CN110445441A - A kind of permanent magnet synchronous motor prediction method for controlling torque - Google Patents

Abstract

The invention discloses a method for controlling the predicted torque of a permanent magnet synchronous motor. The upper and lower bounds of the tracking error in the steady state; (2) Considering the delay compensation, take (k+1)T _s time as the starting point of prediction; (3) if the torque at (k+1)T _s time and The tracking error of the stator flux amplitude cannot satisfy the given upper and lower bound constraints at the same time, and the single-step predictive torque control is adopted, and the control goal is to quickly reduce the torque tracking error and/or the stator flux amplitude tracking error; (4) If the tracking error of torque and stator flux amplitude at time (k+1)T _s satisfies the given upper and lower bound constraints at the same time, multi-step predictive torque control is adopted, and the control target is to reduce torque fluctuation and stator flux While fluctuating, reduce the switching times of the inverter.

Description

A Predictive Torque Control Method for Permanent Magnet Synchronous Motor

technical field

The invention belongs to the field of motor control, in particular to a method for controlling the predicted torque of a permanent magnet synchronous motor, which is suitable for the field of permanent magnet synchronous motor control.

Background technique

Permanent magnet synchronous motor (PMSM) has the advantages of simple structure, high power density, wide range of speed regulation, and high reliability. It has been widely researched and applied in the fields of elevator drive, electric vehicles, and rail transit. In the field of high-performance frequency conversion speed regulation, vector control and direct torque control are considered to be the two most classic control strategies. Vector control is a control strategy based on PWM vector modulation. PWM vector modulation has the advantage of fixed inverter switching frequency, but also has the disadvantage of excessive inverter switching frequency due to some unnecessary switching actions. Direct torque control is a control strategy based on a hysteresis controller. In order to ensure better steady-state performance, such as smaller torque fluctuations, it must rely on a higher switching frequency. In the field of medium and high voltage motor drives, the switching loss of the inverter accounts for a large proportion of the total loss of the inverter. The high switching frequency of the two classic control strategies will inevitably lead to high switching losses.

In recent years, predictive torque control (PTC) has gained widespread attention in the field of PMSM control due to its intuitive method, easy solution to multivariable and multi-constrained problems, and fast dynamic response, and is considered to be a potential of the two classic strategies. alternative strategy. According to the size of the prediction step, PTC can be divided into multi-step PTC (prediction step N _P >1) and single-step PTC (prediction step N _P =1). Studies have shown that compared with single-step PTC, multi-step PTC can obtain better steady-state performance with lower switching frequency. However, the traditional PTC is optimized through enumeration. As the prediction step increases, the calculation amount of PTC increases exponentially. Limited by the performance of the microprocessor, the traditional PTC strategy usually sets the prediction step to 1.

Aiming at the disadvantages of multi-step PTC with a large amount of calculation, some scholars introduce the deadbeat principle, and select several voltage vectors closest to the deadbeat voltage vector as input before each step of prediction. Although this method reduces the candidate voltage vector sequence to a certain extent, it increases the calculation process for solving the deadbeat voltage vector. Some scholars have realized PTC with a prediction step size of 3 by simplifying the prediction model and formulating optimization rules, but it is only applicable to surface-mounted PMSM.

On the other hand, in transient processes such as start-up, acceleration, and load mutation, the tracking error of torque and stator flux is relatively large. At this time, the control goal should be to reduce the tracking of torque and stator flux at the fastest speed. error. Therefore, when the tracking error of torque and stator flux linkage is small, such as under steady-state conditions, the optimization of the number of switching operations should be considered.

In order to achieve multi-step PTC with a small amount of calculation so as to obtain better steady-state performance and lower switching frequency at the same time, and to ensure good transient performance through single-step PTC in transient state, the present invention proposes a A Hybrid Predictive Step Size Predictive Torque Control Method for Permanent Magnet Synchronous Motors.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for predictive torque control of permanent magnet synchronous motors, which can reduce the switching frequency of the inverter as much as possible while ensuring good steady-state performance of the system, and at the same time Fast dynamic response capability in transient process.

The purpose of the present invention is achieved through the following technical solutions:

A method for predictive torque control of a permanent magnet synchronous motor, comprising the following steps:

(1) Establish a tracking error prediction model for the torque of the permanent magnet synchronous motor and the magnitude of the stator flux linkage, and set the upper and lower bound constraints of the tracking error of the torque and the magnitude of the stator flux linkage;

(2) Considering delay compensation, predict the tracking error of torque and stator flux amplitude at (k+1) T _s time;

(3) If the tracking error of torque and stator flux amplitude at time (k+1)T _s cannot satisfy the given upper and lower bound constraints at the same time, single-step predictive torque control is adopted, and the value function only includes torque and stator flux The tracking error item of the flux linkage amplitude, the control target is to quickly reduce the torque tracking error and/or the stator flux amplitude tracking error;

(4) If the tracking error of torque and stator flux amplitude at time (k+1)T _s satisfies the given upper and lower bound constraints at the same time, multi-step predictive torque control is adopted, and the value function excludes torque and stator flux In addition to the tracking error item of the amplitude, it also includes the switching times item of the inverter. The control goal is to reduce the torque tracking error and/or the stator flux amplitude tracking error, and at the same time reduce the switching times of the inverter as much as possible.

Further, the tracking error prediction model of torque and stator flux amplitude in step (1) is

in,

E＝ _ωr (k) _ψs (k)

In the formula, u _x (l|i _l ) and u _y (l|i _l ) are the voltage vector u _il corresponding to lT _s (l=k,k+1,…,k+n-1) time moment x-axis component and y-axis component; i _l represents the serial number of the voltage vector acting at lT _s moment; e _T and e _ψ are torque tracking error and stator flux amplitude tracking error respectively; ψ _s is stator flux amplitude; T _e is the electromagnetic torque; including the superscript ref indicates the reference value of the variable; ω _r is the electrical angular velocity of the rotor rotation; L _d and L _q are the inductance of the stator d-axis and q-axis respectively; ψ _f is the amplitude of the permanent magnet flux linkage; δ represents the load angle, that is, the difference between the stator flux vector angle θ _s and the rotor flux vector angle θ _r ; p is the number of pole pairs; T _s is the sampling period.

The upper and lower bounds of the tracking error of the torque and stator flux amplitude in the steady state are constrained by

In the formula, and are the maximum values of torque fluctuation and stator flux amplitude fluctuation in steady state, respectively; N _p is the prediction step size.

Further, in step (2), the tracking error of torque and stator flux amplitude at time (k+1)T _s is

In the formula, u _x (k|opt) and u _y (k|opt) represent the x-axis component and y-axis component corresponding to the optimal voltage vector u _opt acting at kT _s moment, respectively.

Further, the value function of single-step predictive torque control in step (3) is

J ₁ ＝e _T (k+2) ² +λe _ψ (k+2) ²

In the formula, λ is the weight coefficient;

The optimization problem to be solved is

stS _i =[S _a S _b S _c ] ^T

In the formula, S _opt is the optimal switch state combination; S _i (i=0,1,…,7) are the 8 switch state combinations of the inverter; S _a , S _b and S _c are the inverter The switching state of the three-phase upper bridge arm; u _i is the voltage vector corresponding to S _i ; including (k+1|i) means the value of the variable at (k+1)T _s time under the action of u _i ; including (k+ 2|i) represents the value of the variable at (k+2)T _s time under the action of u _i ; P and C are the Park transformation matrix and Clarke transformation matrix respectively; V _dc is the DC bus voltage.

Further, the value function of multi-step predictive torque control in step (4) is

In the formula, Q and σ are the weight coefficient matrix of the tracking error item and the weight coefficient of the switch item respectively;

The optimization problem to be solved is

stU(k+1)=[S(k+1),S(k+2),...,S(k+N _p )]

S(l)∈S _i

In the formula, U _opt is the optimal switch sequence; U(k+1) is the switch sequence starting at ( _k +1)T _s time, and S(l) (l=k+1, k+2,...,k+N _p ) form; is the average value of the stator flux vector angle in the prediction domain, for the reason Calculate the average voltage vector; for the reason The calculated Park transformation matrix; i _l represents the serial number of the voltage vector acting at the time lT _s ;

Since the predictive control algorithm is rolling optimization, it is only necessary to apply the first item S _opt (k+1) in U _opt (k+1) to the inverter at (k+1)T _s time, and then Repeatedly solve the above optimization problem.

Compared with the prior art, the beneficial effects brought by the technical solution of the present invention are:

(1) Compared with traditional PTC, as described in step (1), the present invention derives the tracking error model of torque and stator flux amplitude, which can directly predict the tracking error of torque and stator flux amplitude , there is no need to calculate the tracking error in the value function, which can effectively reduce the amount of calculation;

(2) The torque and stator flux amplitude prediction model of traditional PTC is a strongly coupled, nonlinear time-varying model, and the calculation is complicated. As described in step (1), the present invention derives torque and stator flux amplitude The tracking error model of , which is a reasonably simplified decoupled, linear time-invariant model, is easy to implement multi-step PTC;

(3) As described in step (3), the present invention adopts single-step PTC in transient processes such as motor start-up, acceleration, and load mutation, and the value function only includes the tracking error term of torque and stator flux linkage, which can ensure fast dynamic responsiveness;

(4) As described in step (4), when the motor is running stably, the present invention adopts multi-step PTC, and the value function contains the tracking error term of torque and stator flux linkage, and the switching number of switches term, which can effectively reduce the speed of rotation. While the torque and stator flux fluctuations, reduce the switching frequency of the inverter.

Description of drawings

Figure 1a is a schematic diagram of a two-level voltage source inverter permanent magnet synchronous motor system.

Figure 1b is the spatial distribution diagram of the voltage vector of the two-level voltage source inverter.

Figure 2a and Figure 2b are schematic diagrams of upper and lower bound constraints of torque and stator flux amplitude in steady state, respectively.

Fig. 3 is a block diagram of predicted torque control in this embodiment.

Figure 4 is an example of the algorithm of hybrid prediction step size PTC.

Detailed ways

Taking a surface-mounted permanent magnet synchronous motor system fed by a two-level voltage source inverter as an example, a method for predictive torque control of a permanent magnet synchronous motor based on a hybrid predictive time domain according to the present invention will be described in detail below. Moreover, the present invention has the potential to be extended to multi-level inverter feed and (or) built-in permanent magnet synchronous motor systems.

As shown in Figure 1a, the two-level voltage source inverter has a total of 8 switching states, which can be written in matrix form

The spatial positions of the voltage vectors corresponding to the eight switching states in the α-β complex plane are shown in Figure 1b. Among them, u ₁ ~ u ₆ are called effective voltage vectors, u ₀ and u ₇ are called zero vectors. The xy rotating coordinate system is established with the orientation of the stator flux vector, and the relationship between the x-axis component and the y-axis component of the voltage vector u _i (i=0,1,…,7) of the inverter and the corresponding switch state is as follows:

in,

They are the Clarke transformation matrix and the Park transformation matrix; V _dc is the DC bus voltage; θ _s is the stator flux vector angle.

In the x-y rotating coordinate system established by the orientation of the stator flux vector, ignoring the influence of the stator resistance, the change rate model of the stator flux amplitude and electromagnetic torque of the surface-mounted PMSM is as follows:

Among them, the expression of the torque coefficient K is

The expression of back electromotive force E is

_E ＝ _ωrψs (7)

In the formula, u _x and u _y are the x-axis component and y-axis component of the stator voltage vector u _s respectively; ψ _s is the amplitude of the stator flux linkage; T _e is the electromagnetic torque; ω _r is the electrical angular velocity of the rotor rotation; L _s is the stator inductance; ψ _f is the flux amplitude of the permanent magnet; δ is the load angle, that is, the difference between the stator flux vector angle θ _s and the rotor flux vector angle θ _r ; p is the number of pole pairs.

Equation (5) is time discretized by Euler approximation, and the discretized mathematical model of stator flux amplitude and torque can be obtained as

In the formula, T _s is the sampling period.

Define the tracking error of torque and stator flux amplitude at time kT _s as

In the formula, and are the reference values of torque and stator flux amplitude, respectively.

From formula (8), it can be obtained that the tracking error prediction value of stator flux amplitude and torque at time (k+1)T _s is

When the motor runs stably (i.e. steady state), it satisfies:

(1) The electrical angular velocity of the rotor rotation is approximately constant in several consecutive sampling periods;

(2) Since the fluctuation of the amplitude of the stator flux linkage is very small, it can be considered that the amplitude of the stator flux linkage is approximately constant in several consecutive sampling periods;

(3) Since the rotational speeds of the stator and rotor flux linkages are synchronized, it can be considered that the load angle δ is approximately constant in several consecutive sampling periods.

Therefore, it can be seen from formula (6) and formula (7) that in the steady state, the torque coefficient K and the electromotive force E can be approximately regarded as constants in several consecutive sampling periods. At this time, the multi-step prediction model of the tracking error of the stator flux amplitude and torque can be recursively obtained by formula (10), and the tracking error prediction value of the stator flux amplitude and torque at the moment (k+n)T _s for

Or write recursively as

As shown in Figure 2a and Figure 2b, the upper and lower bounds of the tracking error of the torque and stator flux amplitude in the steady state are constrained by

In the formula, and are the maximum values of torque fluctuation and stator flux amplitude fluctuation in steady state, respectively; N _p is the prediction step size.

The PTC control block diagram of the permanent magnet synchronous motor system based on the hybrid prediction time domain is shown in Figure 3.

For the surface-mounted permanent magnet synchronous motor, the related expressions of torque and stator flux linkage estimation are as follows:

In the formula, i _α and _{i β} are the α-axis component and β-axis component of the stator current vector is respectively; ψ _sα and ψ _sβ are the α-axis component and β-axis component of the stator flux vector.

As shown in Figure 2a and Figure 2b, considering the delay compensation, the optimal voltage vector applied at kT _s time is obtained in the previous cycle, and this cycle is predicted from (k+1)T _s time as the starting point. Find the optimal voltage vector that needs to be applied at the time of (k+1)T _s .

From formula (10), it can be seen that the tracking errors of torque and stator flux amplitude at time (k+1)T _s are respectively

In the formula, u _x (k|opt) and u _y (k|opt) respectively denote the x-axis component and y-axis component corresponding to the optimal voltage vector u _opt applied at time kT _s .

As shown in Figure 2a and Figure 2b, in steady state, the tracking error of torque and stator flux amplitude satisfies at time (k+1)T _s

If formula (16) is not established, it means that the system is in a transient state, and single-step predictive torque control is adopted at this time.

The value function of single-step predictive torque control is

J ₁ ＝e _T (k+2) ² +λe _ψ (k+2) ² (17)

In the formula, λ is the weight coefficient.

The optimization problem to be solved is

stS _i =[S _a S _b S _c ] ^T

In the formula, including (k+1|i) means the value of the variable at (k+1)T _s time under the action of u _i ; including (k+2|i) means the value of the variable at (k+2) under the action of u _i ) the value at time T _s ;

If Equation (16) is established, it means that the system is in a steady state, and multi-step predictive torque control is adopted at this time.

The value function of multi-step predictive torque control is

In the formula, Q and σ are the weight coefficient matrix of the tracking error item and the weight coefficient of the switch item respectively;

The optimization problem to be solved is

stU(k+1)=[S(k+1),S(k+2),...,S(k+N _p )]

S(l)∈S _i

In the formula, U _opt is the optimal switch sequence; U(k+1) is the switch sequence starting at ( _k +1)T _s time, and S(l) (l=k+1, k+2,...,k+N _p ) form; is the average value of the stator flux vector angle in the prediction domain, for the reason Calculate the average voltage vector; for the reason The calculated Park transformation matrix; i _l represents the serial number of the voltage vector acting at the time lT _s ;

The optimal vector sequence U _opt (k+1) is obtained by solving the multi-step predictive direct torque control, and only the first element, that is, S _opt (k+1), acts on the inverter at (k+1)T _s time. In the next cycle, the above process is repeated to solve a new optimal vector sequence, that is, rolling optimization.

Figure 4 shows an example of a hybrid predictive step size predictive torque control algorithm that uses two-step prediction in steady state and single-step prediction in transient state. In practical applications, the prediction step size of multi-step predictive torque control can be set to 3 or greater.

The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solution of the present invention, and the above specific embodiments are only illustrative and not restrictive. Without departing from the gist of the present invention and the scope of protection of the claims, those skilled in the art can also make many specific changes under the inspiration of the present invention, and these all belong to the protection scope of the present invention.

Claims (5)

1. a permanent magnet synchronous motor predictive torque control method, is characterized in that, comprises the following steps: (1) Establish a tracking error prediction model for the torque of the permanent magnet synchronous motor and the magnitude of the stator flux linkage, and set the upper and lower bound constraints of the tracking error of the torque and the magnitude of the stator flux linkage; (2) Considering delay compensation, predict the tracking error of torque and stator flux amplitude at (k+1) T _s time; (3) If the tracking error of torque and stator flux amplitude at time (k+1)T _s cannot satisfy the given upper and lower bound constraints at the same time, single-step predictive torque control is adopted, and the value function only includes torque and stator flux The tracking error item of the flux linkage amplitude, the control target is to quickly reduce the torque tracking error and/or the stator flux amplitude tracking error; (4) If the tracking error of torque and stator flux amplitude at time (k+1)T _s satisfies the given upper and lower bound constraints at the same time, multi-step predictive torque control is adopted, and the value function excludes torque and stator flux In addition to the tracking error item of the amplitude, it also includes the switching times item of the inverter. The control target is to reduce the torque tracking error and/or the stator flux linkage amplitude tracking error, and at the same time reduce the switching times of the inverter. 2. according to the described a kind of permanent magnet synchronous motor predictive torque control method of claim 1, it is characterized in that, the tracking error prediction model of torque and stator flux linkage amplitude value described in step (1) is in, E＝ _ωr (k) _ψs (k) In the formula, u _x (l|i _l ) and u _y (l|i _l ) are respectively the voltage vectors acting at the time lT _s (l=k,k+1,…,k+n-1) The corresponding x-axis component and y-axis component; i _l represents the number of the voltage vector acting at the time lT _s ; e _T and e _ψ are the torque tracking error and the stator flux amplitude tracking error respectively; ψ _s is the stator flux amplitude T _e is the electromagnetic torque; the superscript ref indicates the reference value of the variable; ω _r is the electrical angular velocity of the rotor rotation; L _d and L _q are the inductance of the stator d-axis and q-axis respectively; ψ _f is the permanent magnet flux linkage amplitude Value; δ represents the load angle, that is, the difference between the stator flux vector angle θ _s and the rotor flux vector angle θ _r ; p is the number of pole pairs; T _s is the sampling period. The upper and lower bounds of the tracking error of the torque and stator flux amplitude in the steady state are constrained by In the formula, and are the maximum values of torque fluctuation and stator flux amplitude fluctuation in steady state, respectively; N _p is the prediction step size. 3. a kind of permanent magnet synchronous motor predictive torque control method according to claim 1, is characterized in that, in step (2), the torque of (k+1) T _s moment and the tracking error of stator flux linkage amplitude value for In the formula, u _x (k|opt) and u _y (k|opt) represent the x-axis component and y-axis component corresponding to the optimal voltage vector u _opt acting at kT _s moment, respectively. 4. according to the described a kind of permanent magnet synchronous motor predictive torque control method of claim 1, it is characterized in that, the cost function of single-step predictive torque control in step (3) is J ₁ ＝e _T (k+2) ² +λe _ψ (k+2) ² In the formula, λ is the weight coefficient; The optimization problem to be solved is stS _i =[S _a S _b S _c ] ^T i=0,1,...,7 In the formula, S _opt is the optimal switch state combination; S _i (i=0,1,…,7) are the 8 switch state combinations of the inverter; S _a , S _b and S _c are the inverter The switching state of the three-phase upper bridge arm; u _i is the voltage vector corresponding to S _i ; including (k+1|i) means the value of the variable at (k+1)T _s time under the action of u _i ; including (k+ 2|i) represents the value of the variable at (k+2)T _s time under the action of u _i ; P and C are the Park transformation matrix and Clarke transformation matrix respectively; V _dc is the DC bus voltage. 5. a kind of permanent magnet synchronous motor predictive torque control method according to claim 1, is characterized in that, the cost function of multi-step predictive torque control in step (4) is In the formula, Q and σ are the weight coefficient matrix of the tracking error item and the weight coefficient of the switch item respectively; The optimization problem to be solved is stU(k+1)=[S(k+1),S(k+2),...,S(k+N _p )] S(l)∈S _i l=k+1,k+2,...,k+N _p i _l =0,1,...,7 In the formula, U _opt is the optimal switch sequence; U(k+1) is the switch sequence starting at ( _k +1)T _s time, and S(l) (l=k+1, k+2,...,k+N _p ) form; is the average value of the stator flux vector angle in the prediction domain, for the reason Calculate the average voltage vector; for the reason The calculated Park transformation matrix; i _l represents the serial number of the voltage vector acting at the time lT _s ; Since the predictive control algorithm is rolling optimization, it is only necessary to apply the first item S _opt (k+1) in U _opt (k+1) to the inverter at (k+1)T _s time, and then Repeatedly solve the above optimization problem.