Design of permanent magnet synchronous motor control system for electric vehicle air conditioning compressor

The permanent magnet synchronous motor (PMSM) is extensively utilized in electric vehicle air conditioning compressor control systems due to its numerous advantages, including high efficiency, lightweight design, compact size, excellent reliability, and low maintenance costs. In order to achieve PMSM without position sensor full speed range operation, this paper designs an optimized control strategy for full speed range operation. At low and zero speed, the I/F control mode is employed to achieve quick motor startup with minimized repetition rate, avoiding the overcurrent problem that is easy to occur by traditional V/F control, and the control is switched to the Phase-locked Loop (PLL) adaptive sliding mode observer (SMO) for position estimation at medium and high speed, avoiding the problems of high-frequency jitter and low position accuracy of traditional SMO. The feasibility of this strategy is confirmed by the simulation results of Simulink.


Introduction
With the continual enhancement of permanent magnet materials' performance, permanent magnet synchronous motors have gained widespread utilization in the aerospace industry, characterized by their reduced repetition rate, industry, and other fields due to their advantages of high operating efficiency, simple structure, small mass and volume, and high power density [1].At present, electric vehicle air conditioning compressors widely use PMSM, due to the high temperature of the air conditioning compressor, high humidity special working environment and the installation of mechanical position sensors will make the motor drive system volume and weight increase.Therefore, the traditional mechanical position sensor is not suitable for air conditioning compressors, and no position sensor control technology can overcome the problems caused by mechanical position sensors.
There are two types of sensorless control for permanent magnet synchronous motors based on different control principles.One type relies on the observation of back electromotive force (EMF) for position detection, typically suitable for medium and high-speed applications.A common method used in this approach is the sliding mode observer method (SMO) model reference adaptive method (MARS), Lomborg observer method (LO), extended Kalman filter algorithm (EKF) [2], etc.The other is based on the position detection method of the motor magnetic field salient pole, generally applicable to the use of the high-frequency injection method at zero low speed of the motor [4].In the motor starting and lowspeed operation stage, the use of I/F control mode reduces the engineering complexity, for the traditional sliding mode observer has high-frequency jitter, phase delay, low estimation accuracy, and other shortcomings.This paper adopts the PLL-based adaptive sliding mode observer method in the medium and high-speed stages.The whole process adopts prepositioning and acceleration.The three-stage mode of mode switching realizes the full-speed sensorless control of the vehicle air conditioning compressor, and the simulation experiment shows that the scheme is effective and feasible and has certain practical use value.

Improved adaptive SMO algorithm
At present, most traditional sliding mode observer algorithms use mathematical models based on stationary coordinate systems, based on the voltage equation of the motor.
Among them, d L and q L are stator inductors; e  is the electric angular velocity; p =d/dt, which is the differential operator; U  and U  are the stator voltage; I  is the stator current; I  is extended back EMF.
According to the surface-mount permanent magnet synchronous motor d L = q L [9], the extended back EMF is simplified to variables related only to the speed of the motor [6], because the actual control quantity is a discontinuous high-frequency switching signal.Therefore, a low-pass filter is added, so that a continuous extended EMF can be extracted.During the low-pass filtering processing of the equivalent control variable, the estimated value of the extended back EMF experiences phase and amplitude variations [5], in order to obtain the position information of the rotor, generally obtained by the arctangent function method [3].Since the back EMF estimation component processed by filtering will cause phase delay, in practical applications, to minimize repetition, an angle compensation is implemented to effectively mitigate the position angle estimation error of the rotor [8].In summary, the implementation principle of the traditional SMO algorithm is shown in Figure 1 Traditional SMO algorithm

Sgn
Low-pass filter Tangent function inversely The conventional synovial film control algorithm exhibits high-frequency jitter in sliding mode, and the estimated back EMF will have high-frequency jitter.Therefore, to minimize estimation error and achieve precise rotor position detection, a phase-locked loop is employed.In the traditional synovial control algorithm, although the back EMF has been filtered by a certain cutoff frequency, it still contains a large number of harmonic highfrequency signals, so this paper designs an adaptive SMO algorithm according to this problem,which is shown in

I/F startup control algorithm
Because in the motor start and low-speed operation stage, the use of the synovial observatory algorithm is difficult to extract the accurate rotor position.A solution is implemented to resolve this problem, and the commonly employed method involves a high-frequency signal injection.However, this approach necessitates precise sensors and complex algorithms.This paper chooses the I/F control algorithm, and I/F control is essentially a speed open loop, current closed-loop semi-open loop start method.Compared to the high-frequency signal injection method, robustness and simpler implementation in the motor starting requirements are not high occasions, more suitable for use in reality.
When the motor starts, it is necessary to pre-locate the rotor position first, the traditional prepositioning method is to introduce a current vector of unchanged size and direction in the stator winding and use the magnetic field generated to drag the rotor to the specified position [7], but this pre-positioning method has an obvious defect, because the initial position of the rotor cannot be determined so that the rotor in some special positions cannot be dragged by the current vector [10].These positions are called positioning blind zone.Due to the internal structural characteristics of the PMSM, bearing friction and cogging positioning form the inherent torque of the motor O T , only when the incoming current vector generates a positioning torque e T greater than the inherent torque of the motor O T , can drag the rotor to achieve positioning, the formula of positioning torque is as follows.
e=2/3 sin In the formula, n P is the number of pole pairs, s I is the amplitude of the incoming current, f  is the flux of the rotor permanent magnet, and L  is the angle between the incoming vector current and the rotor.
It can be seen from the above formula that in the case of other values, the size of the positioning torque e T is closely related to L   .If the angle between the incoming vector current and the rotor is close to 0 o or 180 o , it will cause the prepositioning failure, and the limit angle can be obtained from the above formula. < lim   at this time due to the small angle difference, the impact on the normal start of the motor is also small, but when , if it is close to 180 o , the motor start is easy to produce step loss or overcurrent and other situations, even if the current amplitude is increased, which cannot completely eliminate the prepositioning dead zone In view of the problem of rotor prepositioning blind zone existing in the traditional prepositioning method, this paper adopts the secondary positioning method, as shown in  is obtained.The formula is as follows, where e  is the speed, generated by the slope generator with the slope acceleration coefficient ( ) a t , k is the current-frequency ratio coefficient, q I is the current required to overcome the load torque at the speed of 0, e  is the rotor position determined by the open-loop acceleration stage, and * q I is the q-axis current given at the start time.
In the actual open-loop operation of the motor, there must be a position error e   , because the motor model in this article uses a surface-mount permanent magnet synchronous motor, and the electromagnetic torque generated by the given current vector can be obtained as shown in the following equation.
Only when the given q-axis current vector * q I can overcome the load torque, the motor can be started and the torque balance can be achieved, so that whether the load torque increases or decreases, the motor can return to the balance state to a certain extent, but when the load torque changes drastically, the I/F start control algorithm cannot achieve adaptive adjustment, which is also the deficiency of the I/F control method.
The key point to achieve PMSM with no position sensor is the state switching between low speed and medium and high speed.The more commonly used are the direct switching method and the weighted switching method.The direct switching method has a large switching jitter, so the system stability is poor, the weighted switching method needs to determine the parameter angle, and the calculation amount is large.So, this paper proposes an improved simple switching method, using I/ F to start the control method to give the angle IF  and the difference between the rotor angle SMO  obtained by the synovial observer, to get a new variable e  and then set a threshold s for e  .When B does not reach the threshold s, we use the I/F control method.When e  exceeds the threshold s switch to the adaptive synovial observation method, because the synovial observer detects the value of e  after the motor starts, we observe the actual time required to reach this threshold s ts , and use time ts as the switching point of the switching function, the switching function is as follows.0 ( ) 1 t ts s t t ts

Simulation verification
In this paper, using the Simulink simulation platform included with Matlab software, a simulation model of the full-speed domain sensorless PMSM control system based on the improved adaptive sliding mode observation method and I/F start-up control algorithm is constructed, and the principle is shown in The change curve of the rotor angle Figure 5 below is the estimated rotor position and the actual position of the rotor obtained by the system at 1500 r/min speed.It can be seen that the position waveforms of the two basically coincide.Figure 6 below is the angle difference between the estimated rotor position and the actual rotor position, the rotor error angle is caused by the phase delay, and the delay time is less than 0.001 s.It can be seen that the estimated rotor angle and the actual angle error are very small, and the error waveform is very stable, which can prove that the stability of the system is better.Since the rotor angle obtained by the sliding mode observer fluctuates sharply when the motor is first started, this article sets the motor to run for a certain period of time and then detects the angle error.(2) The change curve of the rotational speed The following figure is the waveform diagram obtained by the actual speed and sliding mode observation speed obtained by setting the speed of 1500 r/min in this experiment.Figure 7 is the waveform diagram of the switching function of low-speed and medium-high speed switching.This article sets the switching algorithm after the running time t=0.028s and the actual speed reaches 674 r/min, and also sets the waveform of the set speed, the actual speed, and the sliding mode observation speed.It can be observed that the actual speed and the speed observed by the sliding mode are stable near the set speed, the speed error is 17 r/min, and there is no high-frequency clutter.But after the acceleration is completed, there is still a certain overshoot to achieve a stable speed waveform, it is less than 3%, which is also where the control scheme needs to continue to improve.

Conclusion
This paper formulates a new scheme for sensorless control of permanent magnet synchronous motor for vehicle air compressor, in the low-speed operation stage of motor startup and setting, IF control is adopted, and improved adaptive sliding mode control is adopted in the medium and high-speed stage, and the error between the predicted rotor angle and motor speed and the actual value is observed through the simulation platform verification, and the error is found to be very small.The robustness of the whole system is strong, which proves the feasibility of the scheme.

Figure 3 .Figure 3 .
Figure 3. Quadratic positioning method.After completing the rotor prepositioning, I / F start, in fact, the motor speed is open-loop control, by integrating the speed, and the command position angle e is obtained.The formula is as follows, where e

Figure 4 .Figure 4 .
Figure 4. Block diagram of the control system of sensorless PMSM in the full-speed domain.(1)The change curve of the rotor angle Figure5below is the estimated rotor position and the actual position of the rotor obtained by the system at 1500 r/min speed.It can be seen that the position waveforms of the two basically coincide.Figure6below is the angle difference between the estimated rotor position and the actual rotor position, the rotor error angle is caused by the phase delay, and the delay time is less than 0.001 s.It can be seen that the estimated rotor angle and the actual angle error are very small, and the error waveform is very stable, which can prove that the stability of the system is better.Since the rotor angle obtained by the sliding mode observer fluctuates sharply when the motor is first started, this article sets the motor to run for a certain period of time and then detects the angle error.

Figure 5 .
Figure 5. Adaptive sliding mode observer rotor position tracking diagram.

Figure 6 .
Figure 6.Rotor position error.(2)The change curve of the rotational speed The following figure is the waveform diagram obtained by the actual speed and sliding mode observation speed obtained by setting the speed of 1500 r/min in this experiment.Figure7is the waveform diagram of the switching function of low-speed and medium-high speed switching.This article sets the switching algorithm after the running time t=0.028s and the actual speed reaches 674 r/min, and also sets the waveform of the set speed, the actual speed, and the sliding mode observation speed.It can be observed that the actual speed and the speed observed by the sliding mode are stable near the set speed, the speed error is 17 r/min, and there is no high-frequency clutter.But after the acceleration is completed, there is still a certain overshoot to achieve a stable speed waveform, it is less than 3%, which is also where the control scheme needs to continue to improve.