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Vector control (motor)
Encyclopedia
Vector control is one method used in variable frequency drive
s to control the torque
(and thus finally the speed
) of three-phase
AC electric motors
by controlling the current
fed to the machine.
phase currents are measured and converted into a corresponding complex (space) vector. This current vector is then transformed to a coordinate system
rotating with the rotor
of the machine. For this the rotor position has to be known. Thus at least speed measurement
is required, the position can then be obtained by integrating
the speed.
Then the rotor flux linkage
vector is estimated by multiplying the stator current vector with magnetizing inductance Lm and low-pass filter
ing the result with the rotor no-load time constant
Lr/Rr, that is the ratio of the rotor inductance to rotor resistance.
Using this rotor flux linkage vector the stator current vector is further transformed into a coordinate system
where the real x-axis is aligned with the rotor flux linkage vector.
Now the real x-axis component of the stator current vector in this rotor flux oriented coordinate system can be used to control the rotor flux linkage and the imaginary y-axis component can be used to control the motor torque.
Typically PI-controllers are used to control these currents to their reference values. However, bang-bang
type current control, that gives better dynamics, is also possible.
With PI-controllers the outputs of the controllers are the x-y components of the voltage reference vector for the stator. Usually due to the cross coupling between the x- and y-axes a decoupling term is further added to the controller output to improve control performance when big and rapid changes in speed, current and flux linkage occur. Usually the PI-controller also needs low-pass filter
ing of either the input or output of the controller to prevent the current ripple due to transistor switching from being amplified excessively and unstabilizing the control. Unfortunately, the filtering also limits the dynamics of the control system. Thus quite high switching frequency (typically more than 10 kHz) is required to allow only minimum filtering for high performance drives such as servo drives.
Next the voltage references are first transformed to the stationary coordinate system (usually through rotor d-q coordinates) and then fed into a modulator that using one of the many Pulse Width Modulation (PWM)
algorithms defines the required pulse widths of the stator phase voltages and controls the transistors (usually IGBTs) of the inverter according to these.
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This control method implies the following properties of the control:
Although the vector control algorithm is more complicated than the Direct Torque Control
(DTC), the algorithm is not needed to be calculated as frequently as the DTC algorithm. Also the current sensors need not be the best in the market. Thus the cost of the processor and other control hardware is lower making it suitable for applications where the ultimate performance of DTC is not required.
Variable frequency drive
A variable-frequency drive is a system for controlling the rotational speed of an alternating current electric motor by controlling the frequency of the electrical power supplied to the motor. A variable frequency drive is a specific type of adjustable-speed drive...
s to control the torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
(and thus finally the speed
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...
) of three-phase
Three-phase
In electrical engineering, three-phase electric power systems have at least three conductors carrying voltage waveforms that are radians offset in time...
AC electric motors
Electric motor
An electric motor converts electrical energy into mechanical energy.Most electric motors operate through the interaction of magnetic fields and current-carrying conductors to generate force...
by controlling the current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
fed to the machine.
Method
The statorStator
The stator is the stationary part of a rotor system, found in an electric generator, electric motor and biological rotors.Depending on the configuration of a spinning electromotive device the stator may act as the field magnet, interacting with the armature to create motion, or it may act as the...
phase currents are measured and converted into a corresponding complex (space) vector. This current vector is then transformed to a coordinate system
Rotation (mathematics)
In geometry and linear algebra, a rotation is a transformation in a plane or in space that describes the motion of a rigid body around a fixed point. A rotation is different from a translation, which has no fixed points, and from a reflection, which "flips" the bodies it is transforming...
rotating with the rotor
Rotor (electric)
The rotor is the non-stationary part of a rotary electric motor, electric generator or alternator, which rotates because the wires and magnetic field of the motor are arranged so that a torque is developed about the rotor's axis. In some designs, the rotor can act to serve as the motor's armature,...
of the machine. For this the rotor position has to be known. Thus at least speed measurement
Wheel speed sensor
A wheel speed sensor or vehicle speed sensor is a type of tachometer. It is a sender device used for reading the speed of a vehicle's wheel rotation...
is required, the position can then be obtained by integrating
Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
the speed.
Then the rotor flux linkage
Flux linkage
Flux linkage is a property of a coil of conducting wire and the magnetic field through which it passes. It is determined by the number of turns in the coil and the flux of the magnetic field....
vector is estimated by multiplying the stator current vector with magnetizing inductance Lm and low-pass filter
Low-pass filter
A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...
ing the result with the rotor no-load time constant
Time constant
In physics and engineering, the time constant, usually denoted by the Greek letter \tau , is the risetime characterizing the response to a time-varying input of a first-order, linear time-invariant system.Concretely, a first-order LTI system is a system that can be modeled by a single first order...
Lr/Rr, that is the ratio of the rotor inductance to rotor resistance.
Using this rotor flux linkage vector the stator current vector is further transformed into a coordinate system
Rotation (mathematics)
In geometry and linear algebra, a rotation is a transformation in a plane or in space that describes the motion of a rigid body around a fixed point. A rotation is different from a translation, which has no fixed points, and from a reflection, which "flips" the bodies it is transforming...
where the real x-axis is aligned with the rotor flux linkage vector.
Now the real x-axis component of the stator current vector in this rotor flux oriented coordinate system can be used to control the rotor flux linkage and the imaginary y-axis component can be used to control the motor torque.
Typically PI-controllers are used to control these currents to their reference values. However, bang-bang
Bang-bang control
In control theory, a bang–bang controller , also known as a hysteresis controller, is a feedback controller that switches abruptly between two states. These controllers may be realized in terms of any element that provides hysteresis...
type current control, that gives better dynamics, is also possible.
With PI-controllers the outputs of the controllers are the x-y components of the voltage reference vector for the stator. Usually due to the cross coupling between the x- and y-axes a decoupling term is further added to the controller output to improve control performance when big and rapid changes in speed, current and flux linkage occur. Usually the PI-controller also needs low-pass filter
Low-pass filter
A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...
ing of either the input or output of the controller to prevent the current ripple due to transistor switching from being amplified excessively and unstabilizing the control. Unfortunately, the filtering also limits the dynamics of the control system. Thus quite high switching frequency (typically more than 10 kHz) is required to allow only minimum filtering for high performance drives such as servo drives.
Next the voltage references are first transformed to the stationary coordinate system (usually through rotor d-q coordinates) and then fed into a modulator that using one of the many Pulse Width Modulation (PWM)
Pulse-width modulation
Pulse-width modulation , or pulse-duration modulation , is a commonly used technique for controlling power to inertial electrical devices, made practical by modern electronic power switches....
algorithms defines the required pulse widths of the stator phase voltages and controls the transistors (usually IGBTs) of the inverter according to these.
This control method implies the following properties of the control:
- Speed or position measurement or some sort of estimation is needed
- Torque and flux can be changed reasonably fast, in less than 5-10 milliseconds, by changing the references
- The step responseStep responseThe step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from...
has some overshootOvershoot (signal)In signal processing, control theory, electronics, and mathematics, overshoot is when a signal or function exceeds its target. It arises especially in the step response of bandlimited systems such as low-pass filters...
if PI control is used - The switching frequency of the transistors is usually constant and set by the modulator
- The accuracy of the torque depends on the accuracy of the motor parameters used in the control. Thus large errors due to for example rotor temperature changes often are encountered.
- Reasonable processor performance is required, typically the control algorithm has to be calculated at least every millisecond.
Although the vector control algorithm is more complicated than the Direct Torque Control
Direct Torque Control
Direct torque control is one method used in variable frequency drives to control the torque of three-phase AC electric motors. This involves calculating an estimate of the motor's magnetic flux and torque based on the measured voltage and current of the motor.-Method:Stator flux linkage is...
(DTC), the algorithm is not needed to be calculated as frequently as the DTC algorithm. Also the current sensors need not be the best in the market. Thus the cost of the processor and other control hardware is lower making it suitable for applications where the ultimate performance of DTC is not required.