CN104915527A - Variational integral-discretization Lagrange model-based Buck-Boost converter modeling and nonlinear analysis method - Google Patents

Abstract

The invention provides a variational integral-discretization Lagrange model-based Buck-Boost converter modeling and nonlinear analysis method. The invention relates to a Buck-Boost converter modeling and nonlinear analysis method. The method of the invention is used for solving the problem that operation of a discrete iterative model is complex because the calculated quantity of an established stroboscopic mapping model is large. The method of the invention is realized by the steps as follows: 1) establishing an Euler-Lagrange function; 2) establishing a Hamiltonian system equation; 3) exporting location momentum of a variational integral; 4) establishing a discrete Lagrange model; 5) exporting a Jacobian matrix characteristic value; 6) calculating non-linear behaviors of a stability region of the Buck-Boost converter and a first branch point of the Buck-Boost converter. The method of the invention is applied to the field of the Buck-Boost converter modeling and nonlinear analysis.

Description

A kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method

Technical field

The present invention relates to One Buck-Boost converter body modeling and nonlinear analysis, particularly a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method.

Background technology

Converters belongs to strongly non-linear system, contains abundant Nonlinear dynamic behaviors.Over the last couple of decades, people have extensive and deep research for the non-linear behavior of the complexity of DC-DC converter, and have defined the method for the analytic system non-linear behavior of complete set.When analyzing the slow yardstick of DC-DC converter and fast yardstick dynamic behavior, the mathematical model of system first will be derived.In modeling, employ State-space Averaging Principle, equivalent circuit method, conservation of energy widely, because DC-DC converter has complicated topological structure and abundant Nonlinear dynamic behaviors, discrete time mapping, modeling method obtains to be applied more and more widely.Chinese scholars is constantly being improved discrete hidden Markov models method and is proposing new method always.Existing document shows, discrete time mapping model is the first-selected model of DC-DC converter nonlinear dynamic analysis.The discrete modeling method of DC-DC converter can be divided into approximate discrete iteration mapping, modeling and accurate discrete iteration mapping, modeling.On the one hand, although approximate discrete iteration model can obtain the roughly mutual relationship between approximate analysis result and transducer inner parameter, but some information may be lost because of approximate, the dynamics of system is made obviously to depart from actual system dynamics behavior; On the other hand, due to the existence of matrix and integration, the calculated amount of accurate discrete model is very large.At present, analyzing the discrete modeling method be most widely used when DC-DC converter Nonlinear dynamic behaviors is stroboscopic map method.But the matrix exponetial in stroboscopic map model and integral operation, usually make the computing of discrete iteration model become complexity very.

Summary of the invention

The object of the invention is to set up the approximate inaccurate problem causing Nonlinear dynamic behaviors calculated amount that is inaccurate and stroboscopic map model to make greatly the computing complexity of discrete iteration model of discrete iteration model to solve, and a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral proposed and nonlinear analysis method.

Above-mentioned goal of the invention is achieved through the following technical solutions:

The Euler-Lagrange function of step one, structure One Buck-Boost converter body;

Step 2, Buck-Boost Euler-Lagrange function is carried out discretize after construct hamiltonian system equation;

Step 3, by hamiltonian system equation, derive the position momentum p of variational integral _kand p _k+1;

Step 4, according to p _kand p _k+1set up the discrete Lagrangian model of One Buck-Boost converter body;

Step 5, utilize the Jacobian matrix eigenwert of the discrete Lagrangian model guiding system of One Buck-Boost converter body;

Step 6, Jacobian matrix eigenwert is utilized to obtain the non-linear behavior of One Buck-Boost converter body stabilized zone and One Buck-Boost converter body bifurcation point first; Namely a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method is completed.

Invention effect

The One Buck-Boost converter body analytical approach of the discrete Lagrangian modeling method based on variational integral of the present invention's research, relative to traditional discrete iteration model, discrete Lagrangian model does not have matrix exponetial item and integration item, reduce computation complexity, computing time is shortened dramatically, makes it be more suitable for computer numerical value calculation and digital control field.Result of study of the present invention has important directive significance and using value to the modeling of DC-DC converter and stability analysis.

The present invention proposes a kind of novel DC-DC converter nonlinear analysis method, discrete Lagrangian modeling method based on variational integral does not have matrix exponetial item and integration item, reduce computation complexity, computing time is shortened dramatically, makes it be more suitable for computer numerical value calculation and digital control field.

The discrete Lagrangian model based on variational integral that the present invention uses analyzes the non-linear behavior of One Buck-Boost converter body, along with the degree of accuracy increasing the method for sample frequency is also more and more higher, good effect is achieved by simulation analysis, from Fig. 4 (b), Fig. 4 (d), Fig. 4 (f) is respectively Fig. 4 (a), Fig. 4 (c), the partial enlarged drawing of Fig. 4 (e). as can be seen from the figure, novel Discrete model and stroboscopic map model are at reference current I _refthe system stability region obtained when changing with pull-up resistor R is almost identical..This modeling method is simple, not containing matrix exponetial and integration item in the model obtained, is suitable for the design of numerical analysis and digitial controller.Conclusion has vital role for the design at converter circuit Selecting parameter and controller.There is certain engineering practical value.

Accompanying drawing explanation

Fig. 1 is the One Buck-Boost converter body schematic diagram of the Controlled in Current Mode and Based that embodiment three proposes;

Fig. 2 is the current-mode exemplary control signal schematic diagram that embodiment three proposes;

Fig. 3 is the track schematic diagram of Jacobian matrix (Jacobian) eigenwert with circuit parameter variations of embodiment eight proposition;

Fig. 4 (a) is under switching frequency that embodiment one proposes is 200k, and when resistance is 0 ~ 500 Ω, Buck-Boost switch converters is with stabilized zone when reference current and pull-up resistor change;

Fig. 4 (b) is under switching frequency that embodiment one proposes is 200k, and when resistance is 50 ~ 150 Ω, Buck-Boost switch converters is with stabilized zone when reference current and pull-up resistor change;

Fig. 4 (c) is under switching frequency that embodiment one proposes is 100k, and Buck-Boost switch converters when resistance is 0 ~ 150 Ω is with stabilized zone when reference current and pull-up resistor change;

Fig. 4 (d) is under switching frequency that embodiment one proposes is the different switching frequency of 100k, and Buck-Boost switch converters when resistance is 50 ~ 150 Ω is with stabilized zone when reference current and pull-up resistor change;

Fig. 4 (e) for embodiment one propose under switching frequency is 50k, Buck-Boost switch converters when resistance is 0 ~ 150 Ω is with stabilized zone when reference current and pull-up resistor change;

Fig. 4 (f) is under switching frequency that embodiment one proposes is 50k, and Buck-Boost switch converters when resistance is 50 ~ 150 Ω is with stabilized zone when reference current and pull-up resistor change;

Fig. 5 (a) for switching frequency that embodiment proposes be that Buck-Boost switch converters under 200k is with stabilized zone when reference current and input direct voltage change;

Fig. 5 (b) for switching frequency that embodiment proposes be that Buck-Boost switch converters under 100k is with stabilized zone when reference current and input direct voltage change;

Fig. 5 (c) for switching frequency that embodiment proposes be that Buck-Boost switch converters under the different switching frequency of 50k is with stabilized zone when reference current and input direct voltage change.

Embodiment

Embodiment one: a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral of present embodiment and nonlinear analysis method, specifically prepare according to following steps:

The Euler-Lagrange function of step one, structure One Buck-Boost converter body;

Step 2, Buck-Boost Euler-Lagrange function is carried out discretize after construct hamiltonian system equation;

Step 3, by hamiltonian system equation, derive the position momentum p of variational integral _kand p _k+1;

Step 4, according to p _kand p _k+1set up the discrete Lagrangian model of One Buck-Boost converter body;

Step 5, utilize the Jacobian matrix eigenwert of the discrete Lagrangian model guiding system of One Buck-Boost converter body;

Step 6, Jacobian matrix eigenwert is utilized to obtain the non-linear behavior of One Buck-Boost converter body stabilized zone and One Buck-Boost converter body bifurcation point first; Namely a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method is completed.

Present embodiment effect:

The One Buck-Boost converter body analytical approach of the discrete Lagrangian modeling method based on variational integral of present embodiment research, relative to traditional discrete iteration model, discrete Lagrangian model does not have matrix exponetial item and integration item, reduce computation complexity, computing time is shortened dramatically, makes it be more suitable for computer numerical value calculation and digital control field.The result of study of present embodiment has important directive significance and using value to the modeling of DC-DC converter and stability analysis.

Present embodiment proposes a kind of novel DC-DC converter nonlinear analysis method, discrete Lagrangian modeling method based on variational integral does not have matrix exponetial item and integration item, reduce computation complexity, computing time is shortened dramatically, makes it be more suitable for computer numerical value calculation and digital control field.

The discrete Lagrangian model based on variational integral that present embodiment is used analyzes the non-linear behavior of One Buck-Boost converter body, along with the degree of accuracy increasing the method for sample frequency is also more and more higher, good effect is achieved by simulation analysis, from Fig. 4 (b), Fig. 4 (d), Fig. 4 (f) is respectively Fig. 4 (a), Fig. 4 (c), the partial enlarged drawing of Fig. 4 (e). as can be seen from the figure, novel Discrete model and stroboscopic map model are at reference current I _refthe system stability region obtained when changing with pull-up resistor R is almost identical..This modeling method is simple, not containing matrix exponetial and integration item in the model obtained, is suitable for the design of numerical analysis and digitial controller.Conclusion has vital role for the design at converter circuit Selecting parameter and controller.There is certain engineering practical value.

Embodiment two: present embodiment and embodiment one unlike: the Euler-Lagrange function constructing One Buck-Boost converter body in step one is specially:

(1) define for the kinetic energy of circuit, ν _u(q _c) be the potential energy of circuit, for the dissipative function of circuit, ν _{u, nc}q forcing function that () is system, u is control signal; During u=0, switch disconnects, switch conduction during u=1, and concrete form is as follows:

$T_u\left({\stackrel{\·}{q}}_L\right)=\frac{1}{2}L{\stackrel{\·}{q}}_L^2,v_u\left(q_C\right)=\frac{1}{2C}{q}_C^2,F_u\left(\stackrel{\·}{q}\right)=\frac{1}{2}R{\left(\right(1-u){\stackrel{\·}{q}}_L-{\stackrel{\·}{q}}_C)}^2,v_{u,nc}\left(q\right)=-{\mathrm{\μ}}^{T}q$

Wherein, q _lbe expressed as the quantity of electric charge stored in inductance, q _crepresent the quantity of electric charge stored in capacitor, q=(q _l, q _c) ^t, be expressed as the electric current flowing through inductance, be expressed as the electric current flowing through capacitor, l is inductance value, and C is capacitance, and R is resistance value, and vector μ is defined as μ=((1-u) E, 0) ^t, E is the input voltage of Buck-Boost circuit;

(2) be then written as with the Euler-Lagrange function of external force and dissipative function:

$L_{nc}(q,\stackrel{\·}{q})=L(q,\stackrel{\·}{q})+F_u\left(\stackrel{\·}{q}\right)-v_{u,nc}\left(q\right)---\left(2\right)$

In formula euler-Lagrange function for traditional:

$L(q,\stackrel{\·}{q})=T_u\left({\stackrel{\·}{q}}_L\right)-v_u\left(q_C\right)=\frac{1}{2}L{\stackrel{\·}{q}}_L^2-\frac{1}{2C}{q}_C^2---\left(3\right)$

(3) formula (2) and (3) are traditional Euler-Lagrange function.Other step and parameter identical with embodiment one.

Embodiment three: present embodiment and embodiment one or two unlike: in step one, the schematic diagram of One Buck-Boost converter body Controlled in Current Mode and Based is as shown in Figure 1, and One Buck-Boost converter body Controlled in Current Mode and Based is specially:

(1) components and parts in circuit are all considered as ideal component; Wherein, the components and parts in circuit comprise inductance, electric capacity, resistance, switching tube, input power, comparer and rest-set flip-flop; Ideal component is have single constant relationship not by the components and parts of the impact of other factors such as material temperature;

(2) by inductive current i _lwith reference current I _refcompare, if i _lbe greater than I _ref, then what rest-set flip-flop R held is input as 1; If i _lbe less than I _ref, then what rest-set flip-flop R held is input as 0;

(3) clock signal is by the S end input of rest-set flip-flop, if rest-set flip-flop R hold be input as 0 and rest-set flip-flop S hold be input as 1 time, then the Q of rest-set flip-flop holds output to be 1, if rest-set flip-flop R hold be input as 1 and rest-set flip-flop S hold be input as 0 time, then rest-set flip-flop Q hold output be 0;

(4) break-make of the output Q gauge tap pipe M of rest-set flip-flop; Shown in circuit waveform Fig. 2, draw the dutycycle in switch periods each time according to the principle of One Buck-Boost converter body Controlled in Current Mode and Based:

$u_k=\frac{I_{ref}-i_{L,k}}{(E/L)T}---\left(1\right)$

Wherein, clock signal is 0 or 1, the T clock period.Other step and parameter identical with embodiment one or two.

Embodiment four: one of present embodiment and embodiment one to three unlike: construct hamiltonian system equation after Buck-Boost Euler-Lagrange function being carried out discretize in step 2;

(1) to Euler-Lagrange function traditional in formula (3) discretize is carried out with time period h:

Construct a sequence increased progressively in time: { t _k=kh|k=0,1 ... N};

Wherein, h=t _k+1-t _k, at each time period [t _k, t _k+1] in Euler-Lagrange function carried out integration obtain L _d(q _k, q _k+1, h):

$L_d(q_k,q_{k+1},h)={\∫}_{t_k}^{t_{k+1}}L(q,\stackrel{\·}{q})dt---\left(4\right)$

(2) by formula (4) with replace, in application, q uses by dot format replace, obtain discrete Euler-Lagrange function L _d:

$L_d=h\{\frac{1}{2}L{\left(\frac{q_{L,k+1}-q_{L,k}}{h}\right)}^2-\frac{1}{2C}{\left(\frac{q_{C,k}+q_{C,k+1}}{2}\right)}^2\}---\left(5\right)$

(3) action of define system is variation and δ S (q) are carried out to S (q):

$\mathrm{\δ}S\left(q\right)=\mathrm{\δ}{\∫}_0^{T}L(q,\stackrel{\·}{q})dt$

(4) δ S (q)=0 is known by Hamilton principle, by the discrete LagrangianL of Euler-Lagrange function in S (q) _dsubstitute, obtain:

$S\left(q\right)={\∫}_0^{T}L(q,\stackrel{\·}{q})dt\≈\underset{k=0}{\overset{N-1}{\Σ}}{L}_d(q_k,q_{k+1})=S_d$

Wherein, q _kfor time t _kthe corresponding quantity of electric charge.Other step and parameter identical with one of embodiment one to three.

Embodiment five: one of present embodiment and embodiment one to four unlike: by hamiltonian system equation in step 3, derive the position momentum p of variational integral _kand p _k+1detailed process:

(1) to S _dchanges persuing divides:

${\mathrm{\δS}}_d=\underset{k=0}{\overset{N-1}{\Σ}}\[D_1{L}_d(q_k,q_{k+1}){\mathrm{\δq}}_k+D_2{L}_d(q_k,q_{k+1}){\mathrm{\δq}}_{k+1}\]$

In formula, D ₁l _drepresent L _dthe partial derivative .D of the first variable ₂l _drepresent L _dbivariate partial derivative;

(2) known end points disturbance is zero, i.e. δ q ₀=δ q _n=0, then extract common factor formula δ q _k, obtain following equation:

${\mathrm{\δS}}_d=\underset{k=1}{\overset{N-1}{\Σ}}\[D_1{L}_d(q_k,q_{k+1})+D_2{L}_d(q_{k-1},q_k)\]{\mathrm{\δq}}_k$

(3) for arbitrary δ q _k≠ 0, δ S _dbe always zero, therefore obtain formula:

D ₁L _d(q _k,q _k+1)+D ₂L _d(q _k-1,q _k)＝0 (6)

(4) definition position momentum p _kfor:

p _k＝D ₂L _d(q _k-1,q _k)＝-D ₁L _d(q _k,q _k+1)

Then formula (6) is by the position momentum representation of variational integral:

p _k＝-D ₁L _d(q _k,q _k+1) (7)

p _k+1＝D ₂L _d(q _k,q _k+1) (8)

(5) owing to there is external force and dissipation in system, the action S (q) of system should be right carry out the result of integration. in S (q), therefore add external force and the dissipation of system apply discrete Lagrange-d'Alembert principle to obtain:

${\mathrm{\δS}}_d=\underset{k=0}{\overset{N-1}{\Σ}}\{D_1{L}_d(q_k,q_{k+1}){\mathrm{\δq}}_k+D_2{L}_d(q_k,q_{k+1})+{F_d}^{-}(q_k,q_{k+1})\·{\mathrm{\δq}}_k+{F_d}^{+}(q_{k-1},q_k)\·{\mathrm{\δq}}_{k+1}\}$

Wherein, for at q _kresult after place F limit on the left discretize, for the result after F limit on the right-right-hand limit discretize, that is:

${F_d}^{-}(q_k,q_{k+1})\·{\mathrm{\δq}}_k+{F_d}^{+}(q_{k-1},q_k)\·{\mathrm{\δq}}_{k+1}={\∫}_{t_k}^{t_{k+1}}F\mathrm{\δ}qdt$

(6) formula (7) after external force is added and (8) are rewritten as:

$p_k=-D_1{L}_d(q_k,q_{k+1})-{F_d}^{-}(q_k,q_{k+1})---\left(9\right)$

$p_{k+1}=D_2{L}_d(q_k,q_{k+1})+{F_d}^{+}(q_k,q_{k+1})---\left(10\right)$

Wherein, ${F_d}^{-}(q_k,q_{k+1})={F_d}^{+}(q_k,q_{k+1})=\frac{h}{2}\left(Q_d\right(q_k,q_{k+1})-{\mathrm{\μ}}^T),$ Q _dfor the result after Q discretize. for oissipation function; Then Q _dfor:

$Q_d=\left(\begin{array}{c}-R\left(\right(1-u_k\left)\right(\frac{q_{L,k+1}-q_{L,k}}{h})-(\frac{q_{C,k+1}-q_{C,k}}{h}\left)\right)(1-u_k)\\ R\left(\right(1-u_k\left)\right(\frac{q_{L,k+1}-q_{L,k}}{h})-(\frac{q_{C,k+1}-q_{C,k}}{h}\left)\right)\end{array}\right)$

In formula, u _kfor the control signal that kth is secondary; q _l,kfor being expressed as the quantity of electric charge stored in the secondary inductance of kth, q _c,kfor being expressed as the quantity of electric charge stored in the secondary capacitor of kth.Other step and parameter identical with one of embodiment one to four.

Embodiment six: one of present embodiment and embodiment one to five unlike: according to p in step 4 _kand p _k+1set up the discrete Lagrangian model of One Buck-Boost converter body:

(1) parameter of One Buck-Boost converter body is brought into the equation that formula (9) releases as follows:

P _k＝Aq _k+1-Aq _k+Bq _k-V (11)

In formula, P _k=(p _l,k, p _c,k) ^t, q _k=(q _l,k, q _c,k) ^t, $A=\left(\begin{array}{cc}\frac{L}{h}+\frac{R{(1-u_k)}^2}{2}& -\frac{-R(1-u_k)}{2}\\ -\frac{R(1-u_k)}{2}& \frac{R}{2}+\frac{h}{4C}\end{array}\right),B=\left(\begin{array}{cc}0& 0\\ 0& \frac{h}{2C}\end{array}\right),$ $V=\left(\begin{array}{c}\frac{(1-u_k)hE}{2}\\ 0\end{array}\right)$

(2) formula (11) is arranged:

q _k+1＝q _k+A ^-1P _k-A ^-1Bq _k+A ^-1V

$q_{L,k+1}=q_{L,k}-\frac{2R(1-u_k)h^2}{{\mathrm{\β}}_k}{q}_{C,k}+\frac{2(2RC+h)h}{{\mathrm{\β}}_k}{P}_{L,k}+\frac{(2RC+h)h^2(1-u_k)E}{{\mathrm{\β}}_k}$

$q_{C,k+1}=q_{C,k}-\frac{2(2L+Rh{(1-u_k)}^2)h}{{\mathrm{\β}}_k}{q}_{C,k}-\frac{4R(1-u_k)hC}{{\mathrm{\β}}_k}{P}_{L,k}-\frac{2R{(1-u_k)}^2{h}^{2}CE}{{\mathrm{\β}}_k}$

Wherein, β _k=4LRC+2Lh+Rh (1-u _k) ²

(3) namely obtain according to formula (10):

$P_{k+1}=-{\mathrm{Aq}}_{k+1}+{\mathrm{Aq}}_k-{\mathrm{Bq}}_k+\stackrel{\‾}{B}{q}_{k+1}+V---\left(12\right)$

Wherein, $\stackrel{\‾}{B}=\left(\begin{array}{cc}\frac{2L}{h}& \frac{2L}{h}\\ 0& 0\end{array}\right).$

(4) formula (12) is opened solution implicit equation to obtain:

$\begin{array}{cc}{P}_{L,k+1}=-P_{L,k}-\frac{4LR(1-u_k)h}{{\mathrm{\β}}_k}{q}_{C,k}+\frac{4L(2RC+h)}{{\mathrm{\β}}_k}{P}_{L,k}+\frac{2L(2RC+h)h(1-u_k)E}{{\mathrm{\β}}_k}& P_{C,k+1}=-P_{C,k}\end{array}$

(5) P is got _{l, k+1}and q _{c, k+1}as variable, set up the discrete Lagrangian model of One Buck-Boost converter body linear iteration system of equations based on the discrete Lagrange of variational integral and One Buck-Boost converter body:

$\left\{\begin{array}{c}{\tilde{x}}_{1,k+1}=-{\tilde{x}}_{1,k}+\frac{{\mathrm{\α}}_{11,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{1,k}-\frac{{\mathrm{\α}}_{12,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{2,k}+\frac{{\mathrm{\α}}_{10,k}}{{\mathrm{\β}}_k}\\ {\tilde{x}}_{2,k+1}={\tilde{x}}_{2,k}-\frac{{\mathrm{\α}}_{21,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{1,k}-\frac{{\mathrm{\α}}_{22,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{2,k}+\frac{{\mathrm{\α}}_{20,k}}{{\mathrm{\β}}_k}\\ x_{1,k}=\frac{{\tilde{x}}_{1,k}}{L}\\ x_{2,k}=\frac{{\tilde{x}}_{2,k}}{C}\end{array}\right.---\left(13\right)$

Wherein, for inductive current, x _{2, k}=q _c/ C is capacitance voltage.

α _11,k＝4(2RC+h)L,α _12,k＝4R(1-u _k)hL,α _10,k＝2(2RC+h)hL(1-u _k)E

α _21,k＝4R(1-u _k)hC,α _22,k＝2h(2L+Rh(1-u _k) ²),α _20,k＝2R(1-u _k) ²h ²CE。Other step and parameter identical with one of embodiment one to five.

Embodiment seven: one of present embodiment and embodiment one to six unlike: utilize the detailed process of the Jacobian matrix eigenwert of the discrete Lagrangian model guiding system of One Buck-Boost converter body to be in step 5:

(1) set the fixed point of system as x ^*, in the Discrete Mapping model that formula (13) represents, make x _n+1=x _n=x ^*, then fixed point x is obtained ^*, the Jacobian matrix J (x of Discrete Mapping model near fixed point of switch Buck-Boost converter ^*) be expressed as:

$J\left(x^{*}\right)=\left[\begin{array}{cc}{J}_{11}& J_{12}\\ J_{21}& J_{22}\end{array}\right]---\left(14\right)$

Wherein, $J_{11}=\frac{\∂x_{1,n+1}}{\∂x_{1,n}},J_{12}=\frac{\∂x_{1,n+1}}{\∂x_{2,n}},J_{21}=\frac{\∂x_{2,n+1}}{\∂x_{1,n}},J_{22}=\frac{\∂x_{2,n+1}}{\∂x_{2,n}};$ X _{1, n}be the inductive current of n-th switch periods, x _{2, n}it is the capacitance voltage of n-th switch periods; x _nfor state variable;

(2) secular equation of Jacobian matrix is expressed as:

det|λI-J(x ^*)|＝0 (15)

Wherein, I is the unit matrix identical with Jacobian matrix exponent number, is namely tried to achieve the eigenvalue λ of Jacobian matrix by formula (15);

(3) now Jacobian poly is:

λ ²-(J ₁₁+J ₂₂)λ+J ₁₁J ₂₂-J ₁₂J ₂₁＝0 (16)

Formula (16) is solved, obtains the eigenvalue λ of second order Jacobian matrix ₁₂for:

${\mathrm{\λ}}_{12}=\frac{1}{2}(J_{11}+J_{22})\±\frac{1}{2}\sqrt{{(J_{11}+J_{22})}^2-4(J_{11}{J}_{22}-J_{12}{J}_{21})}$

(4) input n inductance, electric capacity, resistance and input power parameter, recurring formula (13) ~ (16) obtain the eigenvalue λ of n group second order Jacobian matrix ₁₂;

It can thus be appreciated that shown in formula (14), the Jacobian matrix of discrete system has two nonzero eigenvalues, and its size determines the stability of system.Other step and parameter identical with one of embodiment one to six.

Embodiment eight: one of present embodiment and embodiment one to seven unlike: utilize Jacobian matrix eigenwert to obtain the non-linear behavior detailed process of One Buck-Boost converter body stabilized zone and One Buck-Boost converter body bifurcation point first in step 6:

(1) according to the eigenvalue λ of n group second order Jacobian matrix ₁₂, obtain the track of Jacobian proper value of matrix with circuit parameter variations;

(2) if all eigenwerts of Jacobian matrix are all positioned at unit circle inside, then Buck-Boost system is in steady state (SS); If the eigenvalue of Jacobian matrix has passed the scope of unit circle, then Buck-Boost system there occurs bifurcation thus has determined that the non-linear behavior of One Buck-Boost converter body stabilized zone and One Buck-Boost converter body bifurcation point is first as Fig. 3.Other step and parameter identical with one of embodiment one to seven.

Following examples are adopted to verify beneficial effect of the present invention:

Embodiment one:

A kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral of the present embodiment and nonlinear analysis method, specifically prepare according to following steps:

The Euler-Lagrange function of step one, structure One Buck-Boost converter body is specially:

(1) define for the kinetic energy of circuit, ν _u(q _c) be the potential energy of circuit, for the dissipative function of circuit, ν _{u, nc}q forcing function that () is system, u is control signal; During u=0, switch disconnects, switch conduction during u=1, and concrete form is as follows:

$T_u\left({\stackrel{\·}{q}}_L\right)=\frac{1}{2}L{\stackrel{\·}{q}}_L^2,v_u\left(q_C\right)=\frac{1}{2C}{q}_C^2,F_u\left(\stackrel{\·}{q}\right)=\frac{1}{2}R{\left(\right(1-u){\stackrel{\·}{q}}_L-{\stackrel{\·}{q}}_C)}^2,v_{u,nc}\left(q\right)=-{\mathrm{\μ}}^{T}q$

Wherein, q _lbe expressed as the quantity of electric charge stored in inductance, q _crepresent the quantity of electric charge stored in capacitor, q=(q _l, q _c) ^t, be expressed as the electric current flowing through inductance, be expressed as the electric current flowing through capacitor, l is inductance value, and C is capacitance, and R is resistance value, and vector μ is defined as μ=((1-u) E, 0) ^t, E is the input voltage of Buck-Boost circuit;

(2) be then written as with the Euler-Lagrange function of external force and dissipative function:

$L_{nc}(q,\stackrel{\·}{q})=L(q,\stackrel{\·}{q})+F_u\left(\stackrel{\·}{q}\right)-v_{u,nc}\left(q\right)---\left(2\right)$

In formula euler-Lagrange function for traditional:

$L(q,\stackrel{\·}{q})=T_u\left({\stackrel{\·}{q}}_L\right)-v_u\left(q_c\right)=\frac{1}{2}L{\stackrel{\·}{q}}_L^2-\frac{1}{2C}{q}_C^2---\left(3\right)$

(3) formula (2) and (3) are traditional Euler-Lagrange function;

As shown in Figure 1, One Buck-Boost converter body Controlled in Current Mode and Based is specially the schematic diagram of One Buck-Boost converter body Controlled in Current Mode and Based:

(1) components and parts in circuit are all considered as ideal component; Wherein, the components and parts in circuit comprise inductance, electric capacity, resistance, switching tube, input power, comparer and rest-set flip-flop; Ideal component is have single constant relationship not by the components and parts of the impact of other factors such as material temperature;

(2) by inductive current i _lwith reference current I _refcompare, if i _lbe greater than I _ref, then what rest-set flip-flop R held is input as 1; If i _lbe less than I _ref, then what rest-set flip-flop R held is input as 0;

(3) clock signal is by the S end input of rest-set flip-flop, if rest-set flip-flop R hold be input as 0 and rest-set flip-flop S hold be input as 1 time, then the Q of rest-set flip-flop holds output to be 1, if rest-set flip-flop R hold be input as 1 and rest-set flip-flop S hold be input as 0 time, then rest-set flip-flop Q hold output be 0;

(4) break-make of the output Q gauge tap pipe M of rest-set flip-flop; Shown in circuit waveform Fig. 2, draw the dutycycle in switch periods each time according to the principle of One Buck-Boost converter body Controlled in Current Mode and Based:

$u_k=\frac{I_{ref}-i_{L,k}}{(E/L)T}---\left(1\right)$

Wherein, clock signal is 0 or 1, the T clock period.

Step 2, Buck-Boost Euler-Lagrange function is carried out discretize after construct hamiltonian system equation;

(1) to Euler-Lagrange function traditional in formula (3) discretize is carried out with time period h:

Construct a sequence increased progressively in time: { t _k=kh|k=0,1 ... N};

Wherein, h=t _k+1-t _k, at each time period [t _k, t _k+1] in Euler-Lagrange function carried out integration obtain L _d(q _k, q _k+1, h):

$L_d(q_k,q_{k+1},h)={\∫}_{t_k}^{t_{k+1}}L(q,\stackrel{\·}{q})dt---\left(4\right)$

(2) by formula (4) with replace, in application, q uses by dot format replace, obtain discrete Euler-Lagrange function L _d:

$L_d=h\{\frac{1}{2}L{\left(\frac{q_{L,k+1}-q_{L,k}}{h}\right)}^2-\frac{1}{2C}{\left(\frac{q_{C,k}+q_{C,k+1}}{2}\right)}^2\}---\left(5\right)$

(3) action of define system is variation and δ S (q) are carried out to S (q):

$\mathrm{\δ}S\left(q\right)=\mathrm{\δ}{\∫}_0^{T}L(q,\stackrel{\·}{q})dt$

(4) δ S (q)=0 is known by Hamilton principle, by the discrete LagrangianL of Euler-Lagrange function in S (q) _dsubstitute, obtain:

$S\left(q\right)={\∫}_0^{T}L(q,\stackrel{\·}{q})dt\≈\underset{k=0}{\overset{N-1}{\Σ}}{L}_d(q_k,q_{k+1})=S_d$

Wherein, q _kfor time t _kthe corresponding quantity of electric charge.

Step 3, by hamiltonian system equation, derive the position momentum p of variational integral _kand p _k+1;

(1) to S _dchanges persuing divides:

${\mathrm{\δS}}_d=\underset{k=0}{\overset{N-1}{\Σ}}\[D_1{L}_d(q_k,q_{k+1}){\mathrm{\δq}}_k+D_2{L}_d(q_k,q_{k+1}){\mathrm{\δq}}_{k+1}\]$

In formula, D ₁l _drepresent L _dthe partial derivative .D of the first variable ₂l _drepresent L _dbivariate partial derivative;

(2) known end points disturbance is zero, i.e. δ q ₀=δ q _n=0, then extract common factor formula δ q _k, obtain following equation:

${\mathrm{\δS}}_d=\underset{k=1}{\overset{N-1}{\Σ}}\[D_1{L}_d(q_k,q_{k+1})+D_2{L}_d(q_{k-1},q_k)\]{\mathrm{\δq}}_k$

(3) for arbitrary δ q _k≠ 0, δ S _dbe always zero, therefore obtain formula:

D ₁L _d(q _k,q _k+1)+D ₂L _d(q _k-1,q _k)＝0 (6)

(4) definition position momentum p _kfor:

p _k＝D ₂L _d(q _k-1,q _k)＝-D ₁L _d(q _k,q _k+1)

Then formula (6) is by the position momentum representation of variational integral:

p _k＝-D ₁L _d(q _k,q _k+1) (7)

p _k+1＝D ₂L _d(q _k,q _k+1) (8)

(5) owing to there is external force and dissipation in system, the action S (q) of system should be right carry out the result of integration. in S (q), therefore add external force and the dissipation of system apply discrete Lagrange-d'Alembert principle to obtain:

${\mathrm{\δS}}_d=\underset{k=0}{\overset{N-1}{\Σ}}\{D_1{L}_d(q_k,q_{k+1}){\mathrm{\δq}}_k+D_2{L}_d(q_k,q_{k+1})+{F_d}^{-}(q_k,q_{k+1})\·{\mathrm{\δq}}_k+{F_d}^{+}(q_{k-1},q_k)\·{\mathrm{\δq}}_{k+1}\}$

Wherein, for at q _kresult after place F limit on the left discretize, for the result after F limit on the right-right-hand limit discretize, that is:

${F_d}^{-}(q_k,q_{k+1})\·{\mathrm{\δq}}_k+{F_d}^{+}(q_{k-1},q_k)\·{\mathrm{\δq}}_{k+1}={\∫}_{t_k}^{t_{k+1}}F\mathrm{\δ}qdt$

(6) formula (7) after external force is added and (8) are rewritten as:

$p_k=-D_1{L}_d(q_k,q_{k+1})-{F_d}^{-}(q_k,q_{k+1})---\left(9\right)$

$p_{k+1}=D_2{L}_d(q_k,q_{k+1})+{F_d}^{+}(q_k,q_{k+1})---\left(10\right)$

Wherein, ${F_d}^{-}(q_k,q_{k+1})={F_d}^{+}(q_k,q_{k+1})=\frac{h}{2}\left(Q_d\right(q_k,q_{k+1})-{\mathrm{\μ}}^T),$ Q _dfor the result after Q discretize. for oissipation function; Then Q _dfor:

$Q_d=\left(\begin{array}{c}-R\left(\right(1-u_k\left)\right(\frac{q_{L,k+1}-q_{L,k}}{h})-(\frac{q_{C,k+1}-q_{C,k}}{h}\left)\right)(1-u_k)\\ R\left(\right(1-u_k\left)\right(\frac{q_{L,k+1}-q_{L,k}}{h})-(\frac{q_{C,k+1}-q_{C,k}}{h}\left)\right)\end{array}\right)$

In formula, u _kfor the control signal that kth is secondary; q _l,kfor being expressed as the quantity of electric charge stored in the secondary inductance of kth, q _c,kfor being expressed as the quantity of electric charge stored in the secondary capacitor of kth.

Step 4, according to p _kand p _k+1set up the discrete Lagrangian model of One Buck-Boost converter body:

(1) parameter of One Buck-Boost converter body is brought into the equation that formula (9) releases as follows:

P _k＝Aq _k+1-Aq _k+Bq _k-V (11)

In formula, P _k=(p _l,k, p _c,k) ^t, q _k=(q _l,k, q _c,k) ^t, $A=\left(\begin{array}{cc}\frac{L}{h}+\frac{R{(1-u_k)}^2}{2}& -\frac{-R(1-u_k)}{2}\\ -\frac{R(1-u_k)}{2}& \frac{R}{2}+\frac{h}{4C}\end{array}\right),B=\left(\begin{array}{cc}0& 0\\ 0& \frac{h}{2C}\end{array}\right),$ $V=\left(\begin{array}{c}\frac{(1-u_k)hE}{2}\\ 0\end{array}\right)$

(2) formula (11) is arranged:

q _k+1＝q _k+A ^-1P _k-A ^-1Bq _k+A ^-1V

$q_{L,k+1}=q_{L,k}-\frac{2R(1-u_k)h^2}{{\mathrm{\β}}_k}{q}_{C,k}+\frac{2(2RC+h)h}{{\mathrm{\β}}_k}{P}_{L,k}+\frac{(2RC+h)h^2(1-u_k)E}{{\mathrm{\β}}_k}$

$q_{C,k+1}=q_{C,k}-\frac{2(2L+Rh{(1-u_k)}^2)h}{{\mathrm{\β}}_k}{q}_{C,k}-\frac{4R(1-u_k)hC}{{\mathrm{\β}}_k}{P}_{L,k}-\frac{2R{(1-u_k)}^2{h}^{2}CE}{{\mathrm{\β}}_k}$

Wherein, β _k=4LRC+2Lh+Rh (1-u _k) ²

(3) namely obtain according to formula (10):

$P_{k+1}=-{\mathrm{Aq}}_{k+1}+{\mathrm{Aq}}_k-{\mathrm{Bq}}_k+\stackrel{\‾}{B}{q}_{k+1}+V---\left(12\right)$

Wherein, $\stackrel{\‾}{B}=\left(\begin{array}{cc}\frac{2L}{h}& \frac{2L}{h}\\ 0& 0\end{array}\right).$

(4) formula (12) is opened solution implicit equation to obtain:

$\begin{array}{cc}{P}_{L,k+1}=-P_{L,k}-\frac{4LR(1-u_k)h}{{\mathrm{\β}}_k}{q}_{C,k}+\frac{4L(2RC+h)}{{\mathrm{\β}}_k}{P}_{L,k}+\frac{2L(2RC+h)h(1-u_k)E}{{\mathrm{\β}}_k}& P_{C,k+1}=-P_{C,k}\end{array}$

(5) P is got _{l, k+1}and q _{c, k+1}as variable, set up the discrete Lagrangian model of One Buck-Boost converter body linear iteration system of equations based on the discrete Lagrange of variational integral and One Buck-Boost converter body:

$\left\{\begin{array}{c}{\tilde{x}}_{1,k+1}=-{\tilde{x}}_{1,k}+\frac{{\mathrm{\α}}_{11,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{1,k}-\frac{{\mathrm{\α}}_{12,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{2,k}+\frac{{\mathrm{\α}}_{10,k}}{{\mathrm{\β}}_k}\\ {\tilde{x}}_{2,k+1}={\tilde{x}}_{2,k}-\frac{{\mathrm{\α}}_{21,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{1,k}-\frac{{\mathrm{\α}}_{22,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{2,k}+\frac{{\mathrm{\α}}_{20,k}}{{\mathrm{\β}}_k}\\ x_{1,k}=\frac{{\tilde{x}}_{1,k}}{L}\\ x_{2,k}=\frac{{\tilde{x}}_{2,k}}{C}\end{array}\right.---\left(13\right)$

Wherein, for inductive current, x _{2, k}=q _c/ C is capacitance voltage.

α _11,k＝4(2RC+h)L,α _12,k＝4R(1-u _k)hL,α _10,k＝2(2RC+h)hL(1-u _k)E

α _21,k＝4R(1-u _k)hC，α _22,k＝2h(2L+Rh(1-u _k) ²)，α _20,k＝2R(1-u _k) ²h ²CE。

Step 5, utilize the Jacobian matrix eigenwert of the discrete Lagrangian model guiding system of One Buck-Boost converter body;

(1) set the fixed point of system as x ^*, in the Discrete Mapping model that formula (13) represents, make x _n+1=x _n=x ^*, then fixed point x is obtained ^*, the Jacobian matrix J (x of Discrete Mapping model near fixed point of switch Buck-Boost converter ^*) be expressed as:

$J\left(x^{*}\right)=\left[\begin{array}{cc}{J}_{11}& J_{12}\\ J_{21}& J_{22}\end{array}\right]---\left(14\right)$

Wherein, $J_{11}=\frac{\∂x_{1,n+1}}{\∂x_{1,n}},J_{12}=\frac{\∂x_{1,n+1}}{\∂x_{2,n}},J_{21}=\frac{\∂x_{2,n+1}}{\∂x_{1,n}},J_{22}=\frac{\∂x_{2,n+1}}{\∂x_{2,n}};$ X _{1, n}be the inductive current of n-th switch periods, x _{2, n}it is the capacitance voltage of n-th switch periods; x _nfor state variable;

(2) secular equation of Jacobian matrix is expressed as:

det|λI-J(x ^*)|＝0 (15)

Wherein, I is the unit matrix identical with Jacobian matrix exponent number, is namely tried to achieve the eigenvalue λ of Jacobian matrix by formula (15);

(3) now Jacobian poly is:

λ ²-(J ₁₁+J ₂₂)λ+J ₁₁J ₂₂-J ₁₂J ₂₁＝0 (16)

Formula (16) is solved, obtains the eigenvalue λ of second order Jacobian matrix ₁₂for:

${\mathrm{\λ}}_{12}=\frac{1}{2}(J_{11}+J_{22})\±\frac{1}{2}\sqrt{{(J_{11}+J_{22})}^2-4(J_{11}{J}_{22}-J_{12}{J}_{21})}$

(4) input n inductance, electric capacity, resistance and input power parameter, recurring formula (13) ~ (16) obtain the eigenvalue λ of n group second order Jacobian matrix ₁₂;

It can thus be appreciated that shown in formula (14), the Jacobian matrix of discrete system has two nonzero eigenvalues, and its size determines the stability of system.

Step 6, Jacobian matrix eigenwert is utilized to obtain the non-linear behavior of One Buck-Boost converter body stabilized zone and One Buck-Boost converter body bifurcation point first;

(1) according to the eigenvalue λ of n group second order Jacobian matrix ₁₂, obtain the track of Jacobian proper value of matrix with circuit parameter variations;

(2) if all eigenwerts of Jacobian matrix are all positioned at unit circle inside, then Buck-Boost system is in steady state (SS); If the eigenvalue of Jacobian matrix has passed the scope of unit circle, then Buck-Boost system there occurs bifurcation thus has determined that the non-linear behavior of One Buck-Boost converter body stabilized zone and One Buck-Boost converter body bifurcation point is first as Fig. 3.

One Buck-Boost converter body nonlinear analysis based on discrete Lagrangian model:

Select the systematic parameter of One Buck-Boost converter body as shown in table 1, by the Jacobian matrix of the discrete Lagrangian model constructing system of One Buck-Boost converter body.

Table 1 systematic parameter

Fig. 3 show for, system initial parameter according to table 1 above, when changing One Buck-Boost converter body reference current, the Jacobian proper value of matrix variation track of novel Discrete model. when reference current reaches 0.52A, the eigenwert of Jacobian matrix passes through unit circle from negative real axis direction first, forecasting system generation bifurcation. and design parameter is as shown in table 2.

The different reference current I of table 2 _refunder the eigenwert of system Jacobian matrix

The stabilized zone of the system when different Parameters variation can be drawn out, the system stability scope using above-mentioned novel Discrete iterative model to obtain and reference current I by calculating Jacobian proper value of matrix _refshow with relation such as Fig. 4 of pull-up resistor R, systematic parameter is as shown in table 1. and in figure, dotted line is the stabilized zone that novel Discrete iterative model is drawn out, solid line is the stabilized zone that stroboscopic map modeling rendering goes out. wherein Fig. 4 (b), Fig. 4 (d), Fig. 4 (f) is respectively Fig. 4 (a), the partial enlarged drawing of Fig. 4 (c), Fig. 4 (e). as can be seen from the figure, novel Discrete model and stroboscopic map model are at reference current I _refthe system stability region obtained when changing with pull-up resistor R is almost identical. and along with the increase of switching frequency, the degree of accuracy of novel discrete model is more and more higher.

Fig. 5 (a) ~ (c) compares input voltage to be changed at 0 ~ 50V, reference current stabilized zone of One Buck-Boost converter body under different switching frequency when 0 ~ 1.8A changes, its dotted line is the stabilized zone that novel Discrete iterative model is obtained, and solid line is the stabilized zone that stroboscopic map model is obtained.

By relatively finding out, no matter the pull-up resistor of One Buck-Boost converter body changes at 10 ~ 500 Ω, reference current is when 0-4A changes, or input voltage changes at 0-50V, reference current is when 0-1.8A changes, novel discrete model is compared with stroboscopic map model, the system stability region obtained is all almost identical, and when system switching frequency is higher, the degree of accuracy of novel discrete model is higher, when DC-DC converter switching frequency is more and more higher, novel discrete model has good precision. owing to not having matrix exponetial and integration item, reduce computational complexity, and the operand of calculus of differences is much little compared with the operand of matrix exponetial and integration item, therefore this model reduces the calculated amount of system, namely a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method is completed.

The present invention also can have other various embodiments; when not deviating from the present invention's spirit and essence thereof; those skilled in the art are when making various corresponding change and distortion according to the present invention, but these change accordingly and are out of shape the protection domain that all should belong to the claim appended by the present invention.

Claims (8)

1., based on One Buck-Boost converter body modeling and the nonlinear analysis method of the discrete Lagrangian model of variational integral, it is characterized in that what a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method were specifically carried out according to following steps:

The Euler-Lagrange function of step one, structure One Buck-Boost converter body;

Step 2, Buck-Boost Euler-Lagrange function is carried out discretize after construct hamiltonian system equation;

Step 3, by hamiltonian system equation, derive the position momentum p of variational integral _kand p _k+1;

Step 4, according to p _kand p _k+1set up the discrete Lagrangian model of One Buck-Boost converter body;

Step 5, utilize the Jacobian matrix eigenwert of the discrete Lagrangian model guiding system of One Buck-Boost converter body;

Step 6, Jacobian matrix eigenwert is utilized to obtain the non-linear behavior of One Buck-Boost converter body stabilized zone and One Buck-Boost converter body bifurcation point first; Namely a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method is completed.

2. a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method according to claim 1, is characterized in that: the Euler-Lagrange function constructing One Buck-Boost converter body in step one is specially:

(1) define for the kinetic energy of circuit, ν _u(q _c) be the potential energy of circuit, for the dissipative function of circuit, ν _{u, nc}q forcing function that () is system, u is control signal; During u=0, switch disconnects, switch conduction during u=1, and concrete form is as follows:

$T_u\left({\stackrel{\·}{q}}_L\right)=\frac{1}{2}L{\stackrel{\·}{q}}_L^2,v_u\left(q_C\right)=\frac{1}{2C}{q}_C^2,F_u\left(\stackrel{\·}{q}\right)=\frac{1}{2}R{\left(\right(1-u){\stackrel{\·}{q}}_L-{\stackrel{\·}{q}}_C)}^2,$ v _u，nc(q)＝-μ ^Tq

Wherein, q _lbe expressed as the quantity of electric charge stored in inductance, q _crepresent the quantity of electric charge stored in capacitor, q=(q _l, q _c) ^t, be expressed as the electric current flowing through inductance, be expressed as the electric current flowing through capacitor, l is inductance value, and C is capacitance, and R is resistance value, and vector μ is defined as μ=((1-u) E, 0) ^t, E is the input voltage of Buck-Boost circuit;

(2) be then written as with the Euler-Lagrange function of external force and dissipative function:

$L_{nc}(q,\stackrel{\·}{q})=L(q,\stackrel{\·}{q})+F_u\left(\stackrel{\·}{q}\right)-v_{u,nc}\left(q\right)---\left(2\right)$

In formula euler-Lagrange function for traditional:

$L(q,\stackrel{\·}{q})=T_u\left({\stackrel{\·}{q}}_L\right)-v_u\left(q_c\right)=\frac{1}{2}L{\stackrel{\·}{q}}_L^2-\frac{1}{2C}{q}_C^2---\left(3\right)$

(3) formula (2) and (3) are traditional Euler-Lagrange function.

3. a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method according to claim 2, is characterized in that: in step one, One Buck-Boost converter body Controlled in Current Mode and Based is specially:

(1) components and parts in circuit are all considered as ideal component; Wherein, the components and parts in circuit comprise inductance, electric capacity, resistance, switching tube, input power, comparer and rest-set flip-flop; Ideal component is have single constant relationship not by the components and parts of the impact of other factors such as material temperature;

(2) by inductive current i _lwith reference current I _refcompare, if i _lbe greater than I _ref, then what rest-set flip-flop R held is input as 1; If i _lbe less than I _ref, then what rest-set flip-flop R held is input as 0;

(3) clock signal is by the S end input of rest-set flip-flop, if rest-set flip-flop R hold be input as 0 and rest-set flip-flop S hold be input as 1 time, then the Q of rest-set flip-flop holds output to be 1, if rest-set flip-flop R hold be input as 1 and rest-set flip-flop S hold be input as 0 time, then rest-set flip-flop Q hold output be 0;

(4) dutycycle in switch periods is each time drawn according to the principle of One Buck-Boost converter body Controlled in Current Mode and Based:

$u_k=\frac{I_{ref}-i_{L,k}}{(E/L)T}---\left(1\right)$

Wherein, clock signal is 0 or 1, the T clock period.

4. a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method according to claim 3, is characterized in that: construct hamiltonian system equation after Buck-Boost Euler-Lagrange function being carried out discretize in step 2;

(1) to Euler-Lagrange function traditional in formula (3) discretize is carried out with time period h:

Construct a sequence increased progressively in time: { t _k=kh|k=0,1 ... N};

Wherein, h=t _k+1-t _k, at each time period [t _k, t _k+1] in Euler-Lagrange function carried out integration obtain L _d(q _k, q _k+1, h):

$L_d(q_k,q_{k+1},h)={\∫}_{t_k}^{t_{k+1}}L(q,\stackrel{\·}{q})dt---\left(4\right)$

(2) by formula (4) with replace, in application, q uses by dot format replace, obtain discrete Euler-Lagrange function L _d:

$L_d=h\{\frac{1}{2}L{\left(\frac{q_{L,k+1}-q_{L.k}}{h}\right)}^2-\frac{1}{2C}{\left(\frac{q_{C,k}+q_{C,k+1}}{2}\right)}^2\}---\left(5\right)$

(3) action of define system is variation and δ S (q) are carried out to S (q):

$\mathrm{\δ}S\left(q\right)=\mathrm{\δ}{\∫}_0^{T}L(q,\stackrel{\·}{q})dt$

(4) δ S (q)=0 is known by Hamilton principle, by the discrete LagrangianL of Euler-Lagrange function in S (q) _dsubstitute, obtain:

$S\left(q\right)={\∫}_0^{T}L(q,\stackrel{\·}{q})dt\≈\underset{k=0}{\overset{N-1}{\Σ}}{L}_d(q_k,q_{k+1})=S_d$

Wherein, q _kfor time t _kthe corresponding quantity of electric charge.

5. a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method according to claim 4, is characterized in that: by hamiltonian system equation in step 3, derives the position momentum p of variational integral _kand p _k+1detailed process:

(1) to S _dchanges persuing divides:

${\mathrm{\δS}}_d=\underset{k=0}{\overset{N-1}{\Σ}}\[D_1{L}_d(q_k,q_{k+1}){\mathrm{\δq}}_k+D_2{L}_d(q_k,q_{k+1}){\mathrm{\δq}}_{k+1}\]$

In formula, D ₁l _drepresent L _dthe partial derivative .D of the first variable ₂l _drepresent L _dbivariate partial derivative;

(2) known end points disturbance is zero, i.e. δ q ₀=δ q _n=0, then extract common factor formula δ q _k, obtain following equation:

${\mathrm{\δS}}_d=\underset{k=1}{\overset{N-1}{\Σ}}\[D_1{L}_d(q_k,q_{k+1})+D_2{L}_d(q_{k-1},q_k)\]{\mathrm{\δq}}_k$

(3) for arbitrary δ q _k≠ 0, δ S _dbe always zero, therefore obtain formula:

D ₁L _d(q _k,q _k+1)+D ₂L _d(q _k-1,q _k)＝0 (6)

(4) definition position momentum p _kfor:

p _k＝D ₂L _d(q _k-1,q _k)＝-D ₁L _d(q _k,q _k+1)

Then formula (6) is by the position momentum representation of variational integral:

p _k＝-D ₁L _d(q _k,q _k+1) (7)

p _k+1＝D ₂L _d(q _k,q _k+1) (8)

(5) in S (q), add external force and the dissipation of system apply discrete Lagrange-d'Alembert principle to obtain:

${\mathrm{\δS}}_d=\underset{k=0}{\overset{N-1}{\Σ}}\{D_1{L}_d(q_k,q_{k+1}){\mathrm{\δq}}_k+D_2{L}_d(q_k,q_{k+1})+{F_d}^{-}(q_k,q_{k+1})\·{\mathrm{\δq}}_k+{F_d}^{+}(q_{k-1},q_k)\·{\mathrm{\δq}}_{k+1}\}$

Wherein, F _d ^-(q _k, q _k+1) be at q _kresult after place F limit on the left discretize, F _d ⁺(q _k, q _k+1) be the result after F limit on the right-right-hand limit discretize, that is:

${F_d}^{-}(q_k,q_{k+1})\·{\mathrm{\δq}}_k+{F_d}^{+}(q_{k-1},q_k)\·{\mathrm{\δq}}_{k+1}={\∫}_{t_k}^{t_{k+1}}F\mathrm{\δ}qdt$

(6) formula (7) after external force is added and (8) are rewritten as:

p _k＝-D ₁L _d(q _k,q _k+1)-F _d ^-(q _k,q _k+1) (9)

p _k+1＝D ₂L _d(q _k,q _k+1)+F _d ⁺(q _k,q _k+1) (10)

Wherein, ${F_d}^{-}(q_k,q_{k+1})={F_d}^{+}(q_k,q_{k+1})=\frac{h}{2}\left(Q_d\right(q_k,q_{k+1})-{\mathrm{\μ}}^T),$ Q _dfor the result after Q discretize. for oissipation function; Then Q _dfor:

$Q_d=\left(\begin{array}{c}-R\left(\right(1-u_k\left)\right(\frac{q_{L,k+1}-q_{L,k}}{h})-(\frac{q_{C,k+1}-q_{C,k}}{h}\left)\right)(1-u_k)\\ R\left(\right(1-u_k\left)\right(\frac{q_{L,k+1}-q_{L,k}}{h})-(\frac{q_{C,k+1}-q_{C,k}}{h}\left)\right)\end{array}\right)$

In formula, u _kfor the control signal that kth is secondary; q _l,kfor being expressed as the quantity of electric charge stored in the secondary inductance of kth, q _c,kfor being expressed as the quantity of electric charge stored in the secondary capacitor of kth.

6. a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method according to claim 5, is characterized in that: according to p in step 4 _kand p _k+1set up the discrete Lagrangian model of One Buck-Boost converter body:

(1) parameter of One Buck-Boost converter body is brought into the equation that formula (9) releases as follows:

P _k＝Aq _k+1-Aq _k+Bq _k-V (11)

In formula, P _k=(p _l,k, p _c,k) ^t, q _k=(q _l,k, q _c,k) ^t, $A=\left(\begin{array}{cc}\frac{L}{h}+\frac{R{(1-u_k)}^2}{2}& -\frac{-R(1-u_k)}{2}\\ -\frac{R(1-u_k)}{2}& \frac{R}{2}+\frac{h}{4C}\end{array}\right),b=\left(\begin{array}{cc}0& 0\\ 0& \frac{h}{2C}\end{array}\right),$ $V=\left(\begin{array}{c}\frac{(1-u_k)hE}{2}\\ 0\end{array}\right)$

(2) formula (11) is arranged:

q _k+1＝q _k+A ^-1P _k-A ^-1Bq _k+A ^-1V

$q_{L,k+1}=q_{L,k}-\frac{2R(1-u_k)h^2}{{\mathrm{\β}}_k}{q}_{C,k}+\frac{2(2RC+h)h}{{\mathrm{\β}}_k}{P}_{L,k}+\frac{(2RC+h)h^2(1-u_k)E}{{\mathrm{\β}}_k}$

$q_{C,k+1}=q_{C,k}-\frac{2(2L+Rh{(1-u_k)}^2)h}{{\mathrm{\β}}_k}{q}_{C,k}-\frac{4R+(1-u_k)hC}{{\mathrm{\β}}_k}{P}_{L,k}-\frac{2R{(1-u_k)}^2{h}^{2}CE}{{\mathrm{\β}}_k}$

Wherein, β _k=4LRC+2Lh+Rh (1-u _k) ²

(3) namely obtain according to formula (10):

$P_{k+1}=-{\mathrm{Aq}}_{k+1}+{\mathrm{Aq}}_k-{\mathrm{Bq}}_k+\stackrel{\‾}{B}{q}_{k+1}+V---\left(12\right)$

Wherein, $\stackrel{\‾}{B}=\left(\begin{array}{cc}\frac{2L}{h}& \frac{2L}{h}\\ 0& 0\end{array}\right).$

(4) formula (12) is opened solution implicit equation to obtain:

$\begin{array}{cc}{P}_{L,k+1}=-P_{L,k}-\frac{4LR(1-u_k)h}{{\mathrm{\β}}_k}{q}_{C,k}+\frac{4L(2RC+h)}{{\mathrm{\β}}_k}{P}_{L,k}+\frac{2L(2RC+h)h(1-u_k)E}{{\mathrm{\β}}_k}& P_{C,k+1}=-P_{C,k}\end{array}$

(5) P is got _{l, k+1}and q _{c, k+1}as variable, set up the discrete Lagrangian model of One Buck-Boost converter body linear iteration system of equations based on the discrete Lagrange of variational integral and One Buck-Boost converter body:

$\left\{\begin{array}{c}{\tilde{x}}_{1,k+1}=-{\tilde{x}}_{1,k}+\frac{{\mathrm{\α}}_{11,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{1,k}-\frac{{\mathrm{\α}}_{12,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{2,k}+\frac{{\mathrm{\α}}_{10,k}}{{\mathrm{\β}}_k}\\ {\tilde{x}}_{2,k+1}={\tilde{x}}_{1,k}-\frac{{\mathrm{\α}}_{21,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{1,k}-\frac{{\mathrm{\α}}_{22,k}}{{\mathrm{\β}}_k}{\tilde{x}}_{2,k}+\frac{{\mathrm{\α}}_{20,k}}{{\mathrm{\β}}_k}\\ x_{1,k}=\frac{{\tilde{x}}_{1,k}}{L}\\ x_{2,k}=\frac{{\tilde{x}}_{2,k}}{C}\end{array}\right.---\left(13\right)$

Wherein, ${\tilde{x}}_{1,k}=P_{L,k},{\tilde{x}}_{2,k}=q_{C,k},x_{1,k}={\stackrel{\·}{q}}_L$ For inductive current, $x_{2,k}=q_C/C$ For capacitance voltage.

α _11,k＝4(2RC+h)L,α _12,k＝4R(1-u _k)hL,α _10,k＝2(2RC+h)hL(1-u _k)E

α _21,k＝4R(1-u _k)hC，α _22,k＝2h(2L+Rh(1-u _k) ²)，α _20,k＝2R(1-u _k) ²h ²CE。

7. a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method according to claim 6, is characterized in that: utilize the detailed process of the Jacobian matrix eigenwert of the discrete Lagrangian model guiding system of One Buck-Boost converter body to be in step 5:

(1) set the fixed point of system as x ^*, in the Discrete Mapping model that formula (13) represents, make x _n+1=x _n=x ^*, then fixed point x is obtained ^*, the Jacobian matrix J (x of Discrete Mapping model near fixed point of switch Buck-Boost converter ^*) be expressed as:

$J\left(x^{*}\right)=\left[\begin{array}{cc}{J}_{11}& J_{12}\\ J_{21}& J_{22}\end{array}\right]---\left(14\right)$

Wherein, $J_{11}=\frac{\∂x_{1,n+1}}{\∂x_{1,n}},J_{12}=\frac{\∂x_{1,n+1}}{\∂x_{2,n}},J_{21}=\frac{\∂x_{2,n+1}}{\∂x_{1,n}},J_{22}=\frac{\∂x_{2,n+1}}{\∂x_{2,n}};$ X _{1, n}be the inductive current of n-th switch periods, x _{2, n}it is the capacitance voltage of n-th switch periods; x _nfor state variable;

(2) secular equation of Jacobian matrix is expressed as:

det|λI-J(x ^*)|＝0 (15)

Wherein, I is the unit matrix identical with Jacobian matrix exponent number, is namely tried to achieve the eigenvalue λ of Jacobian matrix by formula (15);

(3) now Jacobian poly is:

λ ²-(J ₁₁+J ₂₂)λ+J ₁₁J ₂₂-J ₁₂J ₂₁＝0 (16)

Formula (16) is solved, obtains the eigenvalue λ of second order Jacobian matrix ₁₂for:

${\mathrm{\λ}}_{12}=\frac{1}{2}(J_{11}+J_{22})\±\frac{1}{2}\sqrt{{(J_{11}+J_{22})}^2-4(J_{11}{J}_{22}-J_{12}{J}_{21})}$

(4) input n inductance, electric capacity, resistance and input power parameter, recurring formula (13) ~ (16) obtain the eigenvalue λ of n group second order Jacobian matrix ₁₂.

8. a kind of One Buck-Boost converter body modeling based on the discrete Lagrangian model of variational integral and nonlinear analysis method according to claim 7, is characterized in that: utilize Jacobian matrix eigenwert to obtain the non-linear behavior detailed process of One Buck-Boost converter body stabilized zone and One Buck-Boost converter body bifurcation point first in step 6:

(1) according to the eigenvalue λ of n group second order Jacobian matrix ₁₂, obtain the track of Jacobian proper value of matrix with circuit parameter variations;

(2) if all eigenwerts of Jacobian matrix are all positioned at unit circle inside, then Buck-Boost system is in steady state (SS); If the eigenvalue of Jacobian matrix has passed the scope of unit circle, then Buck-Boost system there occurs bifurcation thus has determined the non-linear behavior of One Buck-Boost converter body stabilized zone and One Buck-Boost converter body bifurcation point first.