(Source: Hotlight / stock.adobe.com)
Accurate and efficient motor control is a subject of significant academic and real-world interest. Field-oriented control (FOC), sometimes called vector control, benefits both accuracy and efficiency. Although the principle is about 50 years old, it was impractical due to cost and computational requirements until the past few decades. That situation has changed, and FOC has now migrated “down” to markets and applications such as professional power tools and washers/dryers, where it offers improved performance and efficiency.
This blog discusses the evolution and application of field-oriented control (FOC) in efficiently controlling the torque and speed of three-phase AC motors, addressing its computational complexity and growing practicality in various industries.
FOC originated in the late 1960s and early 1970s, with significant contributions by F. Blaschke of Siemens in Germany, leading to a US patent application in 1971. The adoption of FOC was slow, requiring all those calculations and other support electronics. However, as processor speeds and computing capabilities increased while cost and size decreased, it became more practical and cost-effective to use FOC.
FOC is a technique used to control the torque and speed of three-phase AC electric motors, which include three-phase brushless DC (BLDC) and two-phase stepper motors. The purpose of FOC is to direct the motor to achieve maximum torque at a given speed by ensuring that the rotor field is always lagging by 90° concerning the stator, even under continually varying load conditions.
FOC is complex. Essentially, it involves measuring motor currents and continuously converting them into a coordinate system that rotates with the rotor. For this transformation to work, the rotor position must be determined either directly with speed or position sensors (sensored FOC) or indirectly through inference (sensorless FOC).
FOC makes this determination by calculating the rotor flux angle at a kilohertz rate and using the results to control the currents in the stator windings. These transformations involve a significant amount of matrix mathematics and must be performed in real-time with the rotor's rotation, requiring hundreds or even thousands of updates per revolution.
Ultimately, you can understand FOC in two ways: by using electromagnetic theory and complicated equations, or with a more qualitative approach, which we'll use here.
Using a BLDC motor as an example, the wires of all three phases are energized with a sinusoidal current that is 120° apart on each stage. The maximum torque occurs when the rotor’s magnet is at 90° in relation to the stator field. In contrast, if the rotor magnet is at 0° and thus aligned with the stator field, there is a strong pull directly outwards on the magnet, representing wasted power as it produces no torque. Alignments between 0° and 90° deliver some intermediate torque value that is less than optimal versus applied power. But if the angular position of the rotor is known in real-time, the voltages on the trio of phase windings can be controlled to maintain that 90° difference.
While it may seem easy to control the voltages to the windings, the voltage and current to a target winding are not in phase, since it is a magnetic inductive load, and moreover, the magnetic field of interest is the result of current being driven into a coil, not voltage. However, that phase difference is not known in advance and constantly changes.
In FOC, the current is resolved into two perpendicular parts: the part that causes the desired vertical pull—called torque or quadrature current (Iq)—and one that causes the undesired outward pull—called flux or direct current (Id). Once these constituent present components are determined, FOC adjusts these two components by adjusting the voltage phase so the direct current becomes zero and only the desired torque current remains (Figure 1).
Figure 1: FOC requires measurement of motor-coil currents and relative phases concerning each other. (Source: Cblambert, CC BY-SA 3.0, via Wikimedia Commons)
The current on the motor leads alternates while the field inside the stator is a rotating three-phase magnetic field; however, the rotor, which is rotating along with this rotating field, sees a constant force. To get there, a pair of mathematical coordinate transformations called the Clarke transform and the Park transform merge the angle data and the current data to measure the Iq and Id currents, both of which are slowly changing currents as seen from the rotor’s frame of reference.
For practical motor control, a pair of proportional-integral (PI) closed-loop feedback controllers are employed to regulate both the phase and voltage to the coils, ensuring the desired Iq and Id current values. Typically, Id is minimized to zero to reduce wasted torque and maximize useful torque. The Park and Clarke transforms are inverted—requiring intensive calculations—to produce the desired winding currents. This process must be executed at a high frequency, often around 10kHz for most rpm ranges, leading to significant processing demands.
In a sensored FOC, an angle sensor is needed to ensure that rotor flux is in phase with the rotor magnet. However, a basic, low-cost Hall-effect device, regularly used for position sensing, does not offer the needed precision, so a more costly rotary-position encoder is often required. This adds to the complexity of the hardware and cost of the sensor-based version, while also adding something else that can fail in use.
Instead, a sensorless design is used, again with complicated mathematics that are too complex to describe fully here. Keep in mind that the objective of the control loop is to measure the currents in the stator windings, compare them with the desired currents, use the difference to generate an error signal, and then drive the currents to reduce or eliminate the error.
The sensorless design analyzes the relative phases of the three stator currents and voltages. Using these, it is possible to assess the situation in detail and calculate the solution to the closed-loop control vector. Note that even though currents and voltages are scalars, three of each are located 120° apart, so they form vector triplets. As such, their relative displacement (in phase) can be used to adjust the stator currents' timing (again, in phase).
Therefore, a sensor is not needed if the system can “afford” the cost of digitizing each current and voltage at the required update rate—about 10kHz in most cases—with adequate resolution (typically 18 bits) and also perform the numerically intensive matrix math in real-time to determine the constantly changing error and, subsequently, generate a correcting signal.
Sensorless FOC has been used in larger, more costly systems for several decades, but it wasn’t practical for lower-cost consumer products. Once again, however, semiconductor advances are making what was once impractical now effective in terms of cost, size, and power for the mass markets.
Still, sensorless FOC remains “overkill” for some situations, and the incremental benefit may not be worth the cost and effort. It is undeniably complicated, and some designers who implement motor drives and controls don’t want to get involved with that level of advanced design expertise. Further, setting up sensorless FOC and optimizing the parameters for a given motor and load can be somewhat complicated.
However, advances in smarter software, which do not always require artificial intelligence, and development tools are changing that situation. Just as PID controllers used to require careful manual tuning before PID autotuning became quite good, FOC IC and system suppliers have developed advanced auto-tuning, which optimizes the FOC parameters to the desired priorities.
IC vendors have introduced powerful ICs that incorporate nearly all the functions needed for sensor and sensorless FOC. These ICs include high-resolution A/D converters, motor drivers for the external power-switching FETs, analog signal conditioning for the sensors (if any) and current signals, and powerful computation-optimized engines with microcontrollers that can perform critical real-time calculations. The hardware is supported by GUIs and development tools to make setting up the algorithms and testing them more straightforward. As a result, motor FOC is easier to implement and more available for those applications where it makes sense for performance or cost.
Bill Schweber is a contributing writer for Mouser Electronics and an electronics engineer who has written three textbooks on electronic communications systems, as well as hundreds of technical articles, opinion columns, and product features. In past roles, he worked as a technical web-site manager for multiple topic-specific sites for EE Times, as well as both the Executive Editor and Analog Editor at EDN.
At Analog Devices, Inc. (a leading vendor of analog and mixed-signal ICs), Bill was in marketing communications (public relations); as a result, he has been on both sides of the technical PR function, presenting company products, stories, and messages to the media and also as the recipient of these.
Prior to the MarCom role at Analog, Bill was associate editor of their respected technical journal, and also worked in their product marketing and applications engineering groups. Before those roles, Bill was at Instron Corp., doing hands-on analog- and power-circuit design and systems integration for materials-testing machine controls.
He has an MSEE (Univ. of Mass) and BSEE (Columbia Univ.), is a Registered Professional Engineer, and holds an Advanced Class amateur radio license. Bill has also planned, written, and presented on-line courses on a variety of engineering topics, including MOSFET basics, ADC selection, and driving LEDs.