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Hello, and welcome to this TI Precision Labs video for motor drivers, on field-oriented control of brushless-DC motors. My name is Andrew Liu, and in this video, I will discuss the basics of FOC. We will start this video with an overview of BLDC motor construction. Then we will refresh our knowledge on the previously discussed commutation methods of sine and trap control before delving into the details of FOC. The control block diagram will be discussed, and we will talk about the math involved in an FOC system. Lastly, we will close out with emphasizing the characteristics of FOC and some applications where it may be useful.

To better understand the operation of a BLDC motor, let's first talk about its typical construction. This consists mainly of the stator and rotor components. Each phase of the stator has coil windings, which act as electromagnets when injected with current.

The rotor has permanent magnets and interacts with the magnetic fields produced by the stator, generating torque. This process of switching on and off the current to each phase winding is called "motor commutation" and is what causes the motor to spin. For the best performance, these commutation signals should be done in a controlled manner that considers the rotor position.

Now that we have defined motor commutation and how it works, let's discuss some different control methods and the traits of each. First up, we have trapezoidal control, or "trap" for short. This commutation logic is relatively easy to implement and can produce high torque and high speed while maintaining low switching losses.

In this diagram, we observe the motor's voltage and current for each phase, and the six possible states in which each phase is either logic-high, logic-low, or in transition. These inputs result in the system's output torque waveform, below, in which we see a clear torque ripple during each of the state transitions. The ripple occurs at the switching frequency and translates to audible noise and inconsistent torque, which may not be desirable in certain applications.

Next, we will discuss sinusoidal control. Similar to trap commutation, sine control can be described by its phase voltage and current waveforms. The goal is to produce output currents for each phase that are sinusoidal in shape, and we achieve this through the Pulse Width Modulation technique, or PWM. Instead of having the phase voltages either 100% on or off, we can fine-tune the voltage transitions using PWM, which produces much smoother waveforms.

The advantages of this method include low audible noise and high motor efficiency. Some disadvantages are that it is more difficult to implement when compared to trap control, and the PWMs required for each phase will involve higher switching losses. Additionally, the torque ripple is not very good during dynamic loads, such as motor startup and motor braking, in which the speed is changing. With sine control, the system is not reaching its full potential in terms of maximizing torque output and motor efficiency.

Arriving at our main topic today of Field-Oriented Control, or FOC in short, this method aims to produce the most torque possible for our given system, even under dynamic loads like startup and braking. This is done by always applying torque 90 degrees perpendicular to the rotor position, as shown by the direct and quadrature vectors of our phase currents. With FOC, we can achieve the lowest audible noise and the highest motor efficiency. We also retain high motor speed, which can be further increased by using techniques like field weakening, all while keeping our switching losses the same as sine.

So what's the challenge with FOC? We implement FOC through real-time calculations involving motor phase currents and rotor positions. This is a computationally complex activity that usually requires a microcontroller and some user-defined programming code. This overhead takes extra equipment and debugging effort to implement, which is what makes FOC the most difficult of the three methods mentioned here.

Now that we've defined the goal of FOC as maximizing the torque vector perpendicular to the rotor, we should introduce the variables in the control system. Recall our motor phase currents, U, V, and W, which are separated by 120-degree phase angles in a three-phase system. We define a new X,Y fixed coordinate system that will be referred to as alpha and beta.

Lastly, we have the direct and quadrature vectors for our torque components, and note the rotor angle, theta, that separates the rotor and stator positions. The direct component is in line with the rotor, and the quadrature component is 90 degrees perpendicular instead. Combining these coordinate systems in one results in this diagram, which relates all the variables.

Let's take a look at what a motor-control system might look like. The PWM generator will take some input command and apply signals to the inverter for each motor phase, resulting in phase currents and motor rotation. However, commutating a motor is a controlled process, so we need to include a feedback loop in our system to define the position of the rotor, shown as rotor angle, theta.

This feedback is then used to determine the next sequence of phase inputs in order to target some parameter, such as a torque command being fed into a PI controller. In sensored methods, this is usually done with equipment like Hall effect sensors, rotary encoders, and resolvers. In sensorless methods, we can estimate theta by determining the back EMF while the motor is rotating, and relating that to other parameters, like speed and current. There is some more detail on this sensorless method in the TI Precision Labs videos for sinusoidal control and sensored versus sensorless control.

In an FOC system, we can see that the control block diagram becomes more complicated. We will start off with the same variables, like phase current and rotor angle, theta, but now involve the use of Clarke and Park transforms. U, V, and W are converted into alpha and beta terms using the Clarke transform.

The Park transform then takes these two new variables in addition to theta to compute the d and q vectors. Some PI controllers are applied to minimize d and maximize q so that all torque is applied perpendicularly to the rotor. This is then transformed back into U, V, and W terms through the inverse Park and inverse Clarke techniques so that the system can drive the motor using the right PWM inputs.

You might be wondering, how do these Clarke and Park transforms work exactly? Starting with the phase currents U, V, and W in the control feedback loop, we begin the Clarke transformation using these equations for alpha and beta. We note that the original phase currents are each separated by 120 degrees and convert them to the fixed alpha-beta coordinate system using simple trigonometry.

We are essentially breaking down each of the U, V, W phase current vectors into alpha and beta components and then summing them up afterwards. That is, how much of the U phase current is in the direction of the alpha axis? How much of the V phase current is along the alpha axis? And how much of the W phase current is also along the alpha axis? We follow the same process for the beta-axis components, and once we have done this, we will carry forward our alpha and beta currents to the next step of our calculations.

Proceeding with the Park transform, we now involve a new variable in our equations, the rotor angle, theta. With the Park transform equations, we calculate the direct and quadrature components of the phase currents. What we are doing here is relating the stator's phase currents in alpha and beta terms to the rotor's position and field orientation, which is defined by theta.

Now we're thinking of this as, "How much of the alpha current is along the direct axis? How much of the beta current is along the direct axis?" and then summing it up to produce a d vector. The same logic applies here for the quadrature vector, of course, and with this calculation complete, it is possible to assess how much torque is being applied perpendicular to the rotor. And this is something we can maximize using the PI controllers.

In this video, we talked about how an FOC system can achieve the best acoustics, best dynamic torque, and the highest motor efficiency. We also discussed how FOC compares to other methods, like sine and trap. So why does this all matter? When deciding what method to use, it's important to know the intended purpose of your system.

For instance, FOC's low-torque ripple brings an advantage to applications like fans and air purifiers, where quiet operation is desired. Having carefully controlled torque is also extremely valuable in any equipment like robotic servos and washing machines. The efficiency benefits of FOC can result in battery-life improvements and reduce power consumption, while careful control of your motor's magnetic fields and back EMF can increase motor speed through techniques like field weakening. In summary, designing your system around FOC can bring many of these benefits.

This concludes our presentation for this video. Some resources available in this slide will explain the other commutation methods in more detail, as well as some examples of the code and logic to apply in your FOC algorithm, whether that be for a sensored system or a sensorless system. To find more motor driver technical resources and search products, visit ti.com/motordrivers. Thank you for watching.