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Fırçasız Doğru Akım Motorlu Tahrik Sistemlerinde Oniki Darbeli Sürücü

Fırçasız Doğru Akım Motorlu Tahrik Sistemlerinde Oniki Darbeli Sürücü

##### Dosyalar

##### Tarih

1997

##### Yazarlar

Tezduyar, Latif

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

Institute of Science and Technology

Institute of Science and Technology

##### Özet

Bu tez çalışmasının amacı, sürekli mıknatıslı fırçasız motorlu tahrik sistemlerinde moment darbesi bileşeninin en azlanmasına, başka bir ifadeyle moment kalitesinin yükseltilmesine yönelik farklı bir besleme ve denetim yaklaşımı geliştirmektir. Literatürde verilen çalışmalardan ve ticari uygulamaya dönük uygulamalardan, sürekli mıknatıslı fırçasız motorların beslenmesinde temel olarak üç teknikten yararlanıldığı gözlenmektedir. Söz konusu besleme teknikleri sırasıyla, sinusoidal ve 120°- 180° elektriksel iletimli altı darbeli trapezoidal yaklaşımlar olarak tanımlanırlar. Bu bağlamda sürekli mıknatıslı fırçasız motorlu tahrik sistemlerini, besleme yapısına göre sinusoidal ve trapezoidal olarak ikiye ayırmak mümkündür. Tez çalışmasında, sürekli mıknatıslı fırçasız tahrik sistemi uygulaması, özel bir uygulamaya yönelik dış rotorlu doğrudan tahrikli bir motor içermektedir. Yukarıda anılan besleme seçeneklerinin tümü analitik veya durum uzayı yaklaşımını temel alan genelleştirilmiş matematik modeller yardımıyla analiz edilmiş ve sonuçlar irdelenmiştir. Analitik yöntemlerle yapılan irdelemeler sonucunda, sinusoidal yaklaşımın yüksek maliyetli ve karmaşık denetim yapısı gerektirdiği anlaşılmıştır. Bundan sonraki aşamada, altı darbeli trapezoidal 120° ve 180° elektriksel iletimli besleme tekniklerinin durum uzayı yaklaşımı temelli matematik modelleri kurulmuş ve sayısal benzetim sonuçlan analiz edilmiştir. İki besleme yaklaşımının sonuçlarının özel uygulama ölçeğinde irdelenip, yorumlanmasını takiben moment darbesi bileşeninin en azlanmasına yönelik farklı bir besleme tekniği geliştirilmiş ve bu tekniğe oniki darbeli besleme yaklaşımı adı verilmiştir. Oniki darbeli besleme yaklaşımının, bir sonraki aşamada matematik modeli kurulmuş ve model dördüncü dereceden Runge-Kutta algoritması yardımıyla çözülmüştür. Sayısal benzetim sonuçlarından, yeni besleme yaklaşımının uygulanması ile moment darbesi bileşen genliğinin, altı darbeli besleme tekniğine kıyasla yarıya indirildiği saptanmıştır. Bu bağlamda oniki darbeli besleme yaklaşımının pratik uygulamasında akım denetimini sağlayacak ve bu besleme şekline özel, histeresis temelli sabit frekanslı ve doğru akım harasında bir ve yalnız bir algılayıcı içeren, bir akım denetim tekniği geliştirilmiştir. Oniki darbeli besleme ve ona özel akım denetim yaklaşımının Matlab ortamında modelleri kurulmuş ve sayısal benzetim sonuçlan irdelenmiştir. Matlab sonuçlarından, doğru akım harasında yer alan tek algılayıcı ile akım denetiminin başarıldığı anlaşılmaktadır. Ayrıca geliştirilen akım denetimi altı darbeli 120° elektriksel iletimli besleme yaklaşımına da uygulanmış ve bu besleme seçeneğine de katkıları ortaya konulmuştur. Tez çalışmasında yukarıda verilen teorik irdelemenin ardından, altı ve oniki darbeli besleme ve geliştirilen akım denetim yaklaşımı, prototip olarak gerçekleştirilmiş ve tahrik sisteminin tüm hız aralığında temel deneyleri tamamlanmıştır. Böylelikle, ortalama moment anlamında sayısal benzetim ve deney sonuçlarının karşılaştırılması ve doğrulanması amaçlanmıştır. Tez çalışmasında özetle, oniki darbeli besleme ve ona özel geliştirilen sayısal temelli akım denetim tekniğinin uygulanması sonucunda, sürekli mıknatıslı fırçasız motorlu tahrik sistemlerinde moment darbesinin önemli oranda azaltılması ve doğru akım harasında bir ve yalnız bir algılayıcı üzerinden akım denetiminin sağlanması başarılmıştır.

The objective of this thesis which is called "Twelve-Step Drive of Brushless DC Machines" is to develop a new and general drive technique including commutation and current control for permanent magnet brushless machines to minimize the effects of electronic commutation and torque ripple which is the extension of discrete exication due to commutation. Advances in magnetic materials and improvements in silicon technology give new opportunities for permanent magnet brushless motors to move into new application areas. These improvements can be extended by more precise control strategies to improve the performance of these motors. As a result, nowadays there is an increasing tendency to make use of permanent magnet brushless machines in the control of variable-speed high performance applications where torque smoothness is essential. For example, the quality of the surface finish achievable with metal- working machine tools is directly dependent on the smoothness of the instantaneous torque delivered to the rotary tool-piece. In similar manner, the performance specifications of servo motors, which are used in equipment ranging from robots to satellite trackers require minimization of all sources of pulsating torque or torque ripple. Even mass-produced consumer products such as white goods or traction drives demand high levels of ripple free torque and low noise levels to meet user expectations. However, the cost of permanent magnet material will probably always limit the universal use of these motors. As power ratings increase, there comes a point where it is more cost effective to use induction motors or switched reluctance motors. However, this is not a hard task and fast limit as very effective brushless permanent magnet motors can be designed for high power ranges. Permanent magnet brushless motors are candidates for many high-performance applications such as those identified above because of their attractive characteristics in such key categories as power density, torque to inertia and current ratio, noise level, and electrical efficiency. There are two major classes of permanent magnet brushless motor (PMBM) drives which can be characterised by the shapes of their respective back-EMF waveforms that can be defined as sinusoidal and trapezoidal drives respectively. Under idealised conditions, each of these two types of PMBM drives is capable of producing perfectly smooth instantaneous torque waveforms. All is required to understand the torque production of PMBM drives, is the basic knowledge of electronic commutation and the working principle of step motors. This simple operating philosophy makes PMBM drives attractive for many high- performance applications. Although the operating principle seems very simple, the torque production mechanism due to electronic commutation or discrete excitation steps have many specific and scientific problems to be solved. In this manner, only a few of the key relevant characteristics of these sinusoidal and trapezoidal PMBM drives will be briefly reviewed in the following paragraphs. Sinusoidal PMBM drives share many of the basic characteristics of other classic types of polyphase ac machine drive systems. Basically, both the machine back-EMF and current excitation waveforms are perfectly sinusoidal for ideally smooth torque generation. Sinusoidal back-EMF waveforms require that motor's stator windings be sinusoidally distributed around the airgap and/or the radial magnetic flux density amplitude generated by the rotor permanent magnets varies sinusoidally around the airgap. Rotors of sinusoidal permanent magnet brushless motors can be designed either surface-mounted or interior magnet configurations. Sinusoidal phase currents are typically developed using a current-regulated inverter that requires individual phase current sensors and a high-resolution rotor position sensor like resolver or precise encoder to maintain accurate synchronisation of the excitation waveforms with the rotor angular position at any special time instant. Any source of non-ideal properties which causes either the phase current or the back-EMF waveforms to change from their purely sinusoidal shapes, will typically be a reason to the production of undesired pulsating torque components. Trapezoidal PMBM drives, also known as brushless dc or electronically commutated motor drives, have some major differences reference to their sinusoidal counterparts. These machines are designed to develop trapezoidal back-EMF waveforms. It is common to enlarge the flat portion of the trapezoidal back-EMF waveform in trapezoidal PMBM drives to meet the ideal conditions, which are given in textbooks for smooth torque generation [1-5]. To meet this requirement, there is a general tendency in designing the trapezoidal motor with surface-mounted magnets and concentrated stator windings in contrast to the distributed windings preferred in sinusoidal PMBM machines. There are two common excitation strategies of trapezoidal PMBM drives which are called respectively as 120° and 180° electrical conduction modes. Excitation waveforms for three-phase trapezoidal PMBM have the form of quasisquare-wave (six-step) with two 60° electrical intervals of zero- current excitation per cycle for 120° conduction mode of operation. In contrast to 120° electrical conduction mode, there is no zero-current excitation period in 180° electrical conduction mode of operation. The nature of excitation waveforms for trapezoidal PMBM drives give rise to have some important system simplifications compared to sinusoidal PMBM drives. In particular, the resolution requirements for the rotor position sensor are much lower for trapezoidal machines since only six commutation instants per electrical cycle must be sensed. In addition, it has been stated in the literature that, the trapezoidal PMBM drive requires a single current sensor in the inverter dc link, but this is not the case for high power and variable-load drives [6]. Unfortunately, these simplifications leave the trapezoidal PMBM drives to face with some complex mechanisms of pulsating torque generation which don't effect their sinusoidal counterparts. In order to complete the general statement of the pulsating torque problem, it will be very convenient to give pulsating torque definitions in PMBM drive system. Any source of divergence from ideal conditions which are given before in either the motor Will or associated power converter in a PMBM drive typically gives rise to undesired torque pulsations. However, there are various specific sources for these harmonic torque components which can be defined as follows;. Cogging Torque-It is a pulsating torque component generated by the interaction of the rotor magnetic flux and angular variations in the stator magnetic reluctance. By definition, no stator excitation is involved in cogging torque production. »Ripple Torque-It is a pulsating torque component generated by the interaction of stator current magnetomotive forces and rotor electromagnetic properties which can be defined as follows: 1. Mutual or alignment torque-It is generated from the interaction of the current magnetomotive forces with the rotor magnet flux distribution. This is the dominant torque production mechanism in PMBM drive systems. 2. Reluctance torque-It is generated from the interaction of the current magnetomotive forces with the angular variation in the rotor magnetic reluctance. Surface-mounted magnet PMBM generates almost no reluctance torque..Pulsating Torque-It is the sum of cogging and ripple torque components It is clear from the definitions given above that, torque pulsation problem due to the torque production mechanism in PMBM drive systems is one of the most important research topics for that kind of drive systems. For that reason a wide variety of techniques have been proposed in literature during the past fifteen years for minimizing the generation of pulsating torque components. In chapter two of this thesis, these techniques are fully examined, the comments and results are given in details. As a summary it could be stated that these techniques can be classified in two major categories. The first major class consists of techniques related with motor design. It has no importance whether the machine is trapezoidal or sinusoidal. Basically, these techniques tend to eliminate the fundamental electromagnetic sources of the pulsating torque and optimise the design in such a way that to force it toward the ideal conditions. These motor-based techniques are reviewed in first section of Chapter two of this thesis. The second major class of techniques for minimizing pulsating torque are based on active control schemes which modify the excitation to correct for any of the non-ideal characteristics of the machine or its associated power inverter. Many of these techniques involve active elimination techniques of the pulsating torque components which would be generated using classic sinusoidal or square wave current excitation waveforms. The effectiveness of these techniques require preknowledge of the individual machine's design parameters or the use of self-tuning mechanisms to adapt to the torque production characteristics of the PMBM drive system. These approaches are basically depend on observer and estimation techniques. These controller-based approaches are reviewed in second section of Chapter two of this thesis. In this study, the target application is an outer rotor permanent magnet brushless motor which is designed and realised for a special direct drive application. As a first stage, sinusoidal-fed PMBM drives are taken into consideration. This technique is examined by using an analytical approach. It is proved that, sinusoidal excitaion of PMBM has a very complex control algorithm, and requires a precise rotor position transducer and reduces the torque value for the same frame size. As a result, the cost of the drive will be much higher than its trapezoidal counterparts. As a second step of the thesis, trapezoidal drives are folly analysed by the help of a digital simulation technique. A state space model is developed to estimate torque- speed performance of a three phase full-bridge, surface-magnet trapezoidal PMBM drive system for 120° and 180° conduction modes. The power and control electronic circuit deliver square waveforms of current. The power converter topologies of 120° and 180° conduction mode of operation are the same. While two phases are energised at any rotor position in 120° conduction mode, all of three phases are simultaneously ON in 1 80° conduction of mode operation. High frequency pulse width modulation (PWM) of the lower bridge transistors is used to control speed and torque. Broadly speaking, the state space model includes simulations of rectifier/filter or DC link, the resistance/self/mutual inductances^ack EMF circuits of the motor and switching patterns of transistor bridge. They interact at the DC link filter capacitor and their governing equations are solved numerically by using a fourth order Runge- Kutta algorithm in which current or torque is the dependent variable. Thus not only the behaviour of the inverter but also the behaviour of the rectifier are taken into consideration to find out the influences of the drive on torque pulsation. As a result, the generalised set of differential equations which covers PWM technique are obtained and analysis of the overall drive system is described in principle. Analysing the previous studies on pulsating torque minimization in PMBM drives and results of digital simulation of six-step trapezoidal techniques, a new approach is proposed which is called twelve-step excitation of trapezoidal PMBM drive system. The only modification needed is three additional Hall-effect sensors. The new switching scheme works with almost any trapezoidal brushless motor, regardless of the number of poles, phases or motor design configuration. The advantage of twelve-step excitation lies in the increased number of MMF vectors produced during electronic commutation. The six additional vectors reduce torque pulsation when two fields are in quadrature. Unfortunately, adding six more vectors is not the complete solution. The amplitude of torque vectors produced by two conducting phases are not the same with those generated with three phase conduction mode. It could be stated that, if all twelve vectors are not made equal in amplitude, the additional torque vectors can produce a higher frequency torque ripple. For example, in conventional six step excitation, two phases are energised at any time instant and the resultant field is midway between related phases with a magnitude of 1.73 pu. Similarly for twelve-step excitation, if we take one high and two low leg switches conduction, the phase which is connected to dc bus will produce current for the other phases connected to power ground. The amplitude of the resultant torque vector is 1.5 pu in that case. As a result, the unbalanced vectors generate the torque pulsation but can be eliminated by making all vectors produce the same torque vector using current control. In twelve-step excitation system, it could be compensated during three phase ON stages, with phase current which is amplified by a factor of 1.153 to make all vectors equal in amplitude. In order to investigate the behaviour of the new approach, the same procedure which is used for six step techniques, is applied. In other words, the same mathematical modelling approach is also developed for twelve-step excitation of trapezoidal PMBM drives. The simulation results are compared with those of six-step 120° and 180° electrical conduction modes. To have a criteria for comparison, the pulsating factor of torque is defined as: T -T M= j Xl0° 0) The results are very promising and the pulsating factor of torque is decreased by a factor of 50% especially in low speed range. Trapezoidal drive prototypes with six and twelve-step techniques are also designed and realised by using a 8 bit microcontroller-PLD (programmable logic device) based electronic circuits. The average torque values are measured on a dynamometer to compare with those of simulations results. A good agreement between the experimental and analytical results has been observed except very low speeds. In addition to a new excitation approach which is called as "Twelve-Step Trapezoidal-Drive of Permanent Magnet Brushless Machines", a digital current control technique is also introduced to have a reliable drive with special features dedicated to twelve-step excitation approach. It can also be used for 120° conduction mode of six-step trapezoidal drive. A digital technique of current regulation is preferred to ensure a current demand which is the upper limit of hysteresis controller. In order to define the analytical equations of the phase current, the idealised linear behaviour of the hysteresis controller is taken into consideration. The analytical equations of the phase current is proposed in details for all twelve stages of excitation. The combinations of motor phases energised due to the rotor position, is modelled as an equivalent inductance in series with an equivalent back EMF function. Assuming that the DC link voltage exceeds the back-EMF the phase current follows a linear trajectory according to equations which are introduced for every discrete excitation steps. Note that the same technique can also be applied to six-step excitation approaches with different converter topology and equivalent back EMF and inductance value. By combining the advantages of twelve-step excitation, this current control algorithm provide the following key features;. Elimination of all discrete current sensors except one and single one located on dc link. Protection against high circulating current loops during commutation »High degree of drive circuit integration, minimizing the number of drive electronics components. PWM frequency is constant In conclusion, the smooth torque production in trapezoidal PMBM drives is achieved by a package solution which is a combination of a different excitation and current- control strategy.

The objective of this thesis which is called "Twelve-Step Drive of Brushless DC Machines" is to develop a new and general drive technique including commutation and current control for permanent magnet brushless machines to minimize the effects of electronic commutation and torque ripple which is the extension of discrete exication due to commutation. Advances in magnetic materials and improvements in silicon technology give new opportunities for permanent magnet brushless motors to move into new application areas. These improvements can be extended by more precise control strategies to improve the performance of these motors. As a result, nowadays there is an increasing tendency to make use of permanent magnet brushless machines in the control of variable-speed high performance applications where torque smoothness is essential. For example, the quality of the surface finish achievable with metal- working machine tools is directly dependent on the smoothness of the instantaneous torque delivered to the rotary tool-piece. In similar manner, the performance specifications of servo motors, which are used in equipment ranging from robots to satellite trackers require minimization of all sources of pulsating torque or torque ripple. Even mass-produced consumer products such as white goods or traction drives demand high levels of ripple free torque and low noise levels to meet user expectations. However, the cost of permanent magnet material will probably always limit the universal use of these motors. As power ratings increase, there comes a point where it is more cost effective to use induction motors or switched reluctance motors. However, this is not a hard task and fast limit as very effective brushless permanent magnet motors can be designed for high power ranges. Permanent magnet brushless motors are candidates for many high-performance applications such as those identified above because of their attractive characteristics in such key categories as power density, torque to inertia and current ratio, noise level, and electrical efficiency. There are two major classes of permanent magnet brushless motor (PMBM) drives which can be characterised by the shapes of their respective back-EMF waveforms that can be defined as sinusoidal and trapezoidal drives respectively. Under idealised conditions, each of these two types of PMBM drives is capable of producing perfectly smooth instantaneous torque waveforms. All is required to understand the torque production of PMBM drives, is the basic knowledge of electronic commutation and the working principle of step motors. This simple operating philosophy makes PMBM drives attractive for many high- performance applications. Although the operating principle seems very simple, the torque production mechanism due to electronic commutation or discrete excitation steps have many specific and scientific problems to be solved. In this manner, only a few of the key relevant characteristics of these sinusoidal and trapezoidal PMBM drives will be briefly reviewed in the following paragraphs. Sinusoidal PMBM drives share many of the basic characteristics of other classic types of polyphase ac machine drive systems. Basically, both the machine back-EMF and current excitation waveforms are perfectly sinusoidal for ideally smooth torque generation. Sinusoidal back-EMF waveforms require that motor's stator windings be sinusoidally distributed around the airgap and/or the radial magnetic flux density amplitude generated by the rotor permanent magnets varies sinusoidally around the airgap. Rotors of sinusoidal permanent magnet brushless motors can be designed either surface-mounted or interior magnet configurations. Sinusoidal phase currents are typically developed using a current-regulated inverter that requires individual phase current sensors and a high-resolution rotor position sensor like resolver or precise encoder to maintain accurate synchronisation of the excitation waveforms with the rotor angular position at any special time instant. Any source of non-ideal properties which causes either the phase current or the back-EMF waveforms to change from their purely sinusoidal shapes, will typically be a reason to the production of undesired pulsating torque components. Trapezoidal PMBM drives, also known as brushless dc or electronically commutated motor drives, have some major differences reference to their sinusoidal counterparts. These machines are designed to develop trapezoidal back-EMF waveforms. It is common to enlarge the flat portion of the trapezoidal back-EMF waveform in trapezoidal PMBM drives to meet the ideal conditions, which are given in textbooks for smooth torque generation [1-5]. To meet this requirement, there is a general tendency in designing the trapezoidal motor with surface-mounted magnets and concentrated stator windings in contrast to the distributed windings preferred in sinusoidal PMBM machines. There are two common excitation strategies of trapezoidal PMBM drives which are called respectively as 120° and 180° electrical conduction modes. Excitation waveforms for three-phase trapezoidal PMBM have the form of quasisquare-wave (six-step) with two 60° electrical intervals of zero- current excitation per cycle for 120° conduction mode of operation. In contrast to 120° electrical conduction mode, there is no zero-current excitation period in 180° electrical conduction mode of operation. The nature of excitation waveforms for trapezoidal PMBM drives give rise to have some important system simplifications compared to sinusoidal PMBM drives. In particular, the resolution requirements for the rotor position sensor are much lower for trapezoidal machines since only six commutation instants per electrical cycle must be sensed. In addition, it has been stated in the literature that, the trapezoidal PMBM drive requires a single current sensor in the inverter dc link, but this is not the case for high power and variable-load drives [6]. Unfortunately, these simplifications leave the trapezoidal PMBM drives to face with some complex mechanisms of pulsating torque generation which don't effect their sinusoidal counterparts. In order to complete the general statement of the pulsating torque problem, it will be very convenient to give pulsating torque definitions in PMBM drive system. Any source of divergence from ideal conditions which are given before in either the motor Will or associated power converter in a PMBM drive typically gives rise to undesired torque pulsations. However, there are various specific sources for these harmonic torque components which can be defined as follows;. Cogging Torque-It is a pulsating torque component generated by the interaction of the rotor magnetic flux and angular variations in the stator magnetic reluctance. By definition, no stator excitation is involved in cogging torque production. »Ripple Torque-It is a pulsating torque component generated by the interaction of stator current magnetomotive forces and rotor electromagnetic properties which can be defined as follows: 1. Mutual or alignment torque-It is generated from the interaction of the current magnetomotive forces with the rotor magnet flux distribution. This is the dominant torque production mechanism in PMBM drive systems. 2. Reluctance torque-It is generated from the interaction of the current magnetomotive forces with the angular variation in the rotor magnetic reluctance. Surface-mounted magnet PMBM generates almost no reluctance torque..Pulsating Torque-It is the sum of cogging and ripple torque components It is clear from the definitions given above that, torque pulsation problem due to the torque production mechanism in PMBM drive systems is one of the most important research topics for that kind of drive systems. For that reason a wide variety of techniques have been proposed in literature during the past fifteen years for minimizing the generation of pulsating torque components. In chapter two of this thesis, these techniques are fully examined, the comments and results are given in details. As a summary it could be stated that these techniques can be classified in two major categories. The first major class consists of techniques related with motor design. It has no importance whether the machine is trapezoidal or sinusoidal. Basically, these techniques tend to eliminate the fundamental electromagnetic sources of the pulsating torque and optimise the design in such a way that to force it toward the ideal conditions. These motor-based techniques are reviewed in first section of Chapter two of this thesis. The second major class of techniques for minimizing pulsating torque are based on active control schemes which modify the excitation to correct for any of the non-ideal characteristics of the machine or its associated power inverter. Many of these techniques involve active elimination techniques of the pulsating torque components which would be generated using classic sinusoidal or square wave current excitation waveforms. The effectiveness of these techniques require preknowledge of the individual machine's design parameters or the use of self-tuning mechanisms to adapt to the torque production characteristics of the PMBM drive system. These approaches are basically depend on observer and estimation techniques. These controller-based approaches are reviewed in second section of Chapter two of this thesis. In this study, the target application is an outer rotor permanent magnet brushless motor which is designed and realised for a special direct drive application. As a first stage, sinusoidal-fed PMBM drives are taken into consideration. This technique is examined by using an analytical approach. It is proved that, sinusoidal excitaion of PMBM has a very complex control algorithm, and requires a precise rotor position transducer and reduces the torque value for the same frame size. As a result, the cost of the drive will be much higher than its trapezoidal counterparts. As a second step of the thesis, trapezoidal drives are folly analysed by the help of a digital simulation technique. A state space model is developed to estimate torque- speed performance of a three phase full-bridge, surface-magnet trapezoidal PMBM drive system for 120° and 180° conduction modes. The power and control electronic circuit deliver square waveforms of current. The power converter topologies of 120° and 180° conduction mode of operation are the same. While two phases are energised at any rotor position in 120° conduction mode, all of three phases are simultaneously ON in 1 80° conduction of mode operation. High frequency pulse width modulation (PWM) of the lower bridge transistors is used to control speed and torque. Broadly speaking, the state space model includes simulations of rectifier/filter or DC link, the resistance/self/mutual inductances^ack EMF circuits of the motor and switching patterns of transistor bridge. They interact at the DC link filter capacitor and their governing equations are solved numerically by using a fourth order Runge- Kutta algorithm in which current or torque is the dependent variable. Thus not only the behaviour of the inverter but also the behaviour of the rectifier are taken into consideration to find out the influences of the drive on torque pulsation. As a result, the generalised set of differential equations which covers PWM technique are obtained and analysis of the overall drive system is described in principle. Analysing the previous studies on pulsating torque minimization in PMBM drives and results of digital simulation of six-step trapezoidal techniques, a new approach is proposed which is called twelve-step excitation of trapezoidal PMBM drive system. The only modification needed is three additional Hall-effect sensors. The new switching scheme works with almost any trapezoidal brushless motor, regardless of the number of poles, phases or motor design configuration. The advantage of twelve-step excitation lies in the increased number of MMF vectors produced during electronic commutation. The six additional vectors reduce torque pulsation when two fields are in quadrature. Unfortunately, adding six more vectors is not the complete solution. The amplitude of torque vectors produced by two conducting phases are not the same with those generated with three phase conduction mode. It could be stated that, if all twelve vectors are not made equal in amplitude, the additional torque vectors can produce a higher frequency torque ripple. For example, in conventional six step excitation, two phases are energised at any time instant and the resultant field is midway between related phases with a magnitude of 1.73 pu. Similarly for twelve-step excitation, if we take one high and two low leg switches conduction, the phase which is connected to dc bus will produce current for the other phases connected to power ground. The amplitude of the resultant torque vector is 1.5 pu in that case. As a result, the unbalanced vectors generate the torque pulsation but can be eliminated by making all vectors produce the same torque vector using current control. In twelve-step excitation system, it could be compensated during three phase ON stages, with phase current which is amplified by a factor of 1.153 to make all vectors equal in amplitude. In order to investigate the behaviour of the new approach, the same procedure which is used for six step techniques, is applied. In other words, the same mathematical modelling approach is also developed for twelve-step excitation of trapezoidal PMBM drives. The simulation results are compared with those of six-step 120° and 180° electrical conduction modes. To have a criteria for comparison, the pulsating factor of torque is defined as: T -T M= j Xl0° 0) The results are very promising and the pulsating factor of torque is decreased by a factor of 50% especially in low speed range. Trapezoidal drive prototypes with six and twelve-step techniques are also designed and realised by using a 8 bit microcontroller-PLD (programmable logic device) based electronic circuits. The average torque values are measured on a dynamometer to compare with those of simulations results. A good agreement between the experimental and analytical results has been observed except very low speeds. In addition to a new excitation approach which is called as "Twelve-Step Trapezoidal-Drive of Permanent Magnet Brushless Machines", a digital current control technique is also introduced to have a reliable drive with special features dedicated to twelve-step excitation approach. It can also be used for 120° conduction mode of six-step trapezoidal drive. A digital technique of current regulation is preferred to ensure a current demand which is the upper limit of hysteresis controller. In order to define the analytical equations of the phase current, the idealised linear behaviour of the hysteresis controller is taken into consideration. The analytical equations of the phase current is proposed in details for all twelve stages of excitation. The combinations of motor phases energised due to the rotor position, is modelled as an equivalent inductance in series with an equivalent back EMF function. Assuming that the DC link voltage exceeds the back-EMF the phase current follows a linear trajectory according to equations which are introduced for every discrete excitation steps. Note that the same technique can also be applied to six-step excitation approaches with different converter topology and equivalent back EMF and inductance value. By combining the advantages of twelve-step excitation, this current control algorithm provide the following key features;. Elimination of all discrete current sensors except one and single one located on dc link. Protection against high circulating current loops during commutation »High degree of drive circuit integration, minimizing the number of drive electronics components. PWM frequency is constant In conclusion, the smooth torque production in trapezoidal PMBM drives is achieved by a package solution which is a combination of a different excitation and current- control strategy.

##### Açıklama

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1997

Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1997

Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1997

##### Anahtar kelimeler

Doğru akım motorları,
Momentum,
Sürücüler,
Tahrik sistemleri,
Direct current motors,
Momentum,
Drivers,
Propulsion systems