JP6864374B2 - DC / DC converter stability analysis method and system - Google Patents

Description

The present invention takes up a DC / DC converter stability analysis method and system, and specifically, is a DC / DC converter exponential stability analysis method and system based on discontinuous control theory.

Converter system stability is a prerequisite for its industrial application, and only stable systems can be put into industrial production. Theoretical guidance and analysis of stability at the product parameter design stage can ensure that it has strong anti-interference capabilities in practical applications and does not cause system collapse. Stability theory analysis usually relies on the establishment of system mathematical models and the stability determination methods formed on them.
A DC / DC converter is a typical switching discontinuous system, and because of the introduction of "switching", the DC / DC converter system contains continuously changing variables and discrete variables. The interaction of continuous and discrete variables forms various coupling behaviors that greatly complicate the dynamic behavior of the system, so DC / DC converters are typical hybridization systems. Compared to continuous systems, it is more accurate to describe DC / DC converter systems with discontinuous systems, which can reflect the true situation of the system, but the study is more complicated and abstract modern mathematical tools. A complicated control design method is required, and the existing stability judgment theory is also challenged.
Conventional stability analysis methods include small signal analysis methods, discrete model analysis methods, Lyapunov function analysis methods, and the like. Modeling and stability analysis are performed on the DC / DC converter by the small signal analysis method to enhance the function and interference prevention capability of the converter, but when analyzing the DC / DC converter by the small signal analysis method, the small signal analysis method is in a state. Derived by the spatial average model, the temporary information of the state variables is lost, so the analysis results are generally very different from the actual situation, and the range of application is greatly limited; the discrete model analysis method is DC / DC. The system state matrix and output matrix are obtained by the converter's state differential equation, and discrete iterations are performed on the selected state variables, fine linearization is performed on the state variables at immovable points by the averaging method, and the linearization feature matrix. Solving the feature multiplier of, thus obtaining a stability criterion, but not applicable when the parameter disturbance of the converter circuit is large because the discrete model analysis method is a linearization method; Lyapunov stability is a Russian scientist It was submitted by Lyapunov. The key point is to build a joint Lyapunov function or a multi-Lyapunov function, which determines the stability of the system by the law of energy reduction, but when analyzing the DC / DC converter by the Lyapunov function method, the Lyapunov function of the system It is difficult to build, especially a high-dimensional multi-subsystem switching system, and there is currently no good way to build Lyapunov functions, thus limiting the application of Lyapunov stability analysis methods. Especially in multi-subsystem switching systems such as converters, only multi-Lyapunov functions have been discovered at present, and appropriate joint Lyapunov functions have not yet been discovered, making it difficult to proceed with stability analysis.
In addition, the stability obtained by the stability analysis of the conventional DC / DC converter has a slower convergence speed than the exponential stability, and the convergence speed of the system cannot be accurately described.

Chinese Patent Application Publication No. 104578776

In order to solve the above problems in the current technology, an object of the present invention is to provide a DC / DC converter stability analysis method and system, and to describe a DC / DC converter using discontinuous control theory. As a result, the temporary information of the state variable is not lost, the true system state is reflected, and the temporary state of the system can be analyzed.

Another object of the present invention is to provide a DC / DC converter stability analysis method and system, and when it analyzes a DC / DC converter, there is no need to linearize the system, and the analysis for system stability is more. It is accurate and at the same time simplifies the analysis process.

Another object of the present invention is to provide a DC / DC converter stability analysis method and system, avoiding the need for a conventional Lyapunov function analysis method to construct an appropriate Lyapunov function, and at the same time circuit by the method. The parameter design process can be simplified.

Another object of the present invention is to provide a DC / DC converter stability analysis method and system, in which the stability of the DC / DC converter is exponential stable, and the exponential stability is a convergence speed rather than the conventional stability. Is faster, and the exponential description of the system convergence speed can be obtained by the analysis method.

Another object of the present invention is to provide a DC / DC converter stability analysis method and system, and an appropriate exponential stability circuit parameter can be automatically found by a computer calculation tool.

To achieve the above and other objectives, the present invention submits a DC / DC converter stability analysis method, including steps S1 and S2 below:

In step S1, the conversion is derived for the DC / DC converter system model, thereby obtaining the DC / DC converter state-space equation to be applied to the discontinuous control theory stability analysis method;

In step S2, the exponential stability of the DC / DC converter system is determined using the state-space equation of the DC / DC converter derived by the discontinuous control theory exponential stability analysis method, and the exponential convergence speed of the DC / DC converter is determined. To calculate.

Preferentially, said step S1 further includes:

Model the DC / DC converter and obtain the initial state-space equation for the converter;

Transform and derive the initial state-space equation to obtain the DC / DC converter state-space equation to be applied to the discontinuous control theory stability analysis method.

を選択し、

が誘導電流であり、

が容量電圧であり、取得したBUCKコンバータの状態空間方程式が： Preferentially, in step S1, modeling is performed on the BUCK converter, and the state variable

Select and

Is the induced current,

Is the capacitance voltage, and the obtained BUCK converter state-space equation is:

であり、

And

Among them

；

；

；

。

;

;

;

..

The state-space equation of the BUCK converter, which is preferentially applied to the discontinuous control theory stability analysis method, is:

であり、

And

Among them:

Among them, R is the resistance value of the load resistance, C is the capacitance value, L is the inductance value, E is the input voltage value, m is the number of system operation cycles, and τ is the switch. On-time, where T is the system cycle.

Preferentially, in step S2, the state-space equation of the BUCK converter applied to the discontinuity control theory stability analysis method is substituted into the linear inequality of the discontinuity control theory and solved, and the convergence speed of the system is calculated and acquired.

Preferentially, the discontinuous control theory is as follows:

/

が求める必要がある定数であり、Aが状態空間方程式の行列Aであり；A^Tが行列Aの転置を表し；τがスイッチオン時間であり、Tがシステム周期であり、対角行列

である）を成立させる対称の正定値行列

、正の定数

、和

（

）が存在すれば、システムの原点が指数安定する。 (In it

/

Is the constant that needs to be found, A is the matrix A of the state-space equations; A ^T represents the transpose of the matrix A; τ is the switch-on time, T is the system period, and the diagonal matrix

Is a symmetric positive-definite matrix that holds

, Positive constant

,sum

(

) Is present, the origin of the system is exponentially stable.

Preferentially, in step S2

Calculates and obtains the exponential convergence speed of the controlled system.

To achieve the above object, the present invention also submits a DC / DC converter stability analysis system, which includes a conversion derivation unit and a stability discriminant analysis unit:

The conversion derivation unit performs conversion derivation for the DC / DC converter system model, thereby obtaining the DC / DC converter state-space equation to be applied to the discontinuous control theory stability analysis method;

The stability judgment analysis unit judges the exponential stability of the DC / DC converter system by using the state-space equation of the DC / DC converter derived by the discontinuous control theory exponential stability analysis method, and determines the exponential stability of the DC / DC converter. Calculate the exponential convergence rate.

Preferentially, the transformation derivation unit obtains the state-space equation of the BUCK converter applied to the following discontinuous control theory stability analysis method by transformation derivation:

Among them:

Among them, R is the resistance value of the load resistance, C is the capacitance value, L is the inductance value, E is the input voltage value, m is the number of system operation cycles, and τ is the switch. On-time, where T is the system cycle.

Preferentially, the stability judgment analysis unit substitutes the state-space equation of the BUCK converter applied to the discontinuity control theory stability analysis method into the linear inequality of the discontinuity control theory and solves it, and calculates and obtains the convergence speed of the system. To do.

Compared with the existing technology, the DC / DC converter stability analysis method of the present invention and the system linearize the system by applying the stability method of the discontinuous control theory to the stability analysis of the DC / DC converter. Avoid, there is no need to build a Lyapunov function, the exponential stability determination of the DC / DC converter is easily realized, and the convergence speed of the system is described accurately; according to the present invention, the DC / DC converter is exponentially stable. When the judgment is realized and the system is exponentially stable, the convergence speed is faster than the conventional stability, and the present invention allows the parameters of the DC / DC converter exponential stability to be designed quickly and accurately.

FIG. 1 is a step flow diagram of the DC / DC converter stability analysis method according to the present invention; FIG. 2 is a system configuration diagram of the DC / DC converter stability analysis system according to the present invention; FIG. 3 is a schematic diagram of a BUCK converter simulation circuit in a specific embodiment of the present invention; FIG. 4 is a schematic diagram of the load disturbance of the BUCK converter simulation in the specific embodiment of the present invention; FIG. 5 is a schematic representation of the two cycles in the load disturbance of the BUCK converter simulation in a specific embodiment of the present invention; FIG. 6 is a PSIM simulation circuit diagram when the values of the points where the inductance values are not exponentially stable and the points where the inductance values are exponentially stable are selected in a specific embodiment of the present invention; FIG. 7 is a PSIM simulation waveform diagram when the values of the points where the inductance values are not exponentially stable and the points where the inductance values are exponentially stable are selected in a specific embodiment of the present invention.

In order to more clearly explain the examples of the present invention and the technical ideas in the existing technology, the following is a brief introduction to the illustrations that need to be used in the examples and the description of the existing technology. The present invention may be implemented or applied through other different specific examples, and each detail of this document is based on different viewpoints and applications, and various modifications and modifications are made to the premise that does not depart from the spirit of the present invention. Can be done.

Before introducing the present invention, a brief description of discontinuous control theory:

Consider the following systems

（1）

(1)

が状態ベクトルであり；

が

を満たす連続非線形関数であり、且つ対角行列

が存在し

をさせ；

がシステム式（1）の外部制御を表し、

がシステムの初期状態である。 Some of the equations

Is the state vector;

But

It is a continuous nonlinear function that satisfies, and is a diagonal matrix.

Exists

Let me;

Represents the external control of system equation (1),

Is the initial state of the system.

In order to stabilize the system equation (1) at the origin by the method of intermittent feedback control, it is assumed that the control added to the system has the following form.

（2）

(2)

The operating mode of the DC / DC converter is the switch mode, which is essentially a special case of intermittent feedback control.

が制御増益ベクトルであり；

が制御周期を表し；

が制御幅である。こうすれば、被制御システムが下記の方程式により確定される Some of the equations

Is the control profit increase vector;

Represents the control cycle;

Is the control width. In this way, the controlled system is determined by the following equation.

（3）

(3)

m is the number of cycles of system operation, m = 1,2,3, ...

（4）

（5）

（6）

(Four)

(Five)

(6)

/

が求める必要がある定数（工学上の意義がない）であり、Aが状態空間方程式の行列Aであり；A^Tが行列Aの転置を表し；τがスイッチオン時間であり、Tがシステム周期であり、Lが対角行列

である。）を成立させる対称の正定値行列

、正の定数

、和

（

）が存在すれば、 (

/

Is the constant (which has no engineering significance) that needs to be found, where A is the matrix A of the state-space equations; A ^T represents the transpose of the matrix A; τ is the switch-on time and T is the system period. And L is the diagonal matrix

Is. ) Is a symmetric positive-definite matrix

, Positive constant

,sum

(

) Exists

The origin of system equation (3) is exponentially stable and

（7）

(7)

が被制御システムの指数収束速度である。 Among them

Is the exponential convergence speed of the controlled system.

FIG. 1 is a step flow diagram of the DC / DC converter stability analysis method according to the present invention. As Figure 1 shows, the DC / DC converter stability analysis method according to the invention includes steps S1 and S2:

In step S1, the conversion is derived for the DC / DC converter system model, thereby acquiring the DC / DC converter state-space equation to be applied to the discontinuous control theory stability analysis method.

In a specific embodiment of the present invention, a BUCK converter will be described as an example:

を選択し、

が誘導電流であり、

が容量電圧であり、取得したBUCKコンバータの状態空間方程式が First, model the DC / DC converter and state variables

Select and

Is the induced current,

Is the capacitance voltage, and the acquired BUCK converter state-space equation is

である。 （8）

Is. (8)

Among them

；

；

；

。

;

;

;

..

R is the resistance value of the load resistance, C is the capacitance value, L is the inductance value, and E is the input voltage value.

What needs to be explained here is that the present invention takes the BUCK converter as an example, but other converters are also applied to the present invention, and the state-space equation can be expressed by Eq. (8), but only in it. Matrix A and Matrix B are different.

When you let

（9）

(9)

Because there are no non-linear terms in the converter submodality

をさせると、

When you let

Substituting equation (8) into equation (3), the obtained system equation is as follows:

（10）

(Ten)

Among them

。

..

In step S2, the exponential stability of the DC / DC converter system is determined using the state-space equation of the DC / DC converter derived by the discontinuous control theory exponential stability analysis method, and the exponential convergence speed of the DC / DC converter is determined. To calculate.

（4）

（5）

（6） According to the discontinuous control theory:

(Four)

(Five)

(6)

/

が求める必要がある定数（工学上の意義がない）であり、Aが状態空間方程式の行列Aであり；A^Tが行列Aの転置を表し；τがスイッチオン時間であり、Tがシステム周期である。）を成立させる対称の正定値行列

、正の定数

、和

（

）が存在すれば、 (In it

/

Is the constant (which has no engineering significance) that needs to be found, where A is the matrix A of the state-space equations; A ^T represents the transpose of the matrix A; τ is the switch-on time and T is the system period. Is. ) Is a symmetric positive-definite matrix

, Positive constant

,sum

(

) Exists

The origin of system equation (3) is exponentially stable and

（7）

(7)

が被制御システムの指数収束速度である。 Among them

Is the exponential convergence speed of the controlled system.

によりシステムの収束速度を計算し取得する。 Substitute the derived DC / DC converter state-space equation (10) into the linear matrix inequality of equations (4)-(6) above and solve it.

Calculates and obtains the convergence speed of the system.

Assuming the circuit parameters are as shown in Table 1,

Substituting the above parameters into the inequality of Eqs. (4)-Equation (6), the solution of the obtained linear matrix inequality is as follows:

And the system convergence speed is:

である。

Is.

In a specific embodiment of the present invention, a computer tool (for example, MATLAB) can be used to create equations (4)-formulas (6) in the reference, and after determining the functional parameters of the DC / DC converter. By substituting the parameters that cannot be created into equations (4) and (6) in the created criteria and performing stability judgment, the parameters of DC / DC converter exponential stability can be found quickly.

Substitute the circuit component parameters in Table 1 into the Buck converter model, solve the inequality of Eqs. (4)-Equation (6) with the LMI toolbox of a computer tool (for example, MATLAB), and use the desired output voltage (capacitive voltage) as the parameter. Calculated and obtained, under this circuit parameter, the capacitance voltage is within the step-down operating range of 6.7V-11.9V, and the circuit can be exponentially stabilized under appropriate control.

FIG. 2 is a system configuration diagram of the DC / DC converter stability analysis system according to the present invention. As shown in FIG. 2, the DC / DC converter stability analysis system according to the present invention includes a conversion derivation unit 201 and a stability discriminant analysis unit 202:

The conversion derivation unit 201 performs conversion derivation for the DC / DC converter system model, thereby acquiring a DC / DC converter state-space equation to be applied to the discontinuous control theory stability analysis method.

In a specific embodiment of the present invention, taking a BUCK converter as an example, conversion and derivation are performed on the BUCK converter system model, and the following state-space equations are obtained:

Among them

。

..

The stability judgment analysis unit 202 judges the exponential stability of the DC / DC converter system by using the state-space equation of the DC / DC converter derived by the discontinuous control theory exponential stability analysis method, and DC / DC. Calculate the converter exponential convergence rate.

According to the discontinuous control theory:

（4）

（5）

（6）

(Four)

(Five)

(6)

/

が求める必要がある定数（工学上の意義がない）であり、Aが状態空間方程式の行列Aであり；A^Tが行列Aの転置を表し；τがスイッチオン時間であり、Tがシステム周期である。）を成立させる対称の正定値行列

、正の定数

、和

（

）が存在すれば、 (In it

/

Is the constant (which has no engineering significance) that needs to be found, where A is the matrix A of the state-space equations; A ^T represents the transpose of the matrix A; τ is the switch-on time and T is the system period. Is. ) Is a symmetric positive-definite matrix

, Positive constant

,sum

(

) Exists

The origin of system equation (3) is exponentially stable and

（7）

(7)

が被制御システムの指数収束速度である。 Among them

Is the exponential convergence speed of the controlled system.

によりシステムの収束速度を計算し取得する。 Substitute the derived DC / DC converter state-space equation into the linear matrix inequality in the above equation and solve it.

Calculates and obtains the convergence speed of the system.

The present invention will be further described below by circuit simulation:

1. Open-loop BUCK converter circuit simulation

A circuit simulation was performed using PSIM software, and the circuit is shown in Fig. 3. Output load disturbance is performed and the load resistance R is suddenly converted from 10Ω to 5Ω, and the simulation result is as shown in Fig. 4: Two cycles in it are selected and their exponential stability is verified, as shown in Fig. 5. Is.

What can be seen from the discontinuous control theory is that the exponential stability system satisfies the above equation (4), in which the time t = 2.9911s, t1 = 2.99298s, t2 = 2.99303s, and each obtained by simulation. Substitute the numerical value into equation (7) to get the following:

という条件を満たす。

Satisfy the condition.

Therefore, the Buck converter is exponentially stable, and if an appropriate control factor is designed with this parameter, the converter can be exponentially stabilized.

2. Buck converter PSIM simulation controlled by peak current

When the circuit parameters in Table 1 are selected and the value of the inductance L calculated and obtained by the discontinuous control theory stability method with the inductance L as the parameter is larger than 7.2 mH, the circuit can be exponentially stabilized and the simulation circuit is shown in Fig. 6. In it, the inductance value L = 5mH in Fig. 6 (a), the circuit is not exponentially stable at this time, and the inductance value in Fig. 6 (b) is L = 10mH, at this time the circuit. Is index stable. The simulation waveform diagram is as shown in Fig. 7. Obviously, when the inductance value is 10 mH, the circuit is in an exponential stable state, and the induced current ripple at this time is about 0.03046A. When the inductance value is 5 mH, the operating state of the circuit is unstable, and the induced current ripple at this time is 0.07537A.

Based on the above, the DC / DC converter stability analysis method and system according to the present invention avoid the system from being linearized by applying the stability method of the discontinuous control theory to the stability analysis of the DC / DC converter. It is possible to easily determine the exponential stability of the DC / DC converter without having to construct the Lyapunov function, and to accurately describe the convergence speed of the system; the present invention realizes the determination of the exponential stability of the DC / DC converter. When the system is exponentially stable, the convergence speed is faster than the conventional stability, and the present invention allows the parameters of DC / DC converter exponential stability to be designed quickly and accurately.

Compared with the existing technology, the present invention has the following advantages:

1. The small signal analysis method of the conventional DC / DC converter stability analysis method requires linearization of the system, and temporary information of the system is lost. However, the present invention does not need to linearize the system using the stability analysis method of discontinuous control theory, and can accurately describe the stability of the system.

2. The discrete model analysis method is a linearization method, which is not applied when the parameter disturbance of the converter circuit is large, and when the present invention analyzes a DC / DC converter using the stability analysis method of discontinuous control theory, There is no need to linearize the system, the analysis for system stability is more accurate, and at the same time simplifies the analysis process.

3. When analyzing a DC / DC converter by the Lyapunov function method, the Lyapunov function of the system is difficult to build, especially a high-dimensional multi-subsystem switching system, there is currently no good way to build the Lyapunov function, and therefore Lyapunov stable. The application of sexual analysis methods is also limited, especially in multi-subsystem switching systems such as converters, where only multi-Lyapunov functions are currently found, suitable joint Lyapunov functions have not yet been found, making stability analysis difficult to proceed. , The present invention is based on the stability analysis method of the discontinuous control theory, avoids the need for the conventional Lyapunov function analysis method to construct an appropriate Lyapunov function, and at the same time simplifies the circuit parameter design process by the method. be able to.

4. The stability obtained by the stability analysis of the conventional DC / DC converter has a slower convergence speed than the exponential stability, and the convergence speed of the system cannot be described accurately. The stability of the DC / DC converter is judged to be exponential stable by adopting the sex analysis method, and the exponential stability has a faster convergence speed than the conventional stability, and the exponential description of the system convergence speed is obtained by the analysis method. be able to.

5. The present invention can automatically find appropriate exponential stability circuit parameters by a computer calculation tool based on the stability analysis method of discontinuous control theory.

The above is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited to this. Changes and replacements that come to mind through all creative labor are covered by the scope of the invention. Therefore, the scope of protection of the present invention is based on the scope of protection in which the request for rights is limited.

Claims (2)

Includes step S1 and step S2:
In step S1, the conversion is derived for the DC / DC converter system model, thereby obtaining the DC / DC converter state-space equation to be applied to the discontinuous control theory stability analysis method;
In step S2, the exponential stability of the DC / DC converter system is determined using the state-space equation of the DC / DC converter derived by the discontinuous control theory exponential stability analysis method, and the exponential convergence speed of the DC / DC converter is determined. Calculate and
The step S1 further includes:
Model the DC / DC converter and obtain the initial state-space equation for the converter;
Convert and derive the initial state-space equation, obtain the DC / DC converter state-space equation to be applied to the discontinuous control theory stability analysis method, and obtain it.
In step S1, modeling is performed on the BUCK converter, and the state variables

Select and
χ ₁ = i _L
Is the induced current,
χ ₂ = V _C
Is the capacitance voltage, and the obtained BUCK converter state-space equation is:

And
Among them

,
Among them, R is the resistance value of the load resistance, C is the capacitance value, L is the inductance value, and E is the input voltage value.
Discontinuous control theory The state space equation of the BUCK converter applied to the stability analysis method is:

And
Among them:

Among them, m is the number of system operation cycles, τ is the switch-on time, and T is the system cycle.
In step S2, the state-space equation of the BUCK converter applied to the discontinuity control theory stability analysis method is substituted into the linear inequality of the discontinuity control theory and solved, and the convergence speed of the system is calculated and obtained.
The discontinuous control theory is as follows:
^{(1) PA + A T P} + ε 1 P 2 + ε 1 - 1 L + g 1 P + PK + K T P ≦ 0
^{(2) PA + A T P} + ε 2 P 2 + ε 2 - 1 L-g 2 P ≦ 0
(3) τg ₁ − (T−τ) g ₂ > 0
(In it, g ₁ / g ₂ is the constant that needs to be found, A is the matrix A of the state-space equations; A ^T represents the transpose of the matrix A; τ is the switch-on time, T Is the system period, and L is a symmetric definite matrix P> 0 that holds the _{diagonal matrix L = diag (l 1} , l ₂ , ..., l _{n ) ≥ 0), and a positive constant g i.} If> 0, and ε _i > 0 (i = 1,2) exist, the origin of the system is exponentially stable.
In step S2

DC / DC converter stability analysis how include obtaining calculates the exponential convergence rate of the controlled system by. Includes transformation derivation unit and stability discriminant analysis unit
The conversion derivation unit performs conversion derivation for the DC / DC converter system model, thereby obtaining the DC / DC converter state-space equation to be applied to the discontinuous control theory stability analysis method;
The stability judgment analysis unit judges the exponential stability of the DC / DC converter system by using the state-space equation of the DC / DC converter derived by the discontinuous control theory exponential stability analysis method, and determines the exponential stability of the DC / DC converter. Calculate the exponential convergence speed,
The conversion derivation unit obtains the state-space equation of the BUCK converter applied to the following discontinuous control theory stability analysis method by conversion derivation:

Among them:

Among them, R is the resistance value of the load resistance, C is the capacitance value, L is the inductance value, E is the input voltage value, m is the number of system operation cycles, and τ is the switch. On time, T is the system cycle,
The stability judgment analysis unit substitutes the state-space equation of the BUCK converter applied to the discontinuity control theory stability analysis method into the linear inequality of the discontinuity control theory and solves it, and calculates and obtains the convergence speed of the system. it is a DC / DC converter stability analysis system and,
The discontinuous control theory is as follows.
^{(1) PA + A T P} + ε 1 P 2 + ε 1 - 1 L + g 1 P + PK + K T P ≦ 0
^{(2) PA + A T P} + ε 2 P 2 + ε 2 - 1 L-g 2 P ≦ 0
(3) τg ₁ − (T−τ) g ₂ > 0
(In it, g ₁ / g ₂ is the constant that needs to be found, A is the matrix A of the state-space equations; A ^T represents the transpose of the matrix A; τ is the switch-on time, T Is the system period, and L is a symmetric definite matrix P> 0 that holds the _{diagonal matrix L = diag (l 1} , l ₂ , ..., l _{n ) ≥ 0), and a positive constant g i.} If> 0, and ε _i > 0 (i = 1,2) exist, the origin of the system is exponentially stable.
The exponential convergence speed of the controlled system

To be
A DC / DC converter stability analysis system featuring.

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