CN109639192B - Surface-mounted permanent magnet synchronous motor time-sharing control system and time-sharing control method - Google Patents

Abstract

The invention discloses a surface-mounted permanent magnet synchronous motor model prediction control time-sharing control method, which mainly comprises the following steps: (1) setting the enabling signal to be low level at the sampling time k, and enabling the second finite set model predictive controller to carry out i_dAdjusting; (2) predicting the current value at the k +1 moment according to the current moment; (3) selecting the switch state which minimizes the cost function as the optimal switch state to be adopted at the moment k + 1; (4) setting an enabling signal to be a high level at a sampling moment k +1, and enabling the first finite set model prediction controller to carry out rotating speed tracking; (5) predicting the rotating speed value at the k +2 moment according to the current moment; (6) and selecting the switch state which minimizes the cost function as the optimal switch state to be adopted at the moment k + 2. The invention avoids the solution of the nonlinear problem, greatly reduces the calculation workload, improves the real-time performance of control, realizes the high dynamic performance of the motor and reduces the torque pulsation of the motor.

Description

Surface-mounted permanent magnet synchronous motor time-sharing control system and time-sharing control method

Technical Field

The invention belongs to the technical field of permanent magnet synchronous motor control, and particularly relates to a surface-mounted permanent magnet synchronous motor time-sharing control system and a time-sharing control method.

Background

The control of surface-mounted permanent magnet synchronous motors must take into account two issues. One is high dynamic performance. Since the reference rotation speed of the motor may suddenly increase or decrease, the actual rotation speed of the motor must be quickly adjusted to quickly track the reference rotation speed, which may be regarded as an online optimal control problem. Secondly, the actual operation of the motor is subject to constraints such as stator current constraints and voltage limitations. In view of these two problems, the control of the surface-mounted permanent magnet synchronous motor can be regarded as a constrained online optimal control problem. Model predictive control is a method that is applicable to such control problems because it has the ability of the system to handle constraints. Model predictive control methods can be divided into two categories: a continuous control set and a limited control set. In both methods, the finite set model predictive control is more suitable for control of the electric drive system. Since the finite set model predictive control directly uses the switching states (0: off, 1: on) of the power converter as control signals, no complex pulse width modulation is required.

In the finite set model predictive control, a predictive model is employed to predict the state behavior of a controlled object. The predictive model generally prefers a linear state space model because it can eventually be translated into a linear model predictive control problem to solve. However, the surface-mounted permanent magnet synchronous motor is a nonlinear and strong coupling system, and a linear mathematical model is difficult to obtain even in a d-q coordinate system. To solve this problem, different solutions have been proposed in the existing literature. These methods can be roughly classified into a linearization method, a multi-model predictive control method, and a nonlinear model predictive control method based on an intelligent model. The linear method is roughly thought as follows: the nonlinear model is linearized using a feedback linearization technique, handled by a typical linear model predictive control. However, this approach does not deal effectively with constraints, and the linearized model is only effective over a very small working range; the multiple model prediction control methods adopt piecewise linear description of the nonlinear model, have the advantages of simple calculation and real-time operation, but because a new linearized model is used at each sampling moment, the loss of dynamic information is inevitable. Therefore, in the case of a constantly changing model, the feasibility of this method cannot be ensured; there are also some non-linear model predictive controls based on intelligent models, such as neural network model predictive control and fuzzy model predictive control, which aim to overcome such non-linearity. The methods are used for predicting the behavior of a nonlinear system by training a prediction model, however, the methods are difficult to be widely applied at present due to the problems of long model training time, large calculation amount and the like.

Disclosure of Invention

The invention aims to provide a surface-mounted permanent magnet synchronous motor time-sharing control system and a time-sharing control method, so as to solve the problems.

In order to achieve the purpose, the invention adopts the following technical scheme:

a surface-mounted permanent magnet synchronous motor time-sharing control system comprises a control module, an inverter and a surface-mounted permanent magnet synchronous motor; the control module is connected with an inverter, and the inverter is connected with a surface-mounted permanent magnet synchronous motor; the control module comprises a first finite set model predictive controller and a second finite set model predictive controller; the first finite set model prediction controller and the second finite set model prediction controller are connected with the inverter through the gating switch; the first finite set model prediction controller is used for tracking the rotating speed of the surface-mounted permanent magnet synchronous motor, and the second finite set model prediction controller is used for tracking the i of the surface-mounted permanent magnet synchronous motor_dAnd (6) adjusting.

A time-sharing control method of a surface-mounted permanent magnet synchronous motor time-sharing control system is based on the surface-mounted permanent magnet synchronous motor time-sharing control system and comprises the following steps:

step 1, establishing a nonlinear mathematical model of a controlled object, wherein the controlled object is an inverter and a surface-mounted permanent magnet synchronous motor;

step 2, decoupling the nonlinear model in the step 1 into two linear submodels;

and 3, setting an enabling signal as a low level at the sampling time k, and enabling the second finite set model prediction controller to carry out i of the surface-mounted permanent magnet synchronous motor_dAdjusting;

step 4, predicting the current value at the k +1 moment according to the current moment;

step 5, selecting the switch state which minimizes the cost function as the optimal switch state S to be adopted at the moment of k +1_{abc_d}；

Step 6, setting an enabling signal to be a high level at a sampling time k +1, and enabling the first finite set model prediction controller to carry out rotating speed tracking;

step 7, predicting the rotating speed value at the k +2 moment according to the current moment;

step 8, selecting the switch state which minimizes the cost function as the optimal switch state S to be adopted at the moment of k +2_{abc_ω}。

Further, in step 1, the mathematical model includes:

1) two-level inverter modeling

Using vector S ═ S_a，S_b，S_c]^TTo indicate the switching state of the two-level inverter; the switching state per half bridge can be expressed as follows:

x represents a certain phase bridge arm, and A, B or C is taken; in a d-q coordinate system, by using the switching state function, the relationship between the stator voltage and the switching state of the two-level inverter is obtained as follows:

wherein,

here V_dAnd V_qIs d-axis and q-axis stator voltage, V_dcIs the dc bus voltage, θ is the rotor electrical angle; the selected switch state S is used as the optimal control action;

2) surface-mounted permanent magnet synchronous motor modeling

Neglecting the influence caused by magnetic core saturation, hysteresis and eddy current loss, and the influence of external temperature and humidity on the permanent magnet flux linkage when the motor runs; and the magnetic field generated by the permanent magnet is considered to be always sinusoidal, under the condition, the mathematical model of the surface-mount permanent magnet synchronous motor in the d-q coordinate system is as follows:

i herein_d，i_q，V_d，V_qRespectively representing stator current and voltage in a d-q coordinate system, L being the equivalent inductance of the stator winding in the d-q coordinate system, R being the stator resistance, #_fIs a permanent magnet flux linkage, p_nIs the number of pole pairs, ω_mIs the rotor mechanical angular velocity;

the torque equation and the mechanical motion equation are expressed as follows:

T_eis the electromagnetic torque, J is the motor moment of inertia, T_LIs the load torque;

writing (3) - (5) into the form of a state space expression is as follows:

as can be seen from (6), the state space model contains a nonlinear term ω_mi_dAnd ω_mi_q。

Further, in step 2, the decoupling includes the following steps:

1)i_q-ω_mlinear submodel

In the non-linear model (6), i is selected_qAnd ω_mAs state variables, and assume i_d When 0, the model becomes a linear time-invariant state space model, i.e.:

discretizing (7) and S₁＝[S_a1，S_b1，S_c1]^TAsThe input variables, submodels (7) can be written as:

the output equation is:

wherein

T_sIs the sampling period, k represents the sampling instant;

in this equation, the output variable is ω_m(ii) a The linear submodel (8) adopts standard linear finite set model predictive control to realize omega_mAdjusting;

2)i_dlinear submodel

In (6), i is_dSet as a state variable, and i_qAnd ω_mRegarded as constant, the nonlinear model (6) becomes another linear state space sub-model:

(10) further discretized, and when switching state S₂＝[S_a2，S_b2，S_c2]^TAs input variables of the two-level inverter:

the output equation is:

in this connection, it is possible to use,

where the output variable is i_d(ii) a The submodel (11) is also a linear time-invariant model.

Further, in step 6, the first finite set model predictive controller is based on i_q-ω_mThe linear submodels (8) to (9) of (a); at each sampling instant k +1, the cost function of the first finite set model predictive controller is designed to:

here Y₁(k)＝[y₁(k+1|k),y₁(k+2|k),…,y₁(k+H|k)]^T,Y_ref1(k)＝[y_ref1(k+1|k),y_ref1(k+2|k),…,y_ref1(k+H|k)]^T(k + h | k) represents a value at the k + h time predicted based on the available information at the k time; u shape₁(k) Indicating the control sequence at time k, i.e. U₁(k)＝[u₁(k+1),u₁(k+2),…,u₁(k+H)]^T；W_β1＝diag(β₁)and W_1-β1＝diag(1-β₁) Is a weight matrix of two optimization objectives; setting the prediction time domain and the control time domain as H; in the cost function, a predicted value y of the output is calculated according to the state space model (9)₁(k + h | k); thus predicting the output value y₁(k + h | k) with respect to switch state [ u [ ]₁(k),u₁(k+1),…,u₁(k+H)]^TThe function of (a) is expressed as follows:

y₁(k+h|k)＝C₁A₁ ^hx₁(k)+C₁A₁ ^h-1(B₁u₁(k+1)+E₁z₁(k))

+C₁A₁ ^h-2(B₁u₁(k+2|k)+E₁z₁(k+1|k))+C₁A₁ ¹(B₁u₁(k+h|k)+E₁z₁(k+h-1|k)) (14)

Y₁(k) expressed in matrix form as follows:

wherein

In practical applications, the output voltage and current should be limited in consideration of the output capacity of the two-level inverter. We apply the following linear inequality constraint:

-i_q,max≤i_q(k+h|k)≤i_q,max,h＝1,2,...,H (16)

-V_q,max≤V_q(k+h|k)≤V_q,max,h＝1,2,...,H (17)

by the above derivation, the linear expression of the first finite set model predictive controller can be expressed in matrix form as:

s.t.L₁U₁(k)≤K₁(19)

here, the number of the first and second electrodes,

L₁and K₁Is a linear inequality constraint matrix associated with (16) and (17).

Further, in step 3, a second finite set model predictive controller is based on i_dThe linear submodels (11) to (12) of (a); at each sampling instant k, the cost function of the second finite set model predictive controller is designed to:

the voltage and current inequalities are constrained as follows:

-i_d,max≤i_d(k+h|k)≤i_d,max,h＝1,2,...,H (23)

-V_d,max≤V_d(k+h|k)≤V_d,max,h＝1,2,...,H (24)

the second finite set model predictive controller problem is described in matrix form as follows:

s.t.L₂U₂(k)≤K₂ (26)

wherein,

L₂and K₂Is a linear inequality constraint matrix associated with (23) and (24).

Further, in steps 5 and 8, the selected range of the switch states is 18 state space vectors.

Compared with the prior art, the invention has the following technical effects:

the invention is based on_dAnd (3) decoupling the nonlinear state space model of the surface-mounted permanent magnet synchronous motor into two linear state space submodels according to a 0 control principle. Based on the two sub-models, two linear finite set model predictive controllers are designed. Therefore, the problem of the original nonlinear model predictive control can be solved by the enabling control of two linear finite set model predictive controllers, the solution of the nonlinear problem is avoided, and the reduction is greatly reducedThe calculation workload is increased, and the real-time performance of control is improved; meanwhile, the high dynamic performance of the motor is realized; the selection range of the switch state is changed from the traditional 8-state space vector to the 18-state space vector, so that the harmonic wave of a flux linkage is reduced, and the torque ripple of the motor is reduced.

Drawings

FIG. 1 is a finite set model predictive control principle;

FIG. 2 is a diagram of alternative switch states for conventional finite set model predictive control;

fig. 3 shows 18 switching states of the inverter available at each instant;

FIG. 4 is a schematic diagram of a model predictive control time-sharing control method studied by the present invention.

Detailed Description

The invention is further described below with reference to the accompanying drawings:

referring to fig. 1 to 4, a time-sharing control method of a surface-mounted permanent magnet synchronous motor time-sharing control system is based on a surface-mounted permanent magnet synchronous motor time-sharing control system, which includes a control module, an inverter and a surface-mounted permanent magnet synchronous motor; the control module is connected with an inverter, and the inverter is connected with a surface-mounted permanent magnet synchronous motor; the control module comprises a first finite set model predictive controller and a second finite set model predictive controller; the first finite set model prediction controller and the second finite set model prediction controller are connected with the inverter through the gating switch; the first finite set model prediction controller is used for tracking the rotating speed of the surface-mounted permanent magnet synchronous motor, and the second finite set model prediction controller is used for tracking the i of the surface-mounted permanent magnet synchronous motor_dAnd (6) adjusting.

The method comprises the following steps:

step 1, establishing a nonlinear mathematical model of a controlled object, wherein the controlled object is an inverter and a surface-mounted permanent magnet synchronous motor;

step 2, decoupling the nonlinear model in the step 1 into two linear submodels;

and 3, setting an enabling signal as a low level at the sampling time k, and enabling the second finite set model prediction controller to carry out i of the surface-mounted permanent magnet synchronous motor_dAdjusting;

step 4, predicting the current value at the k +1 moment according to the current moment;

step 5, selecting the switch state which minimizes the cost function as the optimal switch state S to be adopted at the moment of k +1_{abc_d}；

Step 6, setting an enabling signal to be a high level at a sampling time k +1, and enabling the first finite set model prediction controller to carry out rotating speed tracking;

step 7, predicting the rotating speed value at the k +2 moment according to the current moment;

step 8, selecting the switch state which minimizes the cost function as the optimal switch state S to be adopted at the moment of k +2_{abc_ω}。

1. System description and modeling

1.1 mathematical model building

In finite set model predictive control, a cost function should be defined to find the optimal control action. In each control cycle, the switching state that minimizes the cost function is selected as the optimal state and applied to the inverter in the next control cycle. In the present invention, we focus on how to select the switching state to achieve high dynamic performance of the surface-mounted permanent magnet synchronous motor, so we need to model the two-level inverter and the surface-mounted permanent magnet synchronous motor.

1.1.1 two-level inverter modeling

We use the vector S ═ S_a，S_b，S_c]^TTo indicate the switching state of the two-level inverter. The switching state per half bridge can be expressed as follows:

and x represents a certain phase bridge arm, and can be A, B or C. By using the switching state function in the d-q coordinate system, we can obtain the relationship between the stator voltage and the switching state of the two-level inverter as follows:

wherein,

here V_dAnd V_qIs d-axis and q-axis stator voltage, V_dcIs the dc bus voltage and θ is the rotor electrical angle. In the proposed finite set model predictive control method, the selected switch state S will be the optimal control action.

1.1.2 surface-mounted permanent magnet synchronous motor modeling

The modeling of the surface-mounted permanent magnet synchronous motor is based on the following assumptions: neglecting the influence caused by saturation, hysteresis and eddy current loss of the magnetic core, and the influence of external conditions (such as temperature and humidity) on the permanent magnet flux linkage when the motor operates. And the magnetic field produced by the permanent magnet is considered to be always sinusoidal. Under the condition, the mathematical model of the surface-mount permanent magnet synchronous motor in the d-q coordinate system is as follows:

i herein_d，i_q，V_d，V_qRespectively representing stator current and voltage in a d-q coordinate system, L being the equivalent inductance of the stator winding in the d-q coordinate system, R being the stator resistance, #_fIs a permanent magnet flux linkage, p_nIs the number of pole pairs, ω_mIs the rotor mechanical angular velocity.

The torque equation and the mechanical motion equation are expressed as follows:

T_eis the electromagnetic torque, J is the motor moment of inertia, T_LIs the load torque.

Writing (3) - (5) into the form of a state space expression is as follows:

as can be seen from (6), the state space model contains a nonlinear term ω_mi_dAnd ω_mi_q. Therefore, the finite set model predictive control based on the model is nonlinear model predictive control and needs to be solved by adopting a nonlinear method, and no effective solution is available for the nonlinear problem of the finite set model predictive control at present.

1.2 decoupling of the nonlinear model into two linear submodels

In the present invention using i_dThe method is characterized in that a control strategy of 0 is used for achieving the aim of tracking the rotating speed of the surface-mounted permanent magnet synchronous motor, so that the finite set model predictive control has two control aims. The main objective is to bring the actual rotational speed of the motor to a reference value, while the second objective is to keep the d-axis current at 0. These two goals can be achieved by using two finite set model predictive controllers. The first controller is responsible for speed tracking, so its predictive model should be i_qAnd ω_mAs a state variable, the second controller is responsible for assigning i_dRemains zero, so its prediction model should be i_dConsidered as state variables.

1.2.1i_q-ω_mLinear submodel

In the non-linear model (6), if i is selected_qAnd ω_mAs state variables, and assume i_dWhen 0, the model becomes a linear time-invariant state space model, i.e.:

discretizing (7) and S₁＝[S_a1，S_b1，S_c1]^TAs input variables, the submodel (7) can be written as:

the output equation is:

wherein

T_sIs the sampling period and k denotes the sampling instant.

In this equation, the output variable is ω_m. The linear submodel (8) can adopt standard linear finite set model predictive control to realize omega_mAnd (6) adjusting.

1.2.2i_dLinear submodel

Similarly, in (6), if i is to be_dSet as a state variable, and i_qAnd ω_mRegarded as constant, the nonlinear model (6) becomes another linear state space sub-model:

(10) can be further discretized, and when in the switch state S₂＝[S_a2，S_b2，S_c2]^TAs input variables of the two-level inverter:

the output equation is:

in this connection, it is possible to use,

where the output variable is i_d. It is clear that the submodel (11) is also a linear time-invariant model.

So far, we have decoupled the nonlinear dynamic model (6) of the surface-mounted permanent magnet synchronous machine into two linear time-invariant models (8) and (11), and both use the switching state of the inverter as input variables for the two submodels. Thus, the nonlinear model predictive control problem can be converted into two linear model predictive control problems, which can be solved by time-sharing enabling of two finite set model predictive controllers.

2 time-sharing control method

As described in the previous section, the present invention requires the implementation of two control objectives, namely speed tracking and d-axis current regulation. In the present invention, these two control objectives are achieved by alternately enabling two finite set model predictive controllers.

2.1 a first finite set model predictive controller for speed tracking;

as described above, our control objectives are achieved by alternately enabling two finite set model predictive controllers. The first finite set model predictive controller is now designed to be responsible for speed tracking.

The first finite set model predictive controller is based on i_q-ω_mThe linear submodels (8) - (9) are designed. Since the control target is the rotation speed tracking, at each sampling moment k, the cost function of the first finite set model predictive controller can be designed as:

here Y₁(k)＝[y₁(k+1|k),y₁(k+2|k),…,y₁(k+H|k)]^T,Y_ref1(k)＝[y_ref1(k+1|k),y_ref1(k+2|k),…,y_ref1(k+H|k)]^TAnd (k + h | k) represents a value at the time k + h predicted based on the available information at the time k. U shape₁(k) Indicating the control sequence at time k, i.e. U₁(k)＝[u₁(k+1),u₁(k+2),…,u₁(k+H)]^T。W_β1＝diag(β₁)and W_1-β1＝diag(1-β₁) Are the weight matrices of the two optimization objectives. For simplicity, the prediction and control time domains are set to H. In the cost function, the output prediction value y can be calculated according to the state space model (9)₁(k + h | k). Thus predicting the output value y₁(k + h | k) with respect to switch state [ u [ ]₁(k),u₁(k+1),…,u₁(k+H)]^TThe function of (a) is expressed as follows:

y₁(k+h|k)＝C₁A₁ ^hx₁(k)+C₁A₁ ^h-1(B₁u₁(k+1)+E₁z₁(k))

+C₁A₁ ^h-2(B₁u₁(k+2|k)+E₁z₁(k+1|k))+C₁A₁ ¹(B₁u₁(k+h|k)+E₁z₁(k+h-1|k)) (14)

Y₁(k) expressed in matrix form as follows:

wherein

In practical applications, the output voltage and current should be limited in consideration of the output capacity of the two-level inverter. We apply the following linear inequality constraint:

-i_q,max≤i_q(k+h|k)≤i_q,max,h＝1,2,...,H (16)

-V_q,max≤V_q(k+h|k)≤V_q,max,h＝1,2,...,H (17)

by the above derivation, the linear expression of the first finite set model predictive controller can be expressed in matrix form as:

s.t.L₁U₁(k)≤K₁(19)

here, the number of the first and second electrodes,

L₁and K₁Is a linear inequality constraint matrix associated with (16) and (17).

2.2 for i_dTuned second finite set model predictive controller

In this subsection, designing a second finite set model predictive controller is responsible for i_dAnd (6) adjusting. The second finite set model predictive controller is based on i_dThe linear submodels (11) - (12) of (1) are designed. The design method is similar to the first finite set model predictive controller. At each sampling instant k, the cost function of the second finite set model predictive controller is designed to:

the voltage and current inequalities are constrained as follows:

-i_d,max≤i_d(k+h|k)≤i_d,max,h＝1,2,...,H (23)

-V_d,max≤V_d(k+h|k)≤V_d,max,h＝1,2,...,H (24)

the second finite set model predictive controller problem is described in matrix form as follows:

s.t.L₂U₂(k)≤K₂(26)

wherein,

L₂and K₂Is a linear inequality constraint matrix associated with (23) and (24).

2.3 time-sharing control of two finite set model predictive controllers

We use the vector S_{abc_d}＝[S_{a_d},S_{b_d},S_{c_d}]^TAnd S_{abc_ω}＝[S_{a_ω},S_{b_ω},S_{c_ω}]^TRespectively, the optimal control actions calculated by the first and second finite-set model predictive controllers. But only one of them will be applied to the inverter at each control moment. To solve this problem, the present invention proposes a time-sharing control strategy aimed at achieving two different control objectives by alternately enabling two controllers.

A schematic diagram of the proposed time-sharing control method is shown in fig. 4. The basic idea is as follows: when the enable signal is at a low level, the second finite set model predictive controller is enabled and the switch state S is applied_{abc_d}To the inverter, thereby controlling the d-axis current of the motor to be 0. Conversely, when the enable signal is high, the first finite set model predictive controller is enabled, and the switch state S is set_{abc_ω}Is applied to an inverter to control the rotation speed of a motorFollowing the reference trajectory. That is, the alternate enabling of the two finite set model predictive controllers is achieved by time-sharing control signals. Thus at time k, the d-axis current is controlled to be near 0, and at time k +1, the d-axis and q-axis currents are considered to be completely decoupled. This ensures the accuracy of the state space submodel (7), which is important for the first finite set model predictive controller.

The first and second finite-set model predictive controllers have different control objectives, and therefore when one of them is enabled, its control action may be detrimental to the other control objective. On the one hand, when the second finite set model predictive controller is operated, the rotation speed is reduced. Similarly, when the first finite set model predictive controller is operating, the d-axis current may run away and may deviate from around 0, so the length of each controller run time is critical to dynamic performance. On the other hand, the enabling frequency of the two finite set model predictive controllers is too high, so that the current is not 0, and the motor rotating speed cannot be tracked. The frequency of the control signal is also important. Therefore, the setting of the time-sharing control enable signal requires attention to the action time and the signal frequency.

In summary, the rotation speed tracking of the surface-mounted permanent magnet synchronous motor can be realized through time-sharing control of the first finite-set model predictive controller and the second finite-set model predictive controller. That is, the original nonlinear model predictive control problem is solved by two linear model predictive control problems.

3. 18 state space vector

Fig. 2 shows conventional 8 space voltage vectors, and if 6 effective space vectors act in sequence once per cycle, that is, the working state is changed every pi/3 degrees, and the switching state is kept unchanged within pi/3 degrees, the formed flux linkage is a six-beat step wave. Obviously, the harmonic components of the flux linkage formed by the 6 effective vector states are larger than the harmonic components of the flux linkage formed after the traditional state space vector modulation, which can cause larger torque ripple. To reduce the torque ripple, it is common to increase the switching frequency of the inverter. However, this would add to the controller's countThe switching losses are also greater, despite the burden. Therefore, in order to reduce the harmonic components, the present invention employs a control method of combining space vectors. The 6-state voltage space vector divides one period into 6 sectors, namely, a plurality of space vectors are inserted into each sector to achieve the purpose of reducing harmonic components. E.g. using V in the I-th sector₁、V₂Synthesis of V₁₂Vector, newly formed combined space vector V₁₂Phase sum V₁、V₂The vectors are different but the magnitudes are the same. Similarly, V can be inserted into other sectors₂₃、V₃₄、V₄₅、V₅₆、V₆₁. Since each combined space vector consists of two space vectors, essentially an 18-state voltage space vector is constructed. The order of combining vectors should place the latter vector in front of it and the former vector behind it, e.g. V₁、V₁₂、V₂The order of deployment is V₁、V₂、V₁、V₂. The above-mentioned 18-state combined vector can be drawn end-to-end as a polygon as shown in fig. 3, which is obviously closer to a circle, indicating that the waveform harmonic component thereof will be smaller than the harmonic of the 6-state space vector, which will facilitate the reduction of the motor torque ripple and at the same time can reduce the switching frequency.

Claims (4)

1. A time-sharing control method of a surface-mounted permanent magnet synchronous motor time-sharing control system is characterized in that the surface-mounted permanent magnet synchronous motor time-sharing control system is based on the surface-mounted permanent magnet synchronous motor time-sharing control system and comprises a control module, an inverter and a surface-mounted permanent magnet synchronous motor; the control module is connected with an inverter, and the inverter is connected with a surface-mounted permanent magnet synchronous motor; the control module comprises a first finite set model predictive controller and a second finite set model predictive controller; the first finite set model prediction controller and the second finite set model prediction controller are connected with the inverter through the gating switch; the first finite set model prediction controller is used for tracking the rotating speed of the surface-mounted permanent magnet synchronous motor, and the second finite set model prediction controller is used for tracking the i of the surface-mounted permanent magnet synchronous motor_dAdjusting;

the method comprises the following steps:

step 1, establishing a nonlinear mathematical model of a controlled object, wherein the controlled object is an inverter and a surface-mounted permanent magnet synchronous motor;

step 2, decoupling the nonlinear model in the step 1 into two linear submodels;

and 3, setting an enabling signal as a low level at the sampling time k, and enabling the second finite set model prediction controller to carry out i of the surface-mounted permanent magnet synchronous motor_dAdjusting;

step 4, predicting the current value at the k +1 moment according to the current moment;

step 5, selecting the switch state which minimizes the cost function as the optimal switch state S to be adopted at the moment of k +1_{abc_d}；

Step 6, setting an enabling signal to be a high level at a sampling time k +1, and enabling the first finite set model prediction controller to carry out rotating speed tracking;

step 7, predicting the rotating speed value at the k +2 moment according to the current moment;

step 8, selecting the switch state which minimizes the cost function as the optimal switch state S to be adopted at the moment of k +2_{abc_ω}。

2. The time-sharing control method of the surface-mounted permanent magnet synchronous motor time-sharing control system according to claim 1, wherein in the step 1, the mathematical model comprises:

1) modeling a two-level inverter:

using vector S ═ S_a，S_b，S_c]^TTo indicate the switching state of the two-level inverter; the switching state function per half bridge is expressed as follows:

x represents a certain phase bridge arm, and A, B or C is taken; in a d-q coordinate system, by using the switching state function, the relationship between the stator voltage and the switching state of the two-level inverter is obtained as follows:

wherein,

here V_dAnd V_qIs d-axis and q-axis stator voltage, V_dcIs the dc bus voltage, θ is the rotor electrical angle; the selected switch state S is used as the optimal control action;

2) modeling a surface-mounted permanent magnet synchronous motor:

neglecting the influence caused by magnetic core saturation, hysteresis and eddy current loss, and the influence of external temperature and humidity on the permanent magnet flux linkage when the motor runs; and the magnetic field generated by the permanent magnet is considered to be always sinusoidal, under the condition, the mathematical model of the surface-mount permanent magnet synchronous motor in the d-q coordinate system is as follows:

i herein_d，i_q，V_d，V_qRespectively representing stator current and voltage in a d-q coordinate system, L being the equivalent inductance of the stator winding in the d-q coordinate system, R being the stator resistance, #_fIs a permanent magnet flux linkage, p_nIs the number of pole pairs, ω_mIs the rotor mechanical angular velocity;

the torque equation and the mechanical motion equation are expressed as follows:

T_eis the electromagnetic torque, J is the motor moment of inertia, T_LIs the load torque;

writing (3) - (5) into the form of a state space expression is as follows:

as can be seen from (6), the state space model contains a nonlinear term ω_mi_dAnd ω_mi_q。

3. The time-sharing control method of the surface-mounted permanent magnet synchronous motor time-sharing control system according to claim 1, wherein in the step 2, the decoupling comprises the following steps:

1)i_q-ω_mlinear submodel

In the non-linear model (6), i is selected_qAnd ω_mAs state variables, and assume i_dWhen 0, the model becomes a linear time-invariant state space model, i.e.:

discretizing (7) and S₁＝[S_a1，S_b1，S_c1]^TAs input variables, the submodel (7) is written as:

the output equation is:

wherein

T_sIs the sampling period, k represents the sampling instant;

in this equation, the output variable is ω_m(ii) a The linear submodel (8) adopts standard linear finite set model predictive control to realize omega_mAdjusting;

2)i_dlinear submodel

In (6), i is_dSet as a state variable, and i_qAnd ω_mRegarded as constant, the nonlinear model (6) becomes another linear state space sub-model:

(10) further discretized, and when switching state S₂＝[S_a2，S_b2，S_c2]^TAs input variables of the two-level inverter:

i_d(k+1)＝A₂i_d(k)+V_dcB_V2C_{sr_2}C_ssS₂+T_s(p_nω_mi_q) (11)

the output equation is: y is₂(k)＝i_d(k) (12)

In this connection, it is possible to use,

where the output variable is i_d(ii) a The submodel (11) is also a linear time-invariant model.

4. The time-sharing control method of the surface-mounted permanent magnet synchronous motor time-sharing control system according to claim 1, wherein the selection range of the switching state in the step 5 and the step 8 is an 18-state space vector.

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