CN110112915A - The control method of Boost DC-DC converter based on Second Order Sliding Mode Control - Google Patents
The control method of Boost DC-DC converter based on Second Order Sliding Mode Control Download PDFInfo
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- CN110112915A CN110112915A CN201910446566.XA CN201910446566A CN110112915A CN 110112915 A CN110112915 A CN 110112915A CN 201910446566 A CN201910446566 A CN 201910446566A CN 110112915 A CN110112915 A CN 110112915A
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M3/00—Conversion of dc power input into dc power output
- H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
- H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
- H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
- H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
- H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators
- H02M3/157—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators with digital control
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M3/00—Conversion of dc power input into dc power output
- H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
- H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
- H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
- H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
- H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators
- H02M3/158—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators including plural semiconductor devices as final control devices for a single load
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- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Dc-Dc Converters (AREA)
Abstract
The control method for the Boost DC-DC converter based on Second Order Sliding Mode Control that the invention proposes a kind of, it include: step 1, the control variable of selected Boost establishes the differential equation according to selected control variable under different circuit structures, establishes the phase plane about control variable；Step 2, finite state machine controller based on Second Order Sliding Mode Control is established to Boost, set effective status and original state, effective status is set to correspond to the controller output quantity, according to the selected control variable analysis differential equation, without output overshoot, the finite state machine controller condition of convergence based on Second Order Sliding Mode Control is obtained；Step 3, according to the finite state machine controller based on Second Order Sliding Mode Control, the finite state machine controller for increasing time lag value is established, in finite frequency, control variable is set to converge to equalization point, i.e. given value in the agonic tracking of the output of Boost.
Description
Technical field
The present invention relates to automation control area more particularly to a kind of Boost DC-DC changes based on Second Order Sliding Mode Control
The control method of parallel operation.
Background technique
Pulsewidth modulation (PWM) control is widely used in direct current --- direct current (DC-DC) converter.It is according to output voltage
Output switching signal is obtained with other state variables, controls DC-DC converter track reference voltage.This method needs to use defeated
The integral term of error guarantees zero error when stable state out.Major advantage is to allow converter work under constant value switching frequency for it
Make, so that it has good Electro Magnetic Compatibility (EMI).However, it there is also some disadvantages:
1) integral term may slow down the dynamic response of converter；
2) it is the control method based on small signal, the dynamic property of a converter only range near equalization point
Inside guaranteed.Therefore, people begin one's study simply, quick control method such as hybrid digital self adaptive control, when approximate
Between optimum control, boundary Control, Raster control.
Sliding formwork control is a kind of nonlinear control method, it has good robust to parameter uncertainty and external disturbance
Property, it can satisfy the big signal and small signal conditioning of converter, be a kind of alternative of DC-DC converter PWM control.Tradition
Sliding formwork control sliding-mode surface s=0 by state control be divided into 2 sub-spaces, in different subspace use different control
It acts on { U+, U- }, generates control output and converter is adjusted, so that system dynamic trajectory is maintained at s=0.Sliding formwork control
It is emphasised that a kind of switching function is used under different circuit structures, but since Boost is non-minimum phase system
System only just can not be completed to control under different circuit structures with a kind of switching function.Boundary control method, similar and High-Order Sliding Mode
Control method can be realized good control effect using high-order diverter surface.But it is applied to the boundary Control of Boost
Method still needs while measuring inductive current and output electric current, and which increase the costs of control method.
Summary of the invention
The present invention is directed at least solve the technical problems existing in the prior art, especially innovatively propose a kind of based on two
The control method of the Boost DC-DC converter of rank sliding formwork control.
The present invention proposes a kind of control method of Boost DC-DC converter based on Second Order Sliding Mode Control.Based on second order
The switching function thought of sliding formwork, this method separately design switching function under two kinds of controller architectures of Boost, make to transport
Dynamic rail mark, according to the movement of regulation track, eventually enters into the limit cycle of stable state under the limitation of switching surface.This method is using a kind of
Controller based on state machine architecture, not needing detection output electric current can be made using the feedback of output voltage and inductive current
Boost has good dynamic response, and has good robustness to Parameter uncertainties and load disturbance.This hair
The control method with time lag of bright proposition, in conjunction with the controller of limited state machine architecture, in the case where limited switching frequency,
Realize zero error when systematic steady state.
In order to realize above-mentioned purpose of the invention, the present invention provides a kind of Boost DC- based on Second Order Sliding Mode Control
The control method of DC converter, it is critical that including:
Step 1, the control variable for selecting Boost, according to selected control variable in different transformer configurations
Under establish the differential equation, establish the phase plane about control variable；
Step 2, the finite state machine controller based on Second Order Sliding Mode Control is established to Boost, sets effective shape
State and original state make effective status correspond to the controller output quantity, according to the selected control variable analysis differential equation,
Without output overshoot, the finite state machine controller condition of convergence based on Second Order Sliding Mode Control is obtained；
Step 3, it according to the finite state machine controller based on Second Order Sliding Mode Control, establishes and increases the limited of time lag value
State machine controller makes control variable converge to equalization point, i.e. the output of Boost is unbiased in finite frequency
Given value in the tracking of difference.
The control method of the Boost DC-DC converter based on Second Order Sliding Mode Control, it is preferred that the step 1
Include:
Step 1-1 establishes the differential equation under controller OFF-state structure according to selected control variable.Selected
Two control variables are respectively inductive current iLWith output voltage Vo, according to OFF-state controller architecture feature, by controller
The input and output differential equation be converted into iL*And VoThe differential equation, thus obtain using two control variables as the phase of reference axis
Equation of locus in plane.
Step 1-2 establishes the differential equation under controller ON-state structure according to selected control variable.Selected two
A control variable is respectively inductive current iLWith output voltage Vo, according to ON-state controller architecture feature, by the defeated of controller
Enter to export the differential equation and is converted into iL*And VoThe differential equation, thus obtain using two control variables as the phase plane of reference axis
On equation of locus.
The control method of the Boost DC-DC converter based on Second Order Sliding Mode Control, it is preferred that the step 2
Include:
The input and output differential equation group of step 2-1, Boost is
Wherein, u is control amount, and as u=1, controller is in ON-state structure, and as u=0, controller is in
OFF-state structure.Four effective statuses of state machineThere is corresponding control amount,WithCorresponding control amount u=0,WithCorresponding control amount u=1.After system electrification, system is initial
Change, is started by original state, as output voltage Vo< VrefWhen, state machine enters Left half-plane work, by stateDriving, when state machine is inIf when output voltage Vo> Vref, then state machine enters right half plane work
Make, by stateDriving.When being inWhen state, if output voltage Vo> VrefThen state machine reenters a left side
Half-plane work.
Step 2-2, it is resulting about i by step 1LAnd VoThe differential equation can be distinguished as follows according to controller architecture.Work as control
When device structure processed is in OFF-state, the differential equation of controller is
As it can be seen that motion profile of the controller in phase plane is with (0, V under OFF-state structureg) be the center of circle circle rail
Mark.When controller architecture is in ON-state, the differential equation of controller is
Wherein, (iL0, Vo0) be track initial point, it is seen that the track of ON-state is the straight line that a slope is negative.
Working trajectory under each structure derived above, can obtain the switching condition jumped between state.
By stateIt jumps toSwitching condition analysis:Controller is in ON-state structure under state,
Motion profile is straight line.Inductance fills energy under this state, and load is risen by output capacitance afterflow, inductive current, and output voltage is with very
Small rate decline.When reference point is passed through in the circular work track locating for the operating point, filling can be completed, and state machine switches to stateSwitching condition is obtained by the intersection point of Circular test and straight path Jing Guo reference point.Switching condition is as follows
For the radius of the Circular test Jing Guo reference point, value is
By stateIt jumps toWithSwitching condition analysis: when state machine is inWhen, output electricity
Pressure rises, inductive current decline.Motion profile under this state is Circular test, is write from memory when inductive current drops to reference value or less
The energy for recognizing inductance storage is insufficient to allow output voltage to continue to rise, and needs to fill energy.Under state, if output voltage is less than
Reference value, inductive current are less than reference value, then state machine still works in Left half-plane, switch toIf output voltage is greater than
Reference value, inductive current are greater than reference value, then state machine enters right half plane, switches toIt can be obtained by above narrationIt switches toSwitching condition be iL≤iLref,It switches toSwitching condition be Vo≥Vref。
By stateIt jumps toSwitching condition analysis:Motion profile under state is Circular test, work
Make point to move along track, until satisfaction is cut when passing through reference point as the motion profile of the ON-state of initial point using current point
Change condition.It will also appreciate that as using current point as initial pointStraight line working trajectory slope be less than or equal to it is current
Meet switching condition when the slope of point and reference point line.The slope of straight-line trajectory under ON-state structure is according to initial
The difference of point obtains different values, and the Movement Locus Equation that can obtain ON-state by step 1 is as follows
The slope of straight line is related with the output voltage of initial point and controller parameter, and value is
When with current point be it is nextThe starting point of stateWhen motion profile passes through reference point, state occurs
It jumps, the condition that can must jump is
Above formula deformation can obtain
(iLref-iL0)*L*Vo0≤R*C*Vg*Vo0-Vref)
To be further simplified above formula, according to input-output power conservation equation
Substitute into Shi Ke get
Wherein, iL*refFor conversion after inductive current reference value,
By stateIt jumps toWithSwitching condition analysis:Inductive current rises under state, defeated
Voltage declines out.State main function is the transition state of state switching, when meeting switching condition iL*≥iL*refAnd still
Work is switched in right half planeWhen meeting condition Vo≤VrefAnd iL*≤iL*refWhen switch toState machine
It works into Left half-plane.
The control method of the Boost DC-DC converter based on Second Order Sliding Mode Control, it is preferred that the step 3
Include:
Step 3, it according to the finite state machine controller based on Second Order Sliding Mode Control, establishes and increases having for time lag value
State machine controller is limited, in finite frequency, control variable is made to converge to equalization point, i.e. the output nothing of Boost
Given value in the tracking of deviation.Time lag value is set as β, in stateIt jumps toSwitching condition in addition time lag value can
Obtain switching condition as follows
After adding time lag value, state machine can cross the boundary into right half plane by limited switching cycle, and can be with
Limit cycle is formed centered on reference point.Into after equilibrium state, the ripple of time lag value β and final steady morphogenetic output voltage ripple
Relationship of Coefficients is explained by derivation below.There are two the switching point of state and controller architecture hairs for finally formed limit cycle
Switching point when raw switching, is set as A (iL*A, VoA)、B(iL*B, VoB).The target ripple factor for concurrently setting output voltage is W,
Because the center of limit cycle is reference point, it can thus be concluded that the expression formula of the coordinate of two o'clock, VoA=Vref-Vref* W/2, VoB=Vref+
Vref* W/2, iL*A=| K | * Vref*W/2+iL*ref, iL*B=iL*ref-|K|*Vref*W/2.Because A, B two o'clock is OFF-state
On Circular test and two intersection points of ON-state straight path.After coordinate wherein is calculated, according to public affairs below
Formula can calculate the expression formula of time lag value
In conclusion by adopting the above-described technical solution, the beneficial effects of the present invention are:
1. improving on the basis of sliding-mode control, detection output electric current is not needed, only with output voltage
With inductive current as feedback；
2. in startup stage, under specific loading condition, it is only necessary to two switchings to act, and track output voltage
Upper reference signal；In stable state, if there is load disturbance, output voltage is set to be restored to steady-state value within a short period of time；
3. the uncertainty of pair controller parameter has good robustness；
Additional aspect and advantage of the invention will be set forth in part in the description, and will partially become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
Above-mentioned and/or additional aspect of the invention and advantage will become from the description of the embodiment in conjunction with the following figures
Obviously and it is readily appreciated that, in which:
Fig. 1 is the Boost DC-DC of the control method of the Boost DC-DC converter the present invention is based on Second Order Sliding Mode Control
The circuit diagram of converter；
Fig. 2 is the Boost DC-DC of the control method of the Boost DC-DC converter the present invention is based on Second Order Sliding Mode Control
The OFF-state structural circuit figure of converter；
Fig. 3 is the Boost DC-DC of the control method of the Boost DC-DC converter the present invention is based on Second Order Sliding Mode Control
The ON-state structural circuit figure of converter；
Fig. 4 is the starting point of the control method of the Boost DC-DC converter the present invention is based on Second Order Sliding Mode Control on a left side
Half-plane (Vo< Vref) when circuit working motion track schematic diagram；
Fig. 5 is the starting point of the control method of the Boost DC-DC converter the present invention is based on Second Order Sliding Mode Control on the right side
Half-plane (Vo> Vref) when circuit working motion track schematic diagram；
Fig. 6 is the Left half-plane of the control method of the Boost DC-DC converter the present invention is based on Second Order Sliding Mode Control
Switching condition schematic diagram between state；
Fig. 7 is the circuit of the control method of the Boost DC-DC converter the present invention is based on Second Order Sliding Mode Control right half
Switching condition schematic diagram between the state of plane；
Fig. 8 is the state machine control of the control method of the Boost DC-DC converter the present invention is based on Second Order Sliding Mode Control
Device structure chart；
Fig. 9 is the addition time lag value of the control method of the Boost DC-DC converter the present invention is based on Second Order Sliding Mode Control
Steady-state analysis schematic diagram afterwards；
Figure 10 is the method signal of the control method of the Boost DC-DC converter the present invention is based on Second Order Sliding Mode Control
Figure；
Figure 11 is the example circuit of the control method of the Boost DC-DC converter the present invention is based on Second Order Sliding Mode Control
Figure；
Specific embodiment
The embodiment of the present invention is described below in detail, examples of the embodiments are shown in the accompanying drawings, wherein from beginning to end
Same or similar label indicates same or similar element or element with the same or similar functions.Below with reference to attached
The embodiment of figure description is exemplary, and for explaining only the invention, and is not considered as limiting the invention.
In the description of the present invention, it is to be understood that, term " longitudinal direction ", " transverse direction ", "upper", "lower", "front", "rear",
The orientation or positional relationship of the instructions such as "left", "right", "vertical", "horizontal", "top", "bottom" "inner", "outside" is based on attached drawing institute
The orientation or positional relationship shown, is merely for convenience of description of the present invention and simplification of the description, rather than the dress of indication or suggestion meaning
It sets or element must have a particular orientation, be constructed and operated in a specific orientation, therefore should not be understood as to limit of the invention
System.
In the description of the present invention, unless otherwise specified and limited, it should be noted that term " installation ", " connected ",
" connection " shall be understood in a broad sense, and also can be the connection inside two elements, energy for example, can be mechanical connection or electrical connection
Enough it is connected directly, also can indirectly connected through an intermediary, for the ordinary skill in the art, it being capable of basis
Concrete condition understands the concrete meaning of above-mentioned term.
Fig. 1 shows the circuit structure of Boost DC-DC converter, and switch S1 and S2 different states determines circuit
Different conditions.When switching tube S1 is turned off, S2 conducting, controller is in OFF-state structure, control amount u=0, by controller
The input and output differential equation following differential equation group can be obtained
For simplifying the analysis, it is set as immunization with gD DNA vaccine, i.e. R → ∞, above equation can be reduced to
With iLAnd VoTwo reference axis of phase plane, above formula can obtain the work of the controller under OFF-state structure by deformation
Equation of locus
For the convenience of geometrical analysis, enable
Finally obtained controller working trajectory equation is the expression formula of circle
Boost DC-DC controller in OFF-state structure is as shown in Figure 2.
Fig. 3 shows the Boost DC-DC controller figure in ON-state structure, and switch S1 is connected at this time, switch
S2 shutdown.Following differential equation group can be obtained by the input and output differential equation of controller in control amount u=1
Here, the intermediate quantity of a derivation process is introduced, the ENERGY E of inductance and capacitor storage, expression formula is as follows
E=L*iL 2/2+C*Vo 2/2
E derivation is obtainedExpression formula it is as follows:
For simplifying the analysis, existR → ∞ is set in formula, above equation can be reduced to
It is rightDerivation obtainsExpression formula it is as follows:
(i is integrated simultaneously to formula (21) both sidesL0For electric current initial value):
iL=(Vg/L)*t+iL0 (22)
Output voltage V can be obtained by deriving through (21)oExpression formula (Vo0For Initial Voltage Value):
I can be obtained by eliminating time t simultaneously for formula (22) and formula (23)LWith VoRelational expression:
ln(Vo/Vo0)=- L* (iL-iL0)/R*C*Vg (24)
In this case, the value very little of output voltage decline, Vo/Vo0Value be approximately equal to 1, approximate processing can be done
ln(Vo/Vo0)≈Vo/Vo0-1 (25)
Formula (25) is brought into (24) and can be obtained:
Fig. 4 shows starting point in Left half-plane (Vo< Vref) when controller working motion track schematic diagram, in figure
The initial value of output voltage is set as 0, first effective status after starting isDue to the Initial Voltage Value of output capacitance
Have the characteristics that equivalent parallel diode for 0 and MOSFET, track is caused " abnormality " phenomenon occur, is i.e. inductive current rises same
When, output voltage also rises.When meeting switching conditionWhen, state switches toIn stateUnder, if controller is in ideal state, i.e., without loss and Parameters variation, then controller will be along
Circular test moves to reference point.But due to being lost with Parameters variation, motion profile is referring to practical controller always
In circle, when meeting switching condition iL≤iLrefAnd controller is still switched back into when Left half-plane worksState.So far one is completed
The movement of a switch periods.It again goes intoEnergy is filled to inductance, the initial voltage for output capacitance of having a surplus is greater than input voltage,
So at this timeTrack is " normal " track, and while inductive current rises, output voltage reduces.The movement of track is same as above
Switch periods are stated, it is the repeating motion period, final because the Left half-plane region of the reasons near reference point such as circuit loss is formed
Stable limit cycle.
The starting point that Fig. 5 is shown is in right half plane (Vo> Vref) when circuit working motion track schematic diagram, output end electricity
The initial value of appearance is greater than reference value, and first effective status entered after starting isController operating point is along Circular test
Movement, output voltage decline, inductive current also reduce (reversed to increase).It is switched to when meeting switching condition Shape
Output voltage declines under state, and inductive current increases, and switches back into if meeting switching conditionSo far a complete switch
Period completes.By figure it can be seen that due to being lost with controller parameter variation, after limited switch periods, movement
Track crosses the boundary into Left half-plane.
Fig. 6 shows the switching condition derivation process schematic diagram between the state of Left half-plane, and starting point is in Zuo Banping
The initial value of face and output capacitor is 0.First effective status beInductance fills energy under this state, and inductive current rises,
Output voltage also rises.If circuit is ideal, it is not lost, then present operating point and the center of circle (0, Vg) distance be equal to by reference
It represents inductance when the radius of the Circular test of point to fill and can complete, if switching at this timeIt operating point will be along the track of circle of reference
Move to reference point.So state can be obtained according to above-mentioned principleIt switches toSwitching conditionWhereinWith reference to square of radius of circle
Switching point is as shown in the C point in figure.But there is loss so actual path moves in reference Circular test always in actual circuit,
In order to keep inductance exoergic sufficiently and close to reference point as quickly as possible,It switches toSwitching condition be iL≤
iLref.Switching point is defaulted as the completion of inductance exoergic as shown in the D point in figure when meeting condition.Hereafter the repeat switch period until
It reaches reference point and is formed about stable limit cycle, while will form the higher-order of oscillation.The effect for adding time lag value is to make rail
Mark crosses the boundary into right plane, and avoids ultimately forming the limit cycle of the higher-order of oscillation.
Fig. 7 shows the schematic diagram that the switching condition between the state of right half plane derives.Such as figure, starting point is put down right half
Face, first effective status after starting areUnder this state, voltage declines, and inductive current reduces.Track it is close
Seemingly it is straight line, slope formula is as follows:
Different switching point (iL*0, Vo0) straight line of Different Slope can be obtained, what above formula indicated is straight line cluster, needs to select
By the straight line of reference point.Different switching point (i is given in figureL*1, Vo1)、(iL*2, Vo2)、(iL*3, Vo3) etc., different cuts
The straight line for a little corresponding to Different Slope is changed, if a point M (i thereinL*4, Vo4) where straight line pass through reference point.Place straight line warp
Crossing reference point, to correspond to switching point equal with the slope of the slope of reference point line and straight path.It can be obtained according to above-mentioned principleIt switches toSwitching condition
When the slope for the straight line working trajectory that the line slope of certain point and reference point is less than or equal to this point, switch toThe straight line for meeting switching condition can pass through reference point (i in the case where circuit is not lost with Parameters variationL*ref,
Vref), but may be caused due to delay, loss and parameter fluctuation etc. in a practical situation track reach reference point before
Cross Vo=VrefNearby belong to the certain point in right half plane region into Left half-plane or arrival reference point.For the ease of meter
It calculates, above formula can be obtained by deformation
According to input-output power conservation, i.e.,Substituting into above formula can obtain
It switches toAfterwards, operating point is moved along straight path, when meeting switching condition iL≥iLref+ A and still on the right side
It is switched to when half-planeWherein A is the constant greater than 0, in order to keep motion profile quickly close to reference point, A
Value should be small as far as possible, enable A=0.SoToThe condition of switching is iL≥iLref。
Fig. 8 shows that the structural schematic diagram of state machine, state machine are made of four effective statuses and an original state.
Switching condition between state has made specific explanations above, and after starting, state machine is according to the inductive current and output fed back to
Jumping between voltage driving condition, into after stable state, the one-way circulation that limit cycle corresponds to four effective statuses is jumped.
Fig. 9 shows the stable state limit cycle schematic diagram after addition time lag value, the track of the ON-state structure of controller
Track for straight line, OFF-state structure is Circular test, into after stable state, two friendships of the track ON-state and OFF-state
Point is set as A (i in figureL*A, VoA)、B(iL*B, VoB), since limit cycle is centered on reference point, according to the performance indicator of circuit
Ripple factor can obtain the coordinate of two intersection points.If the target ripple factor of output voltage is W, then A, B two o'clock can be obtained
Coordinate expressions it is as follows
VoB=Vref-Vref*W/2
iL*B=| K | * Vref*W/2+iL*ref
VoA=Vref+Vref*W/2
iL*A=iL*ref-|K|*Vref*W/2
Wherein, K is the slope of the straight line working trajectory of controller under ON-state structure.According to coordinate energy wherein
Access the calculation formula of time lag value
Figure 10 shows the method signal of the control method of the Boost DC-DC converter based on Second Order Sliding Mode Control
Figure, the switching function thought based on Second Order Sliding Mode improve, this control method is realized by three big steps.From Boost controller
Input and output differential equation group deform to obtain to control variable as the working trajectory equation under the phase plane of reference axis, in conjunction with
The structure and controller working trajectory characteristic of state machine obtain the switching condition in state machine between state, and three big steps are completely chatted
The design cycle and workflow of state machine controller are stated.
Figure 11 shows that example circuit diagram, inductive current and output voltage are back to state machine control as feedback signal
Device, state machine controller output control signals to two switch MOSFET.Controller is using Altera Cyclone IV series
FPGA.Analogue-to-digital converters conversion frequency used in output voltage and inductive current measurement is 30MHz, and resolution ratio is 10,
0-2V input range.
In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show
The description of example " or " some examples " etc. means specific features, structure, material or spy described in conjunction with this embodiment or example
Point is included at least one embodiment or example of the invention.In the present specification, schematic expression of the above terms are not
Centainly refer to identical embodiment or example.Moreover, particular features, structures, materials, or characteristics described can be any
One or more embodiment or examples in can be combined in any suitable manner.
Although an embodiment of the present invention has been shown and described, those skilled in the art can be appreciated that not
In the case where being detached from the principle of the present invention and objective a variety of change, modification, replacement and modification can be carried out to these embodiments, this
The range of invention is defined by the claims and their equivalents.
Claims (8)
1. a kind of control method of the Boost DC-DC converter based on Second Order Sliding Mode Control characterized by comprising
S1 selectes the control variable of Boost, establishes differential under different circuit structures according to selected control variable
Equation establishes the phase plane about control variable；
S2 establishes the finite state machine controller based on Second Order Sliding Mode Control to Boost, setting effective status and initial
State makes effective status correspond to the controller output quantity, according to the selected control variable analysis differential equation, in no output
In the case where overshoot, the finite state machine controller condition of convergence based on Second Order Sliding Mode Control is obtained；
S3 establishes the finite state machine for increasing time lag value according to the finite state machine controller based on Second Order Sliding Mode Control
Controller makes to control variable and converges to equalization point in finite frequency, i.e. the output of Boost it is agonic with
Given value on track.
2. the control method of the Boost DC-DC converter according to claim 1 based on Second Order Sliding Mode Control, feature
It is, the S1 includes:
S1-1 establishes the differential equation in the case where controller OFF-state turns off structure according to selected control variable；Selected two
Controlling variable is respectively inductive current iLWith output voltage Vo, according to OFF-state controller architecture feature, by the defeated of controller
Enter to export the differential equation and is converted into iLAnd VoThe differential equation, thus obtain using two control variables as the phase plane of reference axis
On equation of locus；
S1-2 establishes the differential equation under controller ON-state opening structure according to selected control variable；Selected two
Controlling variable is respectively inductive current iLWith output voltage Vo, according to ON-state controller architecture feature, by the input of controller
The output differential equation is converted into iLAnd VoThe differential equation, controlled in phase plane of the variables as reference axis to obtain using two
Equation of locus.
3. the control method of the Boost DC-DC converter according to claim 2 based on Second Order Sliding Mode Control, feature
It is, the S1-1 includes:
S1-A, it is known that the input and output differential equation group under Boost OFF-state structure is
For simplifying the analysis, it is set as immunization with gD DNA vaccine, i.e. R → ∞, above equation can be reduced to
Here, the intermediate quantity of a derivation process is introduced, the ENERGY E of inductance and capacitor storage, expression formula is as follows
E=L*iL 2/2+C*Vo 2/2 (3)
E derivation is obtainedExpression formula it is as follows:
It is rightDerivation obtainsExpression formula it is as follows:
Formula (4) and formula (5) are mutually multiplied
Enable parameterEquation (6) both sides simultaneously integrate time t:
Formula (4) are substituted into formula (7) and are obtained:
For unknown constant, value is related with the state of controller；For the convenience of geometric representation, enable
Formula (9) are substituted into formula (8) and are obtained:
It can be seen that formula (10) is the expression formula of circle, so far have been set up in iL*And VoUnder the coordinate system of the two control variables
The equation of locus of controller OFF-state structure, wherein L is inductance, C is capacitor, R is resistance, VgFor input voltage.
4. the control method of the Boost DC-DC converter according to claim 1 based on Second Order Sliding Mode Control, feature
It is, the S1-2 includes:
S1-B, it is known that the input and output differential equation group under Boost ON-state structure is
Here, the intermediate quantity of a derivation process is introduced, the ENERGY E of inductance and capacitor storage, expression formula is as follows
E=L*iL 2/2+C*Vo 2/2 (12)
E derivation is obtainedExpression formula it is as follows:
For simplifying the analysis, existR → ∞ is set in formula, above equation can be reduced to
Single order is ledDerivation obtains second order and leadsExpression formula it is as follows:
Following formula are integrated to obtain simultaneously to formula (11) both sides, wherein iL0For electric current initial value:
iL=(Vg/L)*t+iL0 (16)
Output voltage V can be obtained by deriving through formula (11)oExpression formula it is as follows, wherein Vo0For Initial Voltage Value:
I can be obtained by eliminating time t simultaneously for formula (16) and formula (17)LWith VoRelational expression:
ln(Vo/Vo0)=- L* (iL-iL0)/R*C*Vg (18)
In this case, the value very little of output voltage decline, Vo/Vo0Value be approximately equal to 1, approximate processing can be done
ln(Vo/Vo0)≈Vo/Vo0-1 (19)
Formula (19) is brought into (18) and can be obtained:
5. the control method of the Boost DC-DC converter according to claim 1 based on Second Order Sliding Mode Control, feature
It is, the S2 includes:
S2-1 sets the effective status and original state of state machine, makes the output quantity of effective status corresponding states machine controller；Shape
There are four state machines, and effective status isWith an original state；As output voltage Vo< Vref
When, system works in Left half-plane, and state machine is by stateWithDriving；As output voltage Vo> VrefWhen, system work
Make in right half plane, state machine is by stateWithDriving；WithIt represents controller and is in OFF-state
Structure, symbol "-" represent Left half-plane, and symbol "+" represents right half plane；WithIt represents controller and is in ON-
State structure, symbol "-" represent Left half-plane, and symbol "+" represents right half plane；
S2-2, it is resulting about i according to S1LAnd VoThe differential equation, analyze to obtain between state in binding geometry in phase plane
The switching condition jumped mutually is to get the switching surface arrived under different controller architectures.
6. the control method of the Boost DC-DC converter according to claim 5 based on Second Order Sliding Mode Control, feature
It is, the S2-1 includes:
The input and output differential equation group of S2-A, Boost is
Wherein, u is control amount, and as u=1, controller is in ON-state structure, and as u=0, controller is in OFF-
State structure；Four effective statuses of state machineThere is corresponding control amount,
WithCorresponding control amount u=0,WithCorresponding control amount u=1；After system electrification, system initialization,
Started by original state, as output voltage Vo< VrefWhen, state machine enters Left half-plane work, by stateIt drives
It is dynamic, when state machine is inIf when output voltage Vo> Vref, then state machine enters right half plane work, by stateDriving；When being inWhen state, if output voltage Vo> VrefThen state machine reenters Left half-plane work
Make.
7. the control method of the Boost DC-DC converter according to claim 5 based on Second Order Sliding Mode Control, feature
It is, the S2-2 includes:
S2-B, it is resulting about i by step 1LAnd VoThe differential equation can be distinguished as follows according to controller architecture；When controller knot
When structure is in OFF-state, the differential equation of controller is
As it can be seen that motion profile of the controller in phase plane is with (0, V under OFF-state structureg) be the center of circle Circular test；When
When controller architecture is in ON-state, the differential equation of controller is
Wherein, (iL0, Vo0) be track initial point, it is seen that the track of ON-state is the straight line that a slope is negative；More than
The working trajectory under each structure has been obtained, the switching condition jumped between state can be obtained；
By stateIt jumps toSwitching condition analysis:Controller is in ON-state structure under state, movement
Track is straight line；Inductance fills energy under this state, and load is risen by output capacitance afterflow, inductive current, and output voltage is with very little
Rate decline；When reference point is passed through in the circular work track locating for the operating point, filling can be completed, and state machine switches to stateSwitching condition is obtained by the intersection point of Circular test and straight path Jing Guo reference point；Switching condition is as follows
For the radius of the Circular test Jing Guo reference point, value is
By stateIt jumps toWithSwitching condition analysis: when state machine is inWhen, on output voltage
It rises, inductive current decline；Motion profile under this state is Circular test, and electricity is defaulted when inductive current drops to reference value or less
The energy of sense storage is insufficient to allow output voltage to continue to rise, and needs to fill energy；Under state, if output voltage is less than reference
Value, inductive current are less than reference value, then state machine still works in Left half-plane, switch toIf output voltage is greater than reference
Value, inductive current are greater than reference value, then state machine enters right half plane, switches toIt can be obtained by above narration
It switches toSwitching condition be iL≤iLref,It switches toSwitching condition be Vo≥Vref；
By stateIt jumps toSwitching condition analysis:Motion profile under state is Circular test, operating point
It is moved along track, until meeting switching item when passing through reference point as the motion profile of the ON-state of initial point using current point
Part；It will also appreciate that as using current point as initial pointStraight line working trajectory slope be less than or equal to current point with
Meet switching condition when the slope of reference point line；The slope of straight-line trajectory under ON-state structure is according to initial point
Difference obtains different values, and the Movement Locus Equation that can obtain ON-state by S1 is as follows
The slope of straight line is related with the output voltage of initial point and controller parameter, and value is
It is next with current pointThe starting point of stateWhen motion profile passes through reference point, state is jumped,
Condition, which must be jumped, is
Above formula deformation can obtain
(iLref-iL0)*L*Vo0≤R*C*Vg*(Vo0-Vref)
To be further simplified above formula, according to input-output power conservation equation
Substitute into Shi Ke get
Wherein, iL*refFor conversion after inductive current reference value,
By stateIt jumps toWithSwitching condition analysis:Inductive current rises under state, output electricity
Drops；State main function is the transition state of state switching, when meeting switching condition iL*≥iL*refAnd it still works
In right half plane, switch toWhen meeting condition Vo≤VrefAnd iL*≤iL*refWhen switch toState machine enters
Left half-plane work.
8. the control method of the Boost DC-DC converter according to claim 1 based on Second Order Sliding Mode Control, feature
It is, the S3 includes:
S3-1 establishes the limited shape for increasing time lag value according to the finite state machine controller based on Second Order Sliding Mode Control
State machine controller makes control variable converge to equalization point, i.e. the output zero deflection of Boost in finite frequency
Tracking on given value；Time lag value is set as β, in stateIt jumps toSwitching condition in addition time lag value can obtain such as
Under switching condition
After adding time lag value, state machine can cross the boundary into right half plane by limited switching cycle, and can be with reference
Limit cycle is formed centered on point；Into after equilibrium state, the ripple factor of time lag value β and final steady morphogenetic output voltage ripple
Relationship is explained by derivation below；There are two the switching points of state and controller architecture to cut for finally formed limit cycle
Switching point when changing is set as A (iL*A, VoA)、B(iL*B, VoB)；The target ripple factor for concurrently setting output voltage is W, because
The center of limit cycle is reference point, it can thus be concluded that the expression formula of the coordinate of two o'clock, VoA=Vref-Vref* W/2, VoB=Vref+Vref*
W/2, iL*A=| K | * Vref*W/2+iL*ref, iL*B=iL*ref-|K|*Vref*W/2；Because A, B two o'clock is the circle rail of OFF-state
On mark and two intersection points of ON-state straight path；After coordinate wherein is calculated, according to formula energy below
Enough calculate the expression formula of time lag value
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111262426A (en) * | 2020-02-19 | 2020-06-09 | 江苏大学 | Boost power converter control method based on novel second-order sliding mode algorithm |
| CN112865526A (en) * | 2020-12-25 | 2021-05-28 | 重庆大学 | Method for carrying out second-order sliding mode synchronous optimization on time lag value beta and switching frequency in DC-DC boost converter |
| CN112865527A (en) * | 2020-12-25 | 2021-05-28 | 重庆大学 | Control system and control method for fixed frequency of Boost DC-DC converter based on second-order sliding mode control |
| CN114665732A (en) * | 2022-03-23 | 2022-06-24 | 重庆大学 | LCL single-phase grid-connected inverter control method based on circuit energy state |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103378724A (en) * | 2013-07-25 | 2013-10-30 | 重庆大学 | DC-DC buck converter high-order sliding mode control method |
| CN106444367A (en) * | 2015-08-12 | 2017-02-22 | 南京理工大学 | Realization method of input time lag-based motor servo system robust position controller |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103378724A (en) * | 2013-07-25 | 2013-10-30 | 重庆大学 | DC-DC buck converter high-order sliding mode control method |
| CN106444367A (en) * | 2015-08-12 | 2017-02-22 | 南京理工大学 | Realization method of input time lag-based motor servo system robust position controller |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111262426A (en) * | 2020-02-19 | 2020-06-09 | 江苏大学 | Boost power converter control method based on novel second-order sliding mode algorithm |
| CN112865526A (en) * | 2020-12-25 | 2021-05-28 | 重庆大学 | Method for carrying out second-order sliding mode synchronous optimization on time lag value beta and switching frequency in DC-DC boost converter |
| CN112865527A (en) * | 2020-12-25 | 2021-05-28 | 重庆大学 | Control system and control method for fixed frequency of Boost DC-DC converter based on second-order sliding mode control |
| CN112865527B (en) * | 2020-12-25 | 2022-03-25 | 重庆大学 | Control system and control method for fixed frequency of Boost DC-DC converter based on second-order sliding mode control |
| CN114665732A (en) * | 2022-03-23 | 2022-06-24 | 重庆大学 | LCL single-phase grid-connected inverter control method based on circuit energy state |
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