Constrained field-oriented control of permanent magnet synchronous machine with field-weakening utilizing a reference governor

This paper presents a complete solution for constrained control of a permanent magnet synchronous machine. It utilizes field-oriented control with proportional-integral current controllers tuned to obtain a fast transient response and zero steady-state error. To ensure constraint satisfaction in the steady state, a novel field-weakening algorithm which is robust to flux linkage uncertainty is introduced. Field weakening problem is formulated as an optimization problem which is solved online using projected fast gradient method. To ensure constraint satisfaction during current transients, an additional device called current reference governor is added to the existing control loops. The constraint satisfaction is achieved by altering the reference signal. The reference governor is formulated as a simple optimization problem whose objective is to minimize the difference between the true reference and a modified one. The proposed method is implemented on Texas instruments F28343 200 MHz microcontroller and experimentally verified on a surface mounted permanent magnet synchronous machine

Predictive control of interior permanent magnet synchronous motor aiming at minimization of electromagnetic losses

U radu je opisan sustav upravljanja sinkronog stroja s trajnim magnetima s ciljem primjene u električnoj vuči. Zahtjev koji se postavlja na upravljački sustav električnim strojem u vuči je osigurati slijeđenje referentne vrijednosti momenta uz minimizaciju elektromagnetskih gubitaka. Minimizacija gubitaka sinkronog stroja s trajnim magnetima postiže se prikladnim izborom vektora struje. Također, odabirom vektora struje osigurano je i postizanje referentne vrijednosti momenta. Uz minimizaciju gubitaka i slijeđenje referentne vrijednosti momenta uz dobar dinamički odziv, zadatak sustava upravljanja je i osigurati siguran rad sustava i zadovoljenje ogranićenja napona i struje. Sustav upravljanja sinkronim motorom s unutarnjim trajnim magnetima s ciljem minimizacije gubitaka i uz osiguranje rada motora unutar ograničenja predstavljen u radu kaskadne je strukture upravljanja podijeljene na tri zasebna elementa. Prvi element predstavlja računski učinkovit postupak proračuna referentnih vrijednosti struja u d i q osi koje rezultiraju minimalnim gubicima pri zadanom momentu i brzini vrtnje motora. Druga i treća komponenta algoritma upravljanja služe za adaptaciju izlaza iz algoritma minimizacije gubitaka kako bi se osigurao rad motora unutar ogranićenja. Druga komponenta, upravitelj referenci mijenja referentne struje u svrhu izbjegavanja zasićenja strujnih regulatora i nadmodulacije bez gubitka performansi upravljanja ćime se smanjuju gubici pri naglim promjenama momenta karakteristićnima u vuči. Treća komponenta izvedena je u obliku upravljanja utemeljenog na prediktivnim modelima kojim se garantira rad motora unutar limita i minimalni gubici u podrućju slabljenja polja. Predloženi algoritam upravljanja zamišljen je kao računski učinkovit dodatak postojećem klasičnom vektorskom upravljanju sinkronim motorom s unutarnjim trajnim magnetima u cilju poboljšanja performansi. Polazište razvoja algoritma upravljanja je prikladan matematički model sinkronog stroja s trajnim magnetima. Model je zapisan u obliku naponskih jednadžbi stroja i jednadžbe momenta u dvoosnom rotirajućem dq sustavu. Pojednostavljeni model koji se koristi prilikom razvoja algoritama ukljućuje i model elektromagnetskih gubitaka stroja. Gubici u namotima se u ovom modelu računaju kao omski gubici na otporu namota pri ćemu se zanemaruje utjecaj potiskivanja struje u vodiču ili efekt blizine. Gubici u željezu računaju se preko nadomjesnog otpora, što rezultira pogrešnom procjenom gubitaka pri opterećenju. U radu je prikazano detaljno istraživanje gubitaka u željezu izračunatih simulacijama temeljenima na metodi konačnih elemenata i gubitaka dobivenih obradom mjerenja na sinkronom stroju s unutarnjim trajnim magnetima. Prikazan je i novi empirijski model za proračun gubitaka u željezu kojim je greška u procjeni gubitaka smanjena u odnosu na klasičan model gubitaka. Predstavljeni sustav upravljanja ispitan je kroz računalne simulacije i ispitivanja na stvarnom sustavu, i to na dva različita tipa sinkronih strojeva: na sinkronom stroju s trajnim magnetima na površini rotora opće namjene i sinkronom stroju s unutarnjim trajnim magnetima projektiranom za električnu vuču.Permanent magnet synchronous machine (PMSM), due to its inherently high torque density and premium efficiency, stands out as a motor of choice in a wide array of applications and especially proves as a perfect fit in electric traction applications. In order to fully utilize its advantages a proper control system must be employed. In traction applications, the main objective is to ensure reaching the reference torque with a good dynamic performance while achieving loss minimization in the steady state. This can be achieved by a proper current control algorithm which must respect PMSM drive voltage and current limits. High performance control of permanent magnet synchronous machines can be achieved using rotor-field-oriented vector control. Usually, d and q axis currents are controlled independently using two PI controllers with additional decoupling terms. Due to a limited voltage available from the inverter, the current controllers are prone to saturation which leads to disturbed current dynamics, degraded torque production and potentially the system instability. In order to overcome the problem of saturation, the adaptation of current references in the form of a reference governor is implemented in the control structure of a permanent magnet synchronous machine. In order to ensure that voltage and current constraints are not violated in steady state, i.e. to ensure reachability of the torque reference, a novel field-weakening algorithm is also introduced. The presented algorithms are robust to parameter changes, thereby allowing the use of incorrectly assessed motor parameters and implementation on the motor with a high degree of saturation. With addition of loss minimization requirement, the control strategy of a permanent magnet synchronous machine can be divided into three segments: an algorithm for finding the optimal current vector which minimizes the copper losses or total copper and iron losses in a steady state, field-weakening algorithm which ensures that voltage constraints are not violated in steady state, and a control algorithm responsible for tracking of reference current trajectory. In this thesis, a new formulation for minimization of copper and iron losses in interior permanent magnet motor for the purpose of minimum loss control is presented. Motor losses are formulated based on electromagnetic torque to total torque ratio resulting in simplified expression of minimal loss condition which can be easily solved online. The problem of permanent magnet synchronous motor control with the aim of minimizing losses and ensuring machine performance within the limits is implemented as a cascading control structure in three parts. The first part presents a computationally efficient calculation of the reference values of d and q axis current components resulting in minimum losses at the given torque and machine speed. The second and third components of the control algorithm serve to adapt the output from the loss minimization algorithm to ensure machine operation within the limits. The second component, the reference controller, changes the reference current to avoid the saturation of current regulators and over-modulation without loss of control performance, thus reducing losses due to sudden changes in torque reference. The third component is implemented as a management model based on predictive models that guarantee machine performance within the limits and minimum losses in the field weakening regime. The proposed control algorithm is designed as a computationally efficient addition to the existing classical vector-controlled permanent magnet synchronous machine in order to improve its performance. Modern synchronous permanent magnet motors are characterized by high efficiency and high torque density, which are the properties increasingly emphasized in a number of applications like electric traction or aerospace applications. Such machines fully utilize their magnetic circuit which results in saturation phenomena that cause nonlinearities in their mathematical models. The machine model that is able to adequately simulate current, voltage and torque waveforms is one of the key requirements for designing the control system and also for the purpose of the machine design optimization. In the thesis, mathematical model of a permanent magnet synchronous machine which includes saturation effects is presented. To round up mathematical representation of a permanent magnet synchronous machine, the proper model of losses must be included in the machine model used either for simulation purposes or as a cornerstone of control algorithm design. Losses of permanent magnet synchronous machines can be devided into two groups, mechanical and electromagnetic losses, of which control designer can affect only electromagnetic losses. The electromagnetic losses of synchronous motors with permanent magnets can be divided into three categories: copper losses, iron losses and permanent magnet losses. Copper losses are implemented in the mathematical model using winding resistance, while iron losses are implemented using equivalent resistance of iron losses. Losses in permanent magnets are, due to its low value compared to copper and iron losses, neglected during control algorithm design process. Approximation of iron losses with equivalent resistance results in an error under load and at high speeds. In order to obtain a more acurate and detailed model of iron losses in synchronous motors with permanent magnets, an empirical model of iron losses was developed. The presented empirical model of iron losses is compared to the measurement results on the real machine. The subject and focal point of the research problem is the interior permanent magnet synchronous machine designed as the main traction motor of an electric tram. Therefore, an emphasis is placed on the electric traction applications. The thesis is divided into 6 chapters organized as follows: Chapter 1, Introduction draws the attention of the reader to the subject of the research, the permanent magnet synchronous machine, its application, advantages and classification. In brief, the requirements for the control system of this type of machine are presented, as well as a detailed review of the literature. Chapter 2, Permanent magnet synchronous machine model contains derivation of mathematical model of a permanent magnet synchronous machine in three-phase abc reference frame and rotating dq reference frame. This chapter provides a review of models suitable for computer simulation. Chapter 3, Permanent magnet synchronous machine losses presents an upgrade of a mathematical model of the machine by adding the loss model. Breakdown of losses due to their origin on electrical and mechanical losses and a detailed description of the appropriate loss components is presented. A simplified requirement for minimum electrical losses is presented with a proposal for finding solution to a minimum loss problem. Also, the chapter describes a new empirical model of permanent magnet synchronous machine core losses. The chapter contains two original scientific contributions: 1. Simplified model of total electromagnetic losses of interior permanent magnet machine suitable for solving in real-time control systems 2. Empirical model for calculation of iron losses in permanent magnet synchronous machine Chapter 4, Permanent magnet synchronous machine control system describes the classical vector control structure of a permanent magnet synchronous machine based on the field oriented control. The chapter also describes a control algorithm that provides machine operation within the limits in two components. The first component, the reference governor, is an add-on that can be easily embedded into existing classical control structures and whose task is to customize input references to existing current controllers to avoid their saturation and avoid over-modulation without loss of control performance. The second component, the field weakening algorithm, is derived in the form of control based on predictive models to guarantee machine performance within the voltage and current limits with minimum losses in the field weakening regime. These two components represent two distinct original scientific contributions: 1. Algorithm for dynamic modification of permanent magnet synchronous machine current reference values, which ensures machine performance while satisfying the voltage and current limitations 2. Computationally efficient permanent magnet synchronous machine model predictive control which assures field weakening operation while meeting the voltage and current limitations Chapter 5, Experimental results contains a detailed description of the methods and equipment used in the experimental tests. The results of testing and the functionality of the proposed control algorithm are given for two different permanent magnet synchronous machines: an interior permanent magnet synchronous machine and a surface mounted permanent magnet synchronous machine. The results of loss measurement and comparison with the empirical model of losses from Chapter 3 are also included in this chapter. Chapter 6, Conclusion gives an overview of the presented dissertation and sums up the results of the research

Predictive control of interior permanent magnet synchronous motor aiming at minimization of electromagnetic losses

U radu je opisan sustav upravljanja sinkronog stroja s trajnim magnetima s ciljem primjene u električnoj vuči. Zahtjev koji se postavlja na upravljački sustav električnim strojem u vuči je osigurati slijeđenje referentne vrijednosti momenta uz minimizaciju elektromagnetskih gubitaka. Minimizacija gubitaka sinkronog stroja s trajnim magnetima postiže se prikladnim izborom vektora struje. Također, odabirom vektora struje osigurano je i postizanje referentne vrijednosti momenta. Uz minimizaciju gubitaka i slijeđenje referentne vrijednosti momenta uz dobar dinamički odziv, zadatak sustava upravljanja je i osigurati siguran rad sustava i zadovoljenje ogranićenja napona i struje. Sustav upravljanja sinkronim motorom s unutarnjim trajnim magnetima s ciljem minimizacije gubitaka i uz osiguranje rada motora unutar ograničenja predstavljen u radu kaskadne je strukture upravljanja podijeljene na tri zasebna elementa. Prvi element predstavlja računski učinkovit postupak proračuna referentnih vrijednosti struja u d i q osi koje rezultiraju minimalnim gubicima pri zadanom momentu i brzini vrtnje motora. Druga i treća komponenta algoritma upravljanja služe za adaptaciju izlaza iz algoritma minimizacije gubitaka kako bi se osigurao rad motora unutar ogranićenja. Druga komponenta, upravitelj referenci mijenja referentne struje u svrhu izbjegavanja zasićenja strujnih regulatora i nadmodulacije bez gubitka performansi upravljanja ćime se smanjuju gubici pri naglim promjenama momenta karakteristićnima u vuči. Treća komponenta izvedena je u obliku upravljanja utemeljenog na prediktivnim modelima kojim se garantira rad motora unutar limita i minimalni gubici u podrućju slabljenja polja. Predloženi algoritam upravljanja zamišljen je kao računski učinkovit dodatak postojećem klasičnom vektorskom upravljanju sinkronim motorom s unutarnjim trajnim magnetima u cilju poboljšanja performansi. Polazište razvoja algoritma upravljanja je prikladan matematički model sinkronog stroja s trajnim magnetima. Model je zapisan u obliku naponskih jednadžbi stroja i jednadžbe momenta u dvoosnom rotirajućem dq sustavu. Pojednostavljeni model koji se koristi prilikom razvoja algoritama ukljućuje i model elektromagnetskih gubitaka stroja. Gubici u namotima se u ovom modelu računaju kao omski gubici na otporu namota pri ćemu se zanemaruje utjecaj potiskivanja struje u vodiču ili efekt blizine. Gubici u željezu računaju se preko nadomjesnog otpora, što rezultira pogrešnom procjenom gubitaka pri opterećenju. U radu je prikazano detaljno istraživanje gubitaka u željezu izračunatih simulacijama temeljenima na metodi konačnih elemenata i gubitaka dobivenih obradom mjerenja na sinkronom stroju s unutarnjim trajnim magnetima. Prikazan je i novi empirijski model za proračun gubitaka u željezu kojim je greška u procjeni gubitaka smanjena u odnosu na klasičan model gubitaka. Predstavljeni sustav upravljanja ispitan je kroz računalne simulacije i ispitivanja na stvarnom sustavu, i to na dva različita tipa sinkronih strojeva: na sinkronom stroju s trajnim magnetima na površini rotora opće namjene i sinkronom stroju s unutarnjim trajnim magnetima projektiranom za električnu vuču.Permanent magnet synchronous machine (PMSM), due to its inherently high torque density and premium efficiency, stands out as a motor of choice in a wide array of applications and especially proves as a perfect fit in electric traction applications. In order to fully utilize its advantages a proper control system must be employed. In traction applications, the main objective is to ensure reaching the reference torque with a good dynamic performance while achieving loss minimization in the steady state. This can be achieved by a proper current control algorithm which must respect PMSM drive voltage and current limits. High performance control of permanent magnet synchronous machines can be achieved using rotor-field-oriented vector control. Usually, d and q axis currents are controlled independently using two PI controllers with additional decoupling terms. Due to a limited voltage available from the inverter, the current controllers are prone to saturation which leads to disturbed current dynamics, degraded torque production and potentially the system instability. In order to overcome the problem of saturation, the adaptation of current references in the form of a reference governor is implemented in the control structure of a permanent magnet synchronous machine. In order to ensure that voltage and current constraints are not violated in steady state, i.e. to ensure reachability of the torque reference, a novel field-weakening algorithm is also introduced. The presented algorithms are robust to parameter changes, thereby allowing the use of incorrectly assessed motor parameters and implementation on the motor with a high degree of saturation. With addition of loss minimization requirement, the control strategy of a permanent magnet synchronous machine can be divided into three segments: an algorithm for finding the optimal current vector which minimizes the copper losses or total copper and iron losses in a steady state, field-weakening algorithm which ensures that voltage constraints are not violated in steady state, and a control algorithm responsible for tracking of reference current trajectory. In this thesis, a new formulation for minimization of copper and iron losses in interior permanent magnet motor for the purpose of minimum loss control is presented. Motor losses are formulated based on electromagnetic torque to total torque ratio resulting in simplified expression of minimal loss condition which can be easily solved online. The problem of permanent magnet synchronous motor control with the aim of minimizing losses and ensuring machine performance within the limits is implemented as a cascading control structure in three parts. The first part presents a computationally efficient calculation of the reference values of d and q axis current components resulting in minimum losses at the given torque and machine speed. The second and third components of the control algorithm serve to adapt the output from the loss minimization algorithm to ensure machine operation within the limits. The second component, the reference controller, changes the reference current to avoid the saturation of current regulators and over-modulation without loss of control performance, thus reducing losses due to sudden changes in torque reference. The third component is implemented as a management model based on predictive models that guarantee machine performance within the limits and minimum losses in the field weakening regime. The proposed control algorithm is designed as a computationally efficient addition to the existing classical vector-controlled permanent magnet synchronous machine in order to improve its performance. Modern synchronous permanent magnet motors are characterized by high efficiency and high torque density, which are the properties increasingly emphasized in a number of applications like electric traction or aerospace applications. Such machines fully utilize their magnetic circuit which results in saturation phenomena that cause nonlinearities in their mathematical models. The machine model that is able to adequately simulate current, voltage and torque waveforms is one of the key requirements for designing the control system and also for the purpose of the machine design optimization. In the thesis, mathematical model of a permanent magnet synchronous machine which includes saturation effects is presented. To round up mathematical representation of a permanent magnet synchronous machine, the proper model of losses must be included in the machine model used either for simulation purposes or as a cornerstone of control algorithm design. Losses of permanent magnet synchronous machines can be devided into two groups, mechanical and electromagnetic losses, of which control designer can affect only electromagnetic losses. The electromagnetic losses of synchronous motors with permanent magnets can be divided into three categories: copper losses, iron losses and permanent magnet losses. Copper losses are implemented in the mathematical model using winding resistance, while iron losses are implemented using equivalent resistance of iron losses. Losses in permanent magnets are, due to its low value compared to copper and iron losses, neglected during control algorithm design process. Approximation of iron losses with equivalent resistance results in an error under load and at high speeds. In order to obtain a more acurate and detailed model of iron losses in synchronous motors with permanent magnets, an empirical model of iron losses was developed. The presented empirical model of iron losses is compared to the measurement results on the real machine. The subject and focal point of the research problem is the interior permanent magnet synchronous machine designed as the main traction motor of an electric tram. Therefore, an emphasis is placed on the electric traction applications. The thesis is divided into 6 chapters organized as follows: Chapter 1, Introduction draws the attention of the reader to the subject of the research, the permanent magnet synchronous machine, its application, advantages and classification. In brief, the requirements for the control system of this type of machine are presented, as well as a detailed review of the literature. Chapter 2, Permanent magnet synchronous machine model contains derivation of mathematical model of a permanent magnet synchronous machine in three-phase abc reference frame and rotating dq reference frame. This chapter provides a review of models suitable for computer simulation. Chapter 3, Permanent magnet synchronous machine losses presents an upgrade of a mathematical model of the machine by adding the loss model. Breakdown of losses due to their origin on electrical and mechanical losses and a detailed description of the appropriate loss components is presented. A simplified requirement for minimum electrical losses is presented with a proposal for finding solution to a minimum loss problem. Also, the chapter describes a new empirical model of permanent magnet synchronous machine core losses. The chapter contains two original scientific contributions: 1. Simplified model of total electromagnetic losses of interior permanent magnet machine suitable for solving in real-time control systems 2. Empirical model for calculation of iron losses in permanent magnet synchronous machine Chapter 4, Permanent magnet synchronous machine control system describes the classical vector control structure of a permanent magnet synchronous machine based on the field oriented control. The chapter also describes a control algorithm that provides machine operation within the limits in two components. The first component, the reference governor, is an add-on that can be easily embedded into existing classical control structures and whose task is to customize input references to existing current controllers to avoid their saturation and avoid over-modulation without loss of control performance. The second component, the field weakening algorithm, is derived in the form of control based on predictive models to guarantee machine performance within the voltage and current limits with minimum losses in the field weakening regime. These two components represent two distinct original scientific contributions: 1. Algorithm for dynamic modification of permanent magnet synchronous machine current reference values, which ensures machine performance while satisfying the voltage and current limitations 2. Computationally efficient permanent magnet synchronous machine model predictive control which assures field weakening operation while meeting the voltage and current limitations Chapter 5, Experimental results contains a detailed description of the methods and equipment used in the experimental tests. The results of testing and the functionality of the proposed control algorithm are given for two different permanent magnet synchronous machines: an interior permanent magnet synchronous machine and a surface mounted permanent magnet synchronous machine. The results of loss measurement and comparison with the empirical model of losses from Chapter 3 are also included in this chapter. Chapter 6, Conclusion gives an overview of the presented dissertation and sums up the results of the research