 Dear listener, my name is Thomas Dresler and I will introduce you to the basics of the permanent magnet synchronous motors and field oriented control. This lecture demonstrates the principles of the motor and well, doesn't show many equations, they are here only for your understanding and to speed up the following chapters. So let's look at the basic physics that happen in the motor. It's no rocket science and we shall be finished within 10 slides. First let's take a look at our physical system. This is how the motor is constructed and how we will take the parts apart and describe them one by one. Let's begin with the mechanical part. We can see that the motor is connected to the shaft. The shaft is stored in the bearings and provides the rotation let's say momentum or torque to a connected load. The load can be a wheel of the vehicle, a pump or a fan. Now the motor provides a motor torque. The motor torque is lost during the transition to the load in different frictions or initial mechanical resistances. These are typically non-linear and depend on the speed of the shaft. The load has some physical properties, mainly the inertia. Inertia can be described as a mass distributed in the volume of the load and it creates kind of resistance, a dynamical resistance to acceleration or deceleration. Now when we look a little bit to the equation of the speed dependent on the torque over time we can see that the speed can be increased or decreased over time by applying the torque divided by the inertia of the load. So let's wrap it up in the mechanical point of view. The change of speed is equal to the additional torque that if it's a positive the motor accelerates but if it's negative the motor decelerates and can even reverse. Additionally the bigger is the speed, the bigger losses we see in the bearings by the load itself. So it reduces the available torque which means that the acceleration reduces and at one speed the acceleration is reduced down to zero which means we can't mechanically achieve a higher speed with given system parameters. We can call this speed a maximum mechanical. Now only for the reference let's look at the dynamic torque equation that you can take for example in Sylop and simulate the behavior of your system. Further many people are interested in the mechanical power delivered to your load. So typically only the first part is important which we can introduce as a motor torque multiplied by the mechanical speed. If we want to be more precise we can as well deduct the dumping and resistive torque. Both of them rely on the speed of the load itself. Now let's move our attention to the magnetical part of our motor. We can see that this part is the one that drives the conversion from the electrical to mechanical energy. It relies on the Lorenz law which causes attraction of the permanent magnet in the electromagnetic field of the coil. So assuming the coil is fixed in the stator and the permanent magnet is moving on the rotor or on its axis we can deduct from the current the angle between the electromagnetic field and the position of the rotor and other mechanical properties of the rotor like its size the force which the flowing current applies to the shaft and at the same time as well the momentum or torque. The biggest torque is applied when the electromagnetic field of the coil and the magnetic field of the rotor are exactly perpendicular so when their electrical difference is 90 degrees when the sinus of this angle is equal to 1. Now we can look further to the electrical part of our motor. We can see that when we deliver a voltage to the winding of the coil the voltage splits between several different parts of the electrical system. All of it happens in the coil but there are several different properties that need to be taken in account. The first and the main one is the inductive part which can be expressed as inductance Ld or Lq multiplied by the derivation or change of the current over time. This is the thing that's very useful for us because when we apply a voltage the integral of it effectively is transferred as a torque to the rotor and then it creates the mechanical work for us. Second part is the resistive loss which is automatically inserted into the voltage chain and it is the higher the higher is the current through the winding and finally we can see another part of the voltage split which is the back emf voltage. The back emf voltage relies purely on the electrical constant which is the constant of the motor and the rotational speed of the motor. Now to wrap up the electrical part we can see that the speed is proportional to the voltage because the higher voltage we have the higher torque we can generate and the higher speed we can achieve due to the acceleration. Now the torque is proportional to the current that flows through the system. Further let's talk about the back emf voltage. It is induced in the stator by the rotor turning in the windings and it has the opposite direction of the supply current. The back emf is subtracted from the supply voltage and because it's linear with the operating speed of the motor we can tell that the higher the speed the lower voltage is left to the inductive part of our system which at the end limits the maximum electrical speed that we can achieve in our motor. So let's look at the effects of the back emf and the demagnetization of our motor. So when we apply a supply voltage to the motor expressed as a bus voltage we can see that the back emf rises from zero at zero speed to the value of the bus voltage and this happens at the speed maximum electrical. This situation happens if we don't apply any demagnetization. So let's as well look at the same chart when we show the mechanical limits of our motor. You can see that the speed achievable in this case as a maximum electrical is within the limits of the motor when we speak about the mechanical speeds. So for now everything is okay but we feel that the motor could still run faster if it needs to. But to do this we need to apply a little trick called demagnetization. So when we apply demagnetization what happens? We inject a specific angle of the current into the winding that creates a part of our torque and magnetization in the winding that subtracts from the magnetic field of the rotor. This in fact reduces the electrical constant of the rotor which reduces the inducted voltage and this like shown on this picture as a pink line allows us to increase the maximum speed however we could notice that the torque available to the motor was reduced by the same fact of applying the demagnetization. So the maximum speed that we can achieve now is depicted by the dashed pink line. It's still faster than the original electrical speed but you can see that at the same time we are limiting the maximum available torque at this speed. There are some benefits of the demagnetization like higher achievable speed than originally constructed and in some cases it allows smoother speed control. On the other side it reduces the torque at the maximum speed achievable and in case we lose control of the motor at this in this over speed region we need to have an over voltage protection of our power stage. This is because we are running the motor at the speed higher than the maximum electrical and if we remove the demagnetization the inducted voltage starts rising suddenly above the bus voltage which can be dangerous to our power stage to the bulk capacitors and to the transistors. Now let's come back to our principle lecture and let's speak about the construction of the motor. What we see now is the stator. Stator is the fixed part of the motor that is normally fixed somewhere with bolts and joints and doesn't move. Now let's insert a rotor in the motor. Rotor is a permanent magnet fixed on the axis that goes from you through the screen. Now the stator embeds coils that feed the current in a given direction and generate electromagnetic field. This field interferes with a magnetic field of the rotor and creates a torque which causes movement of the rotor. We already described this principle by Lorenz Law. So the current running in the coil causes the rotor to move and in this case when we don't apply any other magnetic field to align in the state with the lowest energy. Now the magnetic fields and many other quantities can be described by vectors which are defined by their size and direction. I can give you an example. The magnetic induction of the permanent magnet has size of half Tesla and its north pole points to the left. To be able to operate with vectors we have to establish coordinate system for example the xy plane with a common point where the rotor axis crosses the screen. Now having a single coil in the motor has no benefit. We could only align the rotor in two ways. Let's add one more coil. When we deliver the current to the second coil instead of the first one the rotor will move towards the newly generated electromagnetic field and will align with it. Now we can spin clockwise and counterclockwise. When we add the third coil and supply the current we finish the construction of the three phase motor and allow full control of the rotor movement. So now we have three coils in the stator each with two terminals. Six terminals are unnecessarily too much. So we connect one end of each coil together creating so called star configuration. Each coil current creates a unique vector of the electromagnetic field. The resulting field applied to the rotor can be expressed as a combination of the three vectors. Mathematics call it a vector sum. The Kirchhoff junction rule tells us that the algebraic sum of the currents in the common point is equal to zero. Consequently the current flowing into one coil must leave through other coil or coils. The common point is normally not connected on motor terminals unlike the three loose ends of the coils. Let's call them U, V and W phases. Okay now let's talk about the permanent magnet synchronous motors and brushless DC motors. First permanent magnet synchronous motor, BMSF. Its construction of the stator consists of three phase windings. Rotor is constructed from permanent magnets that can be either glued on the surface which creates a surface mounted permanent magnet synchronous motors or buried within the rotor so called internal permanent magnet synchronous motors. The stator excitation frequency must be synchronous with the rotor electrical speed. The rotation induces a back EMF or back electromagnetic force which has a sinusoidal shape. The motor gives a best performance and torque steadiness when it's driven by a sinusoidal phase current from our power stage. The permanent magnet brushless motors called in short BLDC are like PMSM in manufacturers like they require alternating stator current like PMSM motors the rotor houses permanent magnets typically glued on the surface of the rotor and like PMSM their stator excitation frequency must be synchronous with the rotor mechanical speed. Unlike permanent magnet synchronous motors the rotor that spins within the stator indexes a trapezoid shaped back electromagnetic force and this motor gives the best performance when driven by rectangular shape currents. Now let's look at the control principles of the permanent magnets synchronous motors. We can see the three phases connected to three parts of the power stage. Each phase is typically driven by two switches transistors one connected to DC bus other to the ground. Periodic switching avoids as much as possible the linear region offering three principal states of the phase connection to the DC bus unconnected or grounded. Combination of phase switches gives eight or in case of using a unconnected 27 possible switch safe configurations of voltages on the motor terminals U, V and W where six combinations are only useful and deliver current to the motor and the two other create short circuit between all phases either grounded or connected to the V bus. The phases U, V and W drive currents I, A, I, B and I, C to the motor. Thanks to the Kirchhoff junction rule one of them is always dependent on two other which allows to simplify the control algorithms and after Clark transformation use only two currents or a current vector to describe them like this or this or even this. The PWM which stands for pulse width modulation is a very useful and simple control technique. The controller generating PWM signals emits periodically at the switching frequency or period a digital pulse with a width whose value represents effective voltage and moves between zero and the length of the switching period. The low side switch is switched on when the pulse has low logical value and high side switch is switched on when the pulse has a high logical value. Cross conduction is avoided by inserting a so-called dead time. The block commutation is the first method to control the permanent magnet synchronous motors. It consists of applying six combinations of the phase voltages in pre-calculated sequence. The periodic change of the phase combination is called a commutation and must appear at correct time. The measurement and setup of the commutation moment as well as of effective phase voltage are principles of this control method. The method I'd like to describe here is the field-oriented control. It's based on control of the stator electromagnetic field as a vector versus the vector of the magnetic field of the rotor. Due to need of regulation of sinusoidal currents some mathematics need to be applied every time the control algorithm is called which requires fast CPU. The processor load is approximately 100 times bigger than with simple block commutation. Let's start with the principle of the field-oriented control. The field-oriented control is a control that takes the electromagnetic field created by the windings and stator which are organized in the slots of the stator creating several independent electromagnetic fields. In this configuration you can see three of them so we have a three pole pair motor in front of us. These windings are driven by three sinusoidal currents with 120 degrees phase shift and this hole creates a time-warring rotating system. Now let's add a stator with its own set of permanent magnets and magnetic fields and now let's put them all together. So the maximum torque is achieved and the maximum energy flow is possible when we align the statoric field in front of the rotoric field and we pull the rotoric field behind us with the angle distance of 90 electrical degrees. By pulling the rotor and maintaining the constant angle difference we can spin the motor with a steady speed. By increasing the amplitude of the vector we can add the torque and acceleration or by reducing the amplitude we can decelerate the spinning. To be able to achieve this control principle we need to read the currents and we can do it with three different methods reading on three shunts on a single shunt or using isolated current sensors. Further we need to read the position of the rotor to be able to align the statoric electromagnetic field properly. For that we need information from sensors like encoder or hole sensor or we can make use of different mathematical algorithms that allow operating without sensors. The currents that we extract from the motor are fed to the current controllers like PID or feedforward. Now because the three currents are interdependent and they are as well placed apart by 120 degrees electrical we can use a Clark transformation that transforms these currents to two independent values that are 90 degrees apart. Further we have to find our reference system and we will lock the axial system to the position of the rotor. With that reference we are able to relate to the rotating currents and create the vector that is perpendicular to the position of our rotor. In case of using the magnets with the internal or inset construction we can make use of a maximum torque per ampere algorithm that modifies this fixed angle to a little bit more than 90 degrees. It's rather difficult to control the two currents when they have a sinusoidal shape and change over time. At this moment we can apply a park transformation which transforms rotating currents i alpha i beta created by the Clark transformation to steady values i q and i d seen from the position of the rotor. This is like if we would sit at the rotor and observe the rotating field that spins around us with the same frequency which means we would see steady values. So let's put it all together in a block diagram. We can notice the three currents at the input of the Clark transformation from the faces a b and c or u v and w converted to two perpendicular currents alpha and beta which are still variable with a sinusoidal shape but 90 degrees apart. Now we demodulated them with the reference to the rotor position by the park transformation and we get two steady currents called d and q. These two steady currents are independent of each other and this means that we can control these currents independently by two different controllers that use for example PID or feed forward principle. The outputs of these two independent controllers the vd and vq are transformed by the inverse park transformation back to the rotating voltages v alpha and v beta and using some type of modulation typically space vector they are brought to the power stage in the form of the three PWM signals. The field oriented control has many benefits over other control strategies like best energy efficiency. It is swell very fast in the speed control when there are load variations or bus voltage variations. They allow decoupled control of both fields related to the position of the rotor the torque part and the magnetization part and because we drive the motor in the perfect angle orientation with a sinusoidal output we are able to reduce the acoustical noise. Because the field oriented control works in four quadrant operation it allows to actively break and get back the energy stored in the system to our power stage and further to the battery or our power distribution system if the construction allows that. Now let's look to these reference frame transformations with a little bit more detail. I won't repeat the equations because you can read yourself and they are here only for your reference.