Field Oriented Control System of Sensorless Permanent Magnet Synchronous Motor Based on DSP

This paper focuses on an improved algorithm, which eliminates the phase current sensor and uses a sliding mode observer to achieve position sensorless speed control.


Permanent magnet synchronous motor (PMSM) is a type of motor that has developed rapidly in recent years. Because its rotor is made of permanent magnet steel, it is a type of brushless motor and has the advantages of simple structure, small size, and long life of general brushless motors [1].
This paper discusses the permanent magnet synchronous motor controlled by space vector control, and uses a magnetic field oriented algorithm to achieve real-time control of the speed with the help of DSP high speed. Since the control algorithm must obtain rotor position information, traditional control systems require photoelectric encoders as rotor position sensors. In order to minimize the number of sensors, this paper changes the phase current detection method, establishes a sliding mode observer using bang-bang control, and introduces a model that can be implemented.
2 Principle of magnetic field orientation
Field oriented control, referred to as FOC. As shown in Figure 1, there are two rectangular coordinate systems: the αβ coordinate system is the stator stationary coordinate system, and the α axis coincides with the a phase axis of the stator winding; dq is the rotor rotating coordinate system, and the d axis coincides with the rotor flux direction and rotates counterclockwise at the synchronous speed ωr. The angle between the two coordinate systems is θe. The stator current integrated vector is can be decomposed on the dq axis of the rotating coordinate system as follows:
is = isd + isq (1)
In an AC permanent magnet synchronous motor, the rotor is a permanent magnet steel, and the magnitude of the rotor current integrated vector can be considered constant, and is usually represented by a constant value IF. According to the universal relationship between the electromagnetic torque T of an AC motor and the integrated vectors of the stator and rotor currents [2]

Where p——pole pair number
L12——mutual inductance between stator and rotor
i1——stator current integrated vector
i2——rotor current integrated vector
δ——angle between stator and rotor integrated vectors
In this way, the electromagnetic torque only changes with |i1| and angle δ. In order to obtain a simple and controllable torque characteristic, the stator current integrated vector instruction can be given so that it is always on the q axis, that is, δ＝90°, thus obtaining

Where Is——modulus of stator current integrated vector
According to the above formula, the modulus of stator current integrated vector can be used to directly control the electromagnetic torque of the motor, so that the permanent magnet synchronous motor can obtain servo performance similar to that of a DC motor, and can obtain fast and static-free adjustment characteristics. Figure 2 is a system control block diagram.

The speed control system is implemented by speed and current double closed loops, and the adopted algorithm is implemented by corresponding modules, including: Park transformation module, Clark transformation module, inverse Park transformation module, rotor position angle estimation module, speed calculation module, weak magnetic control module, PI adjustment module, space vector PWM generation module, etc. The entire control system is based on DSP chip as the core and equipped with simple peripheral circuits. Its complex control algorithms and functions are all implemented by software. Each control module corresponds to a C calling function, and the main function flow is compiled in C language. Compared with the control system with position sensor, the position sensorless system only uses the angle observer module function in the processing of feedback quantity, while other control modules and the system can be implemented in exactly the same way, which further shows the flexibility of software system.

3 Sensorless Algorithm
3.1 Method of Reducing One Current Sensor
Phase current information is required in inverter control. The traditional method is to directly use sensors to obtain the required phase current. This method depends on the layout of the load and requires at least two sensors to be directly applied to the motor group winding. The method introduced in this article is to estimate the three-phase current value on the AC side by collecting only the DC side bus current information. Because the inverter switching state is directly controlled by us, the path of the input current, that is, the relationship between the input line current and the motor phase current, is known. In this way, except for (0, 0, 0) and (1, 1, 1) in the usual eight switching states (Sa, Sb, Sc), in the other six switching states, the DC side line current information always corresponds to a phase current value in a, b, c.

In the switch state (Sa, Sb, Sc) = (0, 0, 1) shown in Figure 3, the phase current ic is equal to the DC line current, and the other two phase currents ia and ib are equal to half of the DC line current. In this way, the line current signal is sent to the DSP through an AD channel, and then the three-phase current information can be obtained after appropriate calculation [4].
3.2 Position sensorless algorithm
In order to obtain excellent torque control performance at low speed or even zero speed, and to improve the efficiency, reliability, mechanical strength and cost of the system, it is necessary to eliminate the position sensor. At this time, the necessary position and speed information can be obtained through the sliding mode observer. This method has strong robustness and is easy to implement.
The observer is a mathematical model that depends on the system structure and parameters, and is implemented through DSP software programming. The model corrects the model by obtaining the difference between the estimated value and the actual measured value, so that the difference between the two disappears. For example, the difference between the estimated current and the actual measured current i is substituted into the sign function sign (), and then multiplied by the constant coefficient K. After that, the adaptive filter is used to compensate for the phase shift of the digital filter. The output result is the sine and cosine function of the rotor position angle.
Figure 4 shows the main variables of PMSM: Vs, is, es, Ψ in the form of comprehensive vectors and their components in the stationary αβ coordinate system and the rotating dq coordinate system. Equation (7) is the mathematical model of PMSM: The

angle observer module is a rotor flux estimation based on the sliding mode current observer. The main part of the module is the sliding mode current observer, which outputs the bang-bang control variable Z. Z is low-pass filtered to obtain the back electromotive force estimate. The angle can be obtained by calculating the components.

Formula (8) is the basic current observer, and formula (9) is the BANG-BANG controller. The two form a sliding mode current observer, the purpose of which is to make the error between the estimated current and the measured current zero by appropriately selecting Z and the estimated back EMF. The discrete forms of the two are

(2) Estimated back EMF

(3) Estimation of rotor flux position θ
The rotor flux position angle is estimated by the back EMF. Formula (14) is the comprehensive vector expression of the back EMF. The rotor flux position angle can be solved according to the components of the back EMF on the α and β axes, that is, Formula

(4) Rotor flux position correction
A low-pass filter is used to obtain the back EMF, which introduces a phase delay. This delay is directly related to the phase response of the low-pass filter. The lower the cutoff frequency, the greater the phase delay corresponding to the fixed frequency. Based
on the phase response of the low-pass filter, a phase delay table is made, and the phase shift angle corresponding to the command speed (frequency) during operation can be obtained by looking up the table. The phase shift angle is added to obtain.
4 System software flow
The main program flow is shown in Figure 6. It only completes the initialization tasks of the system hardware and software, and then enters a waiting state. The complete FOC control algorithm is implemented in the PWM interrupt service program. In an interrupt cycle, the process follows the system control block diagram Figure 2, sampling current from one AD, calculating the rotor position angle, calculating the speed, completing all feedback channel calculations, and then calling the calculation module function in the forward channel, and finally outputting the space vector PWM wave signal of the three-phase inverter bridge.

5 Hardware involved
The output of the three-phase inverter bridge powered by DC voltage is connected to the stator winding of the three-phase motor in star connection. The six PWM outputs provided by the DSP are isolated by optocouplers to drive the three-phase inverter bridge switch devices.
The resistor sensor placed in the DC loop provides the motor line current voltage signal, which is amplified and sent to the ADC channel of the DSP. When implementing the control algorithm, the EVM event of the TMS320C24x controller triggers an interrupt for AD sampling.
In the first half of each symmetrical space vector PWM cycle, the switch state (Sa, Sb, Sc) changes from (0, 0, 0) to (1, 1, 1). The line current signal is sampled at the two intermediate states of this process, which are (1, 0, 0) and (1, 1, 0) in Figure 7. Combined with the three-phase bridge arm switch state defined in Figure 3, the line current corresponds to the a-phase current value ia when (1, 0, 0), and the line current corresponds to the c-phase current value -ic when (1, 1, 0). In this way, two samplings in one cycle respectively obtain the two-phase current values, and the other route is obtained by ia + ib + ic = 0.
6 Conclusion
This paper introduces a solution for PMSM using DSP controller, which uses the DSP structure of TMS320C24x controller and optimized microcontroller peripheral circuit, and adopts intelligent control strategy to obtain rotor position and speed information, thereby eliminating the rotor position sensor, which provides a new idea for designing PMSM control system, reducing system cost and improving system reliability.