two outputs fo the fuzzy logic block: one is diectly multiplied by the P block output, and the othe one is 1543

4 the complement of the fist fuzzy output, then it is multiplied by the GPC block output. This complement is used, since the fuzzy logic typically employs values anging fom zeo to one. In ode to obtain the stategy combining both contolles, thee diffeent egions ae developed fom the contol suface, which ae called NARROW, P-GPC, and BROAD, as shown in Fig.7, whee e(θ ) is the nomalized position eo and μ is the membeship degee. Figue 5. Poposed hybid position contolle block. Table II shows the fuzzy ules used fo the contolle. As displayed, the behavio of the weighting fuzzy action applied to the P contolle and the GPC contolle, changes accoding to the position eo. Fo instance, when the position eo is 0.55, the fuzzy action will be 0.7 and the weighting of the P and GPC contolles will be 0.7 and 0.3, espectively, as shown in Fig.6. Figue 6. Fuzzy contol suface. The position eo is calculated by diffeence of the efeence position and the encode position. The adopted linguistic ules expess the elationship between the vaiables and they ae defined as Positive Big (PB), Positive Medium (PM), Positive Small (PS), Zeo (ZE), Negative Small (NS), Negative Medium (NM) and Negative Big (NB). Position eo TABLE II. Fuzzy action FUZZY RULES LOOP-UP TABLE P contolle weighting GPC contolle weighting NB PB PB PS NM PM PM PS NS PS PS PM ZE ZE ZE PB PS PS PS PM PM PM PM PS PB PB PB PS Figue 7. Membeship functions used in fuzzy logic. The fist stategy involves a pue GPC egion with little elevance elation. The output of this egion aims to keep the steady-state eo in a minimum value o eliminate it. The following egion is the P-GPC, which poduces a single output with both contolles. The pupose of this egion is to smooth an eventual oveshoot when the position efeence suddenly is changed. The last aea involves moe the P action than the GPC, and it is esponsible to bing the system to the efeence as fast as possible. III. EXPERIMENTAL SETUP AND RESULTS A. Expeimental Setup One DSC fom Texas Instuments TMS30F8335 caies out the contolle. The thee-phase squiel cage IM has fou poles, 0.5HP and Y-connected windings. The specifications and paametes of the IM ae given in Table III. TABLE III. Rated Specifications SPECIFICATION AND PARAMETERS OF THE IM Moto s Paametes Rated powe 0.5 HP R Ω Rated speed 175 pm R s Ω Rated voltage 0 V L 0.16 H Rated cuent 1.6 A L s 0.16 H Numbe of poles 4 L m H The schematics and one photo of the expeimental setup ae shown in Fig.8 and Fig. 9, espectively. The invete is a 10-kVA industial voltage-souce thee-phase invete fom Semikon. The mechanical load is a DC-moto fom the manufactue PHYWE. The DSC poduces a PWM switching fequency of 10 khz and an incemental encode, which is coupled to the moto shaft, gives the actual position. The DSC counte is used to count the encode pulses and convet it to adians. The sampling time is 0.1ms. The cuent sensos ae Hall-effect cuent senso fom LEM. 1544

5 B. Expeimental Results In ode to veify the effectiveness of the implemented contol stategy, seveal position tests ae descibed. Fou types of efeence signals wee utilized: step, sinusoidal, tapezoidal and tiangula. The step efeence veifies the contolle s pefomance fo an abupt change in the position efeence. The sinusoidal efeence veifies the contolle s pefomance when the position changes smoothly ove the time. The tapezoidal efeence checks the position tacking when the position inceases linealy. The tiangula efeence veifies the abupt position changing, when it eaches the maximum in eithe positive (o negative) diection. The next esult is the system esponse fo a sinusoidal efeence position signal, which is shown in Fig. 11. Figue 10. Expeimental esultfo the system usinga step position efeence. With this esult, it is possible to note a good tacking chaacteistic of the efeence signal. In the inteval [t 0, t 1 ] the contolle acts like as a mix of P-GPC, conducting the oto of 3 ads to 1 ad steadily. The same esponse duing the descending position in the inteval [t 0, t 1 ] is epeated duing the ascending position in the inteval [t 1, t ]. Figue 8. System s schematics. Figue 11. Expeimental esultsfo the system usinga sinusoidal position efeence. Figue 9. Expeimental setup. The fist esult is shown in Fig. 10, a step efeence ofads is commanded in ode to visualize the pefomance of each membeship function of Fig. 7. In the inteval [t 0, t 1 ] the hybid contolle has the P action until the position eo leaves the BROAD egion. Aftewads, in [t 1, t ] the hybid contolle output is affected mainly by the P-GPC egion. Finally, afte t the contolle output is influenced by the NARROW egion (GPC action), as much as the e(θ )is zeo o nealy zeo. Hence, it is possible to clealy visualize in the measued esult the thee dynamics of the poposed contolle. The next esult is the system esponse fo a tapezoidal efeence position signal. Fig. 1 shows the behavio of the shaft position and the cuents i ds and i qs. The intevals [t 0, t 1 ] and [t, t 3 ] have simila esults. Theefoe, the shaft position emained at stand still fo the given efeence value. On the othe hand, in the inteval [t 1, t ] and afte [t>t 3 ] the shaft position changes linealy, since the cuent i qs is injected allowing the shaft otation. It can be noted in all esults that the cuent i ds emained constant in the efeence value of 0.A, poving the effectiveness of the d-axis cuent contolle. The i ds cuent is esponsible fo the magnetization of the machine and shall not be changed duing the otation of the shaft. 1545

6 Figue 1. Expeimental esultsfo the system using a tapezoidalposition efeence. intevals [t 0, t 1 ] and [t 1, t ] ae simila and with opposite diections, as expected. The last esult is shown in Fig. 14. It is a compaison of step esponses of each contolle individually. Each technique is tested alone in the position loop in ode to analyze its pefomance and chaacteistics in contast to the othes. As it can be seen, the P contolle has the faste settling time, nevetheless, with oveshoot. Fo the GPC esponse, it noted the typical smooth settling motion with long peiods. Finally, the poposed hybid contolle shows the good chaacteistics of both contolles alone in one single contol stuctue. IV. CONCLUSION In this pape, it was shown an oveview fo a hybid position contolle used in an indiect field-oiented induction moto dive. Depending on the position eo, the fuzzy logic block mixes both contolles actions (P and GPC) to achieve a fast and pecise position tacking, and obust pefomance unde load toque distubance. With the given design pocedues and the acquied test esults, it can veify that the poposed contol method is vey obust and toleates extenal system s uncetainties. Futhemoe, this wok shows the feasibility of the given position contolle fo embedded moto dive system. At last, this technique has poven to fulfill the equiements fo obotic applications, e.g., the moto dive located at the joint of a obotic am. ACKNOWLEDGMENT The authos would like to thank the CNPq and the CAPES fo the financial suppot. Figue 13. Expeimental esultsfo the system usinga tiangula position efeence. Figue 14. Expeimental esultsfo the compaison among P, GPC and Hybid contolles. Anothe esult is shown in Fig. 13, whee it is pesented the system esponse fo a tiangula position efeence signal. This test is simila to the esult shown in Fig. 1, howeve, the contolle has to povide the position efeence tacking without a peiod of constant value. The latte esult pesents a good position tacking pefomance, even with the epetitive efeence changes. Indeed, the behavios depicted in the NOMENCLATURE T e = Electomagnetic toque, N.m R s = Stato esistance, Ω L s = Stato magnetizing inductance, H R = Roto esistance, Ω L = Roto magnetizing inductance, H L m = Magnetizing inductance, H P = Numbe of poles ω e = Electical angula speed, ad/sec ω = Roto angula speed, ad/sec ω sl = Slip angula speed, ad/sec θ = Roto angula position, ad θ e = Roto flux linkage angula position, ad θ sl = slip angula position, ad v ds = d-axis stato voltage, V v qs = q-axis stato voltage, V i ds = d-axis stato cuent, A i qs = q-axis stato cuent, A = d-axis stato cuent command, A = q-axis stato cuent command, A λ q = Roto flux align with the q-axis, Wb λ d = Roto flux align with the d-axis, Wb s = Laplace opeato z -1 = Backwad shift opeato Δ = Diffeencing opeato 1546

7 REFERENCES [1] K. Hasse, Zum dynamischen Vehalten de Asynchonmaschine bei Betieb mit vaiable Staendefequenz und Staendespannung( On the dynamic behavio of induction machines diven by vaiable fequency and voltage souces ), ETZ Ach., 1968,89, pp [] B. K. Bose, Powe electonics and AC Dives, Pentice Hall PTR, Knoxville, 001. [3] T. Ying-Yu, DSP-Based obust contol of an AC induction sevo dive fo motion contol, IEEE Tansactions oncontol Systems Technology, vol. 4, no. 6, pp , Nov [4] T.-J. Ho, L.-Y Yeh, Design of a Hybid PID Plus Fuzzy Contolle fo Speed Contol of Induction Motos, IEEE 010 Confeence on Industial Electonics and Applications, 010, pp [5] K. Halbaoui, D. Boukhetala, F. Boudjema, A new obust model efeence adaptative contol fo induction moto dives using a hybid contolle, IEEE 008Intenational Symposium on Powe Electonics, Eletical Dives, Automation and Motion, 008, pp [6] X. Lin-Shi, F. Moel, A. M. Llo, B. Allad, J. -M. Retif, Implementation of Hybid Contol fo Moto Dives, IEEE Tansactions onindustial Electonics, vol. 54, no. 4, pp , Aug [7] A. Jafai, J.-H. Ryu, M. Rezaei, R. Monfaedi, A. Talebi, S. S. Ghiday, Sliding mode hybid inpedance contol of obot manipulatos inteacting with unknown envionments using VSMRC method, 013Intenational Symposium on Robotics, 013, pp [8] J. Xiao, B. Li, D. Zhou, J. Chai, L. Zhang, Speed Contol System Based on Impoved Fuzzy-PID Hybid Contol fo Diect Cuent Moto, 010 Intenational Confeence on Digital Manufactuing and Automation, 010, pp [9] W.-C. Chang, C.-K Shao, Hybid fuzzy contol of an eye-to-hand obotic manipulato fo autonomous assembly tasks, 010 Poceedings of SICEAnnual Confeence, 010, pp [10] L. A. Aguie, Intodução à Identificação de sistemas Técnicaslineaes e não-lineaes aplicadas a sistemas eais,editoa UFMG, Belo Hoizonte, 004. [11] M. Yuwana, D. E. Sebog, A New Method fo On-line Contolle Tuning, AIChE Jounal, vol. 8, no. 3, pp , May198. [1] K. Astöm, T. Hägglund, PID Contolles Theoy, Design and Tunning,Instument Society of Ameica, Reseach Tiangle Pak, [13] D. A. Honóio, E. C. Diniz, A. B. S. Júnio, O. M. Almeida, L. H. S. C. Baeto, Compaison Between Sliding Model Contol and Vecto Contol fo a DSP-Based Position Contol Applied to Squiel-Cage induction Moto, IEEE 010 Intenational Confeence on Industy Applications, 010, pp [14] D. W. Clake, Genealized Pedictive Contol: A Robust Self-Tuning Algoithm, 1987Ameican Contol Confeence, 1987, pp [15] A. B. de S. Júnio, E. C. Diniz, D. de A. Honóio, L. H. S. C. Baeto, L. L. N. dos Reis, Hybid Contol Robust Using Logic Fuzzy Applied to the Position Loop fo Vecto Contol to Induction Motos, Electic Powe Components and Systems, vol. 4, no. 6, pp , Ma