CN116505824A - Permanent magnet synchronous motor control method based on double-prediction control - Google Patents

Abstract

The invention discloses a permanent magnet synchronous motor control method based on double predictive control. The steps are as follows: the present invention studies the current loop part, uses deadbeat predictive control algorithm to optimize the motor current, and introduces a model predictive algorithm in the speed loop , determine the system state variables, design the sliding mode surface and reaching law function, solve the corresponding control output, and finally prove its stability through the Lyapunov equation; introduce the model predictive control algorithm in the speed loop, first discretize the reference trajectory, Carry out two-step prediction, then add model error correction, use quadratic performance index as evaluation function, and finally get the control law. The invention uses a model prediction algorithm to control the speed of the motor for the speed loop part, so as to obtain better dynamic and static control effects, and the PMSM system has faster dynamic response and stronger load interference resistance.

Description

A control method for permanent magnet synchronous motor based on double predictive control

technical field

The invention relates to information and automatic control, in particular to a permanent magnet synchronous motor control method based on double predictive control.

Background technique

Permanent magnet synchronous motors are widely used in various fields such as railway traction, aerospace, machine tools, and military because of their advantages such as high efficiency, high power density, and high power factor. Under this premise, the traditional control method has become more and more difficult to meet the high-performance control requirements, and a high-performance AC motor control strategy is urgently needed to deal with higher-demanding control occasions. Among many advanced control technologies, deadbeat predictive control is widely used in the field of motor control because of its simple structure and easy handling of complex nonlinear systems.

Contents of the invention

Purpose of the invention: The purpose of the present invention is to provide a permanent magnet synchronous motor control method based on double predictive control with good steady-state static difference performance, thereby providing more general performance, faster dynamic response and stronger load resistance Interference ability.

Technical solution: A permanent magnet synchronous motor control method based on double predictive control according to the present invention includes the following steps:

(1) Establish the mathematical model of the permanent magnet synchronous motor: In the PMSM control system, the surface-mounted permanent magnet synchronous motor is used as the research object, from the voltage, AC and DC speed, torque, and mechanical motion equations in the dual synchronous rotating coordinate system. The relevant formulas are derived.

(1.1) Deadbeat predictive current controller

Compared with the traditional current controller, the PI controller is replaced by the deadbeat controller, which has the advantages of constant switching frequency, fast dynamic response, high bandwidth, small current fluctuation, and easy implementation; the most prominent advantage is that it can be realized by The deadbeat tracking between the control object and the control expectation value clarifies the relationship between the input and output of the control object, thereby establishing a clear mathematical formula, so the system has rapid response capabilities;

The current state equation is as follows:

Rewrite the above formula into matrix form:

Laplace transform of the above formula can be obtained:

Among them, _t0 is the initial sampling moment, τ is the integral time constant; since the motor sampling period T = 0.0001s and the motor mechanical time constant is much larger than the current time constant, it can be considered that the motor speed remains unchanged in adjacent sampling periods, Therefore, the electromotive force also remains unchanged; at this time, let t ₀ =kT, t=(k+1)T, the following expression is obtained:

i(k+1)=F(k)i(k)+A ₀ ^-1 (F(k)-E)(B ₀ u(k)+D ₀ ) (4)

in,

Since the sampling period T is very small, it can be considered that: cosω _e T≈1, sinω _e T≈ω _e T, cosω _e T≈1, sinω _e T≈ω _e T,

Then the simplified matrix F(k) is:

At this point, the discretized PMSM state equation is obtained as follows:

i(k+1)=F(k)i(k)+Gu(k)+H(k)(5)

in,

The control voltage can be obtained by solving:

u(k)=G ^-1 (i(k+1)-F(k)i(k)-H(k))(6)

In the deadbeat predictive current control algorithm, it is necessary to meet the requirement that the current can follow the given value, and replace i(k+1) in the above formula with i ^* (k+1), then the output voltage expression is as follows:

Among them, i(k) is the current value sampled in the motor;

Since the present invention takes the surface-mounted permanent magnet synchronous motor as the research object, for this motor, L _d =L _q =L is satisfied, therefore, the electromagnetic torque equation at this moment is:

In the formula, the angle between i _q and i _s is β;

For formula (8), where P _n and Ψ _f are constants, so the magnitude of the electromagnetic torque depends on the q-axis current, and the q-axis current is related to i _s and β. It is known that sinβ=1, that is When β=90°, there is i _q =i _s , that is, the torque current is all composed of the stator current, so the operating efficiency of the motor reaches the maximum at this time; thus, if the motor is expected to run with high performance, its torque The current ratio should be given to the maximum, so that the d-axis current is the maximum, that is, i ^* _d = 0;

(1) Model predictive speed controller

Discrete equation of state for the velocity prediction model:

T is the sampling period, k is the current moment;

In order to facilitate the calculation and ignore the influence of load disturbance, the speed prediction model equation at this time is:

In the above formula, i _q (k) can be written as:

i _q (k)=i _q (k-1)+Δi _q (k)(3)

For ease of calculation, the present invention adopts two-step forecasting, writes respectively as ω _rm (k+1), ω _rm (k+2) to the speed of k+1, k+2 moment predicted at k moment;

Combining formulas (2) and (3), the state equation is obtained as:

make

Bringing (8) into (6) and (7), it can be simplified as follows:

Formula (9) is rewritten into a matrix form, namely:

According to formula (10) into (9), it can be written as:

ω _rm =ω _r0 +GΔi _q (11)

In order to reduce the calculation error of the model, it is necessary to add model error correction. Usually, the deviation between the predicted value and the actual value at the previous moment is used to approximately correct the prediction model; for ω _rm (k+1), ω _rm (k+2) is denoted as ω _rM (k+1) and ω _rM (k+2) respectively, and the corresponding state equations are:

Change the ω _rm (k+1) in the above formula (12) to ω _rM (k+1), then the correction item of the prediction model can be obtained as:

For formula (13), let

According to formula (14), formula (13) can be written as:

ω _rM =ω _rm +e(15)

According to the commonly used performance indicators, the quadratic performance indicators are selected as the evaluation function, namely:

In the above formula, the first item is the constraint item of deviation size, the second item is the constraint item of control quantity, and q _i and r _j are weight coefficients;

In formula (16), because the speed expectation at k+1 and k+2 cannot be directly obtained, so the first-order exponential form is used to obtain its reference trajectory, namely:

In formula (17), Where T _c is a time constant;

According to the principle of rolling optimization, to solve the optimal Δi _q needs to satisfy the equation (16):

Solving formula (18) can get Δi _q as:

In the formula,

Combining formula (5) with the above formula (19), the final control law of the surface-mounted PMSM model predictive controller is:

(2) Load disturbance compensation

Since the load disturbance is ignored in the second part of the model prediction speed controller, in order to improve the control accuracy, the load disturbance is now compensated, combined with the permanent magnet synchronous motor torque equation and motion equation,

The q-axis current that needs to be compensated due to load disturbance is deduced as:

The load torque T _L cannot be obtained directly, so the fractional order integration method is used for current compensation, the purpose is to reduce the system error by means of the integral action, and strengthen the system robustness; the present invention adopts the caputo type fractional order, and its expression is as follows:

In the above formula (22), It is the α-order differential or integral of the function f(t), α>0 means differentiation, α<0 means integral; t ₀ is the initial value of variable t, n∈N and n-1<α<n;

Taking the deviation of the speed as the input quantity, the q-axis compensation current is obtained after the fractional integration of formula (22), that is:

Finally, after combining formula (23) and formula (20) to obtain the compensation current, the control law of the model predictive speed controller becomes:

(2) Design the current loop predictive controller: apply the deadbeat predictive control strategy to the current internal control of the permanent magnet synchronous motor; the deadbeat predictive current control is a digital discrete control, and the motor current obtained mainly through sampling passes through the coordinates The transformation is compared with the given current, the comparison result is controlled by the deadbeat current controller, the output voltage is transformed through the coordinate transformation, and the inverter generates the corresponding switching signal through the space vector pulse width modulation SVPWM modulator module, so that Click the feedback current to follow the given current in the next switching cycle; since the current loop plays an important role in the performance of the motor control system, the inner loop replaces the PI in the traditional vector control with the deadbeat current predictive controller The purpose of this is to improve the operating performance and response speed of the motor current loop;

(3) Design the outer loop speed MPC controller: apply MPC to the speed loop to improve the control performance of the system; The form of optimization determines the optimal solution at the current moment, and adjusts the deviation between the output prediction value and the expected value through feedback correction; MPC mainly includes four parts: reference trajectory, prediction model, feedback correction and rolling optimization. Its control structure is as follows: as shown in the figure;

(4) Establish a control system simulation model: on the basis of the permanent magnet synchronous motor mathematical model, a dual-model prediction strategy is adopted, that is, the model predictive controller is applied to the outer loop of the system, that is, the speed loop, and the deadbeat predictive controller is applied to the system The inner loop is the current loop.

A computer storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the above-mentioned method for controlling a permanent magnet synchronous motor based on bipredictive control is realized.

A computer device, including a memory, a processor, and a computer program stored on the memory and operable on the processor. When the processor executes the computer program, the above-mentioned permanent magnet synchronization based on bi-predictive control is realized. motor control method.

Beneficial effect: compared with the prior art, the present invention has the following advantages:

1. The present invention combines traditional vector control strategy and predictive control research, obtains permanent magnet synchronous motor double predictive control strategy method, conducts research on the current loop part, uses deadbeat predictive control algorithm to optimize the motor current, and obtains more Excellent dynamic and static control effect.

2. The present invention uses a model prediction algorithm to control the motor speed for the speed loop part, and the obtained PMSM system has faster dynamic response and stronger load interference resistance.

3. Through simulation analysis, it is proved that the dual MPC strategy has good control performance. Compared with the traditional control method, the PMSM control system has almost no obvious overshoot, and the quality of the sine wave output phase current is very good.

Description of drawings

Fig. 1 is a flow chart of the steps of the method of the present invention;

Fig. 2 is a block diagram of dual-model predictive control strategy;

Figure 3 is a comparison diagram of the rotational speed waveform; among them, Figure 3(a) is the rotational speed waveform diagram of the dual-model predictive control PMSM, and Figure 3(b) is the rotational speed waveform diagram of the PMSM controlled by PI;

Fig. 4 is a PI control dq axis current waveform diagram;

Fig. 5 is a dual-model predictive control dq axis current waveform diagram;

Fig. 6 is a traditional PID algorithm electromagnetic torque waveform diagram;

Figure 7 is the electromagnetic torque diagram of the dual model prediction algorithm.

Figure 8 shows the technical route of dual model predictive control PMSM.

Detailed ways

The technical solution of the present invention will be further described below in conjunction with the accompanying drawings.

A method for controlling permanent magnet synchronous motors based on double predictive control, comprising the following steps:

(1) Establish the mathematical model of the permanent magnet synchronous motor: In the PMSM control system, the surface-mounted permanent magnet synchronous motor is used as the research object, from the voltage, AC and DC speed, torque, and mechanical motion equations in the dual synchronous rotating coordinate system. The relevant formulas are derived.

(1.1) Deadbeat predictive current controller

Compared with the traditional current controller, the PI controller is replaced by the deadbeat controller, which has the advantages of constant switching frequency, fast dynamic response, high bandwidth, small current fluctuation, and easy implementation; the most prominent advantage is that it can be realized by The deadbeat tracking between the control object and the control expectation value clarifies the relationship between the input and output of the control object, thereby establishing a clear mathematical formula, so the system has rapid response capabilities;

The current state equation is as follows:

Rewrite the above formula into matrix form:

Laplace transform of the above formula can be obtained:

Among them, _t0 is the initial sampling moment, τ is the integral time constant; since the motor sampling period T = 0.0001s and the motor mechanical time constant is much larger than the current time constant, it can be considered that the motor speed remains unchanged in adjacent sampling periods, Therefore, the electromotive force also remains unchanged; at this time, let t ₀ =kT, t=(k+1)T, the following expression is obtained:

i(k+1)=F(k)i(k)+A ₀ ^-1 (F(k)-E)(B ₀ u(k)+D ₀ ) (4)

in,

Since the sampling period T is very small, it can be considered that: cosω _e T≈1, sinω _e T≈ω _e T, cosω _e T≈1, sinω _e T≈ω _e T,

Then the simplified matrix F(k) is:

At this point, the discretized PMSM state equation is obtained as follows:

i(k+1)=F(k)i(k)+Gu(k)+H(k)(5)

in,

The control voltage can be obtained by solving:

u(k)=G ^-1 (i(k+1)-F(k)i(k)-H(k))(6)

In the deadbeat predictive current control algorithm, it is necessary to meet the requirement that the current can follow the given value, and replace i(k+1) in the above formula with i ^* (k+1), then the output voltage expression is as follows:

u(k)=G ^-1 (i ^* (k+1)-F(k)i(k)-H(k))(7)

Among them, i(k) is the current value sampled in the motor;

Since the present invention takes the surface-mounted permanent magnet synchronous motor as the research object, for this motor, L _d =L _q =L is satisfied, therefore, the electromagnetic torque equation at this moment is:

In the formula, the angle between i _q and i _s is β;

For formula (8), where P _n and Ψ _f are constants, so the magnitude of the electromagnetic torque depends on the q-axis current, and the q-axis current is related to i _s and β. It is known that sinβ=1, that is When β=90°, there is i _q =i _s , that is, the torque current is all composed of the stator current, so the operating efficiency of the motor reaches the maximum at this time; thus, if the motor is expected to run with high performance, its torque The current ratio should be given to the maximum, so that the d-axis current is the maximum, that is, i ^* _d = 0;

(1) Model predictive speed controller

Discrete equation of state for the velocity prediction model:

T is the sampling period, k is the current moment;

In order to facilitate the calculation and ignore the influence of load disturbance, the speed prediction model equation at this time is:

In the above formula, i _q (k) can be written as:

i _q (k)=i _q (k-1)+Δi _q (k)(3)

For ease of calculation, the present invention adopts two-step forecasting, writes respectively as ω _rm (k+1), ω _rm (k+2) to the speed of k+1, k+2 moment predicted at k moment;

Combining formulas (2) and (3), the state equation is obtained as:

make

Bringing (8) into (6) and (7), it can be simplified as follows:

Formula (9) is rewritten into a matrix form, namely:

According to formula (10) into (9), it can be written as:

ω _rm =ω _r0 +GΔi _q (11)

In order to reduce the calculation error of the model, it is necessary to add model error correction. Usually, the deviation between the predicted value and the actual value at the previous moment is used to approximately correct the prediction model; for ω _rm (k+1), ω _rm (k+2) is denoted as ω _rM (k+1) and ω _rM (k+2) respectively, and the corresponding state equations are:

Change the ω _rm (k+1) in the above formula (12) to ω _rM (k+1), then the correction item of the prediction model can be obtained as:

For formula (13), let

According to formula (14), formula (13) can be written as:

ω _rM =ω _rm +e(15)

According to the commonly used performance indicators, the quadratic performance indicators are selected as the evaluation function, namely:

In the above formula, the first item is the constraint item of deviation size, the second item is the constraint item of control quantity, and q _i and r _j are weight coefficients;

In formula (16), because the speed expectation at k+1 and k+2 cannot be directly obtained, so the first-order exponential form is used to obtain its reference trajectory, namely:

In formula (17), Where T _c is a time constant;

According to the principle of rolling optimization, to solve the optimal Δi _q needs to satisfy the equation (16):

Solving formula (18) can get Δi _q as:

In the formula,

Combining formula (5) with the above formula (19), the final control law of the surface-mounted PMSM model predictive controller is:

(2) Load disturbance compensation

Since the load disturbance is ignored in the second part of the model prediction speed controller, in order to improve the control accuracy, the load disturbance is now compensated, combined with the permanent magnet synchronous motor torque equation and motion equation,

The q-axis current that needs to be compensated due to load disturbance is deduced as:

The load torque T _L cannot be obtained directly, so the fractional order integration method is used for current compensation, the purpose is to reduce the system error by means of the integral action, and strengthen the system robustness; the present invention adopts the caputo type fractional order, and its expression is as follows:

In the above formula (22), It is the α-order differential or integral of the function f(t), α>0 means differentiation, α<0 means integral; t ₀ is the initial value of variable t, n∈N and n-1<α<n;

Taking the deviation of the speed as the input quantity, the q-axis compensation current is obtained after the fractional integration of formula (22), that is:

Finally, after combining formula (23) and formula (20) to obtain the compensation current, the control law of the model predictive speed controller becomes:

(2) Design the current loop predictive controller: apply the deadbeat predictive control strategy to the current internal control of the permanent magnet synchronous motor; the deadbeat predictive current control is a digital discrete control, and the motor current obtained mainly through sampling passes through the coordinates The transformation is compared with the given current, the comparison result is controlled by the deadbeat current controller, the output voltage is transformed through the coordinate transformation, and the inverter generates the corresponding switching signal through the space vector pulse width modulation SVPWM modulator module, so that Click the feedback current to follow the given current in the next switching cycle; since the current loop plays an important role in the performance of the motor control system, the inner loop replaces the PI in the traditional vector control with the deadbeat current predictive controller The purpose of this is to improve the operating performance and response speed of the motor current loop;

(3) Design the outer loop speed MPC controller: apply MPC to the speed loop to improve the control performance of the system; The form of optimization determines the optimal solution at the current moment, and adjusts the deviation between the output prediction value and the expected value through feedback correction; MPC mainly includes four parts: reference trajectory, prediction model, feedback correction and rolling optimization. Its control structure is as follows: as shown in the figure;

(4) Establish a control system simulation model: on the basis of the permanent magnet synchronous motor mathematical model, a dual-model prediction strategy is adopted, that is, the model predictive controller is applied to the outer loop of the system, that is, the speed loop, and the deadbeat predictive controller is applied to the system The inner loop is the current loop.

A computer storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the above-mentioned method for controlling a permanent magnet synchronous motor based on bipredictive control is realized.

A computer device, including a memory, a processor, and a computer program stored on the memory and operable on the processor. When the processor executes the computer program, the above-mentioned permanent magnet synchronization based on bi-predictive control is realized. motor control method. Simulation results:

In order to verify the feasibility and effectiveness of the control method proposed in the present invention, by comparing the traditional PI control method with the strategy proposed in the present invention, the control performance of the two strategies under the conditions of sudden load increase and speed regulation are discussed. Table 1 shows the parameter values of the permanent magnet synchronous motor simulation in MATLAB/Simulink, and the simulation time is selected as tmax=1.0s.

Table 1 Permanent magnet synchronous motor parameters

Motor parameters value Rated speed(r/min) 1000 Rated load (N·m) 3 Number of pole pairs (P) 4 Stator resistance (Ω) 0.35 Permanent magnet flux linkage (Wb) 0.1827 Inductance (mH) 8.5

The simulation process of the motor begins with no-load operation at the rated speed of 1000r/min, and suddenly increases the load at 0.2s to 3N·m, and the entire simulation time is 0.5s. The comparison of velocity waveforms of PI control and bi-predictive model control is shown in Fig. 3. From the simulation results in Fig. 3, it is concluded that when the motor starts under no-load condition, the PI control algorithm will produce obvious overshoot and vibration, the rise and adjustment time will become longer, and the sudden increase of load will decrease due to the long response time Speed, the start-up speed of the dual predictive model control method is faster, and the performance is improved compared with PI control. There is virtually no overshoot and the response is fast, reaching rated speed seamlessly. When the load suddenly increases and the speed drops, the system responds faster, the speed drops, the adaptability is enhanced, and the system reliability and stability are further improved.

As shown in Figure 4, it can be seen intuitively that the dq axis current error range is wide under the traditional PI control method. After the load is applied under PI control, the id of the system is not maintained at a level close to zero. Under the PMSM system The response time of the q-axis current is relatively fast, but the fluctuation is more obvious.

As shown in Figure 5, in the dual model predictive control method, the q-axis current tracking error range is better optimized, the range is narrower, and the q-axis can track the given value more accurately, so that the system has higher precision and Better dynamic and static control effects, while the dual-model prediction system optimizes the value range of id and maintains it at a level close to zero.

As shown in Figure 6, the PMSM electromagnetic torque waveform under PI control has obvious overshoot and jitter, and there is a large torque fluctuation as a whole.

As shown in Figure 7, although a certain response time is required in the initial stage, the waveform is relatively gentle without large overshoot and chattering. Therefore, the output phase current of the method proposed by the present invention has better sinusoidal quality and can maintain the normal state of the current control, further improving the dynamic performance of the current control.

According to the simulation results and analysis, the double MPC strategy has good control performance. Compared with the traditional control method, the PMSM control system has almost no obvious overshoot, and the quality of the sine wave output phase current is very good. In addition, the dual MPC strategy provides more general performance, faster dynamic response and stronger ability to resist load disturbance.

Claims (5)

1. The control method of the permanent magnet synchronous motor based on the double-prediction control is characterized by comprising the following steps of:

(1) Establishing a mathematical model of the permanent magnet synchronous motor: in a PMSM control system, a surface-mounted permanent magnet synchronous motor is adopted as a research object, and a related formula is deduced from 4 aspects of voltage, AC/DC speed, torque and mechanical motion equation in a double synchronous rotation coordinate system;

(2) Designing a current loop prediction controller: applying a dead beat prediction control strategy to the current internal control of the permanent magnet synchronous motor; the dead beat predictive current control is digital discrete control, the motor current obtained through sampling is compared with a given current through coordinate transformation, the comparison result is controlled by a dead beat current controller, the output voltage is subjected to coordinate transformation, and the space vector pulse width modulation SVPWM modulator module is used for enabling the inverter to generate a corresponding switching signal, so that the click feedback current in the next switching period can follow the given current;

(3) Designing an outer loop speed MPC controller: applying MPC to the speed loop to improve the control performance of the system; the MPC estimates the state of each moment in the future through a corresponding prediction model, takes an evaluation function as a criterion, adopts a rolling optimization mode to determine the optimal solution at the current moment, and adjusts the deviation between the output predicted value and the expected value through feedback correction;

(4) Establishing a simulation model of a control system: a double-model prediction strategy is adopted on the basis of a mathematical model of the permanent magnet synchronous motor, a model prediction controller is applied to an outer ring of the system, namely a speed ring, and a dead beat prediction controller is applied to an inner ring of the system, namely a current ring.

2. The method for controlling a permanent magnet synchronous motor based on double predictive control according to claim 1, wherein the step (1) is specifically:

(1.1) dead beat predictive Current controller

The current state equation is as follows:

the formula (1) is rewritten into a matrix form:

the Lawster transformation of formula (2) can be obtained:

wherein t is ₀ For the sampling initial time, τ is the integration time constant; motor sampling period t=0.0001 s andthe mechanical time constant of the motor is far greater than the current time constant, so that the motor rotating speed is unchanged in the adjacent sampling period, and the electromotive force is unchanged; at this time, let t ₀ =kt, t= (k+1) T, resulting in the following expression:

i(k+1)＝F(k)i(k)+A ₀ ^-1 (F(k)-E)(B ₀ u(k)+D ₀ ) (4)

wherein,,

since the sampling period T is small, it is considered that:cosω _e T≈1、sinω _e T≈ω _e T、/>cosω _e T≈1、sinω _e T≈ω _e T；

the matrix F (k) after simplification is:

at this time, a discretized PMSM state equation is obtained as follows:

i(k+1)＝F(k)i(k)+Gu(k)+H(k) (5)

wherein,,

the control voltage can be obtained by solving:

u(k)＝G ^-1 (i(k+1)-F(k)i(k)-H(k))(6)

in a dead beat predictive current control algorithm, i is used to satisfy the requirement that current can follow a given value ^* (k+1) instead of i (k+1) in the above formula, the output voltage thereof is expressed as follows:

u(k)＝G ^-1 (i ^* (k+1)-F(k)i(k)-H(k)) (7)

wherein i (k) is a current value obtained by sampling in the motor;

as the invention takes the surface-mounted permanent magnet synchronous motor as a research object, the motor meets the L requirement _d ＝L _q =l, so the electromagnetic torque equation at this point is:

wherein i is _q And i _s The included angle is beta;

for formula (8), wherein P _n 、Ψ _f Are all constant, so that the magnitude of the electromagnetic torque depends on the q-axis current, which in turn is equal to i _s In relation to β, where sin β=1 is known, i.e. when β=90°, there is i _q ＝i _s That is, the torque current is entirely composed of the stator current, so that the operation efficiency of the motor reaches the maximum at this time; it is thus obtained that, if high performance operation of the motor is desired, the torque-to-current ratio thereof should be maximized to maximize the d-axis current thereof, i.e., i ^* _d ＝0；

(1.2) model predictive speed controller

Discrete state equation of the velocity prediction model:

t is the sampling period, k is the current time;

in order to facilitate the calculation of the influence of neglecting load disturbance, the speed prediction model equation at this time is:

i in the above _q (k) The method can be written as follows:

i _q (k)＝i _q (k-1)+Δi _q (k) (3)

for the convenience of calculation, the invention adopts two-step prediction, and the speeds at k+1 and k+2 predicted at k moment are respectively written as omega _rm (k+1)、ω _rm (k+2)；

The state equation obtained by combining the formulas (2) and (3) is as follows:

order the

Bringing (8) into (6) and (7) can be simplified to obtain:

let formula (9) rewrite to matrix form, namely:

the carry-over (9) according to formula (10) can be written as:

ω _rm ＝ω _r0 +GΔi _q (11)

in order to reduce the model calculation error, model error correction is required to be added, and the prediction model is generally corrected approximately by adopting the deviation between the predicted value and the actual value at the previous moment; for omega after adding error correction term _rm (k+1)、ω _rm (k+2) are denoted as ω respectively _rM (k+1)、ω _rM (k+2) whose corresponding state equation is:

omega in the above formula (12) _rm (k+1) is changed to ω _rM (k+1), the correction term that can be obtained for the prediction model is:

for formula (13), let

According to formula (14), formula (13) may be written as:

ω _rM ＝ω _rm +e (15)

according to the commonly used performance index, a quadratic performance index is selected as an evaluation function, namely:

in the above formula, the first term is a constraint term of the deviation magnitude, the second term is a constraint term of the control quantity, q _i 、r _j Is a weight coefficient;

in equation (16), since the velocity is expected at the time of k+1, k+2Cannot be directly obtained, so that a first-order exponential form is adopted to obtain the reference track, namely:

in the formula (17), the amino acid sequence of the compound,wherein T is _c Is a time constant;

solving the optimal delta i according to the principle of rolling optimization _q It is necessary that the formula (16) satisfies:

solving for (18) to obtain Δi _q The method comprises the following steps:

in the method, in the process of the invention,

combining the formula (5) with the formula (19), wherein the control law of the final surface-mounted PMSM model predictive controller is as follows:

(2) Load disturbance compensation

Because the second part model predicts the speed controller part and ignores the load disturbance, in order to improve the control precision, the load disturbance is compensated, and the torque equation and the motion equation of the permanent magnet synchronous motor are combined,

the q-axis current to be compensated for load disturbances is derived as:

load torque T _L Cannot be directly obtained, so thatThe current compensation is carried out by a fractional order integration method, so that the system error is reduced by means of the integration effect, and the system robustness is enhanced; the invention adopts a caputo fractional order, and the expression is as follows:

in the above-mentioned (22),an alpha-order derivative or integral of the function f (t), alpha > 0 representing the derivative and alpha < 0 representing the integral; t is t ₀ N is N and N-1 < alpha < N, which is the initial value of the variable t;

taking the deviation amount of the speed as an input quantity, obtaining q-axis compensation current after fractional integration action of a formula (22), namely:

finally, the control law of the model predictive speed controller is changed into after the compensation current is obtained by combining the formula (23) and the formula (20):

3. the method of claim 1, wherein the MPC in step (3) includes reference trajectory, prediction model, feedback correction and rolling optimization.

4. A computer storage medium having stored thereon a computer program which, when executed by a processor, implements a bi-predictive control based permanent magnet synchronous motor control method according to any one of claims 1-3.

5. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements a bi-predictive control based permanent magnet synchronous motor control method according to any of claims 1-3 when executing the computer program.