Permanent Magnet Synchronous Motor ( PMSM )

• PMSM Control
• What is torque control
• FOC and DTC
• FOC (Field Oriented Control)
• DTC (Direct torque control)
• Difference between PMSM and BLDC
• Performance comparison of BLDC and PMSM in low-speed electric vehicle applications
• Experimental verification
• Simulation Verification
• Refer to

PMSM, the full English name is Permanent-magnet Synchronous Motor, which literally means permanent magnet synchronous motor .

The working principle of a permanent magnet synchronous motor is simply that the stator generates a rotating magnetic field by passing alternating current, and the rotor is a permanent magnet. The magnetic field generated by the stator drives the permanent magnet to rotate at the synchronous speed. The characteristic of a synchronous motor is that it runs at the synchronous speed regardless of whether it is loaded or not. As long as it is within the load range of the synchronous motor, the motor will rotate at the synchronous speed. The characteristic of a permanent magnet synchronous motor is that the excitation winding of the rotor is replaced with a permanent magnet.

It needs to meet several characteristics:
1) The three-phase stator is connected to an AC voltage with a phase sequence difference of 120 degrees to generate a rotating stator magnetic field.
2) The rotor is excited by a permanent magnet, regardless of whether its excitation material is AlNiCo, ferrite or NdFeB; regardless of whether it is installed internally or surface mounted, through the special stator and rotor shape design, a sinusoidal NS magnetic field is finally presented in the air gap space.
3) Based on the above two points, the back EMF must be a sine wave, which is the biggest difference between PMSM and BLDC (back EMF trapezoidal wave).

PMSM Control

What is torque control

Any motor control has three different control objectives:

Position control: The motor will rotate as much as you want it to.
Speed ​​control: The motor can rotate as fast as you want it to
Torque control: The motor will produce as much force as you want it to produce
But no matter what the control target is, it is nothing more than the difference between one closed loop, two closed loops or three closed loops. Torque control, as the innermost loop, is indispensable.

To control a motor, it is necessary to first understand the controlled object. After the alternating voltage with a difference of 120 degrees passes through the three phases of the stator, a rotating magnetic field can be seen on the stator core. Under the action of this rotating magnetic field, a force is generated with the rotor magnetic field, driving the rotor to rotate.

How is the motor torque generated? The torque is proportional to the armature (stator) current;

How is the current generated? We can imagine each winding of the motor as a resistor + inductor rotating in the magnetic field, as shown in the equivalent circuit below:

Assuming the motor is running in open loop, when a voltage of 120 degrees is given to the three phases of the motor stator to establish a rotating magnetic field, if there is no load at this time, the motor will rotate rapidly (no load) until the back electromotive force is completely equal to the given voltage; at this time, the current in the stator winding is still 0, and the rotating magnetic field of the stator can be imagined (virtual/equivalent) as a magnet rotating around the motor axis, and the south pole of this imaginary magnet coincides with the north pole axis of the rotor magnet.

When there is a load on the rotor, according to Newton’s law of motion, the motor speed will inevitably slow down, which means that the back electromotive force in the above equivalent circuit decreases, and when the given voltage remains unchanged, the remaining voltage will generate current in the resistor . What else happened during this deceleration process? Because it is dragged by the load, the axis of the rotor magnet lags behind the virtual axis of the stator magnet by an angle, which is what we call the ” power angle “.

The torque control of the motor is to find some combinations of switch tubes to synthesize a given voltage for the motor stator through a certain control algorithm. The torque corresponding to the current generated by this voltage after offsetting the back electromotive force is just balanced with the external load. Various diagrams of the motor vector model can be found on the Internet.

FOC and DTC

There are currently two main schools of thought for motor torque control: field-oriented control (FOC) and direct torque control (DTC) . Of course, in principle, these two control algorithms are applicable to all AC motors. This article only talks about their similarities and differences in permanent magnet synchronous motor control.

FOC (Field Oriented Control)

The FOC control theory was first proposed by Siemens engineers in the 1970s. As mentioned above, the magnetic field generated by the stator can be virtualized as a magnet rotating at high speed around the rotor.

The stator magnetic potential can be decomposed into the d-axis magnetic potential and the q-axis magnetic potential. The d-axis magnetic potential is coaxial with the rotor magnetic potential and cannot generate a tangential torque, but it will affect the magnetic field generated by the permanent magnet of the permanent magnet synchronous motor rotor; the q-axis is 90 degrees out of phase with the rotor magnetic potential, thus generating a tangential torque (similar to the interaction force generated by two vertical bar magnets).

The basic idea of ​​FOC control is to convert the relevant variables in the three-phase static ABC coordinate system to the rotating coordinate system (d, q) for mathematical operations, and control the change of the voltage of the d-axis and q-axis to achieve the purpose of controlling the current of the d-axis and q-axis. However, the voltage of the three-phase motor can only be the voltage in the static coordinate system, so in the control algorithm, it is necessary to convert the voltage of the dq axis into the ABC three-phase voltage again for the drive bridge. That is, there is a process from physical model -> mathematical model -> control algorithm -> physical model.

To realize FOC, the following inputs are essential:

Motor three-phase current (two current sensors as shown in the figure above can be used, or a low-side or high-side bus current sensor can be used to restore the three-phase current using the time-sharing sampling current reconstruction method)
The motor position signal is indispensable
The following control modules are essential:

• Clark-Park Transform
• PI regulation of d-axis and q-axis
• Inverse Clark-Park transform
• SVPWM
  The following figure shows the specific control process.

The process is as follows:

Measure the 3-phase stator current. These measurements give the values ​​of ia and ib, which can be used to calculate ic using the following formula:
ia+ib+ic=0
The 3-phase currents are transformed into a 2-axis system. This transformation results in the variables iα and iβ, which are transformed from the measured ia and ib and the calculated ic values. From the stator point of view, iα and iβ are mutually orthogonal time-varying current values.
The 2-axis system is rotated to align with the rotor flux according to the transformation angle calculated in the last iteration of the control loop. This transformation of the iα and iβ variables yields Id and Iq. Id and Iq are orthogonal currents transformed to the rotating coordinate system. Under steady-state conditions, Id and Iq are constants.
The error signal is obtained by comparing the actual values ​​of Id and Iq with their respective reference values.
· The reference value of Id controls the rotor flux
· The reference value of Iq controls the torque output of the motor
· The error signal is the input to the PI controller
· The output of the controller is Vd and Vq, which are the voltage vectors to be applied to the motor
The new transformation angle is estimated, where Vα, Vβ, iα and iβ are the input parameters. The new angle tells the FOC algorithm where the next voltage vector is.
Using the new angle, the Vd and Vq output values ​​of the PI controller can be inverted to the stationary reference frame. This calculation will produce the next orthogonal voltage values ​​Vα and Vβ.
The Vα and Vβ values ​​are inversely transformed to obtain the 3-phase values ​​Va, Vb and Vc. The 3-phase voltage values ​​can be used to calculate the new PWM duty cycle value to generate the desired voltage vector.
DTC (Direct torque control)
DTC appeared more than ten years later than FOC. It was proposed by German scholar Professor Depenbrock in the mid-1980s. Its basic idea is to no longer convert the relevant variables on the stator side to the rotating coordinate system of the rotor, abandon the control idea of ​​current decoupling in vector control, remove the PI adjustment module, inverse Clark-Park transformation and SVPWM module, and instead directly calculate the motor flux and torque by detecting the bus voltage and stator current, and use two hysteresis comparators to directly realize the decoupling control of the stator flux and torque. (The stator winding itself is a sensor, which directly measures the induced voltage. The direct integration of the stator voltage is the magnetic flux, and the voltage is the differential of the magnetic field. The position and direction of the magnetic field can be determined. This method is called direct torque control (DTC) )

From the above block diagram, we can see that the control algorithm first obtains the voltage and current Uα, Uβ, Iα, Iβ under the stationary two-phase coordinate axis based on the line current and phase voltage of the motor. Then, based on these four quantities, the stator flux and torque are estimated. At the same time, the current rotor position interval must be estimated based on the voltage and current of the motor stator.

Of course, if you are worried that the integral operation in the software may cause inaccuracy due to cumulative errors, or the value of the rotor flux is inaccurate, or the value of the power angle is inaccurate, you can also add an angle sensor to the system, put all the relevant parameters into the rotating coordinate dq axis coordinate system, and then calculate them.

After the stator flux and torque values ​​are calculated, they are compared with their reference values ​​and passed through a hysteresis comparator to obtain two non-zero or 1 state quantities, which represent the relationship between the current magnetic and force and the reference values.

Difference between PMSM and BLDC

Permanent magnet synchronous motor (PMSM) and brushless direct current motor (BLDC) are both permanent magnet motors. The rotor is composed of permanent magnets as the basic structure, and the stator has multi-phase AC windings. The magnetic field generated by the permanent magnet rotor and the AC current of the stator interact to generate the motor torque. The stator current in the winding must be synchronized with the rotor position feedback.

The sinusoidal waveform of the PMSM motor requires the use of a field-oriented control (FOC) algorithm. FOC is often used to maximize the efficiency of a PMSM three-phase motor. Compared to the trapezoidal controller for BLDC, the PMSM sinusoidal controller is more complex and more expensive. However, the increase in cost also brings some advantages, such as reducing noise and harmonics in the current waveform. The main advantage of BLDC is that it is easier to control.

The real difference between the two is the back EMF. The BLDC back EMF is a trapezoidal wave, while the PMSM back EMF is a sine wave.

Back EMF refers to the electromotive force that opposes the tendency of current to pass through, and is essentially an induced EMF. When the motor rotates, an induced EMF is generated in the coil, which has the effect of weakening the power supply EMF, that is, the back EMF, which hinders the rotation of the coil.
The back EMF reflects the parameters of the entire motor magnetic field distribution, which is determined by the electromagnetic design in the motor design, that is, the design of the stator coil winding (generating a stator magnetic field) and the rotor magnetic steel distribution design (generating a rotor magnetic field) determine the back EMF, especially the stator winding design.
The operating current is different. To generate a constant electromagnetic torque, the PMSM uses a sinusoidal stator current, while the BLDC uses a rectangular wave current.
The stator winding distribution is different. PMSM uses short-pitch distributed winding, and sometimes fractional slot or sinusoidal winding to further reduce ripple torque; while BLDC uses full-pitch concentrated winding.
The shapes of permanent magnets are different. The PMSM permanent magnet is parabolic in shape, and the magnetic flux density generated in the air gap is distributed as sinusoidally as possible; the BLDC permanent magnet is tile-shaped, and the magnetic flux density generated in the air gap is distributed in a trapezoidal wave.
The operation modes are different. PMSM uses three phases to work simultaneously, and the current of each phase differs by 120° electrical angle, requiring a position sensor. BLDC uses windings that are turned on in pairs, with each phase turned on for 120° electrical angle, and phase switching every 60° electrical angle, requiring only the phase switching point position detection.
Due to the differences in design and control, the characteristics of PMSM and BLDC are compared as follows:

Torque ripple

Torque ripple is the biggest problem of electromechanical servo systems. It directly affects the difficulty of precise position control and high-performance speed control.
In low-speed and direct drive applications, torque ripple will seriously affect system performance and deteriorate the accuracy and repeatability of the system. Most of the space precision electromechanical servo systems work in low-speed situations, so the motor torque ripple problem is one of the key factors affecting system performance. Both PMSM and BLDCM have torque ripple problems. Torque ripple is mainly caused by the following reasons: cogging effect and flux distortion, torque caused by current commutation, and torque caused by mechanical processing.

Power density

In high-performance applications such as robotics and space actuators, for a given output power, the motor weight is required to be as small as possible. The power density is limited by the heat dissipation capacity of the motor, that is, the surface area of ​​the motor stator. For permanent magnet motors, most of the power losses occur in the stator, including copper losses, eddy current losses and hysteresis losses, while rotor losses are often ignored. Therefore, for a given structural size, the lower the motor losses, the higher the allowable power density. At the same size, BDLC can provide 15% more power output than PMSM. If the iron losses are also the same, the power density of BDLC can be increased by 15% compared to PMSM.

Torque-to-Inertia Ratio

The torque-to-inertia ratio refers to the maximum acceleration that the motor can provide. Because the BDLC can provide 15% more output power than the PMSM, it can obtain 15% more electromagnetic torque than the PMSM. If the BDLC and PMSM have the same speed and their rotor inertia is the same, then the torque-to-inertia ratio of the BDLC is 15% greater than that of the PMSM.

Sensor Rotor position detection:

In BLDC, only two phases of windings are turned on at any one time, and each phase is turned on for 120° electrical angle. As long as these commutation points are detected correctly, the normal operation of the motor can be guaranteed. Usually three Hall sensors are used. In PMSM, sinusoidal current is required. When the motor is working, all three phases of windings are turned on at the same time. Continuous position sensors are required, and the most common ones are high-precision encoders.
Current detection: For three-phase motors, in order to control the winding current, three-phase current information is required. Usually two current sensors are used because the sum of the three-phase current is 0. For some simple brushless DC motor control systems, only one current sensor can be used to detect the bus current to reduce costs.
Performance comparison of BLDC and PMSM in low-speed electric vehicle applications
According to the comparison, BLDCM can provide higher torque in the constant torque range; PMSM has more stable torque and a wider speed range, which better meets the ideal performance requirements of electric vehicles.
The PMSM system is more efficient and has a longer range. The high efficiency area is generally distributed in the medium and high speed range, and the low efficiency area is generally distributed in the heavy load and low speed range.
The low cost of low-speed electric vehicles limits the application of advanced technologies and good materials in their matching motors, and hinders the development of advanced technologies for related motors.
The no-load loss of PMSM is smaller than that of BLDCM, which is why PMSM is more efficient, which has been proved by both experiments and simulations.
Compared with other types of motors, PMSM has many advantages in electric vehicles. With the development of materials and manufacturing technology, PMSM is the most suitable motor for electric vehicles, and it is becoming a trend for more and more low-speed electric vehicles to use PMSM.
PMSM has lower vibration and noise.

Experimental verification

Ideal mechanical characteristics of electric vehicle motors:

PMSM and BLDCM as comparison:

Power and torque characteristics test results:

Both motors have similar power characteristics in the low and medium speed regions, but the power of the BLDCM decreases when the speed exceeds 3000rpm.

Comparison of system efficiency MAP:

High efficiency areas are distributed in the medium and high speed areas, and the efficiency decreases in the low speed area. Considering general operating conditions, PMSM has a longer cruising range.

Simulation Verification

Motor model:

1000rpm magnetic field cloud map:

The magnetic flux density of the rotor yoke and stator teeth of PMSM is lower than that of BLDCM.

Cogging torque:

 

The cogging torque of BLDCM is greater than that of PMSM.

Back EMF waveform:

The back EMF of BLDCM is greater than that of PMSM.

refer to

The difference between BLDC and PMSM motors