## What is principle of AC servo motor vector control?

**1. Vector control of AC induction servo motors**

Vector control is an essential aspect of AC induction servo motors. The concept of vector manipulation was first proposed in 1971 by German scholar F. Blachke. In a servo system, DC servo motors can attain exceptional dynamic and static functions because they can be controlled by the motor magnetic flux (Φ) and armature current (Ia), which are independent variables. Additionally, the electromagnetic torque (Tm = KT Φ Ia) and magnetic flux Φ are directly proportional to the armature current Ia. As a result, the control is straightforward, and the function is linear.

To achieve similar characteristics of a DC motor in an AC motor, one needs to simulate a DC motor, calculate the corresponding magnetic field and armature current of the AC motor, and operate it separately and independently. This requires converting the three intersecting variables (vectors) into equivalent DC quantities (scalars), establishing an equivalent model of an AC motor, and operating it according to the control method of a DC motor.

The three-phase asynchronous AC motor rotates in a magnetic field Φ with an angular velocity of ω0. Figure b shows two sets of windings with a spatial difference of 900, which, when replaced with an AC current with a difference of 900 between the two phases at any time α and β, results in the same angular velocity of ω0’s rotating magnetic field Φ as in Figure a. The two sets of windings in Figures a and b are thus equivalent.

Figure c shows a model with two mutually straight windings d and q. When separately connected with DC currents id and iq, they establish a fixed orientation magnetic field Φ. When the winding rotates at an angular velocity of ω0, the established magnetic field is also a rotating magnetic field, with the same amplitude and speed as that in Figure a.

**Switching from three-phase A, B, and C systems to two-phase systems α、β system**

Transforming from a three-phase A, B, and C system to a two-phase α、β system involves converting a three-phase AC motor into an equivalent two-phase AC motor. The stator windings of the three-phase asynchronous motor in Figure a are 120 degrees apart from each other in space. By applying balanced AC currents iA, iB, and iC with a phase difference of 120 degrees in time, a synchronous rotating magnetic field vector Φ occurs on the stator with an angular velocity of ω 0.

The effect of the three-phase winding can be fully utilized by replacing it with two mutually straight windings α and β in space, and applying balanced AC currents iα and iβ with a phase difference of 90 degrees in time. The amplitude and angular velocity of the rotating magnetic field Φ and ω 0 are the same as those in the three-phase winding, and the two sets of windings in Figures a and b are considered equivalent.

By using the mathematical transformation formula from three-phase to two-phase, the equivalent AC magnetic field of the two-phase AC winding can be calculated. Then, the spatial rotating magnetic field that occurs is the same as the rotating magnetic field that occurs in the three-phase A, B, and C windings. By aligning the axis of the A-phase winding in the three-phase winding with the α coordinate axes, the corresponding current value iα and iβ can be obtained based on the proportional relationship between magnetic potential and current.

Other physical quantities used in the conversion, as long as they are three-phase balance quantities and two-phase balance quantities, can be converted in the same way. This effectively converts a three-phase motor into a two-phase motor.

**Vector rotation transformation**

After converting a three-phase motor into a two-phase motor, it is important to replace the two-phase AC motor with an equivalent DC motor. The excitation winding is represented by d and the excitation current is id. The armature winding is represented by q and the armature current is iq. This generates a fixed fluctuating magnetic field Φ that rotates at an angular velocity ω0 on the stator. The transformation from a two-phase AC motor to a DC motor is essentially a transformation from vector to scalar, and from a stationary Cartesian coordinate system to a rotating Cartesian coordinate system.

This is where iα and iβ are converted to id and iq, while ensuring that the composition of the magnetic field remains unchanged. The composition vector of iα and iβ is represented by i1, which can be obtained by projecting Φ in the direction and perpendicular to iα and iβ. Id and iq rotate in space at angular velocity ω0. The formula for conversion is as follows:

There is a need to change the Cartesian coordinate system and polar coordinate system in vector control. i1 is calculated from id and iq using the formula.

The use of vector transformation in an induction motor provides the same control characteristics as a DC motor, while maintaining a simple and reliable structure. The motor’s capacity is not limited and the mechanical inertia is lower compared to an equivalent DC motor.

**2. Vector control of AC synchronous motors**

Basic Principles

AC synchronous motors are widely used in various industries due to their high efficiency and superior performance. Vector control is a popular method used to regulate the speed and torque of AC synchronous motors. In a DC motor, the torque is directly proportional to the armature current, while in an AC synchronous motor, the torque is determined by the interaction between the rotor magnetic field and the stator magnetic field.

The rotor of an AC synchronous motor consists of permanent magnets, which generates a magnetic field that interacts with the stator magnetic field generated by the three-phase windings. The relative orientation of the rotor magnetic poles and the stator windings is detected by an encoder, which provides the necessary feedback for vector control. By controlling the current flowing through the three-phase windings, it is possible to regulate the torque and speed of the motor.

Vector control ensures that the current flowing through the motor windings is always perpendicular to the magnetic field generated by the rotor, resulting in maximum torque. By establishing a connection between the permanent magnet magnetic field, armature magnetic electromotive force, and torque, vector control enables precise control of the motor’s speed and torque.

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