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

Abstract

The invention discloses a chattering-free sliding mode control method for a buck converter, and belongs to the field of power electronic converters. The invention designs the chattering-free sliding mode control method for the buck converter by a second-order sliding mode control theory on the basis of an average state model of the buck converter. By a constant-frequency PWM mode, on or off is controlled by changing the duty ratio of a switching device, so that target voltage output of the buck converter is achieved. Meanwhile, the whole scheme of a buck converter system under the action of the control method is achieved on the basis of a LabVIEW platform. The widely existed chattering problem in traditional sliding mode control and the problems that a buck converter controlled by a linear PID method is low in response speed, low in voltage output quality, poor in anti-disturbance capability and the like are solved; and the control method overcomes disturbance influences of a load resistance, a DC input voltage and the like and improves the performance of an output voltage by the advantages of strong robustness, high steady accuracy and the like.

Description

Buffeting-free sliding mode control method of buck converter

Technical Field

The invention relates to the field of power electronic converters, in particular to a method for eliminating buffeting widely existing in traditional sliding mode control by utilizing a second-order sliding mode control technology and improving the dynamic performance and the steady-state performance of output voltage of a buck converter.

Background

In recent years, due to the development of power electronic technology, buck converters are widely applied to various direct current buck occasions, such as electric and hybrid electric vehicles, solar power generation, industrial instruments, portable electronic products, military aerospace and other fields. The main function of the buck converter is to convert high-voltage direct current into low-voltage direct current, and provide stable direct current voltage for a load.

The power converter can be realized by adopting a linear control method and can also be realized by adopting a nonlinear control method. As a typical linear control method, a conventional PID control algorithm is often used in various control circuits due to advantages of simple structure, convenient operation, low cost, and the like. However, the power converter has complexity and time-varying property, and meanwhile, large disturbances such as input voltage change and load sudden change exist, so that higher requirements are provided for the requirements of dynamic response speed, disturbance resistance performance, control accuracy and the like, and the traditional PID control method is difficult to meet the actual control requirements. In order to improve the control performance, various superior control algorithms need to be researched and applied in the power converter, such as adaptive control, fuzzy logic control, artificial neural network control, sliding mode control, and the like.

The sliding mode control is taken as a variable structure control method, and when the system motion state is on the sliding mode surface, the method has strong robustness on the uncertain items of system parameters and external interference. Secondly, due to the switching of the switch state, the power converter has the characteristic of a variable structure system, so that the sliding mode variable structure control algorithm is widely adopted in the control design of the power converter. However, when the trajectory of the system reaches the switching surface, the inertia causes the moving point to pass through the switching surface to finally form buffeting, and the buffeting is superimposed on an ideal sliding mode.

The second-order sliding mode expands the idea of the traditional sliding mode, and discontinuous control quantity acts on the second derivative of the sliding modulus instead of the first derivative, so that the advantages of simple design, easy realization, strong robustness and the like of the traditional sliding mode algorithm are kept, the influence of buffeting can be obviously weakened, and the stability of the controller is enhanced.

Disclosure of Invention

In order to solve the problems of buffeting in a traditional sliding mode control method and low response speed, poor disturbance resistance and the like in a traditional linear PID control method, the invention provides a buffeting-free sliding mode control method of a buck converter based on a second-order sliding mode technology, and the buffeting-free sliding mode control method is digitally realized. The adopted specific technical scheme is as follows:

a buffeting-free sliding mode control method of a buck converter comprises the following steps:

step 1, establishing an average state space model of a buck converter containing uncertain factors;

$\left(\begin{array}{c}\frac{{\mathrm{du}}_C}{dt}\\ \frac{{\mathrm{di}}_L}{dt}\end{array}\right)=\left(\begin{array}{cc}-\frac{1}{(C+\mathrm{\Δ}C)(R+\mathrm{\Δ}R)}& \frac{1}{C+\mathrm{\Δ}C}\\ -\frac{1}{L+\mathrm{\Δ}L}& 0\end{array}\right)\left(\begin{array}{c}{u}_C\\ i_L\end{array}\right)+\left(\begin{array}{c}0\\ \frac{U_i+{\mathrm{\ΔU}}_i}{L+\mathrm{\Δ}L}\end{array}\right)d$

wherein R is a resistance value, L is an inductance value, C is a capacitance value, u_CIs the voltage across the capacitor C, i_LIs the inductive current, U_iFor input voltage, Δ C, Δ L, Δ U_iAnd Delta R is respectively a capacitor C, an inductor L and an input voltage U_iD is a switching value, and the value of d is 0 or 1 and represents the open or closed state of the switchState;

step 2, designing a buffeting-free sliding mode control algorithm of the buck converter; the method comprises the following steps:

step 2.1, separating the uncertainty part of the average state space model in the step 1 to obtain:

$\left\{\begin{array}{c}\frac{{\mathrm{du}}_C}{dt}=\frac{1}{C}(i_L-\frac{u_C}{R})+{\mathrm{\θ}}_1\\ \frac{{\mathrm{di}}_L}{dt}=\frac{1}{L}({\mathrm{dU}}_i-u_C)+{\mathrm{\θ}}_2\end{array}\right.$

in the formula, ${\mathrm{\θ}}_1=\frac{u_C\mathrm{\Δ}R}{R(R+\mathrm{\Δ}R)(C+\mathrm{\Δ}C)}+\frac{u_C\mathrm{\Δ}C-i_L\mathrm{\Δ}CR}{RC(C+\mathrm{\Δ}C)},{\mathrm{\θ}}_2=\frac{{\mathrm{d\ΔU}}_{i}L-{\mathrm{d\ΔLU}}_i+{\mathrm{\ΔLU}}_C}{L(L+\mathrm{\Δ}L)};$

step 2.2, defining the deviation of the output voltage as x₁＝u₀-U_refWherein U is_refFor outputting a DC voltage reference value u₀Is the output voltage of the step-down transformer;

for x₁Deriving the voltage deviation change rate x₂：

$x_2={\stackrel{\·}{x}}_1=-\frac{1}{RC}{u}_c+\frac{1}{C}{i}_L+{\mathrm{\θ}}_1;$

Then for x₂The derivation yields:

${\stackrel{\·}{x}}_2=\frac{1}{C}(\frac{{\mathrm{di}}_L}{dt}-\frac{1}{R}\frac{{\mathrm{du}}_c}{dt})=(\frac{1}{R^2{C}^2}-\frac{1}{LC})u_C-\frac{1}{{\mathrm{RC}}^2}{i}_L+\frac{{\mathrm{\θ}}_2}{C}-\frac{{\mathrm{\θ}}_1}{RC}+{\stackrel{\·}{\mathrm{\θ}}}_1+\frac{U_i}{LC}d;$

step 2.3, designing a sliding mode surface function s as x₁+x₂And deriving to obtain:

$\stackrel{\·}{s}=x_2+{\stackrel{\·}{x}}_2=(\frac{1}{R^2{C}^2}-\frac{1}{RC}-\frac{1}{LC})u_C+(\frac{1}{C}-\frac{1}{{\mathrm{RC}}^2})i_L+\frac{{\mathrm{\θ}}_2}{C}-(1-\frac{1}{RC}){\mathrm{\θ}}_1+{\stackrel{\·}{\mathrm{\θ}}}_1+\frac{U_i}{LC}d;$

and then obtaining by derivation: $\stackrel{\·\·}{s}=a(t,x)+b(t,x)v,$ wherein,

$\begin{array}{c}a(t,x)=(-\frac{1}{R^3{C}^3}+\frac{1}{R^2{C}^2}+\frac{2}{{\mathrm{RLC}}^2}-\frac{1}{LC})u_C+(\frac{1}{R^3{C}^3}-\frac{1}{{\mathrm{RC}}^2}-\frac{1}{{\mathrm{LC}}^2})i_L+(\frac{U_i}{LC}-\frac{U_i}{{\mathrm{RLC}}^2})d+(\frac{1}{R^2{C}^2}-\frac{1}{RC}-\frac{1}{LC}){\mathrm{\θ}}_1\\ +(\frac{1}{C}-\frac{1}{{\mathrm{RC}}^2}){\mathrm{\θ}}_2+(1-\frac{1}{RC}){\stackrel{\·}{\mathrm{\θ}}}_1+\frac{1}{C}{\stackrel{\·}{\mathrm{\θ}}}_2+{\stackrel{\·\·}{\mathrm{\θ}}}_1\end{array},$

$b(t,x)=\frac{U_i}{LC};$

step 2.4, designing a second-order sliding mode virtual controller:

$v=-{\mathrm{\β}}_2{\[\mathrm{\σ}({\stackrel{\·}{s}}^{1/{\mathrm{\γ}}_1}+{\mathrm{\β}}_1^{1/{\mathrm{\γ}}_1}\mathrm{\σ}(s\left)\right)\]}^{{\mathrm{\γ}}_2}-\frac{\stackrel{\‾}{a}}{\underset{\‾}{b}}sign({\stackrel{\·}{s}}^{1/{\mathrm{\γ}}_1}+{\mathrm{\β}}_1^{1/{\mathrm{\γ}}_2}\mathrm{\σ}(s\left)\right);$

wherein, bupper and lower bound values of a (t, x), b (t, x), respectively, σ (x) is called the saturation function and is defined as $\mathrm{\σ}\left(x\right)=\left\{\begin{array}{cc}\mathrm{\ϵ}sign\left(x\right),& \left|x\right|>\mathrm{\ϵ}\\ x& \left|x\right|\≤\mathrm{\ϵ}\end{array}\right.,\∀\mathrm{\ϵ}>0,{\mathrm{\β}}_2>{\mathrm{\β}}_1>1;$

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

$u=\∫vdt=-{\mathrm{\β}}_2\∫{\[\mathrm{\σ}({\stackrel{\·}{s}}^{\frac{1}{{\mathrm{\γ}}_1}}+{{\mathrm{\β}}_1}^{\frac{1}{{\mathrm{\γ}}_1}}\mathrm{\σ}(s\left)\right)\]}^{{\mathrm{\γ}}_2}dt-\∫\frac{\stackrel{\‾}{a}}{\underset{\‾}{b}}sign({\stackrel{\·}{s}}^{\frac{1}{{\mathrm{\γ}}_1}}+{{\mathrm{\β}}_1}^{\frac{1}{{\mathrm{\γ}}_1}}\mathrm{\σ}(s\left)\right)dt.$

preferably, the method further comprises the following steps: and 3, digitally realizing the buffeting-free sliding mode control algorithm of the buck converter.

As a preferred scheme, the specific implementation of step 3 includes:

step 3.1, acquiring the output voltage u of the buck converter circuit in real time by using a data acquisition card₀；

Step 3.2, the u₀Sending the processed data to a LabVIEW platform for processing after A/D conversion, and obtaining a control quantity u (k) by utilizing a discrete buffeting-free sliding mode control algorithm;

step 3.3, obtaining a controlled quantity u after D/A/conversion of the u (k);

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

and 3.5, amplifying the PWM square waves with constant frequency and variable duty ratio by a driving circuit, and controlling a switching tube of a buck converter circuit to realize buffeting-free output of the buck converter.

The invention has the beneficial effects that:

the invention considers the uncertain factors existing in the actual circuit in the average state model of the buck converter, and designs the sliding mode control method on the basis of the uncertain factors, so that the buck converter system is closer to the actual state, and the stability and the anti-interference performance of the system are enhanced.

2, the buffeting-free sliding mode controller designed by the second-order sliding mode control theory realizes the limited time tracking of the output signal on the premise of ensuring that the robustness of a closed-loop system is not reduced.

3, the controller designed by the invention is the integral of a discontinuous controller, thereby avoiding the buffeting problem of the traditional sliding mode controller and ensuring that the output signal of the system has higher precision.

4, the designed control method is realized in a digital mode, the control quantity is output based on LabVIEW software, a PWM (pulse-width modulation) fixed-frequency control mode is adopted, and the on-off of the switch device is controlled by changing the duty ratio of the switch device, so that the target voltage output of the buck converter is realized.

5, the controller designed by the invention can obtain a control effect obviously better than PID under the condition of considering large disturbances such as system starting, sudden increase and drop of input voltage, sudden change of load and the like, and is specifically embodied in that:

1) the starting time of the buck converter system controlled by the buffeting-free sliding mode control method is shorter than that of the buck converter system controlled by the traditional PID control method, and the response time is short.

2) Compared with the buck converter system controlled by the traditional PID control method, the start time of the buck converter system controlled by the buffeting-free sliding mode control method is high in control precision and strong in disturbance resistance.

Drawings

FIG. 1 is a schematic circuit diagram of a digitally implemented buck converter for a buffeting-free sliding mode control method of a buck converter in accordance with the present invention;

FIG. 2 is a block diagram of the overall design scheme of a digital implementation of a buffeting-free sliding mode control method for a buck converter of the present invention;

FIG. 3 is a block diagram of a hardware circuit implementation of a buck converter system implemented digitally by a buffeting-free sliding mode control method of the buck converter;

FIG. 4 is a graph of experimental comparison of output voltage for digitally implemented control of a buffeting-free sliding mode control method of a buck converter in accordance with the present invention with conventional PID control method when the buck converter system is started;

FIG. 5 is an experimental comparison of the output voltage for a digitally implemented control action of a buffeting-free sliding mode control method of a buck converter of the present invention versus the action of a conventional PID control method when the input voltage to the buck converter system changes;

fig. 6 is an experimental comparison graph of the output voltage under the control action digitally implemented by the buffeting-free sliding mode control method of the buck converter according to the present invention and the traditional PID control method when the system load of the buck converter changes.

Detailed Description

The invention is further explained below with reference to the figures and the specific embodiments.

Referring to fig. 1 and fig. 2, a buffeting-free sliding mode control method of a buck converter is realized digitally, and is characterized in that the method is realized by the following steps:

step one, establishing an average state model of a buck converter

As shown in fig. 1, the buck converter has corresponding working modes under two conditions of "on" and "off" of the controllable switching tube VT;

(1) when the controllable switch tube VT is in the closed state, the diode D bears the reverse bias voltage and is cut off, and the input direct current voltage source U_iThe capacitor C is connected with the inductor L in series and is in a charging state, and the energy storage stage is performed at the moment. According to kirchhoff's voltage law:

$L\frac{{\mathrm{di}}_L}{dt}=u_i-u_o---\left(1\right)$

(2) when the switching tube VT is in the off state, the diode D continues current, and forms a discharge circuit with the capacitor C and the inductor L. The following relationship is satisfied at this time:

$L\frac{{\mathrm{di}}_L}{dt}=-u_o---\left(2\right)$

combining the two states (1), (2) of one cycle can obtain:

$L\frac{{\mathrm{di}}_L}{dt}=d(u_i-u_o)+(1-d)(-u_o)=U_{i}d-u_o---\left(3\right)$

in the formula (3), d is a switching value, and a value of 0 or 1 indicates an open or closed state of the switch. The value of d is determined by the control quantity u, and the control quantity u is given by the design of the step two.

Similarly, according to kirchhoff's current law, the following can be obtained:

$C\frac{{\mathrm{du}}_o}{dt}=i_L-\frac{u_o}{R}---\left(4\right)$

uncertainty is added to the average state model to account for uncertainty in the actual circuit of the buck converter. Let Δ C, Δ L, Δ U_iAnd Delta R is respectively a capacitor C, an inductor L and an input voltage U_iUncertainty of the load R. Combined with the voltage u across the capacitor_CIs equal to the output voltage u_oAnd obtaining an average state space model expression as follows:

$\left(\begin{array}{c}\frac{{\mathrm{du}}_C}{dt}\\ \frac{{\mathrm{di}}_L}{dt}\end{array}\right)=\left(\begin{array}{cc}-\frac{1}{(C+\mathrm{\Δ}C)(R+\mathrm{\Δ}R)}& \frac{1}{C+\mathrm{\Δ}C}\\ -\frac{1}{L+\mathrm{\Δ}L}& 0\end{array}\right)\left(\begin{array}{c}{u}_C\\ i_L\end{array}\right)+\left(\begin{array}{c}0\\ \frac{U_i+{\mathrm{\ΔU}}_i}{L+\mathrm{\Δ}L}\end{array}\right)d---\left(5\right)$

wherein R is a resistance value, L is an inductance value, C is a capacitance value, u_CIs the voltage across the capacitor C, i_LIs the inductive current, U_iFor input voltage, Δ C, Δ L, Δ U_iAnd Delta R is respectively a capacitor C, an inductor L and an input voltage U_iD is a switching value, the value of d is 0 or 1, and the switching value represents the open or closed state of the switch;

step two, designing buffeting-free sliding mode control algorithm of buck converter

Consider the following nonlinear control system

$\left\{\begin{array}{c}\stackrel{\·}{x}=f(t,x)+g(t,x)v\\ s=s(t,x)\end{array}\right.---\left(6\right)$

Wherein x ∈ RⁿIf the sliding variable has a relative order of 2, the sliding variable is enabled to pass through a discontinuous second-order sliding mode controller vReach stability within a limited time, i.e. ensureIn general, the second derivative of the sliding variable s contains the control input signal v and satisfies: $\stackrel{\·\·}{s}=a(t,x)+b(t,x)v.$ in the formula $a(t,x)=\stackrel{\·\·}{s}{|}_{v=0},b(t,x)=\∂\stackrel{\·\·}{s}/\∂v$ Is an uncertainty term, and assumes $\left|a(t,x)\right|\≤\stackrel{\‾}{a},b(t,x)\≥\underset{\‾}{b}$ This is true.

For convenient calculation, the uncertain item part of the average state space model in the step one is separated, and the expression after deformation is obtained as

$\left\{\begin{array}{c}\frac{{\mathrm{du}}_C}{dt}=\frac{1}{C}(i_L-\frac{u_C}{R})+{\mathrm{\θ}}_1\\ \frac{{\mathrm{di}}_L}{dt}=\frac{1}{L}({\mathrm{dU}}_i-u_C)+{\mathrm{\θ}}_2\end{array}\right.---\left(7\right)$

Wherein ${\mathrm{\θ}}_1=\frac{u_C\mathrm{\Δ}R}{R(R+\mathrm{\Δ}R)(C+\mathrm{\Δ}C)}+\frac{u_C\mathrm{\Δ}C-i_L\mathrm{\Δ}CR}{RC(C+\mathrm{\Δ}C)},{\mathrm{\θ}}_2=\frac{{\mathrm{d\ΔU}}_{i}L-{\mathrm{d\ΔLU}}_i+{\mathrm{\ΔLu}}_C}{L(L+\mathrm{\Δ}L)}.$

Referring to FIGS. 2 and 3, the deviation of the output voltage is x₁＝u₀-U_refWherein U is_refTo output a dc voltage reference. For x₁Deriving the voltage deviation change rate x₂I.e. by

$x_2={\stackrel{\·}{x}}_1=-\frac{1}{RC}{u}_c+\frac{1}{C}{i}_L+{\mathrm{\θ}}_1---\left(8\right)$

${\stackrel{\·}{x}}_2=\frac{1}{C}(\frac{{\mathrm{di}}_L}{dt}-\frac{1}{R}\frac{{\mathrm{du}}_c}{dt})=(\frac{1}{R^2{C}^2}-\frac{1}{LC})u_C-\frac{1}{{\mathrm{RC}}^2}{i}_L+\frac{{\mathrm{\θ}}_2}{C}-\frac{{\mathrm{\θ}}_1}{RC}+{\stackrel{\·}{\mathrm{\θ}}}_1+\frac{U_i}{LC}d---\left(9\right)$

Designing the sliding mode surface function as s ═ x₁+x₂After derivation, there are

$\stackrel{\·}{s}=x_2+{\stackrel{\·}{x}}_2=(\frac{1}{R^2{C}^2}-\frac{1}{RC}-\frac{1}{LC})u_C+(\frac{1}{C}-\frac{1}{{\mathrm{RC}}^2})i_L+\frac{{\mathrm{\θ}}_2}{C}-(1-\frac{1}{RC}){\mathrm{\θ}}_1+{\stackrel{\·}{\mathrm{\θ}}}_1+\frac{U_i}{LC}d---\left(10\right)$

Then, the above formula is derived byIn the form of (1). Wherein:

$\begin{array}{c}a(t,x)=(-\frac{1}{R^3{C}^3}+\frac{1}{R^2{C}^2}+\frac{2}{{\mathrm{RLC}}^2}-\frac{1}{LC})u_C+(\frac{1}{R^3{C}^3}+\frac{1}{{\mathrm{RC}}^2}-\frac{1}{{\mathrm{LC}}^2})i_L+(\frac{U_i}{LC}-\frac{U_i}{{\mathrm{RLC}}^2})d+(\frac{1}{R^2{C}^2}-\frac{1}{RC}-\frac{1}{LC}){\mathrm{\θ}}_1\\ +(\frac{1}{C}-\frac{1}{{\mathrm{RC}}^2}){\mathrm{\θ}}_2+(1-\frac{1}{RC}){\stackrel{\·}{\mathrm{\θ}}}_1+\frac{1}{C}{\stackrel{\·}{\mathrm{\θ}}}_2+{\stackrel{\·\·}{\mathrm{\θ}}}_1\end{array},b(t,x)=\frac{U_i}{LC},$

all variables or parameters in a (t, x), b (t, x) are bounded quantities and there is some constant η that makes $|(\frac{1}{R^2{C}^2}-\frac{1}{RC}-\frac{1}{LC}){\mathrm{\θ}}_1+(\frac{1}{C}-\frac{1}{{\mathrm{RC}}^2}){\mathrm{\θ}}_2+(1-\frac{1}{RC}){\stackrel{\·}{\mathrm{\θ}}}_1+\frac{1}{C}{\stackrel{\·}{\mathrm{\θ}}}_2+{\stackrel{\·\·}{\mathrm{\θ}}}_1|\≤\mathrm{\η}$ It holds that the uncertainty terms a (t, x), b (t, x) satisfy the constant upper bound assumption. The value of d is determined by the actual control input u,is determined by the virtual control input v.

The second-order sliding mode virtual controller is designed as

$v=-{\mathrm{\β}}_2{\[\mathrm{\σ}({\stackrel{\·}{s}}^{1/{\mathrm{\γ}}_1}+{\mathrm{\β}}_1^{1/{\mathrm{\γ}}_1}\mathrm{\σ}(s\left)\right)\]}^{{\mathrm{\γ}}_2}-\frac{\stackrel{\‾}{a}}{\underset{\‾}{b}}sign({\stackrel{\·}{s}}^{1/{\mathrm{\γ}}_1}+{\mathrm{\β}}_1^{1/{\mathrm{\γ}}_2}\mathrm{\σ}(s\left)\right)---\left(11\right)$

Wherein, bupper and lower bound values of a (t, x), b (t, x), respectively, σ (x) is called the saturation function and is defined as $\mathrm{\σ}\left(x\right)=\left\{\begin{array}{cc}\mathrm{\ϵ}sign\left(x\right),& \left|x\right|>\mathrm{\ϵ}\\ x& \left|x\right|\≤\mathrm{\ϵ}\end{array}\right.,\∀\mathrm{\ϵ}>0,{\mathrm{\β}}_2>{\mathrm{\β}}_1>1;$ Then the sliding variableStable for a limited time.

The actual controller is designed as the integral of a virtual controller, so that the buffeting problem of sliding mode control can be effectively weakened, and the precision of the output voltage of the buck converter is improved, namely the following form:

$u=\∫vdt=-{\mathrm{\β}}_2\∫{\[\mathrm{\σ}({\stackrel{\·}{s}}^{\frac{1}{{\mathrm{\γ}}_1}}+{{\mathrm{\β}}_1}^{\frac{1}{{\mathrm{\γ}}_1}}\mathrm{\σ}(s\left)\right)\]}^{{\mathrm{\γ}}_2}dt-\∫\frac{\stackrel{\‾}{a}}{\underset{\‾}{b}}sign({\stackrel{\·}{s}}^{\frac{1}{{\mathrm{\γ}}_1}}+{{\mathrm{\β}}_1}^{\frac{1}{{\mathrm{\γ}}_1}}\mathrm{\σ}(s\left)\right)dt---\left(12\right)$

in order to implement the designed controller on LabVIEW software, the controller is discretized as follows. Discrete voltage deviations of e (k) u_o(k)-U_refWherein U is_refIs the reference output voltage. Then, the voltage deviation ratio can be expressed as

de(k)＝(e(k)-e(k-1))/ts(13)

In the above formula, ts is the sampling period, and is derived from de (k)

dde(k)＝(de(k)-de(k-1))/ts(14)

Then, the discretized sliding-mode surface function is expressed as

$\left\{\begin{array}{c}s\left(k\right)=e\left(k\right)+de\left(k\right)\\ ds\left(k\right)=de\left(k\right)+dde\left(k\right)\end{array}\right.---\left(15\right)$

To sum up, the discretized sliding mode controller is

$\left\{\begin{array}{c}du\left(k\right)=-{\mathrm{\β}}_2{\[\mathrm{\σ}(ds{\left(k\right)}^{\frac{1}{{\mathrm{\γ}}_2}}+{{\mathrm{\β}}_1}^{\frac{1}{{\mathrm{\γ}}_2}}\mathrm{\σ}(s\left(k\right)\left)\right)\]}^{{\mathrm{\γ}}_3}-\frac{\stackrel{\‾}{a}}{\underset{\‾}{b}}*sign(ds{\left(k\right)}^{\frac{1}{{\mathrm{\γ}}_2}}+{{\mathrm{\β}}_1}^{\frac{1}{{\mathrm{\γ}}_2}}\mathrm{\σ}(s\left(k\right)\left)\right)\\ u\left(k\right)=u(k-1)+du\left(k\right)*ts\end{array}\right.---\left(16\right)$

Step three, realizing digitization of buffeting-free sliding mode control algorithm of buck converter

The basic principle of the virtual instrument technology is that based on a hardware platform, a proper virtual instrument software program is written out, and the functions of different required instruments can be realized by executing the software program. As a virtual instrument development platform released by NI company, LabVIEW has the advantages of visual, simple and convenient programming mode, convenient and fast data processing and the like.

Referring to fig. 2 and 3, the digital implementation of the buffeting-free sliding mode control algorithm of the buck converter comprises two parts, namely hardware and software. The software part is a buffeting-free sliding mode control method which is designed by using LabVIEW software as a platform in the second step. The hardware part comprises a data acquisition card module and a buck converter bottom layer circuit module. The buck converter bottom layer circuit module comprises a buck converter main circuit module, a PWM (pulse width modulation) generating circuit module and a driving circuit module.

As shown in fig. 2 and 3, the main circuit module of the buck converter is composed of a direct current voltage source U_iA switch tube VT, a diode D,Inductor L, capacitor C and load R. The switching tube VT adopts IRF 630. The data acquisition card is used for acquiring output signals. The output voltage signal is acquired by the data acquisition card in a voltage division manner through the load resistor of the main circuit module of the buck converter, so that the output voltage is ensured to be within the acquisition range of the data acquisition card.

Referring to fig. 2 and 3, an output signal u (k) under the action of a controller designed by taking LabVIEW software as a platform is converted into an analog output signal u through a D/a conversion module, and after the output signal u is collected by a data collection card, the output signal u is connected with a feedback (fb) pin in a PWM generation circuit module through a collection card output pin, and a control signal is input into the PWM generation circuit module. The sawtooth wave signal frequency of the PWM generating module is composed of a TL494 chip and a resistor R of a peripheral device thereof_TCapacitor C_TAnd (6) adjusting.

As shown in fig. 2 and 3, the input end of the driving circuit module is connected to the PWM generating circuit module to output the PWM square wave. The driving circuit module is used for amplifying the PWM square wave and then controlling the on-off of a switching tube of the buck converter circuit. The power switch tube IRF630 in the voltage reduction circuit main body module meets the switching-on condition, so that the duty ratio control signal d obtained after amplification can normally control the on-off of the voltage reduction circuit. And a Feedback (FB) pin is connected with an output pin of the data acquisition card, and the output signal of the data acquisition card is compared with the sawtooth wave signal according to the voltage of the FB input pin, so that the PWM square wave with constant output frequency and different duty ratios is output. The driving circuit is composed of the IR2110 and peripheral devices.

Referring to fig. 2 and 3, the overall implementation process of the digital implementation of the buffeting-free sliding mode control method of the buck converter is as follows: data acquisition card module real-time acquisition voltage reduction circuit output voltage u_oCarrying out A/D conversion by using a self-contained module of a LabVIEW development board, and obtaining a discrete voltage deviation e (k) through data processing; based on a LabVIEW development platform, obtaining a control quantity u (k) by using a sliding mode control method designed in the discretization step two; the control quantity u is obtained through the D/A conversion module, and the bottom layer hardware circuit obtains the PWM square wave D with constant frequency and variable duty ratio according to the given control quantity u_oPWM square wave signal d_oAnd a duty ratio control signal d is output after passing through the driving circuit module to control the on and off of the switching tube, and finally the purpose of controlling the buck converter to output the buffeting-free voltage is achieved.

In order to effectively illustrate the effectiveness and the practicability of the digital realization of the buffeting-free sliding mode control algorithm of the buck converter. In the following, the three conditions that input voltage signal disturbance exists in the system and load disturbance exists in the system at the start-up stage of the buck converter system are considered respectively, and the output voltage signals of the buck converter system controlled by the buffeting-free sliding mode control method and the buck converter system controlled by the traditional PID control method are compared in an experiment. Setting the value of an inductor L in a voltage reduction circuit to be 330 mu H, the value of a capacitor C to be 1000pF, the value of a load resistor R to be 110 omega, the sampling period ts to be 0.001s, and the proportionality coefficient k of a PID control algorithm_p0.2, integral coefficient k_i2, coefficient of differentiation k_d1. the parameter of the sliding mode control algorithm without buffeting is 1, tau is-2/5, β₁＝1.2，β₂＝10，γ₁＝3/5,γ₂＝1/5，

Case 1: a buck converter system start-up phase.

As shown in fig. 4, the control target of both controllers is an output voltage of 12V. The dashed line in the figure represents the buck converter system output voltage waveform under the action of the PID controller, and the solid line represents the buck converter system output voltage waveform under the action of the buffeting-free sliding mode controller, marked with CFSM (Chattering-freeslidingmode). Under the condition that the steady-state error is not large, the starting time of the buck converter system under the action of the buffeting-free sliding mode controller is shortened by nearly half compared with the starting time of the buck converter system under the action of the PID controller.

Case 2-buck converter system there is input voltage signal disturbance and the experiment assumes that the input signal voltage varies from 18V to 24V.

As shown in fig. 5, the control target of both controllers is an output voltage of 12V. In the figure, the dotted line represents the output voltage waveform of the buck converter system under the action of the PID controller, and the solid line represents the output voltage waveform of the buck converter system under the action of the chattering-free sliding mode controller, which is marked by CFSM. When input voltage signal disturbance exists, the buck converter system under the action of the PID controller has obvious transient voltage change, and the output voltage change of the buck converter system under the action of the buffeting-free sliding mode controller is relatively small.

Case 3. in the presence of load disturbances in the buck converter system, experiments assume that the load jumps from 110 Ω to 50 Ω.

As shown in fig. 6, the control target of both controllers is an output voltage of 12V. In the figure, the dotted line represents the output voltage waveform of the buck converter system under the action of the PID controller, and the solid line represents the output voltage waveform of the buck converter system under the action of the chattering-free sliding mode controller, which is marked by CFSM. When the load suddenly changes, compared with a PID (proportion integration differentiation) controller, the buffeting-free sliding mode controller enables the output voltage variation amplitude of the buck converter system to be obviously reduced.

The above description is only intended to illustrate the technical solution and the specific embodiments of the present invention, and not to limit the scope of the present invention, and it should be understood that any modifications, equivalents and the like may be made within the scope of the present invention without departing from the spirit of the present invention.

Claims (3)

1. A buffeting-free sliding mode control method of a buck converter is characterized by comprising the following steps:

step 1, establishing an average state space model of a buck converter containing uncertain factors;

$\left(\begin{array}{c}\frac{{\mathrm{du}}_C}{dt}\\ \frac{{\mathrm{di}}_L}{dt}\end{array}\right)=\left(\begin{array}{cc}-\frac{1}{(C+\mathrm{\Δ}C)(R+\mathrm{\Δ}R)}& \frac{1}{C+\mathrm{\Δ}C}\\ -\frac{1}{L+\mathrm{\Δ}L}& 0\end{array}\right)\left(\begin{array}{c}{u}_C\\ i_L\end{array}\right)+\left(\begin{array}{c}0\\ \frac{U_i+{\mathrm{\ΔU}}_i}{L+\mathrm{\Δ}L}\end{array}\right)d$

wherein R is a resistance value, L is an inductance value, C is a capacitance value, u_CIs the voltage across the capacitor C, i_LIs the inductive current, U_iFor input voltage, Δ C, Δ L, Δ U_iAnd Delta R is respectively a capacitor C, an inductor L and an input voltage U_iD is a switching value, the value of d is 0 or 1, and the switching value represents the open or closed state of the switch;

step 2, designing a buffeting-free sliding mode control algorithm of the buck converter; the method comprises the following steps:

step 2.1, separating the uncertainty part of the average state space model in the step 1 to obtain:

$\left\{\begin{array}{c}\frac{{\mathrm{du}}_C}{dt}=\frac{1}{C}(i_L-\frac{u_C}{R})+{\mathrm{\θ}}_1\\ \frac{{\mathrm{di}}_L}{dt}=\frac{1}{L}({\mathrm{dU}}_i-u_C)+{\mathrm{\θ}}_2\end{array}\right.$

in the formula, ${\mathrm{\θ}}_1=\frac{u_C\mathrm{\Δ}R}{R(R+\mathrm{\Δ}R)(C+\mathrm{\Δ}C)}+\frac{u_C\mathrm{\Δ}C-i_L\mathrm{\Δ}CR}{RC(C+\mathrm{\Δ}C)},{\mathrm{\θ}}_2=\frac{{\mathrm{d\ΔU}}_{i}L-{\mathrm{d\ΔLU}}_i+{\mathrm{\ΔLu}}_C}{L(L+\mathrm{\Δ}L)};$

step 2.2, defining the deviation of the output voltage as x₁＝u₀-U_refWherein U is_refFor outputting a DC voltage reference value u₀Is the output voltage of the step-down transformer;

for x₁Deriving the voltage deviation change rate x₂：

$x_2={\stackrel{\·}{x}}_1=-\frac{1}{RC}{u}_c+\frac{1}{C}{i}_L+{\mathrm{\θ}}_1;$

Then for x₂The derivation yields:

${\stackrel{\·}{x}}_2=\frac{1}{C}(\frac{{\mathrm{di}}_L}{dt}-\frac{1}{R}\frac{{\mathrm{du}}_c}{dt})=(\frac{1}{R^2{C}^2}-\frac{1}{LC})u_C-\frac{1}{{\mathrm{RC}}^2}{i}_L+\frac{{\mathrm{\θ}}_2}{C}-\frac{{\mathrm{\θ}}_1}{RC}+{\stackrel{\·}{\mathrm{\θ}}}_1+\frac{U_i}{LC}d;$

step 2.3, designing a sliding mode surface function s as x₁+x₂And deriving to obtain:

$\stackrel{\·}{s}=x_2+{\stackrel{\·}{x}}_2=(\frac{1}{R^2{C}^2}-\frac{1}{RC}-\frac{1}{LC})u_C+(\frac{1}{C}-\frac{1}{{\mathrm{RC}}^2})i_L+\frac{{\mathrm{\θ}}_2}{C}-(1-\frac{1}{RC}){\mathrm{\θ}}_1+{\stackrel{\·}{\mathrm{\θ}}}_1+\frac{U_i}{LC}d;$

and then obtaining by derivation: $\stackrel{\·\·}{s}=a(t,x)+b(t,x)v,$ wherein,

$\begin{array}{c}a(t,x)=(-\frac{1}{R^3{C}^3}+\frac{1}{R^2{C}^2}+\frac{2}{{\mathrm{RLC}}^2}-\frac{1}{LC})u_C+(\frac{1}{R^2{C}^3}-\frac{1}{{\mathrm{RC}}^2}-\frac{1}{{\mathrm{LC}}^2})i_L+(\frac{U_i}{LC}-\frac{U_i}{{\mathrm{RLC}}^2})d+(\frac{1}{R^2{C}^2}-\frac{1}{RC}-\frac{1}{LC}){\mathrm{\θ}}_1\\ +(\frac{1}{C}-\frac{1}{{\mathrm{RC}}^2}){\mathrm{\θ}}_2+(1-\frac{1}{RC}){\stackrel{\·}{\mathrm{\θ}}}_1+\frac{1}{C}{\stackrel{\·}{\mathrm{\θ}}}_2+{\stackrel{\·}{\mathrm{\θ}}}_1\end{array},$ $b(t,x)=\frac{U_i}{LC};$

step 2.4, designing a second-order sliding mode virtual controller:

$v=-{\mathrm{\β}}_2{\[\mathrm{\σ}({\stackrel{\·}{s}}^{1/{\mathrm{\γ}}_1}+{\mathrm{\β}}_1^{1/{\mathrm{\γ}}_1}\mathrm{\σ}(s\left)\right)\]}^{{\mathrm{\γ}}_2}-\frac{\stackrel{\‾}{a}}{\underset{\‾}{b}}sign({\stackrel{\·}{s}}^{1/{\mathrm{\γ}}_1}+{\mathrm{\β}}_1^{1/{\mathrm{\γ}}_2}\mathrm{\σ}(s\left)\right);$

wherein, ${\mathrm{\&gamma;}}_1=\mathrm{\&tau;}+1,{\mathrm{\&gamma;}}_2={\mathrm{\&gamma;}}_1+\mathrm{\&tau;},-\frac{1}{2}<\mathrm{\&tau;}<0,$ bupper and lower bound values of a (t, x), b (t, x), respectively, σ (x) is called the saturation function and is defined as $\mathrm{\&sigma;}\left(x\right)=\left\{\begin{array}{cc}\mathrm{\&epsiv;}sign\left(x\right),& \left|x\right|>\mathrm{\&epsiv;}\\ x& \left|x\right|\&le;\mathrm{\&epsiv;}\end{array}\right.,\&ForAll;\mathrm{\&epsiv;}>0,{\mathrm{\&beta;}}_2>{\mathrm{\&beta;}}_1>1;$

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

$u=\&Integral;vdt=-{\mathrm{\&beta;}}_2\&Integral;{\&lsqb;\mathrm{\&sigma;}({\stackrel{\&CenterDot;}{s}}^{\frac{1}{{\mathrm{\&gamma;}}_1}}+{{\mathrm{\&beta;}}_1}^{\frac{1}{{\mathrm{\&gamma;}}_1}}\mathrm{\&sigma;}(s\left)\right)\&rsqb;}^{{\mathrm{\&gamma;}}_2}dt-\&Integral;\frac{\stackrel{\&OverBar;}{a}}{\underset{\&OverBar;}{b}}sign({\stackrel{\&CenterDot;}{s}}^{\frac{1}{{\mathrm{\&gamma;}}_1}}+{{\mathrm{\&beta;}}_1}^{\frac{1}{{\mathrm{\&gamma;}}_2}}\mathrm{\&sigma;}(s\left)\right)dt.$

2. the buffeting-free sliding-mode control method of a buck converter according to claim 1, further comprising: and 3, digitally realizing the buffeting-free sliding mode control method of the buck converter.

3. The buffeting-free sliding mode control method of the buck converter according to claim 2, wherein the step 3 is realized by the following steps:

step 3.1, acquiring the output voltage u of the buck converter circuit in real time by using a data acquisition card₀；

Step 3.2, the u₀Sending the processed data to a LabVIEW platform for processing after A/D conversion, and obtaining a control quantity u (k) by utilizing a discrete buffeting-free sliding mode control algorithm;

step 3.3, obtaining a controlled quantity u after D/A/conversion of the u (k);

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

and 3.5, amplifying the PWM square waves with constant frequency and variable duty ratio by a driving circuit, and controlling a switching tube of a buck converter circuit to realize buffeting-free output of the buck converter.