CN105576972A

CN105576972A - Chattering-free sliding mode control method for buck converter

Info

Publication number: CN105576972A
Application number: CN201610051865.XA
Authority: CN
Inventors: 马莉; 王常青; 丁世宏
Original assignee: Jiangsu University
Current assignee: Jiangsu University
Priority date: 2016-01-26
Filing date: 2016-01-26
Publication date: 2016-05-11
Anticipated expiration: 2036-01-26
Also published as: CN105576972B

Abstract

The invention discloses a vibration-free sliding mode control method of a step-down converter, which belongs to the field of power electronic converters. Based on the average state model of the step-down converter, the present invention utilizes the second-order sliding mode control theory to design a chattering-free sliding mode controller for the step-down converter, adopting the fixed-frequency PWM mode, and changing the duty cycle of the switching device To control its turn-on or turn-off, and then realize the target voltage output of the step-down converter. At the same time, the overall scheme of the buck converter system under the action of the control method is realized based on the LabVIEW platform. The invention solves the chattering problem widely existing in traditional sliding mode control and the problems of slow response speed, low voltage output quality and poor anti-disturbance ability of the step-down converter controlled by the linear PID method. The control method utilizes its strong robustness, high steady-state precision and other advantages to overcome the disturbance influence of load resistance, DC input voltage, etc., and improve the performance of the output voltage.

Description

A Chattering-Free Sliding Mode Control Method for Buck Converter

技术领域technical field

本发明涉及电力电子变换器领域，具体是利用二阶滑模控制技术来消除传统滑模控制中广泛存在的抖振，提高降压变换器输出电压的动态性能和稳态性能。The invention relates to the field of power electronic converters, and specifically utilizes second-order sliding mode control technology to eliminate chattering widely existing in traditional sliding mode control, and improve the dynamic performance and steady-state performance of the output voltage of a step-down converter.

背景技术Background technique

近年来，由于电力电子技术的发展，降压变换器被广泛运用到各类直流降压场合，如电动及混合动力汽车、太阳能发电、工业仪器仪表、便携式电子产品和军事航天等领域。降压变换器的主要作用是将高压直流电变为低压直流电，给负载提供稳定的直流电压。In recent years, due to the development of power electronics technology, buck converters have been widely used in various DC step-down applications, such as electric and hybrid vehicles, solar power generation, industrial instrumentation, portable electronic products and military aerospace and other fields. The main function of the step-down converter is to convert high-voltage direct current into low-voltage direct current and provide a stable direct-current voltage to the load.

功率变换器既可以采用线性控制方法来实现，也可以采用非线性控制方法来实现。传统的PID控制算法作为一种典型的线性控制方法，由于结构简单、操作方便、成本低等优点常被用于各种控制电路中。然而，功率变换器内部具有复杂性和时变性，同时存在输入电压变化、负载突变等较大扰动，这就对动态响应速度、抗扰动性能和控制精度等方面要求提出了更高要求，传统PID控制方法难以满足实际控制需求。为了改善控制性能，各种更加优越的控制算法需要在功率变换器中得以研究和应用，例如自适应控制、模糊逻辑控制、人工神经网络控制、滑模控制等。The power converter can be implemented either by a linear control method or by a nonlinear control method. As a typical linear control method, the traditional PID control algorithm is often used in various control circuits due to its simple structure, convenient operation, and low cost. However, the power converter is complex and time-varying, and there are large disturbances such as input voltage changes and load mutations, which put forward higher requirements for dynamic response speed, anti-disturbance performance and control accuracy. Traditional PID The control method is difficult to meet the actual control needs. In order to improve the control performance, various more superior control algorithms need to be researched and applied in power converters, such as adaptive control, fuzzy logic control, artificial neural network control, sliding mode control, etc.

值的提出的是，滑模控制作为一种变结构控制方法,当系统运动状态在滑模面上时,对系统参数的不确定项以及外界干扰有着很强的鲁棒性。滑模控制器可以使得闭环系统具有鲁棒性强、收敛速度快等优点.其次，由于开关状态的切换，功率变换器本身具有变结构系统的特点，因而滑模变结构控制算法在功率变换器的控制设计中被广泛采用。但是，当系统的轨迹到达切换面时，惯性使运动点会穿越切换面最终形成抖振，叠加在理想的滑动模态上。What is worth mentioning is that sliding mode control is a variable structure control method. When the system motion state is on the sliding mode surface, it has strong robustness to the uncertain items of system parameters and external disturbances. The sliding mode controller can make the closed-loop system have the advantages of strong robustness and fast convergence speed. Secondly, due to the switching of the switch state, the power converter itself has the characteristics of a variable structure system, so the sliding mode variable structure control algorithm in the power converter widely used in control design. However, when the trajectory of the system reaches the switching surface, the inertia causes the moving point to cross the switching surface and eventually form chattering, which is superimposed on the ideal sliding mode.

二阶滑模扩展了传统滑模的思想，将不连续控制量作用在滑模量的二阶导数上而不是一阶导数上，这样不仅保留了传统滑模算法设计简单、容易实现且鲁棒性强等优点，而且可以很明显地削弱抖振的影响、增强控制器的稳定性。The second-order sliding mode expands the idea of the traditional sliding mode, and applies the discontinuous control quantity to the second derivative of the sliding mode instead of the first derivative, which not only retains the simple design, easy implementation and robustness of the traditional sliding mode algorithm It has the advantages of strong performance, and can obviously weaken the influence of chattering and enhance the stability of the controller.

发明内容Contents of the invention

为了解决传统滑模控制方法存在抖振和传统线性PID控制方法存在响应速度慢、抗扰动能力较弱等问题，本发明提出了一种基于二阶滑模技术的降压变换器无抖振滑模控制方法，并进行数字化实现，本发明在大扰动工况条件下，包括启动、负载突变和输入电压突变等，利用二阶滑模控制技术设计无抖振滑模控制器，并基于LabVIEW软件实现，提高降压变换器的输出电压的快速性和稳定性。采用的具体技术方案如下：In order to solve the problems of chattering in the traditional sliding mode control method and slow response speed and weak anti-disturbance ability in the traditional linear PID control method, the present invention proposes a chattering-free buck converter based on second-order sliding mode technology. mode control method, and carry out digital realization, the present invention under the conditions of large disturbance, including start-up, load sudden change and input voltage sudden change, etc., utilizes second-order sliding mode control technology to design chattering-free sliding mode controller, and based on LabVIEW software Realize that the rapidity and stability of the output voltage of the step-down converter are improved. The specific technical scheme adopted is as follows:

一种降压变换器的无抖振滑模控制方法，包括如下步骤：A chattering-free sliding mode control method for a step-down converter, comprising the steps of:

步骤1，建立包含不确定因素的降压变换器的平均状态空间模型；Step 1, establishing an average state-space model of the buck converter including uncertain factors;

$(\begin{matrix} \frac{{du du}_{C C}}{d d t t} \\ \frac{{di di}_{L L}}{d d t t} \end{matrix}) = = (\begin{matrix} - - \frac{11}{((C C + + Δ Δ C C)) ((R R + + Δ Δ R R))} & \frac{11}{C C + + Δ Δ C C} \\ - - \frac{11}{L L + + Δ Δ L L} & 00 \end{matrix}) (\begin{matrix} {u u}_{C C} \\ {i i}_{L L} \end{matrix}) + + (\begin{matrix} 00 \\ \frac{{U u}_{i i} + + {ΔU Δ U}_{i i}}{L L + + Δ Δ L L} \end{matrix}) d d$

式中，R为电阻值，L为电感值，C为电容值，u_C是电容C两端的电压，i_L是电感电流，U_i为输入电压，ΔC、ΔL、ΔU_i、ΔR分别为电容C、电感L、输入电压U_i、负载电阻R的不确定因素，d是开关量，其取值为0或1，表示开关的断开或闭合状态；In the formula, R is the resistance value, L is the inductance value, C is the capacitance value, u _C is the voltage across the capacitor C, i _L is the inductor current, U _i is the input voltage, ΔC, ΔL, ΔU _i and ΔR are the capacitance C. Uncertain factors of inductance L, input voltage U _i , load resistance R, d is the switch value, and its value is 0 or 1, indicating the open or closed state of the switch;

步骤2，设计降压变换器的无抖振滑模控制算法；包括：Step 2, design the chattering-free sliding mode control algorithm of the buck converter; including:

步骤2.1，分离步骤1所述的平均状态空间模型的不确定项部分，得到：Step 2.1, separate the uncertain item part of the average state space model described in step 1 to obtain:

$\{\begin{matrix} \frac{{du du}_{C C}}{d d t t} = = \frac{11}{C C} (({i i}_{L L} - - \frac{{u u}_{C C}}{R R})) + + {θ θ}_{11} \\ \frac{{di di}_{L L}}{d d t t} = = \frac{11}{L L} (({dU U}_{i i} - - {u u}_{C C})) + + {θ θ}_{22} \end{matrix}$

式中， $θ_{1} = \frac{u_{C} Δ R}{R (R + Δ R) (C + Δ C)} + \frac{u_{C} Δ C - i_{L} Δ C R}{R C (C + Δ C)}, θ_{2} = \frac{{dΔU}_{i} L - {dΔLU}_{i} + {ΔLU}_{C}}{L (L + Δ L)};$ In the formula, $θ_{1} = \frac{u_{C} Δ R}{R (R + Δ R) (C + Δ C)} + \frac{u_{C} Δ C - i_{L} Δ C R}{R C (C + Δ C)}, θ_{2} = \frac{{dΔU}_{i} L - {dΔLU}_{i} + {ΔLU}_{C}}{L (L + Δ L)};$

步骤2.2，定义输出电压偏差为x₁＝u₀-U_ref，其中U_ref为输出直流电压参考值，u₀为降压变压器的输出电压；Step 2.2, define the output voltage deviation as x ₁ =u ₀ -U _ref , where U _ref is the reference value of the output DC voltage, and u ₀ is the output voltage of the step-down transformer;

对x₁求导得到电压偏差变化率x₂：Deriving x ₁ to obtain the rate of change of voltage deviation x ₂ :

${x x}_{22} = = {\overset{\cdot &Center Dot;}{x x}}_{11} = = - - \frac{11}{R R C C} {u u}_{c c} + + \frac{11}{C C} {i i}_{L L} + + {θ θ}_{11};;$

再对x₂求导得到：Then take the derivative of x ₂ to get:

${\overset{\cdot \cdot}{x x}}_{22} = = \frac{11}{C C} ((\frac{{di di}_{L L}}{d d t t} - - \frac{11}{R R} \frac{{du du}_{c c}}{d d t t})) = = ((\frac{11}{{R R}^{22} {C C}^{22}} - - \frac{11}{L L C C})) {u u}_{C C} - - \frac{11}{{RC RC}^{22}} {i i}_{L L} + + \frac{{θ θ}_{22}}{C C} - - \frac{{θ θ}_{11}}{R R C C} + + {\overset{\cdot &Center Dot;}{θ θ}}_{11} + + \frac{{U u}_{i i}}{L L C C} d d;;$

步骤2.3，设计滑模面函数s＝x₁+x₂，并求导得到：Step 2.3, design the sliding mode surface function s=x ₁ +x ₂ , and derive:

$\overset{\cdot \cdot}{s the s} = = {x x}_{22} + + {\overset{\cdot \cdot}{x x}}_{22} = = ((\frac{11}{{R R}^{22} {C C}^{22}} - - \frac{11}{R R C C} - - \frac{11}{L L C C})) {u u}_{C C} + + ((\frac{11}{C C} - - \frac{11}{{RC RC}^{22}})) {i i}_{L L} + + \frac{{θ θ}_{22}}{C C} - - ((11 - - \frac{11}{R R C C})) {θ θ}_{11} + + {\overset{\cdot &Center Dot;}{θ θ}}_{11} + + \frac{{U u}_{i i}}{L L C C} d d;;$

再求导得到： $\overset{\cdot\cdot}{s} = a (t, x) + b (t, x) v,$ 其中，Then find the derivative to get: $\overset{\cdot\cdot}{the s} = a (t, x) + b (t, x) v,$ in,

$\begin{matrix} a a ((t t,, x x)) = = ((- - \frac{11}{{R R}^{33} {C C}^{33}} + + \frac{11}{{R R}^{22} {C C}^{22}} + + \frac{22}{{RLC RLC}^{22}} - - \frac{11}{L L C C})) {u u}_{C C} + + ((\frac{11}{{R R}^{33} {C C}^{33}} - - \frac{11}{{RC RC}^{22}} - - \frac{11}{{LC LC}^{22}})) {i i}_{L L} + + ((\frac{{U u}_{i i}}{L L C C} - - \frac{{U u}_{i i}}{{RLC RLC}^{22}})) d d + + ((\frac{11}{{R R}^{22} {C C}^{22}} - - \frac{11}{R R C C} - - \frac{11}{L L C C})) {θ θ}_{11} \\ + + ((\frac{11}{C C} - - \frac{11}{{RC RC}^{22}})) {θ θ}_{22} + + ((11 - - \frac{11}{R R C C})) {\overset{\cdot &Center Dot;}{θ θ}}_{11} + + \frac{11}{C C} {\overset{\cdot &Center Dot;}{θ θ}}_{22} + + {\overset{\cdot\cdot \cdot\cdot}{θ θ}}_{11} \end{matrix},,$

$b b ((t t,, x x)) = = \frac{{U u}_{i i}}{L L C C};;$

步骤2.4，设计二阶滑模虚拟控制器：Step 2.4, design a second-order sliding mode virtual controller:

$v v = = - - {β β}_{22} {[[σ σ (({\overset{\cdot &Center Dot;}{s the s}}^{11 / / {γ γ}_{11}} + + {β β}_{11}^{11 / / {γ γ}_{11}} σ σ ((s the s))))]]}^{{γ γ}_{22}} - - \frac{\overset{&OverBar; &OverBar;}{a a}}{\underset{&OverBar; &OverBar;}{b b}} s the s i i g g n no (({\overset{\cdot &Center Dot;}{s the s}}^{11 / / {γ γ}_{11}} + + {β β}_{11}^{11 / / {γ γ}_{22}} σ σ ((s the s))));;$

其中， b分别为a(t,x)，b(t,x)的上界值和下界值，σ(x)称为饱和函数，并定义为 $σ (x) = \{\begin{matrix} ϵ s i g n (x), & | x | > ϵ \\ x & | x | \leq ϵ \end{matrix}, &ForAll; ϵ > 0, β_{2} > β_{1} > 1;$ in, b are the upper and lower bounds of a(t,x) and b(t,x) respectively, σ(x) is called the saturation function and is defined as $σ (x) = \{\begin{matrix} ϵ the s i g no (x), & | x | > ϵ \\ x & | x | \leq ϵ \end{matrix}, &ForAll; ϵ > 0, β_{2} > β_{1} > 1;$

步骤2.5，对步骤2.4所述虚拟控制器积分得到实际控制器：Step 2.5, integrating the virtual controller described in step 2.4 to obtain the actual controller:

$u u = = &Integral; &Integral; v v d d t t = = - - {β β}_{22} &Integral; &Integral; {[[σ σ (({\overset{\cdot &Center Dot;}{s the s}}^{\frac{11}{{γ γ}_{11}}} + + {β β}_{11}^{\frac{11}{{γ γ}_{11}}} σ σ ((s the s))))]]}^{{γ γ}_{22}} d d t t - - &Integral; &Integral; \frac{\overset{&OverBar; &OverBar;}{a a}}{\underset{&OverBar; &OverBar;}{b b}} s the s i i g g n no (({\overset{\cdot \cdot}{s the s}}^{\frac{11}{{γ γ}_{11}}} + + {β β}_{11}^{\frac{11}{{γ γ}_{11}}} σ σ ((s the s)))) d d t t . .$

作为优选方案，还包括：步骤3，数字化实现所述降压变换器无抖振滑模控制算法。As a preferred solution, it also includes: Step 3, digitally implementing the chattering-free sliding mode control algorithm of the step-down converter.

作为优选方案，所述步骤3的具体实现包括：As a preferred solution, the specific realization of said step 3 includes:

步骤3.1，利用数据采集卡实时采集降压变换器电路的输出电压u₀；Step 3.1, using the data acquisition card to collect the output voltage u ₀ of the step-down converter circuit in real time;

步骤3.2，所述u₀经A/D转换后送给LabVIEW平台处理，利用离散后的无抖振滑模控制算法得到控制量u(k)；In step 3.2, the u ₀ is sent to the LabVIEW platform for processing after A/D conversion, and the control variable u(k) is obtained by using the discrete chattering-free sliding mode control algorithm;

步骤3.3，所述u(k)经D/A/转换后得到控制量u；Step 3.3, said u(k) obtains the control quantity u after D/A/ conversion;

步骤3.4，所述控制量u作用在PWM信号产生电路得到频率不变、占空比变化的PWM方波；Step 3.4, the control quantity u acts on the PWM signal generating circuit to obtain a PWM square wave with constant frequency and variable duty ratio;

步骤3.5，所述频率不变、占空比变化的PWM方波经驱动电路放大后控制降压变换器电路的开关管，实现降压变换器的无抖振输出。In step 3.5, the PWM square wave with constant frequency and variable duty cycle is amplified by the driving circuit and then controls the switching tube of the step-down converter circuit to realize chatter-free output of the step-down converter.

本发明的有益效果是：The beneficial effects of the present invention are:

1，本发明在降压变换器的平均状态模型中考虑了实际电路存在的不确定因素，并在此基础上设计滑模控制方法，使降压变换器系统更接近于实际，增强了系统的稳定性和抗干扰性。1. The present invention considers the uncertain factors existing in the actual circuit in the average state model of the step-down converter, and designs a sliding mode control method on this basis, so that the step-down converter system is closer to reality, and the stability of the system is enhanced. Stability and anti-interference.

2，本发明利用二阶滑模控制理论设计的无抖振滑模控制器，在保证闭环系统不降低鲁棒性的前提下，实现了对输出信号的有限时间跟踪。2. The chattering-free sliding mode controller designed by the present invention using the second-order sliding mode control theory realizes the limited time tracking of the output signal under the premise of ensuring that the closed-loop system does not reduce the robustness.

3，本发明设计的控制器为非连续控制器的积分，避免了传统滑模控制器存在的抖振问题，使系统输出信号具有更高的精度。3. The controller designed by the present invention is the integral of the discontinuous controller, which avoids the chattering problem existing in the traditional sliding mode controller, and makes the system output signal have higher precision.

4，本发明对所设计的控制方法运用数字化方式实现，基于LabVIEW软件输出控制量，采用PWM定频控制方式，通过改变开关器件的占空比来控制其导通或关断，进而实现降压变换器的目标电压输出。4. The present invention implements the designed control method in a digital way, based on LabVIEW software output control amount, adopts PWM fixed frequency control mode, controls its on or off by changing the duty cycle of the switching device, and then realizes step-down Converter target voltage output.

5，本发明设计的控制器在考虑系统启动、输入电压突增突降、负载突变等大扰动情况下，可以取得比PID明显要好的控制效果，具体体现在：5. The controller designed by the present invention can achieve significantly better control effects than PID in consideration of large disturbances such as system start-up, sudden increase and drop of input voltage, and sudden load change, which are specifically reflected in:

1)采用无抖振滑模控制方法控制的降压变换器系统启动时间比传统PID控制方法控制的降压变换器系统启动时间短，反应时间快。1) The start-up time of the step-down converter system controlled by the chattering-free sliding mode control method is shorter than that of the step-down converter system controlled by the traditional PID control method, and the response time is faster.

2)采用无抖振滑模控制方法控制的降压变换器系统启动时间比传统PID控制方法控制的降压变换器系统控制精度高，抗扰动性能强。2) The start-up time of the step-down converter system controlled by the chattering-free sliding mode control method is higher than that of the step-down converter system controlled by the traditional PID control method, and the anti-disturbance performance is stronger.

附图说明Description of drawings

图1为本发明降压变换器的一种无抖振滑模控制方法数字化实现的降压变换器的电路原理图；Fig. 1 is the circuit schematic diagram of the step-down converter realized digitally by a kind of non-chattering sliding mode control method of the step-down converter of the present invention;

图2是本发明降压变换器的一种无抖振滑模控制方法数字化实现的总体设计方案结构框图；Fig. 2 is a kind of chattering-free sliding mode control method digital realization structural block diagram of the overall design scheme of step-down converter of the present invention;

图3是降压变换器的一种无抖振滑模控制方法数字化实现的降压变换器系统硬件部分电路实现结构图；Fig. 3 is a buck converter system hardware partial circuit realization structural diagram of a kind of chattering-free sliding mode control method digitally realized;

图4是当降压变换器系统启动时，本发明降压变换器的一种无抖振滑模控制方法数字化实现的控制作用与传统PID控制方法作用的输出电压的实验对比图；Fig. 4 is when the step-down converter system starts up, the experimental contrast diagram of the output voltage of the control action of a kind of non-chattering sliding mode control method of the step-down converter of the present invention realized digitally and the effect of traditional PID control method;

图5是当降压变换器系统输入电压改变时，本发明降压变换器的一种无抖振滑模控制方法数字化实现的控制作用与传统PID控制方法作用的输出电压的实验对比图；Fig. 5 is when the step-down converter system input voltage changes, the control action of a kind of non-chattering sliding mode control method of the step-down converter of the present invention digitally realizes the control effect and the experimental comparison diagram of the output voltage of traditional PID control method effect;

图6是当降压变换器系统负载发生变化时，本发明降压变换器的一种无抖振滑模控制方法数字化实现的控制作用与传统PID控制方法作用下的输出电压的实验对比图。Fig. 6 is an experimental comparison diagram of the output voltage under the control effect of a non-chattering sliding mode control method digitally realized by the step-down converter of the present invention and the traditional PID control method when the load of the step-down converter system changes.

具体实施方式detailed description

下面结合附图和具体实施例对本发明做进一步的解释。The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments.

如图1和图2，降压变换器的一种无抖振滑模控制方法数字化实现,其特征在于所述方法的实现过程为：As shown in Fig. 1 and Fig. 2, a kind of chattering-free sliding mode control method of step-down converter is realized digitally, it is characterized in that the realization process of described method is:

步骤一、建立降压变换器的平均状态模型Step 1. Establish the average state model of the buck converter

如图1，降压变换器有可控开关管VT“开通”和“关断”两种情况下对应的工作模式；As shown in Figure 1, the step-down converter has two corresponding working modes under the controllable switch tube VT "on" and "off";

(1)当可控开关管VT处于闭合状态时，二级管D承受反向偏压而截止，输入直流电压源U_i与电感L串联，电容C处于充电状态，此时为蓄能阶段。根据基尔霍夫电压定律有：(1) When the controllable switch tube VT is in the closed state, the diode D is cut off under reverse bias, the input DC voltage source U _i is connected in series with the inductor L, and the capacitor C is in the charging state, which is the energy storage stage. According to Kirchhoff's voltage law:

$L L \frac{{di di}_{L L}}{d d t t} = = {u u}_{i i} - - {u u}_{o o} - - - - - - ((11))$

(2)当开关管VT处于断开状态时，二极管D续流，与电容C、电感L构成放电回路。此时满足下面关系：(2) When the switch tube VT is in the off state, the diode D freewheels and forms a discharge circuit with the capacitor C and the inductor L. At this time, the following relationship is satisfied:

$L L \frac{{di di}_{L L}}{d d t t} = = - - {u u}_{o o} - - - - - - ((22))$

合并一个周期的两种状态(1)、(2)可得：Combining the two states (1) and (2) of one cycle can be obtained:

$L L \frac{{di di}_{L L}}{d d t t} = = d d (({u u}_{i i} - - {u u}_{o o})) + + ((11 - - d d)) ((- - {u u}_{o o})) = = {U u}_{i i} d d - - {u u}_{o o} - - - - - - ((33))$

式(3)中，d是开关量，其取值为0或1表示开关的断开或闭合状态。d的取值由控制量u决定，控制量u由步骤二设计给出。In formula (3), d is the switching value, and its value of 0 or 1 indicates the open or closed state of the switch. The value of d is determined by the control quantity u, which is given by the design of step two.

同理，根据基尔霍夫电流定律还可以得到：Similarly, according to Kirchhoff's current law, we can also get:

$C C \frac{{du du}_{o o}}{d d t t} = = {i i}_{L L} - - \frac{{u u}_{o o}}{R R} - - - - - - ((44))$

考虑降压变换器实际电路存在不确定因素，因此在平均状态模型中加入不确定项。设ΔC,ΔL,ΔU_i,ΔR分别为电容C，电感L，输入电压U_i，负载R的不确定项。结合电容两端电压u_C等于输出电压u_o，得到其平均状态空间模型表达式如下：Considering that there are uncertain factors in the actual circuit of the buck converter, an uncertain item is added to the average state model. Let ΔC, ΔL, ΔU _i , ΔR be the uncertain items of capacitance C, inductance L, input voltage U _i and load R respectively. Combining that the voltage u _C across the capacitor is equal to the output voltage u _o , the expression of its average state space model is as follows:

$(\begin{matrix} \frac{{du du}_{C C}}{d d t t} \\ \frac{{di di}_{L L}}{d d t t} \end{matrix}) = = (\begin{matrix} - - \frac{11}{((C C + + Δ Δ C C)) ((R R + + Δ Δ R R))} & \frac{11}{C C + + Δ Δ C C} \\ - - \frac{11}{L L + + Δ Δ L L} & 00 \end{matrix}) (\begin{matrix} {u u}_{C C} \\ {i i}_{L L} \end{matrix}) + + (\begin{matrix} 00 \\ \frac{{U u}_{i i} + + {ΔU Δ U}_{i i}}{L L + + Δ Δ L L} \end{matrix}) d d - - - - - - ((55))$

步骤二、设计降压变换器的无抖振滑模控制算法Step 2. Design the chattering-free sliding mode control algorithm for the buck converter

考虑如下非线性控制系统Consider the following nonlinear control system

$\{\begin{matrix} \overset{\cdot &Center Dot;}{x x} = = f f ((t t,, x x)) + + g g ((t t,, x x)) v v \\ s the s = = s the s ((t t,, x x)) \end{matrix} - - - - - - ((66))$

其中x∈Rⁿ为系统的状态变量，v∈R为系统的控制输入量；s(t,x)是滑模量；f(t,x)和g(t,x)是不确定光滑函数。若滑动变量具有相对阶2，通过非连续二阶滑模控制器v，使得滑动变量在有限时间内达到稳定，即保证有一般来说，滑动变量s的二阶导数显含控制输入信号v，且满足： $\overset{\cdot\cdot}{s} = a (t, x) + b (t, x) v .$ 式中 $a (t, x) = \overset{\cdot\cdot}{s} |_{v = 0}, b (t, x) = \partial \overset{\cdot\cdot}{s} / \partial v$ 为不确定项，且假设 $| a (t, x) | \leq \overset{&OverBar;}{a}, b (t, x) &GreaterEqual; \underset{&OverBar;}{b}$ 成立。where x∈R ⁿ is the state variable of the system, v∈R is the control input of the system; s(t,x) is the sliding modulus; f(t,x) and g(t,x) are uncertain smooth functions . If the sliding variable has a relative order of 2, through a discontinuous second-order sliding mode controller v, the sliding variable Stability is reached in a finite time, that is, guaranteed to have In general, the second derivative of the sliding variable s explicitly contains the control input signal v, and satisfies: $\overset{\cdot\cdot}{the s} = a (t, x) + b (t, x) v .$ In the formula $a (t, x) = \overset{\cdot\cdot}{the s} |_{v = 0}, b (t, x) = \partial \overset{\cdot\cdot}{the s} / \partial v$ is an uncertain item, and it is assumed that $| a (t, x) | \leq \overset{&OverBar;}{a}, b (t, x) &Greater Equal; \underset{&OverBar;}{b}$ established.

为方便计算，将步骤一的平均状态空间模型的不确定项部分分离，得到变形后的表达式为For the convenience of calculation, the uncertain part of the average state space model in step 1 is separated, and the transformed expression is obtained as

$\{\begin{matrix} \frac{{du du}_{C C}}{d d t t} = = \frac{11}{C C} (({i i}_{L L} - - \frac{{u u}_{C C}}{R R})) + + {θ θ}_{11} \\ \frac{{di di}_{L L}}{d d t t} = = \frac{11}{L L} (({dU U}_{i i} - - {u u}_{C C})) + + {θ θ}_{22} \end{matrix} - - - - - - ((77))$

其中 $θ_{1} = \frac{u_{C} Δ R}{R (R + Δ R) (C + Δ C)} + \frac{u_{C} Δ C - i_{L} Δ C R}{R C (C + Δ C)}, θ_{2} = \frac{{dΔU}_{i} L - {dΔLU}_{i} + {ΔLu}_{C}}{L (L + Δ L)} .$ in $θ_{1} = \frac{u_{C} Δ R}{R (R + Δ R) (C + Δ C)} + \frac{u_{C} Δ C - i_{L} Δ C R}{R C (C + Δ C)}, θ_{2} = \frac{{dΔU}_{i} L - {dΔLU}_{i} + {ΔLu}_{C}}{L (L + Δ L)} .$

如图2、3，输出电压偏差为x₁＝u₀-U_ref，其中U_ref为输出直流电压参考值。对x₁求导得到电压偏差变化率x₂，即As shown in Figures 2 and 3, the output voltage deviation is x ₁ =u ₀ -U _ref , where U _ref is the reference value of the output DC voltage. Deriving x ₁ to obtain the rate of change of voltage deviation x ₂ , namely

${x x}_{22} = = {\overset{\cdot \cdot}{x x}}_{11} = = - - \frac{11}{R R C C} {u u}_{c c} + + \frac{11}{C C} {i i}_{L L} + + {θ θ}_{11} - - - - - - ((88))$

${\overset{\cdot &Center Dot;}{x x}}_{22} = = \frac{11}{C C} ((\frac{{di di}_{L L}}{d d t t} - - \frac{11}{R R} \frac{{du du}_{c c}}{d d t t})) = = ((\frac{11}{{R R}^{22} {C C}^{22}} - - \frac{11}{L L C C})) {u u}_{C C} - - \frac{11}{{RC RC}^{22}} {i i}_{L L} + + \frac{{θ θ}_{22}}{C C} - - \frac{{θ θ}_{11}}{R R C C} + + {\overset{\cdot \cdot}{θ θ}}_{11} + + \frac{{U u}_{i i}}{L L C C} d d - - - - - - ((99))$

设计滑模面函数为s＝x₁+x₂，求导后有The sliding mode surface function is designed as s=x ₁ +x ₂ , after derivation, there is

$\overset{\cdot \cdot}{s the s} = = {x x}_{22} + + {\overset{\cdot \cdot}{x x}}_{22} = = ((\frac{11}{{R R}^{22} {C C}^{22}} - - \frac{11}{R R C C} - - \frac{11}{L L C C})) {u u}_{C C} + + ((\frac{11}{C C} - - \frac{11}{{RC RC}^{22}})) {i i}_{L L} + + \frac{{θ θ}_{22}}{C C} - - ((11 - - \frac{11}{R R C C})) {θ θ}_{11} + + {\overset{\cdot \cdot}{θ θ}}_{11} + + \frac{{U u}_{i i}}{L L C C} d d - - - - - - ((1010))$

再对上式求导，则有的形式。其中：Then take the derivative of the above formula, then we have form. in:

$\begin{matrix} a a ((t t,, x x)) = = ((- - \frac{11}{{R R}^{33} {C C}^{33}} + + \frac{11}{{R R}^{22} {C C}^{22}} + + \frac{22}{{RLC RLC}^{22}} - - \frac{11}{L L C C})) {u u}_{C C} + + ((\frac{11}{{R R}^{33} {C C}^{33}} + + \frac{11}{{RC RC}^{22}} - - \frac{11}{{LC LC}^{22}})) {i i}_{L L} + + ((\frac{{U u}_{i i}}{L L C C} - - \frac{{U u}_{i i}}{{RLC RLC}^{22}})) d d + + ((\frac{11}{{R R}^{22} {C C}^{22}} - - \frac{11}{R R C C} - - \frac{11}{L L C C})) {θ θ}_{11} \\ + + ((\frac{11}{C C} - - \frac{11}{{RC RC}^{22}})) {θ θ}_{22} + + ((11 - - \frac{11}{R R C C})) {\overset{\cdot &Center Dot;}{θ θ}}_{11} + + \frac{11}{C C} {\overset{\cdot &Center Dot;}{θ θ}}_{22} + + {\overset{\cdot\cdot \cdot\cdot}{θ θ}}_{11} \end{matrix},, b b ((t t,, x x)) = = \frac{{U u}_{i i}}{L L C C},,$

a(t,x)，b(t,x)中所有变量或参数都为有界量，且存在某一常数η使 $| (\frac{1}{R^{2} C^{2}} - \frac{1}{R C} - \frac{1}{L C}) θ_{1} + (\frac{1}{C} - \frac{1}{{RC}^{2}}) θ_{2} + (1 - \frac{1}{R C}) {\overset{\cdot}{θ}}_{1} + \frac{1}{C} {\overset{\cdot}{θ}}_{2} + {\overset{\cdot\cdot}{θ}}_{1} | \leq η$ 成立，因此不确定项a(t,x)，b(t,x)满足常数上界假设。d的取值由实际控制输入量u决定，的取值由虚拟控制输入量v决定。All variables or parameters in a(t,x) and b(t,x) are bounded quantities, and there is a certain constant η that makes $| (\frac{1}{R^{2} C^{2}} - \frac{1}{R C} - \frac{1}{L C}) θ_{1} + (\frac{1}{C} - \frac{1}{{RC}^{2}}) θ_{2} + (1 - \frac{1}{R C}) {\overset{&Center Dot;}{θ}}_{1} + \frac{1}{C} {\overset{\cdot}{θ}}_{2} + {\overset{\cdot\cdot}{θ}}_{1} | \leq η$ Established, so the uncertain items a(t,x), b(t,x) satisfy the constant upper bound assumption. The value of d is determined by the actual control input u, The value of is determined by the virtual control input v.

二阶滑模虚拟控制器设计为The second-order sliding mode virtual controller is designed as

$v v = = - - {β β}_{22} {[[σ σ (({\overset{\cdot &Center Dot;}{s the s}}^{11 / / {γ γ}_{11}} + + {β β}_{11}^{11 / / {γ γ}_{11}} σ σ ((s the s))))]]}^{{γ γ}_{22}} - - \frac{\overset{&OverBar; &OverBar;}{a a}}{\underset{&OverBar; &OverBar;}{b b}} s the s i i g g n no (({\overset{\cdot &Center Dot;}{s the s}}^{11 / / {γ γ}_{11}} + + {β β}_{11}^{11 / / {γ γ}_{22}} σ σ ((s the s)))) - - - - - - ((1111))$

其中， b分别为a(t,x)，b(t,x)的上界值和下界值，σ(x)称为饱和函数，并定义为 $σ (x) = \{\begin{matrix} ϵ s i g n (x), & | x | > ϵ \\ x & | x | \leq ϵ \end{matrix}, &ForAll; ϵ > 0, β_{2} > β_{1} > 1;$ 则滑动变量在有限时间内稳定。in, b are the upper and lower bounds of a(t,x) and b(t,x) respectively, σ(x) is called the saturation function and is defined as $σ (x) = \{\begin{matrix} ϵ the s i g no (x), & | x | > ϵ \\ x & | x | \leq ϵ \end{matrix}, &ForAll; ϵ > 0, β_{2} > β_{1} > 1;$ then the sliding variable Stable for a limited time.

实际控制器设计为虚拟控制器的积分，可以有效减弱滑模控制的抖振问题，提高降压变换器输出电压的精度，即如下形式：The actual controller is designed as the integral of the virtual controller, which can effectively reduce the chattering problem of sliding mode control and improve the accuracy of the output voltage of the buck converter, that is, the following form:

$u u = = &Integral; &Integral; v v d d t t = = - - {β β}_{22} &Integral; &Integral; {[[σ σ (({\overset{\cdot \cdot}{s the s}}^{\frac{11}{{γ γ}_{11}}} + + {β β}_{11}^{\frac{11}{{γ γ}_{11}}} σ σ ((s the s))))]]}^{{γ γ}_{22}} d d t t - - &Integral; &Integral; \frac{\overset{&OverBar; &OverBar;}{a a}}{\underset{&OverBar; &OverBar;}{b b}} s the s i i g g n no (({\overset{\cdot &Center Dot;}{s the s}}^{\frac{11}{{γ γ}_{11}}} + + {β β}_{11}^{\frac{11}{{γ γ}_{11}}} σ σ ((s the s)))) d d t t - - - - - - ((1212))$

为了将所设计的控制器在LabVIEW软件上实现，下面对控制器进行离散化处理。离散的电压偏差为e(k)＝u_o(k)-U_ref，其中U_ref是参考输出电压。那么，电压偏差率可以表示为In order to implement the designed controller on the LabVIEW software, the controller is discretized as follows. The discrete voltage deviation is e(k)=u _o (k)−U _ref , where U _ref is the reference output voltage. Then, the voltage deviation rate can be expressed as

de(k)＝(e(k)-e(k-1))/ts(13)de(k)=(e(k)-e(k-1))/ts(13)

上式中ts为采样周期，对de(k)求导得In the above formula, ts is the sampling period, and the derivation of de(k) is obtained

dde(k)＝(de(k)-de(k-1))/ts(14)dde(k)=(de(k)-de(k-1))/ts(14)

那么，离散化的滑模面函数表示为Then, the discretized sliding mode surface function is expressed as

$\{\begin{matrix} s the s ((k k)) = = e e ((k k)) + + d d e e ((k k)) \\ d d s the s ((k k)) = = d d e e ((k k)) + + d d d d e e ((k k)) \end{matrix} - - - - - - ((1515))$

综上，离散化的滑模控制器为In summary, the discrete sliding mode controller is

$\{\begin{matrix} d d u u ((k k)) = = - - {β β}_{22} {[[σ σ ((d d s the s {((k k))}^{\frac{11}{{γ γ}_{22}}} + + {β β}_{11}^{\frac{11}{{γ γ}_{22}}} σ σ ((s the s ((k k))))))]]}^{{γ γ}_{33}} - - \frac{\overset{&OverBar; &OverBar;}{a a}}{\underset{&OverBar; &OverBar;}{b b}} * * s the s i i g g n no ((d d s the s {((k k))}^{\frac{11}{{γ γ}_{22}}} + + {β β}_{11}^{\frac{11}{{γ γ}_{22}}} σ σ ((s the s ((k k)))))) \\ u u ((k k)) = = u u ((k k - - 11)) + + d d u u ((k k)) * * t t s the s \end{matrix} - - - - - - ((1616))$

步骤三、降压变换器无抖振滑模控制算法的数字化实现Step 3. Digital implementation of the chattering-free sliding mode control algorithm for buck converters

虚拟仪器技术基本原理是基于硬件平台，编写出合适的虚拟仪器软件程序，执行软件程序就可以实现所需要的不同仪器的功能。作为NI公司推出的虚拟仪器开发平台，LabVIEW具有直观简便的编程方式、数据处理便捷快速等优点.The basic principle of virtual instrument technology is based on the hardware platform, writing a suitable virtual instrument software program, and executing the software program can realize the functions of different instruments required. As a virtual instrument development platform launched by NI, LabVIEW has the advantages of intuitive and simple programming, convenient and fast data processing, etc.

如图2、3，所述降压变换器无抖振滑模控制算法的数字化实现，包括硬件和软件两个部分。所述软件部分是以LabVIEW软件为平台设计步骤二所述的无抖振滑模控制方法。硬件部分包括数据采集卡模块和降压变换器底层电路模块组成。所述降压变换器底层电路模块包括降压变换器主电路模块、PWM产生电路模块和驱动电路模块。As shown in Figures 2 and 3, the digital realization of the chattering-free sliding mode control algorithm of the step-down converter includes two parts: hardware and software. The software part uses LabVIEW software as the platform to design the chattering-free sliding mode control method described in step two. The hardware part consists of the data acquisition card module and the bottom circuit module of the step-down converter. The bottom circuit module of the step-down converter includes a main circuit module of the step-down converter, a PWM generating circuit module and a driving circuit module.

如图2，3，所述降压变换器主电路模块由直流电压源U_i、开关管VT、二极管D、电感L、电容C和负载R组成。所述开关管VT采用IRF630。所述数据采集卡用于采集输出信号。输出电压信号通过数据采集卡对降压变换器主电路模块负载电阻分压采集，从而保证输出电压在数据采集卡的采集范围内。As shown in Figures 2 and 3, the main circuit module of the step-down converter is composed of a DC voltage source U _i , a switch tube VT, a diode D, an inductor L, a capacitor C and a load R. The switch tube VT adopts IRF630. The data acquisition card is used for collecting output signals. The output voltage signal is collected by dividing the load resistance of the main circuit module of the step-down converter through the data acquisition card, so as to ensure that the output voltage is within the acquisition range of the data acquisition card.

如图2、3，在以LabVIEW软件为平台设计的控制器作用下的输出信号u(k)经过D/A转换模块转换为模拟输出信号u，数据采集卡采集输出信号u后，通过采集卡输出引脚与PWM产生电路模块中Feedback(FB)引脚相连，将控制信号输入到PWM产生电路模块中。所述PWM产生模块的锯齿波信号频率由TL494芯片及其外围器件电阻R_T、电容C_T调节。As shown in Figures 2 and 3, the output signal u(k) under the action of the controller designed with LabVIEW software as the platform is converted into an analog output signal u by the D/A conversion module. After the data acquisition card collects the output signal u, it passes through the acquisition card The output pin is connected to the Feedback (FB) pin in the PWM generating circuit module, and the control signal is input to the PWM generating circuit module. The frequency of the sawtooth wave signal of the PWM generation module is adjusted by the TL494 chip and its peripheral device resistor R _T and capacitor C _T .

如图2、3，驱动电路模块输入端接入PWM产生电路模块输出PWM方波。驱动电路模块的作用是将PWM方波放大后控制降压变换器电路的开关管通断。降压电路主体模块中功率开关管IRF630满足开通条件，从而经过放大后得占空比控制信号d能正常控制降压电路的通断。Feedback(FB)引脚与数据采集卡输出引脚相连，根据FB输入引脚的电压大小，将数据采集卡输出信号与锯齿波信号比较，输出频率不变，占空比不同的PWM方波。所述驱动电路由IR2110及外围器件组成。As shown in Figures 2 and 3, the input terminal of the drive circuit module is connected to PWM to generate a PWM square wave output from the circuit module. The function of the driving circuit module is to amplify the PWM square wave and control the on-off of the switching tube of the step-down converter circuit. The power switch tube IRF630 in the main module of the step-down circuit meets the turn-on condition, so the amplified duty cycle control signal d can normally control the on-off of the step-down circuit. The Feedback (FB) pin is connected to the output pin of the data acquisition card. According to the voltage of the FB input pin, the output signal of the data acquisition card is compared with the sawtooth wave signal, and the PWM square wave with the same frequency and different duty ratios is output. The driving circuit is composed of IR2110 and peripheral devices.

如图2、3，所述降压变换器的一种无抖振滑模控制方法数字化实现的整体实现过程为：数据采集卡模块实时采集降压电路的输出电压u_o，经过LabVIEW开发板自带模块进行A/D转换，在经过数据处理得到离散电压偏差e(k)；基于LabVIEW开发平台，利用离散化的步骤二所设计的滑模控制方法得到控制量u(k)；经过D/A转换模块得到控制量u，底层硬件电路依据所给控制量u得到频率不变，占空比变化的PWM方波d_o，PWM方波信号d_o经过驱动电路模块后输出占空比控制信号d，控制开关管的导通和关断，最终实现控制降压变换器输出无抖振电压的目的。As shown in Figures 2 and 3, the overall realization process of the digital realization of a chatter-free sliding mode control method for the step-down converter is as follows: the data acquisition card module collects the output voltage u _o of the step-down circuit in real time, and after the LabVIEW development board automatically Carry out A/D conversion with the module, and obtain the discrete voltage deviation e(k) after data processing; based on the LabVIEW development platform, use the sliding mode control method designed in the discretization step 2 to obtain the control variable u(k); after D/ The A conversion module obtains the control variable u, and the underlying hardware circuit obtains the PWM square wave d _o with constant frequency and variable duty cycle according to the given control value u, and the PWM square wave signal d _o outputs the duty cycle control signal after passing through the drive circuit module d. Control the turn-on and turn-off of the switch tube, and finally achieve the purpose of controlling the output voltage of the step-down converter without chattering.

为了有效地说明本发明降压变换器无抖振滑模控制算法的数字化实现的有效性与实用性。下面分别考虑在降压变换器系统启动阶段，系统存在输入电压信号扰动，系统存在负载扰动时这三种情况，将无抖振滑模控制方法控制的降压变换器系统与传统PID控制方法控制的降压变换器系统的输出电压信号进行实验对比。设定降压电路中电感L的值为330μH，电容C的值为1000pF，负载电阻R为110Ω，采样周期ts＝0.001s，PID控制算法的比例系数k_p＝0.2，积分系数k_i＝2，微分系数k_d＝1。无抖振滑模控制算法参数ε＝1,τ＝-2/5，β₁＝1.2，β₂＝10，γ₁＝3/5,γ₂＝1/5， In order to effectively illustrate the effectiveness and practicability of the digital realization of the chattering-free sliding mode control algorithm of the step-down converter of the present invention. The following three situations are considered in the startup stage of the buck converter system, the system has input voltage signal disturbance, and the system has load disturbance, and the buck converter system controlled by the non-chattering sliding mode control method and the traditional PID control method control The output voltage signal of the buck converter system is compared experimentally. Set the value of the inductance L in the step-down circuit to 330μH, the value of the capacitor C to 1000pF, the load resistance R to 110Ω, the sampling period ts=0.001s, the proportional coefficient k _p =0.2 of the PID control algorithm, and the integral coefficient k _i =2 , the differential coefficient k _d =1. Chattering-free sliding mode control algorithm parameters ε=1, τ=-2/5, β ₁ = 1.2, β ₂ = 10, γ ₁ = 3/5, γ ₂ = 1/5,

情况1：降压变换器系统启动阶段。Case 1: Buck converter system start-up phase.

如图4，两种控制器的控制目标为输出电压为12V。图中虚线表示PID控制器作用下的降压变换器系统输出电压波形，实线表示无抖振滑模控制器作用下的降压变换器系统输出电压波形，用CFSM(Chattering-freeslidingmode)标记。在稳态误差相差不大的条件下，无抖振滑模控制器作用下的降压变换器系统的启动时间比PID控制器作用下的降压变换器系统启动时间缩短了近一半。As shown in Figure 4, the control target of the two controllers is an output voltage of 12V. The dotted line in the figure indicates the output voltage waveform of the buck converter system under the action of the PID controller, and the solid line indicates the output voltage waveform of the buck converter system under the action of the non-chattering sliding mode controller, marked with CFSM (Chattering-freesliding mode). Under the condition that the steady-state error is not much different, the start-up time of the buck converter system under the action of the non-chattering sliding mode controller is shortened by nearly half of that of the buck converter system under the action of the PID controller.

情况2:降压变换器系统存在输入电压信号扰动，实验假设输入信号电压由18V变化到24V。Case 2: There is input voltage signal disturbance in the buck converter system, and the experiment assumes that the input signal voltage changes from 18V to 24V.

如图5，两种控制器的控制目标为输出电压为12V。图中虚线表示PID控制器作用下的降压变换器系统输出电压波形，实线表示无抖振滑模控制器作用下的降压变换器系统输出电压波形，用CFSM标记。当存在输入电压信号扰动时，PID控制器作用下的降压变换器系统有明显的瞬态电压变化，而无抖振滑模控制器作用下的降压变换器系统输出电压变化相对很小。As shown in Figure 5, the control target of the two controllers is an output voltage of 12V. The dotted line in the figure indicates the output voltage waveform of the buck converter system under the action of the PID controller, and the solid line indicates the output voltage waveform of the buck converter system under the action of the non-chattering sliding mode controller, marked with CFSM. When there is an input voltage signal disturbance, the step-down converter system under the action of the PID controller has obvious transient voltage changes, while the output voltage change of the step-down converter system under the action of the sliding mode controller without chattering is relatively small.

情况3:降压变换器系统存在负载扰动时，实验假设负载由110Ω突变到50Ω。Case 3: When there is a load disturbance in the buck converter system, the experiment assumes that the load changes from 110Ω to 50Ω.

如图6，两种控制器的控制目标为输出电压为12V。图中虚线表示PID控制器作用下的降压变换器系统输出电压波形，实线表示无抖振滑模控制器作用下的降压变换器系统输出电压波形，用CFSM标记。在突变负载时，相比于PID控制器，无抖振滑模控制器使得降压变换器系统输出电压变化幅度明显减小。As shown in Figure 6, the control target of the two controllers is an output voltage of 12V. The dotted line in the figure indicates the output voltage waveform of the buck converter system under the action of the PID controller, and the solid line indicates the output voltage waveform of the buck converter system under the action of the non-chattering sliding mode controller, marked with CFSM. When the load is suddenly changed, compared with the PID controller, the non-chattering sliding mode controller can significantly reduce the range of output voltage variation of the buck converter system.

以上所述仅为本发明的技术方案和具体实施例说明，并不用于限定本发明的保护范围，应当理解，在不违背本发明实质内容的前提下，所作任何修改、等同替换等都将落入本发明的保护范围内。The above description is only a description of the technical solutions and specific embodiments of the present invention, and is not intended to limit the protection scope of the present invention. It should be understood that any modifications, equivalent replacements, etc. will fall under the premise of not violating the essence of the present invention Into the protection scope of the present invention.

Claims

1. a chattering-free sliding mode control method for a step-down converter, characterized in that, comprising the steps:

Step 1, establishing an average state-space model of the buck converter including uncertain factors;

(\begin{matrix} \frac{{du du}_{C C}}{d d t t} \\ \frac{{di di}_{L L}}{d d t t} \end{matrix}) = = (\begin{matrix} - - \frac{11}{((C C + + Δ Δ C C)) ((R R + + Δ Δ R R))} & \frac{11}{C C + + Δ Δ C C} \\ - - \frac{11}{L L + + Δ Δ L L} & 00 \end{matrix}) (\begin{matrix} {u u}_{C C} \\ {i i}_{L L} \end{matrix}) + + (\begin{matrix} 00 \\ \frac{{U u}_{i i} + + {ΔU Δ U}_{i i}}{L L + + Δ Δ L L} \end{matrix}) d d

In the formula, R is the resistance value, L is the inductance value, C is the capacitance value, u _C is the voltage across the capacitor C, i _L is the inductor current, U _i is the input voltage, ΔC, ΔL, ΔU _i and ΔR are the capacitance C. Uncertain factors of inductance L, input voltage U _i , load resistance R, d is the switch value, and its value is 0 or 1, indicating the open or closed state of the switch;

Step 2, design the chattering-free sliding mode control algorithm of the buck converter; including:

Step 2.1, separate the uncertain part of the average state-space model described in step 1 to obtain:

\{\begin{matrix} \frac{{du du}_{C C}}{d d t t} = = \frac{11}{C C} (({i i}_{L L} - - \frac{{u u}_{C C}}{R R})) + + {θ θ}_{11} \\ \frac{{di di}_{L L}}{d d t t} = = \frac{11}{L L} (({dU U}_{i i} - - {u u}_{C C})) + + {θ θ}_{22} \end{matrix}

In the formula,

θ_{1} = \frac{u_{C} Δ R}{R (R + Δ R) (C + Δ C)} + \frac{u_{C} Δ C - i_{L} Δ C R}{R C (C + Δ C)}, θ_{2} = \frac{{dΔU}_{i} L - {dΔLU}_{i} + {ΔLu}_{C}}{L (L + Δ L)};

Step 2.2, define the output voltage deviation as x ₁ =u ₀ -U _ref , where U _ref is the reference value of the output DC voltage, and u ₀ is the output voltage of the step-down transformer;

Deriving x ₁ to obtain the rate of change of voltage deviation x ₂ :

{x x}_{22} = = {\overset{\cdot &Center Dot;}{x x}}_{11} = = - - \frac{11}{R R C C} {u u}_{c c} + + \frac{11}{C C} {i i}_{L L} + + {θ θ}_{11};;

Then take the derivative of x ₂ to get:

{\overset{\cdot &Center Dot;}{x x}}_{22} = = \frac{11}{C C} ((\frac{{di di}_{L L}}{d d t t} - - \frac{11}{R R} \frac{{du du}_{c c}}{d d t t})) = = ((\frac{11}{{R R}^{22} {C C}^{22}} - - \frac{11}{L L C C})) {u u}_{C C} - - \frac{11}{{RC RC}^{22}} {i i}_{L L} + + \frac{{θ θ}_{22}}{C C} - - \frac{{θ θ}_{11}}{R R C C} + + {\overset{\cdot &Center Dot;}{θ θ}}_{11} + + \frac{{U u}_{i i}}{L L C C} d d;;

Step 2.3, design the sliding mode surface function s=x ₁ +x ₂ , and derive:

\overset{\cdot &Center Dot;}{s the s} = = {x x}_{22} + + {\overset{\cdot &Center Dot;}{x x}}_{22} = = ((\frac{11}{{R R}^{22} {C C}^{22}} - - \frac{11}{R R C C} - - \frac{11}{L L C C})) {u u}_{C C} + + ((\frac{11}{C C} - - \frac{11}{{RC RC}^{22}})) {i i}_{L L} + + \frac{{θ θ}_{22}}{C C} - - ((11 - - \frac{11}{R R C C})) {θ θ}_{11} + + {\overset{\cdot \cdot}{θ θ}}_{11} + + \frac{{U u}_{i i}}{L L C C} d d;;

Then find the derivative to get:

\overset{\cdot\cdot}{the s} = a (t, x) + b (t, x) v,

in,

\begin{matrix} a a ((t t,, x x)) = = ((- - \frac{11}{{R R}^{33} {C C}^{33}} + + \frac{11}{{R R}^{22} {C C}^{22}} + + \frac{22}{{RLC RLC}^{22}} - - \frac{11}{L L C C})) {u u}_{C C} + + ((\frac{11}{{R R}^{22} {C C}^{33}} - - \frac{11}{{RC RC}^{22}} - - \frac{11}{{LC LC}^{22}})) {i i}_{L L} + + ((\frac{{U u}_{i i}}{L L C C} - - \frac{{U u}_{i i}}{{RLC RLC}^{22}})) d d + + ((\frac{11}{{R R}^{22} {C C}^{22}} - - \frac{11}{R R C C} - - \frac{11}{L L C C})) {θ θ}_{11} \\ + + ((\frac{11}{C C} - - \frac{11}{{RC RC}^{22}})) {θ θ}_{22} + + ((11 - - \frac{11}{R R C C})) {\overset{\cdot &Center Dot;}{θ θ}}_{11} + + \frac{11}{C C} {\overset{\cdot &Center Dot;}{θ θ}}_{22} + + {\overset{\cdot &Center Dot;}{θ θ}}_{11} \end{matrix},,

b b ((t t,, x x)) = = \frac{{U u}_{i i}}{L L C C};;

Step 2.4, design a second-order sliding mode virtual controller:

v v = = - - {β β}_{22} {[[σ σ (({\overset{\cdot &Center Dot;}{s the s}}^{11 / / {γ γ}_{11}} + + {β β}_{11}^{11 / / {γ γ}_{11}} σ σ ((s the s))))]]}^{{γ γ}_{22}} - - \frac{\overset{&OverBar; &OverBar;}{a a}}{\underset{&OverBar; &OverBar;}{b b}} s the s i i g g n no (({\overset{\cdot &Center Dot;}{s the s}}^{11 / / {γ γ}_{11}} + + {β β}_{11}^{11 / / {γ γ}_{22}} σ σ ((s the s))));;

in,

γ_{1} = τ + 1, γ_{2} = γ_{1} + τ, - \frac{1}{2} < τ < 0,

b are the upper and lower bounds of a(t,x) and b(t,x) respectively, σ(x) is called the saturation function and is defined as

σ (x) = \{\begin{matrix} ϵ the s i g no (x), & | x | > ϵ \\ x & | x | \leq ϵ \end{matrix}, &ForAll; ϵ > 0, β_{2} > β_{1} > 1;

Step 2.5, integrating the virtual controller described in step 2.4 to obtain the actual controller:

u u = = &Integral; &Integral; v v d d t t = = - - {β β}_{22} &Integral; &Integral; {[[σ σ (({\overset{\cdot &Center Dot;}{s the s}}^{\frac{11}{{γ γ}_{11}}} + + {β β}_{11}^{\frac{11}{{γ γ}_{11}}} σ σ ((s the s))))]]}^{{γ γ}_{22}} d d t t - - &Integral; &Integral; \frac{\overset{&OverBar; &OverBar;}{a a}}{\underset{&OverBar; &OverBar;}{b b}} s the s i i g g n no (({\overset{\cdot &Center Dot;}{s the s}}^{\frac{11}{{γ γ}_{11}}} + + {β β}_{11}^{\frac{11}{{γ γ}_{22}}} σ σ ((s the s)))) d d t t . .

2 . The chattering-free sliding mode control method for a buck converter according to claim 1 , further comprising: step 3, digitally implementing the chattering-free sliding mode control method for a buck converter. 3 .

3. The chattering-free sliding mode control method of a step-down converter according to claim 2, wherein the specific realization of the step 3 comprises:

Step 3.1, using the data acquisition card to collect the output voltage u ₀ of the step-down converter circuit in real time;

In step 3.2, the u ₀ is sent to the LabVIEW platform for processing after A/D conversion, and the control variable u(k) is obtained by using the discrete chattering-free sliding mode control algorithm;

Step 3.3, said u(k) obtains the control quantity u after D/A/ conversion;

Step 3.4, the control quantity u acts on the PWM signal generating circuit to obtain a PWM square wave with constant frequency and variable duty ratio;

In step 3.5, the PWM square wave with constant frequency and variable duty cycle is amplified by the drive circuit to control the switching tube of the step-down converter circuit, so as to realize chatter-free output of the step-down converter.