Got Field-Oriented Control in Your Servos? This article includes online material.

Field-oriented control—sometimes called flux-vector control—is a method that enables highest performance from permanent magnet (pm) synchronous (or brushless servo) motors throughout their speed range. FOC algorithms model the torque-generating efficiency of dc motors and allow linear torque control.




  • High-performance servo control

  • Minimize motor torque ripple

  • Servo control for all speeds

  • Digital processors essential

Field-oriented control—sometimes called flux-vector control—is a method that enables highest performance from permanent magnet (pm) synchronous (or brushless servo) motors throughout their speed range. FOC algorithms model the torque-generating efficiency of dc motors and allow linear torque control.

Better known in connection with ac induction motors, for which the technique was first developed more than 30 years ago by Felix Blaschke at Siemens, FOC is available from many manufacturers for brushless servo motors, yet not widely touted. FOC has different flavors and tag names, much like vector control of induction motors. (Read more about FOC and alternative control methods in an online sidebar at

For highest performance

Digital drives based on FOC are considered "standard" fare for brushless dc motors (and other motor types) at Bosch Rexroth Corp., Electric Drives & Controls, to meet the demands of higher positioning accuracy, power density, speed, and efficiency not possible with traditional controls—like trapezoidal or sinusoidal commutation.

"With field-oriented control, the current vector is controlled in its optimized orientation, resulting in maximized torques with minimized losses," says Peter Fischbach, manager, component sales. "Safe operation during voltage limitation and field weakening would not be possible using conventional control methods."

Fischbach attributes various advantages to FOC that overcome inherent limitations of earlier controls. Bosch Rexroth's latest FOC design, a fifth-generation multivariable current-control system, reportedly provides high torque at low speeds (down to 0 rpm) with less than 0.5% torque ripple; high efficiency, even at high speeds; and full control during voltage limitation and field weakening. Among other benefits, he also cites:

  • Torque and current response times under 0.2 ms; and

  • Current controller bandwidth greater than 2,000 Hz.

Charles Rollman, Copley Controls Corp.'s technical director of motion products, differentiates FOC from sinusoidal commutation (see section on "alternatives"). In the latter method, the commanded current is modulated by sinusoidal waveforms to produce a rotating magnetic field in the motor stator; however, the sine-wave frequency is speed limited, he explains. At higher speeds it results in current phase lag, causing misalignment of the magnetic fields, leading to motor heating and speed limitations.

FOC gets around this problem by direct control of the current space vector in the d-q reference frame of the rotor, which ideally fixes the vector's magnitude and quadrature direction (90°) relative to the rotor—independent of rotation. "The PI controllers operate on dc, rather than sinusoidal signals. With field-oriented control, the quality of current control is largely unaffected by motor speed," says Rollman.

To implement FOC, various reference frame transformations must be made, involving complex calculations. Measured motor currents are first transformed mathematically from the stator windings' three-phase static reference frame to the two-axis rotating d-q reference frame, prior to processing by the two PI controllers (see FOC diagram). The controller handling the d (direct) current component is driven to zero, forcing the current space vector exclusively in the desired quadrature direction. The second PI controller operates on the q (quadrature) component of current and tracks the torque command, Rollman explains.

Outputs from the two PI controllers represent a voltage space vector with respect to the rotor. A series of reverse transformations then converts these signals back to the stator's reference frame for three-phase PWM modulator output to the motor. Success of FOC depends on making these transformations efficiently. Rollman considers high-performance processors as enabling that task. And wide availability of digital signal processors (DSPs) in recent years has helped advance FOC for servos.

Stressing an important architectural difference between FOC and sine commutation in the sequence of current control and commutation processes, Rollman explains that PI control of current happens first in FOC, followed by fast commutation processes. The reverse is true for sinusoidal commutation. "PI controllers are therefore isolated from time-varying currents and voltages, and the system is not limited by PI control-loop bandwidth and phase shift," he says.

Quietly at work

Siemens likewise advocates FOC for pm synchronous servo motors, but with little fanfare about the naming.

"Field-oriented control is based on the transformation of the time-dependent three-phase stator system into a time-invariant d-q reference frame," explains Martin Gertz, product manager, Motion Control Drives and Motors, at Siemens Energy & Automation. This rotating system has two orthogonal current vectors: one parallel and one orthogonal to the rotor field. Since only the latter component produces useful torque, the parallel component is regulated to zero and the space vector is kept in the quadrature direction. "The [final] transformation back to a three-phase system results in sinusoidal stator currents via pulse-width modulation, without phase error of the current-space vector," says Gertz.

Simovert MasterDrives Motion Control and Simodrive 611U from Siemens use FOC exclusively to control pm synchronous motors. These servo drives use high-pulse frequencies up to 10 kHz, enabling control of oscillating torques without the need for damping cages. It satisfies applications that demand extremely short cycle times with highest dynamic response and precision, according to Siemens.

Field-oriented control allows PI controllers to operate in the rotor’s d-q reference frame, isolated from sinusoidal motor current and voltage changes, for equally good performance at high and low speeds.

Emerson Control Techniques (ECT) also put FOC to work quietly for brushless servo motors years ago. The occasion was its introduction of Unidrive, a so-called "universal" drive for multiple motor types. (ECT has applied the algorithms substantially longer to induction motors.) Alex Harvey, product line manager of Industrial Drives, Control Techniques Americas, says, "FOC is embedded in our servo drives, but not promoted specifically."

He mentions feedback devices as another important factor in FOC's success with brushless servo motors. UnidriveSP, the latest in the Unidrive family, supports incremental and absolute encoders, resolvers, and newer SinCos feedback, among others. "For high-performance applications, absolute devices that provide over 500,000 equivalent lines/revolution feedback are commonly used," Harvey, says. Of course, absolute devices also eliminate the need for time-consuming machine homing after a power-up.

Another proponent of field-oriented control, Delta Tau Data Systems, enhanced its control algorithm for brushless servo motors (as well as induction motors) to include digital current-loop closure 10 years ago. "We transformed the phase-current measurements taken in the 'stator frame' to the rotating 'field frame,' where the values are dc quantities, explains," Curtis Wilson, VP of engineering & research. "This eliminated the high-frequency problems associated with ac current loops."

While these algorithms continue to suit most of Delta Tau's customers, Wilson cites recent innovations for special users, such as "field weakening" techniques borrowed from induction motor vector control that permits significant changes on the fly to a servo motor's torque/speed curves. He also mentions a recent advance for the startup of synchronous servo motors, which require an absolute phase reference. In the past, this meant use of a costly absolute sensor or substantial motor motion during a "phasing search" move on power-up. "We are now employing an excitation technique that exploits the magnetic saturation properties of the iron core to establish the phase reference with no motion required," adds Wilson.

Rockwell Automation considers field-oriented control an integral part of its servo drives for brushless motors. Example products incorporating FOC include such lower power servos as Ultra3000—a one-axis 230/460 V drive with 22 kW (30 hp) maximum output—and recently introduced multiaxis Kinetix 6000 drive for 230/460 V input and rated output of 7.5 kW, slated to expand to 22 kW by end of 2004. Even so, reference to FOC is absent in typical spec literature, amid a gamut of other performance features, for example, digital interfaces, high bandwidth, high-resolution feedback options, and software.

Corey Morton, Rockwell Automation product line manager of standard drives, notes the company's added experience with FOC for ac induction motors. He points to PowerFlex 700S ac drive, rated at 0.37-250 kW, designed to control induction as well as brushless motors. FOC is cited in this drive's reference literature, but you have to drill down a bit to find it. Morton also mentions the evolution of FOC algorithms to include sensorless operation, a control mode that's available in PowerFlex 700S.

Baldor Electric Co. applies different control methods to brushless synchronous motors to suit specific application needs. Its full-featured FlexDriveII and MintDriveII use FOC to obtain torque and velocity regulation typically required in high-performance servo positioning applications.

John Mazurkiewicz, servo products manager, sees only negligible differences between FOC and sine commutation for ac brushless synchronous motors. "With FOC, a mathematical model of the motor is implemented using techniques that decouple the flux and torque-producing components of the current demand. It allows for independent monitoring and control of each component," says Mazurkiewicz. "Sine commutation naturally provides correct decoupling of flux and torque producing current components." He adds that FOC offers the benefit of higher rotor speeds (beyond available bus voltage) through field weakening by reducing the back EMF.

Board and chip level

"Field orientation is the only method to attain linear torque regulation for an ac machine, including induction and permanent magnet motors," remarks Toshio Takahashi, director of engineering for International Rectifier's (IR) Digital Control IC Design Center. IR is unreservedly keen on FOC. It considers FOC "essential technology" for new designs, even for replacing existing ones. "Implementation costs of FOC are becoming not so much different than those of traditional non-FOC control," according to Takahashi.

International Rectifier refers to its control method as "sinusoidal commutation by FOC." IR has found FOC superior to traditional controls for torque control and smoothness, particularly for an interior pm motor —an emerging motor design for appliance applications, such as a compressor drive. Moreover, FOC provides ability to extract saliency torque (an additional torque) generated by interior pm motors. "Complexity of the [FOC] algorithm can be overcome by the dedicated hardware control method, such as Motion Control Engine in IR's iMotion product," concludes Takahashi.

Texas Instruments (TI) notes several benefits of FOC, which it calls "sinusoidal field-oriented control"—mainly, better dynamic performance of the servo system and less motor torque ripple. Potential resizing of motors is an adjunct benefit due to the improved performance. "The historical downside to using FOC has been its implementation challenge," says Kedar Godbole, TI senior applications engineer for motors. FOC demands intensive computation, making it hard to apply without very efficient processors. "Due to this complexity, FOC had previously been reserved for very advanced or very large motor control," he adds.

Availability of highly integrated, embedded signal processors aimed at motor control has changed all that. For example, TI's TMS320C28x generation controllers now supply the necessary mix of computation power and on-chip peripherals to enable application of FOC in low- and medium-end systems, explains Godbole.

Alternative solutions

What came before FOC? Trapezoidal and sinusoidal commutation, especially with analog servo drives—and other methods if you go back far enough—provided ac servo motor control alternatives, but at lesser performance.

Siemens mentions a simple control method from servo drives' early days. It detected rotor position and speed with a position sensor and applied square-wave currents via a current controller to obtain basic positioning with synchronous servo motors. However, square-wave currents produced high torque ripple, especially at low speeds.

Pulse-width modulation applied to the inverter output voltage solved that problem, resulting in sine-wave stator currents. Known as sinusoidal commutation, this was a step forward, though still not optimal for cyclic high-dynamic applications, according to Siemens. "At high speeds, a phase error of the current space vector creates an unwanted reactive current, which....doesn't produce any useful torque, but increases the stator current," states Gertz. Sinusoidal commutation is no longer used on Siemens' servo drives.

Trapezoidal ("trap") commutation is a coarse brushless motor control that's simple to implement using just Hall sensor feedback. It's adequate for many adjustable-speed applications, according to Baldor's Mazurkiewicz. Sine commutation offers control improvement for motors with encoder plus Hall sensor feedback. "Sine commutation uses less current for a given torque compared to trap," he adds. Baldor MicroFlex drive supports trap and sine commutation with feedback type software selectable by the user.

Texas Instruments regards trapezoidal commutation and the associated brushless motor as a low-cost control for applications where "some torque ripple might be acceptable." It's a six-step approach, where rotor position feedback no finer than 1/6thof a rotation suffices. TI also mentions the usefulness of trapezoidal commutation for brushless motors running at speeds above 10,000 rpm.

"Trapezoidal controls can cause a misalignment of the optimal current vector of up to 30 degrees, which can result in torque ripple of up to 15% plus significant losses in efficiency and very limited precision at low speeds," says Bosch Rexroth's Fischbach. Sinusoidal control methods help at the low-speed end but offer no advantage to high-speed performance. "Since the current controller has to track time-variant current values, the limited gain and frequency response of the PI controller causes phase lag and gain errors in the motor current," explains Fischbach. "As a result, the current vector loses its optimized orientation and the motor efficiency deteriorates."

FOC overcomes limitations of earlier methods, providing optimal low and high-speed performance for brushless servo motors. And powerful processors are lowering implementation costs. It's time to beat the drum louder for the virtues of field-oriented control.

Online Extra to February 2004 Control Engineering article on‘Field-Oriented Control for Servos’

Frank J.Bartos, Control Engineering

Field-oriented control (FOC) produces the best performance available today in permanent magnet (pm) synchronous motors or brushless servo motors. And FOC does so at all operating speeds of the motor.

FOC has come a long way, since it was first developed to control torque and speed in ac induction motors in the early 1970s by Felix Blaschke at Siemens. Subsequently, it was adapted to optimize brushless servo motor performance, and today it’s the control method of choice for virtually all high-performance electric servo-motion systems.

Still, FOC for servo motors doesn’t get the same recognition as with induction motors, where the method—also known as flux vector control—is widely advertised. Field-oriented control also suffers from some confusion with sinusoidal commutation. “Some technology suppliers and users refer to sinusoidal commutation, even with fixed-field,‘stator-frame’ ac current-loop closure as field-oriented control,” says Curtis Wilson, VP of engineering & research at Delta Tau Data Systems.

Differences in the methods are explained in a sidebar on “alternative methods” and in the main article.
Sophisticated applications

Field-oriented control caters to high-performance needs.

Bosch Rexroth applies FOC in its digital intelligent drives that achieve positioning accuracies down to 0.001 in., at speeds exceeding 3,000 ft/min—even in multi-axis applications. For high positioning accuracy from zero to full speed, FOC is used in combination with feedback having resolution up to 16 million increments/revolution plus other technologies. “Any of the conventional control methods would lack in bandwidth and dynamics,” says Peter Fischbach, manager, component sales. Also featured is shaftless drive technology, which eliminates gears and other wear-prone parts between different motion axes. The company has championed shaftless drive technology for some time.

Bosch Rexroth also mentions high-speed metal cutting as an important FOC application (see photo in main article). For example, IndraDyn H permanent magnet motors achieve speeds up to 30,000 rpm using IndraDrive series controls. Motor temperature management becomes critical in this type of application, because additional losses in the rotor can cause thermal growth and affect machining accuracy, explains Fischbach.

International Rectifier cites a new dental drill design that uses a 24-V sensorless (encoderless) FOC system capable of operating at up to 100,000 rpm. It replaces a 6-step trapezoidal drive that produced unacceptable torque ripple and motor temperature rise at less than half that speed.

‘Sensorless’ FOC

Traditional field-oriented control requires a feedback device for positional information. Consequently, significant development is ongoing in “sensorless” (or encoderless) approaches to simplify the method, eliminate a separate feedback device and reduce costs, but still obtain the high performance of FOC.

Delta Tau Data Systems mentions an energy storage application of FOC involving flywheel control for up to 100,000 rpm, and in “sensorless mode”—that is, control without a shaft-mounted sensor, but relying on parameter sensing in the servo drive to estimate rotor angle. Wilson also mentions other “sensorless” FOC applications by Delta Tau with motor speeds up to 40,000 rpm. “Few sensors can handle that speed,” he adds.

Internal (or interior) permanent magnet synchronous motors are drawing attention, particularly in Japan. These motors embed permanent magnets inside the rotor rather than mounting them on the rotor surface for improved acceleration and other benefits. However, applying sensorless control to interior pm motors becomes more complex because rotor position information cannot be derived from electromotive force (EMF) estimation alone. Inductance of the stator also affects rotor position estimation, which emerging motor mathematical models seek to include.

Mitsubishi Electric Automation ( and Yaskawa Electric ( are among manufacturers that presently offer internal pm servo motors. One application mentioned by Yaskawa is in elevator drives.

FOC and alternative methods for brushless servo motor control

Trapezoidal (or six-step) commutation

One of the simplest control methods for brushless dc motors is termed “trapezoidal” commutation. Current is controlled through motor terminals one pair at a time, with the third terminal always electrically disconnected from the power source. Three Hall-effect devices embedded in the motor usually provide the digital signals which measure rotor position within 60-degree sectors and send information to the motor controller. Because at any time, currents in two of the windings are equal in magnitude and the third is zero, this method can only produce current space vectors having one of six directions. As the motor turns, current to its terminals is electrically switched (commutated) every 60 degrees of rotation so that the current space vector is always within the nearest 30 degrees of the quadrature direction.

Current waveform for each winding is therefore a staircase from zero, to positive current, to zero, and then to negative current. This produces a current space vector that approximates “smooth” rotation as it steps among six distinct directions as the rotor turns.
[The method is also known as six-step commutation.]

A PI controller is used for current control. Desired torque is compared against the measured current to produce an error signal. The current error is then integrated (I) and amplified (P) to produce an output correction, which tends to reduce the error. PI controller output is subsequently pulse-width modulated (PWM) and provided to the output bridge. This works to maintain a constant current in whatever windings are being driven.

Commutation is done independently of the current control. Position signals from the Hall devices in the motor select the appropriate pair of motor terminals to be driven by the output bridge. The remaining terminal is left disconnected. Current sensing circuitry is designed so that current is always measured in the active winding pair and fed back to the current-control loop.

Trapezoidal commutation performs adequately for many applications, but has its shortcomings. Because the current space vector can only point in six discrete directions, it’s misaligned from the optimal direction by anywhere from 0 to 30 degrees. This causes torque ripple of about 15% (1-cos30) at a frequency of six times the motor’s electrical rotational speed. Misalignment of the current space vector also represents a loss in efficiency, since some of the winding current produces no torque. Also, switching of active terminals introduces a transient to the current-control loop six times per electrical revolution of the motor. This causes an audible “click” and can make precise motor difficult at slow speeds.

Sinusoidal commutation
Another electric phase switching method—known as sinusoidal commutation—solves this problem by having the motor controller drive all three motor windings with currents that vary sinusoidally as the motor turns. The relative phases of these currents are chosen to result in a smoothly rotating current space vector that is always in the quadrature direction with respect to the rotor and has constant magnitude. This eliminates torque ripple and commutation spikes associated with trapezoidal commutation.

However, accurate rotor position measurement is needed to generate smooth sinusoidal modulation of motor currents. Hall devices are inadequate as they provide only a coarse measure of rotor position. For this reason, angle feedback from an encoder, or similar device, is needed. This method uses a separate current loop for each of two motor winding currents. Because the motor is “wye” wired, current in the third motor winding is equal to the negative sum of the currents in the first two windings (Norton current law), and therefore cannot be separately controlled.

Currents in each winding must be sinusoidal, phase shifted by 120 degrees (because the stator windings are oriented 120 degrees apart), and combined to produce a smoothly rotating current space vector of constant magnitude. Position information from the encoder is used to synthesize two sinusoids, phase shifted from the other by 120 degrees. These signals are then multiplied by the torque command so that sine-wave amplitudes are proportional to the desired torque. The result is two sinusoidal current-command signals appropriately phased to produce a rotating stator current space vector in the quadrature direction.

The sinusoidal current command signals are provided as inputs to a pair of PI controllers that regulate current in the two appropriate motor windings. Current in the third motor winding is the negative sum of currents in the controlled windings (as noted earlier). Output from each PI controller is fed to a PWM modulator and then to the output bridge and two of the motor terminals. Voltage applied to the third motor terminal is derived as the negative sum of the outputs to the first two windings. To the extent that the actual output current waveform accurately tracks the sinusoidal current command signals, the resulting current space vector will rotate smoothly, have constant magnitude and be oriented in the quadrature direction, as desired.

Sinusoidal commutation results in control smoothness generally unachievable with trapezoidal commutation. While it is very effective at low motor speeds, the sinusoidal method tends to fall apart at high speeds. This is because as speed goes up the current-loop controllers must track a sinusoidal signal of increasing frequency. At the same time, they must overcome the motor’s back-EMF that also increases in amplitude and frequency with speed.

Because PI controllers have limited gain and frequency response, time-variant perturbations to the current-control loop cause phase lag and gain error in the motor currents. Higher speeds result in larger errors. This perturbs the direction of the current space vector relative to the rotor, causing it to shift away from the desired quadrature direction. When this happens, less torque is produced by a given amount of current and therefore more current is required to maintain torque. Efficiency deteriorates.

This degradation continues as speed increases. At some point motor current phase shift crosses through 90 degrees—at which point torque is reduced to zero. With sinusoidal commutation, speeds above this point result in negative torque and are therefore not achievable.

Field-oriented control
The fundamental weakness of sinusoidal commutation is that it attempts to control motor currents that are time variant. This breaks down as speeds and frequencies increase due to the limited bandwidth of PI controllers. Field-oriented control (FOC) isolates the controllers from the time-variant winding currents and voltages [by translating the current space vector directly to the rotor’s d-q reference frame] and therefore eliminates the limitation of controller frequency response and phase shift on motor torque and speed.

Although the reference frame transformations can be performed in a single step, they are best described as a two-step process [see FOC diagram in the main article]. Motor currents are first translated from the 120-degree physical frame of the stator windings to a fixed orthogonal reference frame. They are then translated to the rotating frame of the rotor, which must be done at the update rate of the PI controllers to ensure valid results. The process is [later] reversed to transform voltage signals from the PI controllers in the d-q reference frame to the terminals of the stator windings.

Once the motor currents are transformed to the rotor reference, control becomes straightforward. Outputs from the two PI controllers represent a voltage space vector with respect to the rotor. Mirroring the transformation performed on motor currents, these static signals are processed by a series of reference frame transformations to produce voltage control signals for the output bridge. They are first translated from the rotating d-q frame of the rotor to the fixed x-y frame of the stator. Voltage signals are then converted from an orthogonal frame to the 120-degree physical frame of the U,V and W motor windings.

This results in three voltage signals appropriate for control of the PWM output modulator. The reference frame transformations do the work of converting between the sinusoidal time-variant current and voltage signals at the motor windings into the dc signal representations in the d-q space.

Why is FOC better?
Sinusoidal commutation produces smooth motion at slow speeds, but is inefficient at high speeds. Trapezoidal commutation can be relatively efficient at high speeds, but causes torque ripple at slow speeds. Field-oriented control provides smooth motion at slow speeds as well as efficient operation at high speeds. FOC provides the best of both worlds.

Excerpted and edited from “What is‘Field Oriented Control’ and what good is it?” by Charles Rollman, technical director of motion products at Copley Controls Corp.

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