Low Computational Complexity Control of a Three-Phases Open-Windings AC Brushless Motor

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1 Low Computational Complexity Control of a Three-Phases Open-Windings AC Brushless Motor Alerto Cologni, Mirko Mazzoleni, Faio Previdi Dipartimento di Ingegneria Gestionale, dell Informazione e della Produzione Universita degli Studi di Bergamo 444 Dalmine (BG), Italy alerto.ologni@unig.it Astrat The omputational omplexity of a modulating ontrol is always one of the iggest limitation in the real ontrol of rushless motor. This paper presents a low omputational omplexity ontrol for a three phases open-windings AC rushless motor. The ontrol strategy is ased on a modified version of the D-Q frame: this solution allows to exploit the motor ontrol liraries, already availale on some motor ontrol miroproessors. The PWM is generated in aordane to a novel algorithm ased on a omination of two standard SVM algorithms, one for eah inverter. The urrent ontroller has een tested on a real open-windings motor, installed as an ative virations damper for aerospae appliations. The experiments demonstrate the good quality of the urrent traking and the high effiieny of the inverter, ontrolled with the proposed approah. Index Terms Current ontrol, Brushless motor, Open windings, High effiieny inverter, Spae vetor pulse width modulation I. INTRODUCTION Nowadays, the need of more powerful, lightest and safer motors is eome one of the most important request of the industry. In this ontext, the introdution of the open-winding tehnology for the rushless motors, allowed to inrease the power-weight ratio, the reliaility and to redue the energy onsumption []. This evolution, allowed to start a researh ranh in this motor arhiteture. Most of the early works are foused on the fault-tolerant apailities [], []. Further researh ativities demonstrate the power inrease with the same swith rating of the omponents, ompared with standard losed-windings motors [4]. The last ativities on this topi are related to the omparison, in terms of effiieny, of different ontrol approahes []. Comparing the standard star-onneted motor with the openwindings one, it is easy to understand that the atuation approah must e redefined. During the last deade some ontrol solutions have een proposed [6] [8]. Considering one of the first researh ativities in this ontext [9] (with the introdution of a two stages atuation system), the possile 4 β 6 α Fig.. SVM Atuation setors in the star-windings (left) and open-windings (right) motors onfigurations of the two inverters lead to a total numer of 64 ominations of the swithes. This huge numer of possile onditions, implies an inrease of the instrutions in the SVM (Spae Vetor Modulation) ode. In Figure the SVM setors are represented in oth ases (star-windings and open-windings): the identifiation of the setor with the dual inverter onfiguration auses a signifiant rise of the omputational effort on the miro-ontroller. In this paper, a novel ontrol algorithm for the openwindings AC rushless motor is proposed. Speifially, the first ontriution of this doument is to desrie a low omputational omplexity ontrol of a three-phases open-windings AC rushless motor. The main idea ehind this tehnique is to guarantee alaned urrents during the atuation: driving the two inverters in a ertain way, also without an high omplexity, it is possile to otain symmetri urrents in the windings. A seond ontriution of the paper is the implementation of the designed algorithm for the ontrol of a real motor. This ativity allowed to experimentally verify the effiieny of the proposed solution. The onsidered ase study is an ative viration damper for aerospae appliations []. The use of ative damping allows to introdue energy into the system and aurately and effetively ahieve the designed performane y means of ontrol systems [] [4]. An ative β α /6/$. 6 IEEE

2 damping system requires sensors, atuators, a soure of power and an eletroni ontrol system. The use of ative damping strategies an provide fine frequeny tuning, also varying with time, higher ontrol ation intensity, ontrol of power effiieny and greater auray in traking []. Moreover, in aerospae appliations the atuator must also have small weight and high reliaility (see [6] as an example). In partiular, ative viration damping systems ased on Eletro- Mehanial Atuators (EMAs) have een already suessfully used, espeially in those appliations where high fore values at quite low frequeny are neessary (see [7] as an example). The use of this type of motors allows to optimize some of the ritial limits of the appliation of eletro-mehanial atuator in the aerospae field. It allows to: inrease the power-weight ratio; inrease the maximum urrent, and onsequently the torque, with a ertain DC us voltage; inrease the reliaility of the atuation system thanks to the fault-tolerant struture of the open-windings motor In this ontext, the design, the implementation and the testing of a new ontrol solution for an innovative atuation system allows to move forward the researh limit. The remainder of the paper is as follows. In Setion II, the ontrol approah for the open-windings AC rushless motor is detailed. In Setion III the layout of the experimental setup is desried, and a desription of the experiments has een arried out. Setion IV is devoted to the results desription and analysis. Some onluding remarks end the paper. II. PROPOSED APPROACH The motor ontrol requires to atuate a set of output that determine the voltages of the motor windings. In this setion, the ontrol algorithms neessary for this purpose are desried. A. Control of a star-windings motor Considering the lassi star-windings motor, the defined voltages are three (one for eah phase), usually atuated using the PWM (Pulse-Width Modulation). In Figure it is possile to oserve the input signals neessary to drive the motor. The signals are, generally, two for eah terminal: one that ommands the upper mosfet (onneted to the positive line of the DC us) and the other one that ommands the lower one (onneted to the ground of the DC us). Considering, however, the struture of the iruit, it is easy to understand that, the upper ommand (e.g P + a,h ) and the lower one on the same leg (P + a,l ) an t e ativated simultaneously; for this reason it is possile to onsider the signals as one for eah winding (the two ommands are one the negate of the other, negleting the dead time neessary for the mosfet ommutation). V d P + a,h P + a,l P +,h P +,l P +,h P +,l V a + V + Ia Phase A I Phase B Rotor Stator Fig.. Struture of a single inverter Phase C In the star-windings ase, using Kirkoff, it is possile to write the simple urrent alane: I a +I +I = () It means that, in order to ontrol a star-windings motor it is neessary to aquire two of the three urrents. One extrated (y means of measure or alulus) the three urrents, it is possile to otain, using the Clarke transformation, the two urrents I α and I β that represent the urrent omponent in the diretion of the first winding, and the perpendiular one (oth integral with the stator). I a I α,β,γ = I I I () Comining the equations and it is easy to alulate the value of I γ : it is always zero (the urrents are automatially alaned). Using the Park transformation, it is possile to otain the quadrature urrent I q and the diret urrent I d : these urrents depend from the rotor position θ and represent, respetively, the motor torque and the power losses (I γ doesn t hange eause it represents the urrent on the rotation axis). os(θ) sin(θ) I α I d,q,γ = sin(θ) os(θ) I β () I γ One otained the d-q measures, it is possile to lose two ontrol loops, in order to provide the defined voltages to the motor.

3 Vd P + a,h P + a,l P a,h P a,l P +,h P +,l V a + Va P,h P,l P +,h P +,l V + P,h P,l V PWM values for eah yle. The proposed approah is ased on this onept: exploit the standard SVM algorithm in order to extend the numer of outputs, guaranteeing an high effiieny (low I d and I γ ). In order to guarantee the alane of the urrents in the windings (I γ = ), the onept is to feed a seond standard SVM using the negate V α and V β signals. Phase B Modified SVM Iq;ref Id regulator Iq regulator Id Iq Iγ Phase A Rotor Stator Phase C Fig.. Struture of a dual inverter Vd Vq Park transformation Inverse Park transformation Iα Iβ Iγ Vα Vβ Clarke transformation Modified SVM Ia I I Motor θ A. Standard SVM: exeute the standard SVM with the inputs V α and V β. B. Calulate the opposite stator voltages: ompute the two opposite stator voltages V α,neg = V α and V β,neg = V β. C. Opposite SVM: exeute the standard SVM with the inputs V α,neg and V β,neg. D. Assign outputs: assign the output of the standard SVM to the first inverter and the outputs of the opposite SVM to the lower one. The details of the algorithm are defined in Tale I, where φ represents the angle formed y the V α and V β omponenents in the V α - V β spae with respet to the V α axis. In order to evaluate the performane of this approah, a real experiment is arried out, and an effiieny analysis is presented. Fig. 4. Struture of the open-windings ontrol B. Control of a open-windings motor Considering an open-windings motor (the struture of whih is depited in Figure ), it is easy to understand that the atuation algorithm must e redesigned, in order to manage the numer of output to the motor (6 voltages instead of ). The ontrol tehniques for this type of motors, are ased on the sheme represented in Figure 4. The layout is similar to that used in the star-windings motors: starting from the urrent measures (in this ase of the three windings, eause Equation is not valid), it is possile to extrat, using Clark and Park transformation, the I d and I q measures, and, using two ontrol loops, the two (diret and quadrature) voltages an e defined. The stator urrents, extrated through the inverse Park transformation, enter in the SVM module, that determines the six PWM to the windings. The SVM alulus is the ompletely redesigned part in respet to the star-windings motor. Considering the lassial two-levels approah, the numer of possile swithes in funtion of the ative setor is 4. This huge numer of onditions implies an inrease of the omputation needed to define the III. EXPERIMENTAL SETUP The low omplexity ontrol has een implemented on a real atuator, in order to verify its performane. The atuator has een designed for the use in a lassi layout for dynami viration damping. The damper is onneted to an un-damped main mass-spring system, and tuned to the resonant frequeny of the main mass-spring. When a fore, with the same frequeny of the tuned resonant frequeny of the damping system, is applied, there is no motion of the main mass, and no net reation fore (other than stati equilirium fore) is required at the mehanial onstraint. This an e ahieved y measuring the viration fore and applying the orret ounterating fore with the atuator (see Figure ). The system an e desried y the equations of motion of a lumped parameter model (see Figure 6). The allsrew joint an e assumed to e an infinite wedge with angle α: Mx m m vẍ v = k s(x i x M)+k eq(x v +y vtan(α) x M)+ + s( x i x M)+ ( x v + y vtan(α) x M)(4) = k v(x i x v) k eq(x v +y vtan(α) x M)+ + v( x i x v) ( x v + y vtan(α) x M) () m eqÿ vtan(α) = k eq(x v +y vtan(α) x M)+ ( x v + y vtan(α) x M) (6)

4 Three phases AC rushless motor Flexile struture Ballsrew atuator Load ell high dynami urrent sensors with a range of ± A The ontrol system for the presented ativity is ased on two nested ontrol loops. The inner one is the urrent ontrol systems (the ore of the puliation); while the seond one is a fore ontroller. This atuator is designed in order to work in a defined frequeny (in partiular the resonane frequeny of the spring - mass struture). For this reason, the tests (desried in Setion IV) are exeuted with a referene sinusoidal signal at Hz. y Struture stiffness ks,s where: x Fig.. Atuator sheme Main mass M xi, xi x, x h LC Load sensor kl k, mv xv, xv,yv, yv tan(α) = p πr Asorer mass and allsrew atuator kv,v Fig. 6. Mehanial model of the atuator M is the main mass; m v is the mass of the atuator; k s and s are respetively the elasti onstant and the damping oeffiient of the load spring; k and are respetively the elasti onstant and the damping oeffiient of the load sensor; k v and v are respetively the elasti onstant and the damping oeffiient of the onnetion etween the sensor and the atuator; k l is the elasti onstant of the load sensor; k eq = kk l k +k l is the equivalent elastiity of the load sensor and its onnetion to the atuator. All the mehanial strutures are designed in order to have parameters (masses, stiffness and damping) as lose as possile aligned to the required resonane ( Hz). The eletroni layout is ased on a freesale miroontroller (DSP 68). The tehnial details are the following: Three phases motor with sinusoidal BEMF; DC us at 8 V; nominal power of 7 W; two three phases ridges with A of maximum urrent; IV. RESULTS The experiments of the real system allow to analyze the performane of the proposed approah. During the tests a ertain I q referene is defined (as already disussed a sine at Hz), while a zero referene is seleted for I d. One otained the measures on the real system (I d, I q and I γ ) it is possile to alulate the effiieny of the inverter [8]. The atuator has een tested on a test enh with an elasti load. The atuator performane have een assessed in experiments at the target working frequeny f w, y measuring the generated fore, the kinemati parameters (angular and linear displaement/veloity/aeleration) and urrent/power asorption. The tested I q referene is a sine with an amplitude of A and a frequeny of Hz. The performane of the ontrol loop are depited in Figure 7: the quality of the traking is good; the RMSEs (Root Mean Square Errors) are the followings: I q :.8 A; I d :.78 A; I γ :.9 A. In order to evaluate the performane it is neessary to alulate the overall effiieny of the ontrol. Starting from the I d, I q and I γ, the overall effiieny an e alulated as: Iq (t) η(t)[%] = (7) Id (t) +I q (t) +I γ (t) The result of this alulus are depited in Figure 8: the average effiieny is 9 % (with the sinusoidal I q referene). Another important result of the introdution of this openwindings arhiteture, is the possiility of inrease the reliaility of the motor: with this onfiguration, the motor is ale to atuate (in eah rotor position) also disaling one of the three phases. In order to verify the performane in these onditions, a test has een performed, disonneting one of the motor phases (simulating a failure on a winding or on a omponent of the three phases ridge). The results of this experiment are depited in Figure 9; the RMSEs are, in this ase, the followings:

5 Quadrature urrent Quadrature urrent Diret urrent Diret urrent - Referene Measure Gamma urrent Gamma urrent Fig. 7. Control performane in the nominal onditions Fig. 9. Control performane with a phase fault Effiieny [%] Effiieny [%] Fig. 8. Control effiieny in the nominal onditions Fig.. Control effiieny with a phase fault I q :.48 A; I d :. A; I γ :.64 A. The overall effiieny, in ase of one phase fault, is represented in Figure : the average effiieny is 8.8 %. V. CONCLUSIONS In this paper, a low-omputational omplexity algorithm, for the ontrol of a three-phases open-windings AC rushless motor has een proposed. The main idea is to exploit the standard Spae Vetor Modulation in order to alulate the ommand signals to the lower ridge, using a modifiation of the inputs of this algorithm. In this way, the omplexity of the alulus is redued, omparing to the ommon multilevels open-windings ontrol arhitetures [4]. The approah has een first presented qualitatively and then disussed in detail on an experimental ase study. Speifially, the ontrol of an ative damper for an aerospae appliation has een oped with and satisfatory results have een otained. From a pratial point of view, the ontrol performane denote a very high effiieny of the inverter (9 %) and the possiility of work with only two phases with an aeptale effiieny (8.8 %). Future work will e devoted to the optimization of the effiieny in ase of failure, swithing the SVM to another modified version. 4

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