CN114826075A - Double-time-scale parallel double-ring control method for high-speed permanent magnet motor - Google Patents

Abstract

The invention discloses a dual-time-scale parallel double-loop control method for a high-speed permanent magnet motor. Considering the speed tracking problem of the high-speed motor in the running process, the state parameters of the high-speed permanent magnet motor are collected, and a nonlinear system is established for the high-speed permanent magnet motor. The singular perturbation model, for the nonlinear singular perturbation model, decouples the d-axis, q-axis current and rotational speed of the high-speed permanent magnet motor, and obtains a linear current sub-model on a fast time scale and a nonlinear rotational speed sub-model on a slow time scale. . The sliding mode control law is designed based on the linear current tachyon model to improve the response speed and robustness of the current loop, and the H _∞ robust control law is designed based on the nonlinear slow speed sub-model to eliminate chattering and improve the speed loop resistance Interference ability. The present invention adopts a double-time-scale parallel double-loop control method, which effectively reduces the coupling degree and interaction degree of the inner and outer loops.

Description

A dual-time-scale parallel dual-loop control method for high-speed permanent magnet motors

technical field

The invention relates to the technical field of electric power transmission, in particular to a dual-time-scale parallel dual-loop control method for a high-speed permanent magnet motor.

Background technique

At present, the mainstream control methods in the motor field are mostly double-loop control strategies with a series structure. The input of the current loop is the output of the speed loop, and the two sub-controllers are connected in series. The cascade double closed-loop control strategy alleviates the contradictory and conflicting control indicators, and improves the control quality and control accuracy. In particular, if the response speed of the inner loop is significantly higher than that of the outer loop and the controller gain of the inner loop is greater than the gain of the outer loop, the resonance of the inner and outer loops can be effectively avoided. However, the cascade control strategy also has shortcomings: it requires measurable or appreciable internal and external loop variables, adding additional auxiliary measurement units or computational complexity, which greatly increases the complexity of the system model and the design cost of the controller. Moreover, the inner and outer loops of the cascade double closed-loop control are interactive, and the current dynamic characteristics of the inner loop will greatly affect the tracking performance of the outer loop speed, which leads to the complicated design process of the series inner and outer loop controllers with good control performance. ,difficulty.

In addition, in the high-speed motor drive system, the dynamic change rate of the current loop is on the order of milliseconds, and the dynamic change rate of the rotational speed loop is on the order of seconds. More specifically, in the transient process of the high-speed permanent magnet synchronous motor, the current response speed is fast, resulting in a huge current shock, threatening the reliability of the system, and the speed increase is slow. Due to the inherent characteristics of the dynamic performance of the electromechanical system, the electrical time constant is much smaller than the mechanical time constant, especially for high-speed motors, the inductance parameter is very small (about 10-4 order of magnitude), there are time scale differences between the state variables, and the system has a dual time Scale (Two TimeScale, TTS) characteristics. However, in the traditional motor series double-loop control algorithm, the same execution cycle is used for the sampling, observation, control signal calculation and parameter correction of the electromagnetic state and mechanical state. For the control problem of the dual time scale system, if the time scale is based on the slow scale of mechanical dynamics, it is difficult to make an appropriate and timely response to the electromagnetic dynamics on the fast time scale; if the time scale is based on the fast time scale of electromagnetic dynamics, Then the difference of the slow time scale dynamics is almost zero, resulting in a serious loss of significant digits, and then a huge error; and if the intermediate time scale is used as the benchmark, due to the significant difference between the fast and slow time scales, the processing of fast and slow dynamics will encounter similar problems at the same time. The ill-conditioned characteristic of , that is, the rigid characteristic. When a single time scale control strategy is applied to a dual time scale high-speed motor system, it will inevitably lead to the loss of effective information of the system or the numerical ill-conditioned problem in the process of digital control.

SUMMARY OF THE INVENTION

In view of the problems existing in the prior art, the present invention provides a dual-time-scale parallel-type dual-loop control method for high-speed permanent magnet motors, proposes a parallel-type dual-loop control strategy for the motor system, and breaks through the existing high-speed permanent-magnet synchronous motors. Control the bottleneck, realize the complete decoupling of the current loop and the speed loop, and improve the accuracy and robustness of the high-speed permanent magnet motor control.

In order to achieve the above-mentioned technical purpose, the present invention adopts the following technical scheme: a dual-time-scale parallel dual-loop control method for a high-speed permanent magnet motor, which specifically includes the following steps:

Step 1: Collect the state parameters of the high-speed permanent magnet motor, and determine the singular perturbation parameter ε according to the magnitude of the equivalent inductance of the d-axis winding and the equivalent inductance of the q-axis winding in the state parameters, and establish a singular perturbation nonlinear mathematical model;

Step 2: Use the singular perturbation theory to reduce the order and decouple the singular perturbation nonlinear mathematical model to obtain a nonlinear slow time scale sub-model, and linearize the nonlinear slow time scale sub-model to obtain n linear slow time scales. Invariant submodel;

Step 3: For n linear slow-time-invariant sub-models, combined with the threshold γ of the influence degree of noise on the state and each operating point, the H _∞ robust control law is obtained, and the slow time-scale control input u _s (t _k ) is calculated;

Step 4: Calculate the fast time scale parameter τ, change the time scale of the singularly perturbed nonlinear mathematical model to obtain a fast time scale sub-model, select the diagonal matrix M to solve the first positive definite matrix O and the second positive definite matrix Q, and calculate control input u _f (τ) of the fast time scale submodel;

Step 5: Input the calculated control input u(t _k ) of the slow time scale and the control input u _f (τ) of the fast time scale sub-model into the ultra-high-speed permanent magnet motor to perform dual-time-scale parallel dual-loop control.

Further, the collected state parameters of the high-speed permanent magnet motor include: the equivalent inductance of the d-axis winding, the equivalent inductance of the q-axis winding, the equivalent resistance of the winding, the permanent magnet flux linkage, the number of pole pairs of the motor, the moment of inertia, and the load torque. .

Further, the singular perturbation nonlinear mathematical model is:

为d轴绕组电流导数，r为绕组等效电阻，ω_e为角速度，L_q为q轴绕组等效电感，u_d为d轴绕组电压，

i_q为q轴绕组电流，

为q轴绕组电流导数，L_d为d轴绕线等效电感，u_q为q轴绕组电压，

为角速度导数，P_n为电机的极对数，J为转动惯量，ψ_f为永磁体磁链，T_l为负载转矩。where id is the _d -axis winding current,

is the d-axis winding current derivative, r is the winding equivalent resistance, ω _e is the angular velocity, L _q is the q-axis winding equivalent inductance, _ud is the d-axis winding voltage,

i _q is the q-axis winding current,

is the q-axis winding current derivative, L _d is the equivalent inductance of the d-axis winding, u _q is the q-axis winding voltage,

is the angular velocity derivative, P _n is the number of pole pairs of the motor, J is the moment of inertia, ψ _f is the permanent magnet flux linkage, and T _l is the load torque.

Further, the nonlinear slow time scale sub-model is:

为角速度的慢分量，

为角速度慢分量的导数，u_d为d轴绕组电压，u_q为q轴绕组电压，T_l为负载转矩，P_n为电机的极对数，J为转动惯量，

in,

is the slow component of the angular velocity,

is the derivative of the slow component of the angular velocity, ud is the _d -axis winding voltage, u _q is the q-axis winding voltage, T _l is the load torque, P _n is the number of pole pairs of the motor, J is the moment of inertia,

Further, the process of linearizing the nonlinear slow time-scale sub-model in step 2 is specifically: arranging the angular velocities of the high-speed permanent magnet motor in sequence, and dividing the angular velocity interval, the division is the operating point, and there are n operating points in total, and Linearize the nonlinear slow time-scale sub-model at the angular velocity interval division to obtain n linear slow-time-invariant sub-models, each of which is:

u_s(θ_j)为在θ_j处的慢子控制输入。Among them, θ _j is the operating point index, δω _e is the error between the measured value of the slow component of the current angular velocity and the operating point in the corresponding angular velocity interval,

u _s (θ _j ) is the bradyron control input at θ _j .

Further, step 3 includes the following substeps:

求出H_∞鲁棒控制律K(θ_j)；Step 3.1. The threshold of the influence degree of noise on the state is γ > 0. If there is a positive definite matrix P > 0, the following inequality conditions are satisfied

Find the H _∞ robust control law K(θ _j );

Step 3.2. Measure the angular velocity ω _e (t _k ) at time t _k , and calculate the first weighting coefficient α ₁ (t _k ) and the second weighting coefficient α ₂ (t _k ) according to the divided interval of the angular velocity:

ω _e (t _k )=α ₁ (t _k )θ _m +α ₂ (t _k )θ _m+1

α ₁ (t _k )+α ₂ (t _k )=1,

Among them, θ _m is the mth operation point, θ _m+1 is the m+1th operation point, ω _e (t _k )∈[θ _m , θ _m+1 ];

Step 3.3. According to the first weight coefficient α ₁ (t _k ) and the second weight coefficient α ₂ (t _k ), describe the H _∞ robust control law K(θ(t _k )) at time t k as: K(θ(t _k )) (t _k ))=α ₁ (t _k )K _m (θ _m )+α ₂ (t _k )K _m+1 (θ _m+1 ), and then calculate the slow time scale control input u _s (t _k )= K(θ(t _k ))δω _e (t _k ).

Further, step 4 includes the following sub-steps:

将奇异摄动非线性数学模型进行时间尺度更改，得到快时间尺度子模型：Step 4.1. Calculate fast time scale parameters

Change the time scale of the singularly perturbed nonlinear mathematical model to get the fast time scale submodel:

为d轴电流变量的快分量，

为q轴电流变量的快分量，

为d轴电压变量的快分量，

为q轴电压变量的快分量，t为时间变量，t₀初始时刻，

为慢变量ω_e的值。in,

is the fast component of the d-axis current variable,

is the fast component of the q-axis current variable,

is the fast component of the d-axis voltage variable,

is the fast component of the _q -axis voltage variable, t is the time variable, and t is the initial moment,

is the value of the slow variable ω _e .

其中，

为快时间尺度子模型的控制输入中忽略不确定输入的标称输入，s(τ)为滑模函数，||s(τ)||₂为滑模函数的二范数，h小正数。Step 4.2. Select the diagonal matrix M=diag{λ ₁ λ ₂ }>0 to solve the first positive definite matrix O and the second positive definite matrix Q, and calculate the control input of the fast time scale sub-model

in,

is the nominal input that ignores the uncertain input in the control input of the fast time scale sub-model, s(τ) is the sliding mode function, ||s(τ)|| ₂ is the second norm of the sliding mode function, h is a small positive number .

Compared with the prior art, the present invention has the following beneficial effects:

(1) In the traditional series double-loop control strategy, the control effect of the outer loop greatly affects the performance of the inner loop, the controller design is complex, and the parameter adjustment process is cumbersome; while the dual-time-scale parallel double-loop control method of the present invention fully considers high-speed permanent For the dual time scale characteristics of the magnetic motor, the singular perturbation method is used, and a parallel dual loop control method is proposed, which completely decouples the electromagnetic dynamic part and the mechanical dynamic part, reduces the model order, and weakens the interaction between the inner and outer loops;

(2) The present invention designs the sliding mode function in the fast time scale sub-model to meet the requirement of fast response in the fast time scale sub-model, and designs the H _∞ robust control law in the linear slow time-invariant sub-model to eliminate the sliding mode The "chattering" side effect brought by the mode control improves the anti-interference ability of the high-speed permanent magnet motor and ensures the safe performance of the operation;

(3) The dual-time-scale parallel dual-loop control method of the present invention is not limited to the control problem of high-speed permanent magnet motors, and can be applied to other electromechanical systems with obvious dual-time-scale characteristics.

Description of drawings

Fig. 1 is the flow chart of the dual-time-scale parallel dual-loop control method for high-speed permanent magnet motor of the present invention;

Fig. 2 is the simulation schematic diagram of the dual-time-scale parallel dual-loop control method for the high-speed permanent magnet motor according to the embodiment;

Fig. 3 is the control input effect diagram of the fast time scale sub-model in the embodiment, (a) in Fig. 3 is the input diagram of the d-axis winding tachyon controller, and (b) in Fig. 3 is the q-axis winding tachyon control the input graph of the device;

Fig. 4 is an input effect diagram of slow time scale control in the embodiment, (a) the input diagram of the d-axis winding slow sub-controller in Fig. 4, and (b) in Fig. 4 is the input diagram of the q-axis winding slow sub-controller ;

Figure 5 is a phase current diagram of phase A;

Figure 6 is a waveform diagram of the motor speed;

Fig. 7 is the q-axis winding current diagram;

Figure 8 is a d-axis winding current diagram.

Detailed ways

The technical solutions of the present invention will be further explained below with reference to the accompanying drawings.

Fig. 1 is the flow chart of the dual-time-scale parallel-type dual-loop control method for the high-speed permanent magnet motor of the present invention, and the dual-time-scale parallel-type dual-loop control method specifically includes the following steps:

Step 1: Collect the state parameters of the high-speed permanent magnet motor, including: the equivalent inductance of the d-axis winding, the equivalent inductance of the q-axis winding, the equivalent resistance of the winding, the permanent magnet flux linkage, the number of pole pairs of the motor, the moment of inertia, and the load torque ; And according to the order of magnitude of the equivalent inductance of the d-axis winding and the equivalent inductance of the q-axis winding in the state parameters, the singular perturbation parameter ε is determined, and the singular perturbation nonlinear mathematical model is established. The nonlinear mathematical model of the singular perturbation model can effectively describe The dual time scale characteristics of the engineering system, the main idea of the singular perturbation method is: decoupling-separate design-combination, by using the time scale difference of high-speed permanent magnet motor dynamics, implement forced decoupling on different time scales to achieve fast and slow decomposition 、Reduce the order of the high-speed permanent magnet motor, and design the fast and slow subsystem controllers separately, and combine them to form the controller of the high-speed permanent magnet motor. The establishment of the singular perturbation nonlinear mathematical model fully considers the time scale difference between the mechanical dynamics and the electromagnetic dynamics inside the high-speed motor, which can effectively improve the dynamic response performance. The singular perturbation nonlinear mathematical model in the present invention is:

为d轴绕组电流导数，r为绕组等效电阻，ω_e为角速度，L_q为q轴绕组等效电感，u_d为d轴绕组电压，

i_q为q轴绕组电流，

为q轴绕组电流导数，L_d为d轴绕线等效电感，u_q为q轴绕组电压，

为角速度导数，P_n为电机的极对数，J为转动惯量，ψ_f为永磁体磁链，T_l为负载转矩。where id is the _d -axis winding current,

is the d-axis winding current derivative, r is the winding equivalent resistance, ω _e is the angular velocity, L _q is the q-axis winding equivalent inductance, _ud is the d-axis winding voltage,

i _q is the q-axis winding current,

is the q-axis winding current derivative, L _d is the equivalent inductance of the d-axis winding, u _q is the q-axis winding voltage,

is the angular velocity derivative, P _n is the number of pole pairs of the motor, J is the moment of inertia, ψ _f is the permanent magnet flux linkage, and T _l is the load torque.

Step 2: The singular perturbation nonlinear mathematical model is reduced in order and decoupled by the singular perturbation theory, and the nonlinear slow time scale sub-model is obtained, thereby realizing the decoupling of the slow state and the fast state. In order to deal with the nonlinear characteristics of the slow time-scale sub-model, the nonlinear slow-time-scale sub-model is linearized by using the linear variable parameter theory, and n linear slow-time invariant sub-models are obtained, which greatly reduces the controller design difficulty of the slow sub-system. ;

Specifically: set ε=0 in formula (1)-(2), and inversely obtain the slow component id ^{s of the d-axis winding current and the slow component i q s} _{of the} ^q -axis winding current,

Substituting into formula (3), we get:

则本发明中非线性慢时间尺度子模型为：remember

Then the nonlinear slow time scale sub-model in the present invention is:

为角速度的慢分量，

为角速度慢分量的导数，u_d为d轴绕组电压，u_q为q轴绕组电压，T_l为负载转矩，P_n为电机的极对数，J为转动惯量。in,

is the slow component of the angular velocity,

is the derivative of the slow component of the angular velocity, ud is the _d -axis winding voltage, u _q is the q-axis winding voltage, T _l is the load torque, P _n is the number of pole pairs of the motor, and J is the moment of inertia.

The process of linearizing the nonlinear slow time scale sub-model in the present invention is as follows: arranging the angular velocities of the high-speed permanent magnet motor in sequence, and dividing the angular velocity interval. The nonlinear slow-time-scale sub-model is linearized at the division, and n linear slow-time-invariant sub-models are obtained. Each linear slow-time-invariant sub-model is:

It is further assumed that there is an interference signal δv in the model, c is the coefficient of the interference signal, and considering that the output of the slow subsystem is the rotational speed itself, then there are

y=δω _e (10)

u_s(θ_j)为在θ_j处的慢子控制输入。Among them, θ _j is the operating point index, δω _e is the error between the measured value of the slow component of the current angular velocity and the operating point in the corresponding angular velocity interval,

u _s (θ _j ) is the bradyron control input at θ _j .

The invention utilizes the linear variable parameter theory to realize the simplified processing of the nonlinear characteristics of the slow time scale sub-model. On the one hand, the design difficulty of the controller is reduced, and the calculation space of the controller design algorithm is saved; It is linearized at the high-speed motor and preserves the nonlinear dynamic characteristics of the high-speed motor. Step 3: Considering that there must be external interference in the system, the present invention designs H _∞ robust control law for the rotation speed loop to overcome the influence of external interference on the rotation speed, so that the rotation speed can stably follow the ideal rotation speed. Therefore, for n linear slow-time-invariant sub-models, the H _∞ robust control law is obtained by combining the threshold γ and each operating point of noise influence on the state, so that the closed-loop linear slow sub-model at the operating point θ _j is robust Stable, computes the slow timescale control input u _s (t _k ); includes the following sub-steps:

Step 3.1. Design a state feedback controller: u _s (t)=K(θ _j )δω _e , and substitute it into formulas (9)-(10) to obtain:

For the threshold γ>0 of the influence of noise on the state, if there is a positive definite matrix P>0, the following inequality conditions are satisfied

Find the H _∞ robust control law K(θ _j ); then formula (11) is asymptotically stable at the operating point θ _j , and the transfer function T _δvy (s) from disturbance δv to output y(t) satisfies robust Rod performance indicators

Next, in order to verify the reasonable validity of the proposed control scheme, a robust stability proof is carried out.

(1) First, it is proved that the closed-loop system is asymptotically stable in the case of zero disturbance.

Assuming δv=0, construct the Lyapunov function V(δω _e ,t)=δω _e ^T (t)Pδω _e (t), and derive the function V(δω _e ,t) for time t along equation (11) ,Available

According to Schur's complement lemma, the inequality (12) is equivalently transformed into

那么根据(13)式，显然有

由此可得，当扰动δv＝0时，公式(11)的平衡点是渐近稳定的。According to formula (14), it is obvious that

Then according to (13), it is obvious that

Therefore, when the disturbance δv=0, the equilibrium point of formula (11) is asymptotically stable.

(2) Next, it is proved that when δv≠0, under the condition of matrix inequality (12), the system is robust.

Taking the derivative of the function V(δω _e ,t) with respect to time t along Equation (11), we get

According to inequalities (14) and (15), it can be rewritten as

that is

further,

Based on the proof of the asymptotic stability of part (1), it can be known that δω _e (∞) = 0, now assuming δω _e (0) = 0, integrating both sides of inequality (16), we can get:

由此明显可得：which is

From this it is evident that:

也就是

that is

Step 3.2. Measure the angular velocity ω _e (t _k ) at time t _k , and calculate the first weighting coefficient α ₁ (t _k ) and the second weighting coefficient α ₂ (t _k ) according to the divided interval of the angular velocity:

ω _e (t _k )=α ₁ (t _k )θ _m +α ₂ (t _k )θ _m+1

α ₁ (t _k )+α ₂ (t _k )=1,

Among them, θ _m is the mth operation point, θ _m+1 is the m+1th operation point, ω _e (t _k )∈[θ _m , θ _m+1 ];

Step 3.3. According to the first weight coefficient α ₁ (t _k ) and the second weight coefficient α ₂ (t _k ), describe the H _∞ robust control law K(θ(t _k )) at time t k as: K(θ(t _k )) (t _k ))=α ₁ (t _k )K _m (θ _m )+α ₂ (t _k )K _m+1 (θ _m+1 ), and then calculate the slow time scale control input u _s (t _k )= K(θ(t _k ))δω _e (t _k ).

Step 4: Considering the rapidity of the current loop, the present invention selects the sliding mode control with good rapidity and robustness as the control method of the current loop, calculates the fast time scale parameter τ, and performs the singular perturbation nonlinear mathematical model. Change the time scale to obtain the fast time scale sub-model, select the diagonal matrix M to solve the first positive definite matrix O and the second positive definite matrix Q, and calculate the control input u _f (τ) of the fast time scale sub-model; including the following sub-steps:

将奇异摄动非线性数学模型进行时间尺度更改，即对公式(1)-(2)进行变换，得到：Step 4.1. Calculate fast time scale parameters

Change the time scale of the singular perturbation nonlinear mathematical model, that is, transform the formulas (1)-(2), and get:

和

为伪输入，将公式(9)-(10)整理为快时间尺度子模型，可以有效地描述解耦的快状态的动态特性；本发明中快时间尺度子模型为：where d(τ) is the noise, and the noise is bounded ||d(τ)|| ₂ <δ,δ>0, take

and

For pseudo input, formulas (9)-(10) are organized into fast time scale sub-models, which can effectively describe the dynamic characteristics of the decoupled fast state; the fast time scale sub-model in the present invention is:

为d轴电流变量的快分量，

为q轴电流变量的快分量，

为d轴电压变量的快分量，

为q轴电压变量的快分量，t为时间变量，t₀初始时刻，

为慢变量ω_e的值。in,

is the fast component of the d-axis current variable,

is the fast component of the q-axis current variable,

is the fast component of the d-axis voltage variable,

is the fast component of the _q -axis voltage variable, t is the time variable, and t is the initial moment,

is the value of the slow variable ω _e .

Step 4.2. Select the diagonal matrix M=diag{λ ₁ λ ₂ }>0 to solve the first positive definite matrix O and the second positive definite matrix Q, and calculate the control input of the fast time scale sub-model:

为快时间尺度子模型的控制输入中忽略不确定输入的标称输入，s(τ)为滑模函数，||s(τ)||₂为滑模函数的二范数，h小正数。in,

is the nominal input that ignores the uncertain input in the control input of the fast time scale sub-model, s(τ) is the sliding mode function, ||s(τ)|| ₂ is the second norm of the sliding mode function, h is a small positive number .

The first positive definite matrix O and the second positive definite matrix Q satisfy:

Next we prove the validity of formula (21):

If the parameters h>0, l>0 and the upper bound δ of interference are known, under the action of formula (21), the tracking error e(τ) of formula (20) tends to 0,

Construct the Lyapunov function

Taking the derivative of V(τ) with respect to τ, we get

where V _eq (τ)=-s ^T (τ)Qs(τ), V _N (τ)=-s ^T (τ)Osgn(s(τ)), where O and Q satisfy:

或者

or

The derivative of s(τ) can be expressed as:

Substitute formula (25) into formula (24) to obtain:

Inversely find u _f from the above formula:

和不确定部分

In fact, u _eq (τ) contains the nominal part

and the uncertain part

in

获得快子系统的控制器Based on the assumption ||d(t)|| ₂ <δ, the uncertainty component in u _eq (τ) can be ignored

Get the controller of the fast subsystem

已知l是小正数。将公式(25)代入公式(27)-(28)可得：In order to make the system converge in a finite time, it is necessary to

It is known that l is a small positive number. Substitute formula (25) into formulas (27)-(28) to obtain:

According to Schwarz's inequality, the sufficient conditions of (29) inequality can be obtained as follows:

Further, the above formula is equivalent to

In addition, in order to avoid chattering caused by the sign function, the following approximate function is introduced

Step 5: Input the calculated control input u(t _k ) of the slow time scale and the control input u _f (τ) of the fast time scale sub-model into the high-speed permanent magnet motor to perform dual-time-scale parallel dual-loop control.

The dual-time-scale parallel double-loop control method of the present invention for the high-speed permanent magnet motor fully considers the dual-time-scale characteristics of the high-speed motor, avoids the drawbacks of the single-time-scale series double-loop control, effectively reduces the dimension of the high-speed motor, and simplifies the The complexity of the controller design can significantly improve the dynamic response performance.

Example

The present embodiment adopts a high-speed rare earth permanent magnet motor as the experimental object, and the specific parameters of the high-speed rare earth permanent magnet motor are shown in Table 1:

Table 1 18000rmp/110W high-speed permanent magnet motor parameters

Phase equivalent resistance 0.22Ω Number of pole pairs 1 Phase equivalent inductance 0.0001H bus voltage 36V Magnet Flux Amplitude 0.0004 rated power 200W Rated speed 18000rpm Sampling frequency 20kHz

快时间尺度子模型采用滑模控制方法，慢时间尺度子模型采用基于线性变参数理论的H_∞控制方法。图3展示了快时间尺度子模型的控制输入效果图，图3中的(a)为d轴绕组快子控制器的输入图，图3中的(b)为q轴绕组快子控制器的输入图，可以看出快子控制器变化快速，响应快速；如图4为实施例中慢时间尺度控制输入效果图，图4中的(a)d轴绕组慢子控制器的输入图，图4中的(b)为q轴绕组慢子控制器的输入图，慢子控制器相对平稳，该实验结果与本发明双时间尺度并联式双环控制方法的设计预期一致。图5展示了A相相电流图，由图5可见在加入负载后，电流非常快速的收敛为正弦波形；图6为电机转速波形图，在负载突变后，转速在极短的时间内恢复平稳；图7展示了q轴绕组电流的波形图，可见q轴电流可以快速地跟踪理想值，跟踪效果很好；图8展示了d轴绕组电流波形图，纹波较小，静态性能很好。Figure 2 is a schematic diagram of the simulation of the dual-time-scale parallel dual-loop control method based on the high-speed permanent magnet motor in the embodiment. The function of the PI controller is to provide an ideal signal for the tachyon model.

The fast time scale sub-model adopts the sliding mode control method, and the slow time scale sub-model adopts the H _∞ control method based on the linear variable parameter theory. Figure 3 shows the control input effect diagram of the fast time scale sub-model. Figure 3 (a) is the input diagram of the d-axis winding tachyon controller, and Figure 3 (b) is the q-axis winding tachyon controller. In the input diagram, it can be seen that the tachyon controller changes rapidly and responds quickly; Figure 4 is the input effect diagram of the slow time scale control in the embodiment, and (a) the input diagram of the d-axis winding tachyon controller in Figure 4, Figure 4 (b) in 4 is the input diagram of the q-axis winding slow sub-controller, the slow sub-controller is relatively stable, and the experimental result is consistent with the design expectation of the dual-time-scale parallel dual-loop control method of the present invention. Figure 5 shows the current diagram of phase A. It can be seen from Figure 5 that after adding the load, the current converges very quickly to a sine waveform; Figure 6 is the waveform of the motor speed. After the load suddenly changes, the speed returns to a stable state in a very short time. ; Figure 7 shows the waveform of the q-axis winding current. It can be seen that the q-axis current can quickly track the ideal value, and the tracking effect is very good; Figure 8 shows the d-axis winding current waveform. The ripple is small and the static performance is good.

The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions that belong to the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims (7)

1. a dual-time scale parallel dual-loop control method for high-speed permanent magnet motor, is characterized in that, specifically comprises the steps: Step 1: Collect the state parameters of the high-speed permanent magnet motor, and determine the singular perturbation parameter ε according to the magnitude of the equivalent inductance of the d-axis winding and the equivalent inductance of the q-axis winding in the state parameters, and establish a singular perturbation nonlinear mathematical model; Step 2: Use the singular perturbation theory to reduce the order and decouple the singular perturbation nonlinear mathematical model to obtain a nonlinear slow time scale sub-model, and linearize the nonlinear slow time scale sub-model to obtain n linear slow time scales. Invariant submodel; Step 3: For n linear slow-time-invariant sub-models, combined with the threshold γ of the influence degree of noise on the state and each operating point, the H _∞ robust control law is obtained, and the slow time-scale control input u _s (t _k ) is calculated; Step 4: Calculate the fast time scale parameter τ, change the time scale of the singular perturbation nonlinear mathematical model to obtain a fast time scale sub-model, select the diagonal matrix M to solve the first positive definite matrix O and the second positive definite matrix Q, and calculate control input u _f (τ) of the fast time scale submodel; Step 5: Input the calculated control input u(t _k ) of the slow time scale and the control input u _f (τ) of the fast time scale sub-model into the high-speed permanent magnet motor to perform dual-time-scale parallel dual-loop control. 2. according to claim 1, it is characterized in that, the state parameter of the high-speed permanent magnet motor collected comprises: d-axis winding equivalent inductance, q-axis winding equivalent Inductance, equivalent resistance of winding, flux linkage of permanent magnet, number of pole pairs of motor, moment of inertia, load torque. 3. according to claim 1, it is characterized in that, described singular perturbation nonlinear mathematical model is:

where id is the _d -axis winding current,

is the d-axis winding current derivative, r is the winding equivalent resistance, ω _e is the angular velocity, L _q is the q-axis winding equivalent inductance, _ud is the d-axis winding voltage,

i _q is the q-axis winding current,

is the q-axis winding current derivative, L _d is the equivalent inductance of the d-axis winding, u _q is the q-axis winding voltage,

is the angular velocity derivative, P _n is the number of pole pairs of the motor, J is the moment of inertia, ψ _f is the permanent magnet flux linkage, and T _l is the load torque. 4. The dual-time-scale parallel dual-loop control method for high-speed permanent magnet motor according to claim 3, wherein the nonlinear slow time-scale sub-model is:

in,

is the slow component of the angular velocity,

is the derivative of the slow component of the angular velocity, ud is the _d -axis winding voltage, u _q is the q-axis winding voltage, T _l is the load torque, P _n is the number of pole pairs of the motor, J is the moment of inertia,

5. according to claim 4, it is characterized in that, in step 2, the process of linearizing the nonlinear slow time scale sub-model is specifically: by the high-speed permanent magnet motor The angular velocities are arranged in order, and the angular velocity interval is divided. The division is the operating point, and there are n operating points in total. At the angular velocity interval division, the nonlinear slow time-scale sub-model is linearized to obtain n linear slow-time invariant sub-models. , each linear slow-time-invariant submodel is:

Among them, θ _j is the operating point index, δω _e is the error between the measured value of the slow component of the current angular velocity and the operating point in the corresponding angular velocity interval,

u _s (θ _j ) is the bradyron control input at θ _j . 6. The dual-time-scale parallel dual-loop control method for high-speed permanent magnet motor according to claim 5, wherein step 3 comprises the following sub-steps: Step 3.1. The threshold of the influence degree of noise on the state is γ > 0. If there is a positive definite matrix P > 0, the following inequality conditions are satisfied

Find the H _∞ robust control law K(θ _j ); Step 3.2. Measure the angular velocity ω _e (t _k ) at time t _k , and calculate the first weighting coefficient α ₁ (t _k ) and the second weighting coefficient α ₂ (t _k ) according to the divided interval of the angular velocity: ω _e (t _k )=α ₁ (t _k )θ _m +α ₂ (t _k )θ _m+1 α ₁ (t _k )+α ₂ (t _k )=1, Among them, θ _m is the mth operation point, θ _m+1 is the m+1th operation point, ω _e (t _k )∈[θ _m , θ _m+1 ]; Step 3.3. According to the first weight coefficient α ₁ (t _k ) and the second weight coefficient α ₂ (t _k ), describe the H _∞ robust control law K(θ(t _k )) at time t k as: K(θ(t _k )) (t _k ))=α ₁ (t _k )K _m (θ _m )+α ₂ (t _k )K _m+1 (θ _m+1 ), and then calculate the slow time scale control input u _s (t _k )= K(θ(t _k ))δω _e (t _k ). 7. The dual-time-scale parallel dual-loop control method for high-speed permanent magnet motor according to claim 1, wherein step 4 comprises the following sub-steps: Step 4.1. Calculate fast time scale parameters

Change the time scale of the singularly perturbed nonlinear mathematical model to get the fast time scale submodel:

in,

is the fast component of the d-axis current variable,

is the fast component of the q-axis current variable,

is the fast component of the d-axis voltage variable,

is the fast component of the _q -axis voltage variable, t is the time variable, and t is the initial moment,

is the value of the slow variable ω _e . Step 4.2. Select the diagonal matrix M=diag{λ ₁ λ ₂ }>0 to solve the first positive definite matrix O and the second positive definite matrix Q, and calculate the control input of the fast time scale sub-model

in,

is the nominal input that ignores the uncertain input in the control input of the fast time scale sub-model, s(τ) is the sliding mode function, ||s(τ)|| ₂ is the second norm of the sliding mode function, h is a small positive number .

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