CN113395028B - Method for forming flux linkage observer based on voltage and current hybrid model - Google Patents

Abstract

The invention discloses a method for forming a voltage-current hybrid model flux linkage observer. At the same time, it is ensured that with the increase of frequency, the real part of the characteristic function F(s) gradually increases from 0 to 1; Step B: Stability analysis of the improved voltage-current hybrid model flux linkage observer. The present invention can realize the smooth switching of the current model and the voltage model, reduce the flux linkage estimation error, and thus solve the problem of poor robustness in the medium-speed region of the traditional hybrid model flux linkage observer. When there is an error in the motor parameters, the improved hybrid model flux observer can observe the accurate rotor flux in the full speed range, which solves the problems of amplitude attenuation and phase shift at different speeds.

Description

Formation method of flux linkage observer based on voltage-current hybrid model

technical field

The invention belongs to the field of power electronics, in particular to a method for forming a flux linkage observer based on a voltage-current hybrid model.

Background technique

The key in the induction motor control system is to accurately obtain the magnitude and spatial position of the rotor flux linkage vector. The direct detection of rotor flux linkage is difficult. The existing literature points out that most of the flux linkage estimation adopts voltage model, current model and full-order flux linkage observation model. Since the current model includes the rotor time constant and mutual inductance parameters, when the motor temperature rises and the magnetic circuit is saturated, these parameters will have a great impact, resulting in flux linkage observation errors. But in general, the current model does not require a voltage signal and has no influence of DC bias, so it is more suitable for low-speed operation. The rotor resistance is not included in the voltage model, and the motor parameters are more robust, so the performance is better than the current model at medium and high speeds. However, there are two main problems in the practical application of the voltage model: one is that the low-speed occasion is more sensitive to the change of stator resistance; the other is that the pure integral link in the model is easy to cause the flux linkage observation error. The former can reduce the influence of the stator resistance parameters through online parameter self-adaptation; while the latter in practical applications, due to electromagnetic interference, sensor measurement and sampling errors, the problems of pure integral link DC bias and integral saturation are more significant.

In the existing literature, in order to improve the estimation accuracy of the rotor flux linkage observer, many improved flux linkage observers have been proposed. For example, the document "A New Quick-response And High-efficiency Control Strategy Of AnInduction Motor" proposes a voltage-current hybrid model rotor flux linkage observer, which makes full use of the advantages of the current model in the low-speed region and the advantages of the voltage model in the high-speed region. In the medium-speed switching region, the flux linkage estimation is sensitive to motor parameters due to the influence of voltage dead zone and other factors, so solving the robustness problem in the medium-speed switching region becomes the key to research.

In order to solve the problem of poor robustness in the medium-speed region, some scholars have proposed some solutions, but most of these methods have changed the structure of the mixture model. For example, the document "Novel Rotor-Flux Observer Using ObserverCharacteristic Function in Complex Vector Space For Field-Oriented InductionMotor Drives" adds an angle compensation module based on the traditional hybrid model, which not only increases the amount of calculation, but also includes online parameters in its expression, which has a negative impact on the control system. Real-time computing power is required. Some scholars have also proposed to improve the voltage model in the hybrid model, adding a high-pass filter on the basis of the pure integrator to eliminate the DC component in the back EMF and solve the DC bias problem in the integration result. Although the observation performance of the flux linkage was improved at medium and high speed, the observation performance in the low speed region was not improved. At present, there is no better method that can simultaneously satisfy: 1) the estimation of the flux linkage in the medium-speed switching region is accurate; 2) the calculation amount is small; 3) the structure of the hybrid model is not changed. Therefore, it is necessary to design a simple and practical method to make the hybrid model obtain better flux linkage observation performance in the medium-speed switching region.

SUMMARY OF THE INVENTION

Aiming at the problems that the traditional hybrid model flux linkage observer is sensitive to motor parameters in the medium-speed switching region, the present invention proposes an improved voltage-current hybrid model flux linkage observer. Without changing the structure of the mixed model, through the theoretical analysis of the eigenfunction of the mixed model in the frequency domain, a set of complex coefficient PI parameters are designed to replace the traditional real coefficient PI parameters, so that the imaginary part of the eigenfunction is 0 and the real part is 0. Gradually increase from 0 to 1 as the frequency increases. The smooth switching between the current model and the voltage model is realized, and the flux linkage estimation error is reduced, thereby solving the problem of poor robustness of the traditional hybrid model flux linkage observer in the medium-speed region. The technical scheme adopted in the present invention is as follows:

Step A: Based on the eigenfunction of the traditional mixed model, a set of complex coefficient PI parameters are designed to make the imaginary part of the eigenfunction as small as possible, and at the same time ensure that the real part of the eigenfunction gradually increases from 0 to 1 as the frequency increases ;

Step B: Perform stability analysis on the improved hybrid model obtained according to Step A, so that its characteristic root is in the left half-plane of the complex plane to ensure the stability of the system.

In some embodiments, the step A includes:

According to the characteristic function of the flux linkage observer based on the voltage-current hybrid model:

When the motor is running in a steady state, let s=jω _e , get:

make

Among them, K _p and K _i are PI parameters, and ω _e is the synchronization angular frequency;

In the middle and high frequency bands, F(jω _e )=1, that is, the voltage-current hybrid model observer only functions as a voltage-type flux linkage observer. At this time, as long as A=0, we can get:

K _i = -jω _e K _p

In the low frequency band, if the real part of F(jω _e ) slowly rises from 0 to 1, the following design is performed:

get:

Among them, ω _b is the boundary angular frequency of the switching between the current model and the voltage model flux linkage observer.

In some embodiments, the step B includes:

The mathematical model of the voltage-current hybrid model flux observer in the static coordinate system:

为转子时间常数；L_m、L_r、L_s、R_s、R_r、ω_r、σ、p、

分别为互感、转子电感、定子电感、定子电阻、转子电阻、转子角速度、漏感、微分算子、电流模型转子磁链估计值、电压模型转子磁链估计值；in,

is the rotor time constant; L _m , L _r , L _s , R _s , R _r , ω _r , σ, p,

Mutual inductance, rotor inductance, stator inductance, stator resistance, rotor resistance, rotor angular velocity, leakage inductance, differential operator, estimated value of rotor flux linkage of current model, estimated value of rotor flux linkage of voltage model;

Transforming Equation (3-1), the state space equation of the closed-loop voltage-current hybrid model flux observer is:

State variables

state matrix

The state equation is:

The characteristic equation is:

的根在复平面的左半平面，所以通过使

的根在复平面的左半平面，则保证改进后的电压电流混合模型磁链观测器的稳定性；because

The root of is in the left half-plane of the complex plane, so by making

The root of is in the left half plane of the complex plane, then the stability of the improved voltage-current hybrid model flux linkage observer is guaranteed;

In the low frequency band (0≤ω _e <ω _b ), the relationship between K _p and K _i is:

Simultaneous equations (3-4) and (3-5) get:

Solve it to get:

Assuming K _p = a+b*j, substitute K _p into formula (3-7) to get:

It can be seen from formula (3-8) that as long as a is greater than 0, the system can be stable and the characteristic function F(jω _e ) is in the low frequency band, the imaginary part is always 0, and the real part gradually increases from 0 as the frequency increases to 1;

In the mid and high frequency bands, the relationship between K _p and K _i is:

K _i = -jω _e K _p (3-9)

Simultaneous equations (3-4) and (3-5) get:

s ² +K _p s-jω _e K _p =0

Solve it to get:

得到a和b的值：Assuming K _p = a+b*j, substitute K _p into formula (3-10) to ensure that the real part of the characteristic root is less than zero; for the convenience of calculation, let

Get the values of a and b:

Using the values of a and b in the above formula, the obtained characteristic root is in the left half plane of the complex plane, so the closed-loop voltage-current hybrid model system is stable.

The present invention has the following features and advantages: compared with the traditional improvement scheme, there is no need to add another module, and the calculation amount is small. The improved hybrid model can switch smoothly between the current model and the voltage model in the medium-speed switching region, reducing the flux linkage estimation error. Making full use of the advantages of the current model and the voltage model, the hybrid model has good robustness to changes in motor parameters. When there is an error in the motor parameters, the improved hybrid model flux observer can observe the accurate rotor flux in the full speed range, which solves the problems of amplitude attenuation and phase shift at different speeds.

Description of drawings

Fig. 1 is the real part and imaginary part of the improved mixed model characteristic function F(s);

Figure 2 is a block diagram of the induction motor model predicting the flux linkage control structure;

Figure 3 is a comparison of the estimated waveforms of the flux linkage when the rotor resistance is changed;

(300r/min空载)；图4b中：

(300r/min满载)；Figure 4a and Figure 4b are the comparison of the estimated waveforms of rotor flux linkage when the rotor resistance is changed. In Figure 4a:

(300r/min no load); in Figure 4b:

(300r/min full load);

(300r/min满载)；图5b中：

(300r/min空载)；Figure 5a and Figure 5b are the comparison of the estimated flux linkage waveforms when the stator resistance is changed, in which, in Figure 5a:

(300r/min full load); in Figure 5b:

(300r/min no load);

(300r/min空载)；图6b中：

300r/min满载)。Figure 6a and Figure 6b are the comparison of the flux linkage estimation waveforms when the mutual inductance is changed, in which, in Figure 6a:

(300r/min no load); in Figure 6b:

300r/min full load).

Detailed ways

The following examples may enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way.

The present invention provides an improved voltage-current hybrid model flux linkage observer, comprising the following steps:

Step A: Through the design of the PI parameters of the voltage-current hybrid model flux linkage observer, the imaginary part of the characteristic function F(s) is minimized, and the real part of the characteristic function F(s) is gradually guaranteed as the frequency increases. grow from 0 to 1;

Step B: Stability analysis of the improved voltage-current hybrid model flux observer.

In some embodiments, step A includes:

According to the characteristic function of the flux linkage observer based on the voltage-current hybrid model:

When the motor is running in a steady state, let s=jω _e , get:

make

Among them, K _p and K _i are PI parameters; ω _e is the synchronization angular frequency.

In the middle and high frequency bands, F(jω _e )=1, that is, the voltage-current hybrid model observer only has the function of the voltage-type flux linkage observer. At this time, it is only necessary to set A=0. get:

K _i = -jω _e K _p

In the low frequency band, if the real part of F(jω _e ) slowly rises from 0 to 1, the following design is performed:

get:

Among them, ω _b is the boundary angular frequency of the switching between the current model and the voltage model flux linkage observer.

In some embodiments, step B includes:

The mathematical model of the voltage-current hybrid model flux observer in the static coordinate system:

为转子时间常数；L_m、L_r、L_s、R_s、R_r、ω_r、σ、p、

分别为互感、转子电感、定子电感、定子电阻、转子电阻、转子角速度、漏感、微分算子、电流模型转子磁链估计值、电压模型转子磁链估计值。in,

is the rotor time constant; L _m , L _r , L _s , R _s , R _r , ω _r , σ, p,

They are mutual inductance, rotor inductance, stator inductance, stator resistance, rotor resistance, rotor angular velocity, leakage inductance, differential operator, estimated value of rotor flux linkage of current model, and estimated value of rotor flux linkage of voltage model.

Transforming Equation (3-1), the state space equation of the closed-loop voltage-current hybrid model flux observer is:

State variables

state matrix

The state equation is:

The characteristic equation is:

的根在复平面的左半平面，所以只需使

的根在复平面的左半平面，就可以保证改进后的电压电流混合模型磁链观测器的稳定性。because

The root of is in the left half-plane of the complex plane, so just make

The root of is in the left half plane of the complex plane, which can ensure the stability of the improved voltage-current hybrid model flux observer.

In the low frequency band (0≤ω _e <ω _b ), the relationship between K _p and K _i is:

Simultaneous equations (3-4) and (3-5) get:

Solve it to get:

Assuming K _p = a+b*j, substitute K _p into formula (3-7) to get:

It can be seen from formula (18) that as long as a is greater than 0, the system can be stable and the characteristic function F(jω _e ) is in the low frequency band, the imaginary part is always 0, and the real part gradually increases from 0 to 1 as the frequency increases .

In the mid and high frequency bands, the relationship between K _p and K _i is:

K _i = -jω _e K _p (3-9)

Simultaneous equations (3-4) and (3-5) get:

s ² +K _p s-jω _e K _p =0

Solve it to get:

得到a和b的值：Assuming K _p =a+b*j, substitute K _p into equation (3-10) to ensure that the real part of the characteristic root is less than zero. For ease of calculation, we can make

Get the values of a and b:

The solutions of a and b above are not unique. Using the values of a and b in the above formula, the characteristic root obtained is in the left half-plane of the complex plane, so the closed-loop voltage-current hybrid model system can be stable.

The present invention is further described below with reference to the accompanying drawings, wherein the feasibility of the improved model is verified by combining the model to predict the flux linkage control, but it is only used to explain the present invention, rather than to limit the scope of the present invention.

Figure 1 shows the changes of the real and imaginary parts of the improved hybrid model characteristic function F(jω _e ) when the motor is in a steady state.

Fig. 2 is the structural block diagram of the voltage-current hybrid model. The voltage-current hybrid model consists of a current model, a voltage model and a PI regulator. By controlling the PI regulator, the current model plays a major role in the low-speed region, and the voltage model plays a major role in the middle and high-speed regions, so as to obtain a more accurate rotor flux linkage in the full-speed range.

Figure 3 is a block diagram of the model predicted flux linkage control. The effectiveness of the method proposed in the present invention can be obtained by comparing the simulation results of Figs. 4a, 4b, 5a, 5b, 6a and 6b. It can be seen from Fig. 4a and Fig. 4b that when there is an error in the rotor resistance, the estimated flux linkage of the hybrid model and the new improved hybrid model proposed in this paper can keep up with the actual flux linkage in both no-load and full-load conditions. However, compared with the two, the observation performance of the improved mixed model of the present invention is better. It can be seen from Figure 5a and Figure 5b that when there is an error in the stator resistance, in both no-load and full-load conditions, the estimated flux linkage of the hybrid model has errors in amplitude and phase compared with the actual flux linkage. However, the estimated flux linkage of the improved hybrid model of the present invention can keep up with the actual flux linkage and has better observation performance. It can be seen from Fig. 6a and Fig. 6b that in both no-load and full-load conditions, when there is an error in the mutual inductance, the estimated flux linkage of the hybrid model has errors in amplitude and phase compared with the actual flux linkage. However, the estimated flux linkage of the improved hybrid model of the present invention can keep up with the actual flux linkage.

Those skilled in the art should understand that the above embodiments are only exemplary embodiments, and various changes, substitutions and alterations may be made without departing from the spirit and scope of the present application.

Claims (1)

1. A forming method of a voltage and current hybrid model flux linkage observer is characterized by comprising the following steps:

step A: through the design of PI parameters of a voltage-current hybrid model flux linkage observer, the imaginary part of the characteristic function F(s) is reduced, and meanwhile, the real part of the characteristic function F(s) is ensured to gradually increase from 0 to 1 along with the increase of frequency;

and B, step B: performing stability analysis on the improved voltage-current hybrid model flux linkage observer;

wherein the step A comprises the following steps:

according to the characteristic function of the voltage-current hybrid model flux linkage observer:

when the motor is in steady operation, let s be j omega_eObtaining:

order to

Wherein, K_p、K_iIs the PI parameter, ω_eIs the synchronous angular frequency;

in the medium and high frequency band, F (j omega)_e) When the voltage-current hybrid model observer only functions as a voltage flux linkage observer, only a is 0, and the following results are obtained:

K_i＝-jω_eK_p

in the low frequency band, want F (j ω_e) The real part of (a) rises slowly from 0 to 1, and the following design is made:

obtaining:

wherein, ω is_bBoundary angular frequency for switching of the current model and the voltage model flux linkage observer;

The step B comprises the following steps:

the mathematical model of the voltage and current mixed model flux linkage observer in a static coordinate system is as follows:

wherein,

is the rotor time constant; l is_m、L_r、L_s、R_s、R_r、ω_r、σ、p、

Mutual inductance, rotor inductance, stator resistance, rotor angular velocity, leakage inductance, differential operator, current model rotor flux linkage estimation value and voltage model rotor flux linkage estimation value;

and (3) converting the formula (3-1), wherein the state space equation of the closed-loop voltage-current hybrid model flux linkage observer is as follows:

variable of state

State matrix

The state equation is:

the characteristic equation is as follows:

because of the fact that

Is in the left half plane of the complex plane, so that

The root of the improved voltage-current hybrid model flux linkage observer is positioned on the left half plane of the complex plane, so that the stability of the improved voltage-current hybrid model flux linkage observer is ensured;

in the low frequency range (0 ≦ omega)_e＜ω_b),K_pAnd K_iThe relationship between is:

the combined vertical type (3-4) and (3-5) are as follows:

solving the following steps:

suppose K_pA + b j, and K_pSubstituting into equation (3-7) yields:

as can be seen from the equations (3-8), the system is stable and the characteristic function F (j ω) is stable as long as a is guaranteed to be greater than 0_e) In the low frequency bandThe imaginary part is always 0, and the real part gradually increases from 0 to 1 along with the rise of the frequency;

in the medium-high frequency band, K_pAnd K_iThe relationship between is:

K_i＝-jω_eK_p (3-9)

Combined vertical type (3-4) and (3-5) are obtained:

s²+K_ps-jω_eK_p＝0

solving the following steps:

suppose K_pA + b j, K_pSubstituting into the formula (3-10) to ensure that the real part of the characteristic root is less than zero; for convenience of calculation, order

Values for a and b were obtained:

by adopting the values of a and b in the formula, the obtained characteristic root is on the left half plane of the complex plane, so that the closed-loop voltage-current mixed model system is stable.

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