阅读说明：本技术 一种直流升压变换器的非连续二阶滑模控制方法 (Discontinuous second-order sliding mode control method of direct current boost converter ) 是由 刘富 丁世宏 刘陆 于 2021-07-14 设计创作，主要内容包括：本发明公开了一种直流升压变换器的非连续二阶滑模控制方法,属于电力电子变换器领域。直流升压变换器为变结构、非线性系统,传统的线性控制方法难以获得较好的动静态性能,进而提出了一种非连续二阶滑模控制方案。主要步骤：1、根据直流升压变换器工作原理,考虑系统扰动,建立非线性数学模型；2、设计滑动面使闭环系统具有期望的运动轨迹；3、设计滑模控制器使运动轨迹可以沿着滑动面滑动至平衡点。本发明的优点：一,基于更加贴近实际的直流升压变换器数学模型设计,可以从本质上削弱直流升压变换器的非线性扰动带来的不利影响；二,不仅实现输出电压快速跟踪目标电压值,而且使闭环系统具有更好的动态和稳态性能。(The invention discloses a discontinuous second-order sliding mode control method of a direct current boost converter, and belongs to the field of power electronic converters. The direct current boost converter is a variable structure and nonlinear system, and the traditional linear control method is difficult to obtain better dynamic and static performances, so that a discontinuous second-order sliding mode control scheme is provided. The method mainly comprises the following steps: 1. according to the working principle of the direct-current boost converter, considering system disturbance, and establishing a nonlinear mathematical model; 2. designing the sliding surface to enable the closed-loop system to have a desired motion track; 3. the sliding mode controller is designed to enable the motion track to slide along the sliding surface to a balance point. The invention has the advantages that: firstly, based on the mathematical model design of the direct current boost converter which is closer to the reality, the adverse effect caused by the nonlinear disturbance of the direct current boost converter can be weakened essentially; and secondly, the target voltage value is quickly tracked by the output voltage, and the closed-loop system has better dynamic and steady-state performance.)

1. A discontinuous second-order sliding mode control method of a direct current boost converter is characterized by comprising the following steps:

the method comprises the following steps: analyzing the working principle of the direct current boost converter, considering the disturbance of the system, and establishing a nonlinear mathematical model and a second-order sliding mode kinetic equation of the direct current boost converter;

step two: according to the second-order sliding mode kinetic equation established in the first step, a non-continuous second-order sliding mode controller based on the direct-current boost converter is established;

step three: and selecting appropriate condition parameters for the second-order sliding mode kinetic equation established in the first step and the second step and the discontinuous second-order sliding mode controller respectively.

2. The discontinuous second-order sliding-mode control method for the DC boost converter according to claim 1, wherein in the step one, in consideration of system disturbance factors, a nonlinear mathematical model of the DC boost converter system is established as follows:

in the formula i_LIs the inductive current, V_cIs the output voltage, V_refIs a reference voltage, C is a capacitance, R is a load, u is a system control input, u is 1 and 0 represent the on and off of the switching tube, S is a sliding variable whose relative order to the controller u is 2, d (t) is the lumped disturbance of the system;

order S₁＝S，Then the second order sliding mode kinetic equation of the dc boost converter system is:

in the formula S₁Sliding variables, S, being second order sliding mode kinetic equations₂Is the first derivative of the slip variable,is the second derivative of the sliding variable, an

Wherein (x)₁,x₂)^T＝(i_L,V_c)^T，d₁(t) and d₂(t) represents the disturbance of the system caused by the change of the input voltage and the load variation, respectively, and

3. the discontinuous second-order sliding-mode control method for the dc boost converter according to claim 1, wherein in the second step, the discontinuous second-order sliding-mode controller is established as follows:

wherein the content of the first and second substances,

where sign is a sign function, xi₁>0 by selecting the appropriate parameter ε₁And ε₂A limited time tracking of the output voltage to the reference voltage can be made.

4. The discontinuous second-order sliding-mode control method for the direct-current boost converter according to claim 1, characterized in that in step three, the bounded condition of the nonlinear function in the second-order sliding-mode kinetic equation needs to satisfy:

and is b>0。

5. The discontinuous second-order sliding-mode control method for the dc boost converter according to claim 1, wherein in the third step, the condition that the control parameter needs to satisfy in the discontinuous second-order sliding-mode controller is as follows:

ε₂>ε₁and is epsilon₁>0，ε₂>0。

6. The discontinuous second-order sliding-mode control method of the DC boost converter according to claim 3, characterized in that σ (S) is introduced into the controller₁) Function xi₁The thickness of the boundary layer can realize smooth transition in a sliding mode, the buffeting of the system is weakened, and the robustness of the system in the boundary layer is improved.

7. The discontinuous second-order sliding-mode control method of the direct-current boost converter according to claim 1, characterized in that the output voltage can track the target voltage value quickly, the adverse effect of nonlinear disturbance is weakened, and the system is stable in a limited time.

Technical Field

The invention relates to a control technology of a direct current boost converter system, belongs to the field of power electronic converters, and particularly relates to a control method for improving the control performance of the output voltage of a boost converter by using a designed discontinuous second-order sliding mode control method, accelerating the response speed and enhancing the anti-interference capability.

Background

With the rapid development of power electronic technology, the application field of switching power supplies is continuously expanded, and a DC boost converter, which is currently a commonly used DC boost device, is one of DC-DC switching power supplies and has been widely applied in the fields of electronics, computers, aerospace, and the like. Because the dc boost converter is a typical nonlinear time-varying system, modeling, stability and output voltage performance under the condition of non-ideal components are the focus and difficulty of control. The conventional linear control method is a typical control method based on a linear theory, and the most representative of the conventional linear control method is a PID control method. For the characteristics of the dc boost converter, although the conventional linear control method is simple and easy to implement, it is difficult to obtain good dynamic and static performances, and a satisfactory control effect cannot be obtained. Accordingly, engineers have developed nonlinear control methods as needed.

The sliding mode control is also called sliding mode variable structure control, which is different from the traditional linear control method, and the control has discontinuity. The sliding mode variable structure control is developed to the present, and is applied to the field of direct current boost converter control. Compared with a conventional linear control strategy, the sliding mode control is more suitable for a time-varying and nonlinear system of a direct current converter. The method not only has strong robustness, but also has quick response speed. Compared with other nonlinear control methods, the sliding mode control method is simple in physical realization and insensitive to parameter change. The method is designed for the nonlinear system, the robustness of the system is enhanced, and the dynamic performance and the steady-state performance of the system are improved.

Disclosure of Invention

The invention provides a discontinuous second-order sliding mode control method of a direct current boost converter, and aims to solve the problems of poor anti-interference capability, low output voltage quality, low voltage output response speed and the like in the traditional control method. Aiming at the direct current boost converter, the control method improves the robustness and stability of the system. The specific technical scheme is as follows:

a discontinuous second-order sliding mode control method of a direct current boost converter comprises the following steps:

the method comprises the following steps: analyzing the working principle of the direct current boost converter, considering the disturbance of the system, and establishing a nonlinear mathematical model and a second-order sliding mode kinetic equation of the direct current boost converter;

step two: according to the second-order sliding mode kinetic equation established in the first step, a non-continuous second-order sliding mode controller based on the direct-current boost converter is established;

step three: and selecting appropriate condition parameters for the second-order sliding mode kinetic equation established in the first step and the second step and the discontinuous second-order sliding mode controller respectively.

Further, in the step one, according to the operating principle of the dc boost converter, the state space average model of the dc boost converter can be obtained as follows:

where E is a DC voltage source, i_LIs the inductive current, V_cIs the output voltage, L is the inductance, C is the capacitance, R is the load,u is a switching value and takes the values of 0 and 1. When u is 1, the switching tube is considered to be closed, and when u is 0, the switching tube is considered to be open.

When considering system disturbances, the above expression may be written as:

in the formula (x)₁,x₂)^T＝(i_L,V_c)^TDisturbance d caused to the system by changes in the input voltage₁(t) disturbance d to the system caused by load changes₂(t), the specific expressions are respectively expressed as:

according to the state space average model of the direct current boost converter after considering the system disturbance, a nonlinear mathematical model is established as follows:

in the formula V_cIs the output voltage, V_refIs a reference voltage, S is a sliding variable having a relative order of 2 to controller u, d (t) is a variable comprising d₂Lumped perturbation of the system of (t).

According to the nonlinear mathematical model, the selected sliding variables are:

S₁＝S

according to the nonlinear mathematical model and the sliding variable of the direct current boost converter, a second-order sliding mode kinetic equation is established as follows:

in the formula S₁Sliding variables, S, being second order sliding mode kinetic equations₂Is the first derivative of the slip variable,is the second derivative of the sliding variable, and a (t, i)_L,V_c)，b(t,i_L,V_c) Is a non-linear function.

The first derivative of the slip variable is:

a derivative is obtained from the above equation:

nonlinear function in formula

Further, in the second step, the non-continuous second-order sliding mode controller based on the dc boost converter is established as follows:

wherein the content of the first and second substances,

where sign is a sign function, xi₁Is the thickness of the boundary layer and xi₁>0 by selecting the appropriate parameter ε₁And ε₂A limited time tracking of the output voltage to the reference voltage can be made.

Further, in the third step, the bounded condition that the nonlinear function in the second-order sliding mode kinetic equation needs to satisfy is as follows:

and is b>0。

Further, in the third step, the parameters of the control conditions that the discontinuous second-order sliding mode controller needs to satisfy are as follows:

ε₂>ε₁and is epsilon₁>0，ε₂>0。

The invention has the beneficial effects that:

the discontinuous second-order sliding mode controller designed by the invention has good rapidity, and can enable the output voltage to quickly track the upper reference voltage; the anti-interference performance of the system is enhanced, and the influence of external interference on the system is weakened; the robustness of the system is enhanced, and the dynamic performance and the steady-state performance of the system are improved.

Drawings

Fig. 1 is a system configuration diagram of a dc boost converter.

Fig. 2 is a circuit schematic of the dc boost converter.

Fig. 3 is a waveform diagram of a start-up phase of the dc boost converter.

Fig. 4 is a waveform diagram of the load change phase of the dc boost converter.

Fig. 5 is a waveform diagram of a transformation phase of the dc boost converter.

Detailed Description

The invention discloses a discontinuous second-order sliding mode control method which is used for controlling the output voltage of a direct current boost converter. In order to make the objects, technical solutions and advantages of the present invention clearer and clearer, the present invention is further described below with reference to the accompanying drawings.

Fig. 1 is a system configuration diagram of a dc boost converter, which includes: (1) a boost power converter model; (2) a second-order sliding mode dynamic equation module; (3) a discontinuous second order sliding mode controller module; (4) a comparator module.

With reference to fig. 1 and fig. 2, a discontinuous second-order sliding mode control method for a dc boost converter is characterized in that the control method is implemented by the following steps:

the method comprises the following steps: the working principle of the direct current boost converter is analyzed, the disturbance of the system is considered, and a nonlinear mathematical model and a second-order sliding mode kinetic equation of the direct current boost converter are established.

As shown in the schematic diagram of the dc boost converter circuit shown in fig. 2, according to the operation principle, the method for establishing the state space average model is as follows:

(1) when the switch tube is turned on, the expression written in the column is:

(2) when the switch tube is disconnected, the expression written in the column is:

combining (1) and (2), the state space average model under the ideal state of the system can be obtained as follows:

where E is a DC voltage source, i_LIs the inductive current, V_cIs the output voltage, L is the inductance, C is the capacitance, R is the load,u is switching value, and the values of 1 and 0 represent the on and off of the switching tube.

Considering that the dc boost converter may be disturbed by disturbance during actual operation, the state space average model may be rewritten as:

wherein (x)₁,x₂)^T＝(i_L,V_c)^TDisturbance d caused to the system by changes in the input voltage₁(t) disturbance d to the system caused by load changes₂(t), the specific expressions are respectively expressed as:

the nonlinear mathematical model obtained according to the state space average model after disturbance is added is as follows:

wherein, V_cIs the output voltage, V_refIs a reference voltage, S is a sliding variable having a relative order of 2 to controller u, d (t) is a variable comprising d₂Lumped perturbation of the system of (t).

The parameters of the dc boost converter used are shown in table 1.

TABLE 1 DC boost converter parameters

Input voltage	E(V)	24
			Inductance	L(μH)	100
Capacitor with a capacitor element	C(μF)	4400
			Resistance (RC)	R(Ω)	50
Reference voltage	Vref(V)	48

According to the established nonlinear mathematical model, the selected sliding variables are as follows:

S₁＝S

according to the selected sliding variables and the nonlinear mathematical model, the established second-order sliding mode kinetic equation is as follows:

in the formula S₁Sliding variables, S, being second order sliding mode kinetic equations₂Is the first derivative of the slip variable,is the second derivative of the sliding variable, and a (t, i)_L,V_c)，b(t,i_L,V_c) Is a non-linear function.

The first derivative of the sliding mode variable can be found by the above formula:

then the following equation can be found:

wherein the non-linear function

Step two: and D, establishing a non-continuous second-order sliding mode controller based on the direct-current boost converter according to the second-order sliding mode kinetic equation established in the step one.

Then the non-continuous second-order sliding mode controller based on the direct current boost converter is established as follows:

wherein the content of the first and second substances,

where sign is a sign function, xi₁Is the thickness of the boundary layer and xi₁>0 by selecting the appropriate parameter ε₁And ε₂A limited time tracking of the output voltage to the reference voltage can be made.

Step three: and selecting appropriate condition parameters for the second-order sliding mode kinetic equation established in the first step and the second step and the discontinuous second-order sliding mode controller respectively.

The bounded conditions which need to be met by the nonlinear function in the second-order sliding mode kinetic equation of the direct current boost converter are as follows:

and is b>0。

The parameters of the control conditions selected by the discontinuous second-order sliding mode controller of the direct current boost converter are as follows:

ε₂>ε₁and is epsilon₁>0，ε₂>0。

Example (b): the method of the invention is verified by the following simulation results:

the comparison under three conditions is given below, namely the comparison of the output waveforms of the discontinuous second-order sliding mode control method (SOSM) in the invention and the PID algorithm and the traditional first-order sliding mode algorithm (SMC) in the starting stage of the system; comparing the output waveforms of the PID algorithm and the traditional first-order sliding mode algorithm with the output waveforms of the control method of the invention when the load resistance of the system is changed; and comparing the PID algorithm and the traditional first-order sliding mode algorithm of the system with the output waveform of the control method under the condition of changing the input voltage.

Case 1: DC boost converter start-up phase comparison

As shown in fig. 3: under the condition that the input voltage is given to be 24V and the reference output voltage is 48V, the second-order sliding mode control method is compared with the overshoot and the response speed of a PID algorithm and a traditional first-order sliding mode algorithm. Compared with the other two algorithms, the second-order sliding mode control method has the advantages of high response speed, no overshoot and good robustness, and shows that the control method has good dynamic performance and steady-state performance.

Case 2: DC boost converter load change phase comparison

As shown in fig. 4: given an input voltage of 24V and a reference output voltage of 48V, the load abruptly changes when t is 1s, and the load resistance abruptly changes from 50 Ω to 80 Ω. It can be seen from the comparison graph of the variable load stage that when the load resistance is suddenly changed, the PID and the traditional first-order sliding mode have the jitter phenomenon, and the variable load amplitude is higher than that of a second-order sliding mode.

Case 3: DC boost converter voltage transformation phase comparison

As shown in fig. 5: given an input voltage of 24V and a reference output voltage of 48V, the input voltage abruptly changes from 24V to 30V when t equals 1 s. It can be seen from the comparison graph of the voltage transformation stage that when the input voltage has a sudden change, the voltage transformation amplitude of the second-order sliding mode is between the PID and the traditional first-order sliding mode, but compared with the other two algorithms, the second-order sliding mode control method has the advantages of high response speed and good stability, and the buffeting problem occurring in the first-order sliding mode is weakened. On the whole, the second-order sliding mode control method is superior to the traditional first-order sliding mode and PID algorithm.

According to the simulation results, the discontinuous second-order sliding mode controller can reach a stable state within a limited time under the condition that the direct current boost converter is in a constant voltage state and disturbance interference exists, and output is stabilized at an expected output voltage. This characteristic is precisely what is required for many power electronic power supply devices. In the application of power supply and utilization of a storage battery, the voltage of the storage battery can be boosted to the voltage required by the electric equipment through the boost converter, and the voltage can be kept; in photovoltaic power generation application, the electric energy and voltage converted by the photovoltaic cell panel can be converted by the boost converter so as to supply power to a load; in the wind power generation application, the peak power tracking of a power generation system is easily realized by controlling the boost converter, and the maximum output power is obtained at a certain wind speed. A power converter with stable performance and strong robustness cannot be used in these practical applications. Therefore, the second-order sliding mode control method for the boost converter, which is designed by the invention, has good anti-interference performance and stronger robustness and stability, and meets the requirements.

The embodiments of the present invention have been shown and described, and are not intended to limit the scope of the present invention, and any obvious modifications, substitutions and variations therein may be made by those skilled in the art without departing from the principles of the present invention.