What is principle of AC servo motor vector control?

AC Servo Motor Vector Control: What Clarke and Park Do

Why Vector Control Exists

A separately excited DC machine is straightforward to control because its field flux Φ and armature current Ia can be adjusted independently. Its torque is Tm = KT · Φ · Ia. Since the field has a separate winding, changing Ia does not directly change Φ, so torque can be regulated through the armature-current loop.

In a three-phase AC machine, the same stator currents contribute to both magnetisation and torque. Scalar V/f control keeps voltage proportional to frequency to maintain roughly constant flux, but it does not directly regulate torque-producing current. The load determines the resulting torque, so V/f can suit a fan but may not provide the response or position holding a servo axis needs.

Vector control addresses this problem through a change of coordinates, without changing the motor hardware. Resolving stator current into components parallel and perpendicular to rotor flux lets the drive control them much like the field and armature currents of a DC machine. The method is usually credited to Felix Blaschke at Siemens in 1971.

Vector control depends on a usable rotor angle and reasonably accurate motor parameters. Errors in either can affect torque control, particularly as speed or load rises. A comparison with a general-purpose motor on a variable-speed drive is available in VFD motor versus normal motor.

Three Frames, One Rotating Field

Vector control uses three coordinate frames to describe the same current field from different reference points. Keeping track of the frame makes the transformations easier to follow.

The αβ transform reduces three variables to two because, in a balanced three-wire system, the third current follows from the other two: ia + ib + ic = 0. The αβ currents still oscillate at the electrical frequency. They become constant only after the Park transform moves them into the rotating rotor frame.

Mechanical angle versus electrical angle

The transform uses electrical angle, which advances p times per mechanical revolution for a motor with p pole pairs. The relationship between pole count and pole pairs is explained in number of poles in a motor.

Clarke: Three Phases to Two

The Clarke transform maps the three phase currents to two stationary axes, with the α axis aligned to phase A. The amplitude-invariant form below preserves the current peak value and is commonly used in drive implementations:

Because the neutral is not connected in a normal three-wire machine, ic = −ia − ib, and the pair simplifies to something a microcontroller can compute in a few instructions:

Two conventions that are not interchangeable

The amplitude-invariant and power-invariant forms use different scaling and should not be mixed. The amplitude-invariant form preserves peak current; the power-invariant form uses √(2/3) as its leading coefficient and preserves power. Under the conventions shown here, current scaling differs by √(3/2). Mixing conventions in one implementation can create a 50% torque-constant error.

A worked example

Consider a balanced three-phase set with a 10 A peak. The table shows the currents and Clarke components at three points in the cycle:

The vector’s magnitude stays at 10 A while its direction changes. The Clarke transform describes that rotating vector in the stationary αβ frame; the three phase currents are another representation of the same quantity.

The αβ representation can also be pictured as two orthogonal windings, 90° apart, carrying currents 90° apart in time. They produce the same rotating field as the original three-phase winding arrangement, with the same amplitude and speed.

Park: Two Axes to a Rotating Frame

The Park transform rotates the stationary αβ pair into a frame aligned with the rotor flux, using the electrical angle θ:

The inverse, which the drive needs on the way back out to the modulator:

Continuing the example, with the same 10 A vector but the frame rotated by 30° relative to it:

Why the result is constant

In the middle row, the current vector and reference frame have both rotated by 30°. Their relative angle has not changed, so the dq projections remain the same even while the phase currents continue to vary sinusoidally.

A PI controller is simplest to use with a constant reference. Tracking a sinusoidal current directly is harder because the reference keeps changing. The Park transform expresses the current feedback as DC values in steady state, allowing the current loops to regulate them in the rotating frame.

A typical implementation uses separate PI loops to regulate id and iq. Their voltage commands pass through the inverse Park transform and then a space-vector modulator, which produces inverter switching signals. For a broader drive overview, see how a variable speed motor works.

What id and iq Physically Are

id and iq are stator-current components along and perpendicular to the chosen flux axis. In a permanent-magnet motor, the d-axis aligns with the rotor magnets. In an induction motor, it aligns with rotor flux, which the drive estimates from the motor model.

Torque from the two components

For a surface permanent-magnet machine, this simplified model treats the d- and q-axis inductances as equal. Its torque equation is:

In this surface-PM model, torque is proportional to iq, so drives commonly set id to zero. Interior permanent-magnet motors have different d- and q-axis inductances, so their torque equation includes a reluctance term:

When Lq is greater than Ld, negative id can add reluctance torque. This relationship underlies maximum-torque-per-ampere control. With a typical saliency ratio, an interior design gains roughly 10–20% torque per ampere over a surface-mount design at the same current, though the figure moves with rotor geometry and current angle.

Rotor flux in an induction machine

In rotor-flux-oriented induction-motor control, the drive estimates rotor flux from the motor model. In this simplified representation, flux responds to id through a first-order lag:

and the slip frequency that keeps the frame aligned is the ratio of the two currents:

This relation is central to indirect field orientation. Since Tr depends on rotor resistance, temperature-related changes can shift the estimated slip frequency and flux angle. Winding resistance can rise by roughly 40% between a cold start and a hot steady state, which shortens Tr and moves the slip frequency the drive computes. Background is available in squirrel-cage induction motor applications, with a comparison to synchronous motors in induction motor versus AC motor.

The Decoupling Problem

The id and iq loops are coupled by speed-dependent terms in the rotating-frame voltage equations:

These terms couple the axes: a change in iq affects d-axis voltage, while a change in id affects q-axis voltage. They are zero at standstill and increase with electrical speed, so they become more significant as the motor accelerates.

Feedforward, not feedback

A common approach is feedforward decoupling. The drive estimates ωe·Lq·iq and ωe·(Ld·id + ψf) from its commands and compensates for these terms alongside the PI outputs. The PI loops then correct the remaining error. Without those terms the two loops fight each other, and a drive that holds torque cleanly at low speed can lose authority well below its base speed. Decoupling terms can account for a large share of the voltage command at speed. Incorrect Ld or Lq values may show up as high-speed torque ripple before a steady-state error.

Where the Rotor Angle Comes From

Vector control requires electrical angle θ, measured or estimated. The main approaches are:

Measured

An absolute encoder or resolver measures rotor position for the drive. Industrial servo motors commonly use one of these devices, connected separately from the power leads. Absolute encoders are available at resolutions such as 17 to 23 bits. That resolution can exceed what the mechanics can use; actual positioning accuracy depends on the complete mechanical and feedback system.

Indirect

With indirect field orientation, the drive measures speed, estimates slip frequency from iq and id, then integrates rotor and slip speeds to estimate θ. This is a standard approach for induction-machine vector drives and requires no direct flux sensor. Accuracy depends on the rotor time constant used by the model.

Estimated, or sensorless

Sensorless methods estimate angle from back-EMF or the motor’s response to an injected high-frequency signal. Back-EMF falls with speed and is unavailable at standstill. High-frequency injection can estimate angle at zero speed in suitable motors, but adds noise and relies on detectable saliency. Back-EMF methods can suit fans, while their low-speed limits may make sensorless control a poor fit for some positioning axes.

id = 0, and What Happens Above Base Speed

In a surface-PM motor, the rotor magnets provide the main flux. In the usual operating region, setting id to zero avoids spending current on the d-axis and gives the expected torque per ampere. The exact command can depend on the drive strategy and operating point.

Above base speed, the inverter’s available voltage limits further acceleration as back-EMF rises. A surface-PM drive may use negative id to weaken effective flux and extend the speed range. In this field-weakening region, torque generally falls as speed rises; the operating point depends on both voltage and current limits.

The operating point must satisfy both current and voltage limits, often shown as a current circle and voltage ellipse across the id and iq axes. For each speed, the controller selects a point within those limits that meets the torque demand. This produces the familiar constant-torque region followed by a constant-power region. Related sizing background is available in how to calculate motor torque and understanding electric motors.

What the Drive Actually Does Every 100 µs

A 10 kHz current loop runs once every 100 µs. During each cycle, the drive samples current, updates its control calculations and sets the next PWM output.

The nested loop structure

The speed and position loops usually run more slowly than the inner current loop, typically five to ten times slower for the speed loop and slower again for position. A speed loop tuned too close to the current-loop bandwidth can oscillate and, in severe cases, may stress the switching devices. An implementation example for a specific motor family is described in FOC control of a BLDC motor.

Where the Method Stops Helping

Vector control relies on rotor-angle estimates and motor parameters. Errors and delays affect how closely a real drive follows the ideal model. Common sources include:

• Resistance rises with temperature. Copper resistance climbs roughly 40 % over a 100 K rise, which shifts the decoupling terms and, in an induction machine, moves the slip frequency and therefore the flux angle.
• Inductance falls with saturation. Ld and Lq are functions of current, not constants. A drive tuned at light load will over- or under-compensate at rated torque.
• The angle has delay. Sampling, computation and PWM update together cost one to two periods. At low speed that is a small angle; at high electrical frequency it is a large one, and the torque error it produces is proportional to speed.
• Dead time distorts small voltages. Inverter dead time of a few microseconds is negligible at full output and dominant at 2 % output, which is exactly the condition at low speed. It is the main reason sensorless drives behave badly just off standstill.

These effects come from hardware limits and model uncertainty, so a practical drive must account for them.

Some drives reduce these errors with online resistance estimation, inductance mapping or dead-time compensation. These features add cost and can improve performance near the operating limits.

Vector Control Against V/f and DTC

The choice depends on the application’s control requirements. V/f may be sufficient when precise torque or position control is not needed; vector control is useful when the drive must regulate torque through current control. For motor-selection background, see servo motor basics and BLDC motor versus servo motor.

Stepper motors move in discrete increments and may operate without position feedback, so the controller may not measure rotor angle. The differences are covered in servo versus stepper and how stepper motors work. A vector-driven general-purpose induction motor also differs from a servo system: the drive estimates rotor flux rather than reading a rotor position sensor. See general purpose motor.

For applications that prioritize torque density over positioning accuracy, see the high-torque BLDC technical guide and how a BLDC motor works.

References

1. International Electrotechnical Commission. (2022). IEC 60034-1:2022 — Rotating electrical machines, Part 1: Rating and performance. IEC. https://webstore.iec.ch/en/publication/65446
2. International Electrotechnical Commission. (2014). IEC 60034-2-1:2014 — Standard methods for determining losses and efficiency from tests. IEC. https://webstore.iec.ch/en/publication/121
3. International Electrotechnical Commission. (2016). IEC TS 60034-30-2:2016 — Efficiency classes of variable speed AC motors (IE code). IEC. https://webstore.iec.ch/en/publication/30830
4. International Electrotechnical Commission. (2025). IEC 60034-30-1:2025 — Efficiency classes of line operated AC motors (IE code). IEC. https://webstore.iec.ch/en/publication/91195
5. International Electrotechnical Commission. (2017). IEC 61800-9-2:2017 — Ecodesign for power drive systems, motor starters and power electronics. IEC. https://webstore.iec.ch/en/publication/111276
6. International Electrotechnical Commission. (2013). IEC 60529:1989+AMD2:2013 — Degrees of protection provided by enclosures (IP code). IEC. https://webstore.iec.ch/en/publication/2452
7. National Electrical Manufacturers Association. (2021). NEMA MG 1 — Motors and Generators. NEMA. https://www.nema.org/standards
8. European Parliament and Council. (2019). Commission Regulation (EU) 2019/1781 laying down ecodesign requirements for electric motors and variable speed drives. Official Journal of the EU. https://eur-lex.europa.eu/eli/reg/2019/1781/oj
9. European Parliament and Council. (2023). Regulation (EU) 2023/1230 on machinery and repealing Directive 2006/42/EC. Official Journal of the EU. https://eur-lex.europa.eu/eli/reg/2023/1230/oj
10. U.S. Department of Energy. (2024). Motor systems — energy efficiency and system optimisation. Advanced Manufacturing Office. https://www.energy.gov/eere/amo/motor-systems

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